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Examining geographies of opportunity for households with limited means : an investigation of transit accessibility and housing affordability in eight U.S. metropolitan areas

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Title:
Examining geographies of opportunity for households with limited means : an investigation of transit accessibility and housing affordability in eight U.S. metropolitan areas
Creator:
Luckey, Kara S.
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Doctorate ( Doctor of philosophy)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
College of Architecture and Planning, CU Denver
Degree Disciplines:
Design and planning
Committee Chair:
Nemeth, Jeremy
Committee Members:
Krizek, Kevin J.
Marshall, Wesley
Heikkila, Tanya

Notes

Abstract:
The role of transit in maximizing geographies of opportunity for low- and moderateincome individuals is well-established, although emerging concerns about direct and exclusionary displacement in transit-rich neighborhoods call into question the ability of those with limited means to benefit from transit access. In the face of these questions, a ‘location efficiency narrative’ suggests that displacement may be less of a threat than commonly thought because lower transportation costs in transit-accessible neighborhoods are likely to offset higher housing costs. Yet it remains unclear whether this narrative is supported by onthe- ground empirics, especially given concerns about the robustness of typical measures of affordability. This study takes as its starting point a puzzle about whether transit-rich neighborhoods are indeed more affordable, as a location efficiency approach would suggest, when affordability is examined using measures and methods that address key shortcomings in the literature. I therefore introduce an improved ‘location-sensitive residual income’ (LSRI) measure – which accounts for the nuances of household composition, financial circumstances, and residential location – and demonstrate how more typical measures are likely to under-estimate the challenges faced by low- and moderate-income households as they seek affordable housing. I then employ LSRI measures to investigate current landscapes of accessibility and affordability experienced by low- and moderateincome renters in eight U.S. metros. I first examine the extent to which supplies of affordable rental housing are located in transit-accessible neighborhoods. I then isolate the complex relationship between transit accessibility and affordability using a series of spatial error and geographically-weighted regression models that control for key characteristics of the built and social environments, as well as for spatial dependence. Results indicate that geographies of opportunity as shaped by accessibility and affordability are surprisingly strong in several metros – Denver and Los Angeles most notably – but are quite weak others. While findings for some metros are largely consistent with a location efficiency narrative, results for a larger number challenge it, underscoring that high housing costs in transit-accessible areas cannot be assumed to be offset by lower transportation costs. Further implications for transportation justice and potential policy prescriptions to promote transit-accessible affordable housing are also discussed.
Restriction:
Embargo ended 05/02/2018
General Note:
n3p

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University of Colorado Denver
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Auraria Library
Rights Management:
Copyright Kara S. Luckey. Permission granted to University of Colorado Denver to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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Full Text
EXAMINING GEOGRAPHIES OF OPPORTUNITY FOR HOUSEHOLDS WITH LIMITED
MEANS: AN INVESTIGATION OF TRANSIT ACCESSIBILITY AND HOUSING AFFORDABILITY IN EIGHT U.S. METROPOLITAN AREAS
by
KARA S. LUCKEY
B.S.C.E., The Cooper Union for the Advancement of Art and Science, 2003
A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Design and Planning Program
2017


This thesis for the Doctor of Philosophy degree by Kara S. Luckey has been approved for the Design and Planning Program by
Jeremy Nemeth, Chair Kevin J. Krizek, Advisor Wesley Marshall Tanya Heikkila
Date: May 13, 2017


Luckey, Kara S. (PhD, Design and Planning)
Examining Geographies of Opportunity for Households with Limited Means: An Investigation of Transit Accessibility and Housing Affordability in Eight U.S. Metropolitan Areas Thesis directed by Professor Kevin J. Krizek
ABSTRACT
The role of transit in maximizing geographies of opportunity for low- and moderate-income individuals is well-established, although emerging concerns about direct and exclusionary displacement in transit-rich neighborhoods call into question the ability of those with limited means to benefit from transit access. In the face of these questions, a ‘location efficiency narrative’ suggests that displacement may be less of a threat than commonly thought because lower transportation costs in transit-accessible neighborhoods are likely to offset higher housing costs. Yet it remains unclear whether this narrative is supported by on-the-ground empirics, especially given concerns about the robustness of typical measures of affordability. This study takes as its starting point a puzzle about whether transit-rich neighborhoods are indeed more affordable, as a location efficiency approach would suggest, when affordability is examined using measures and methods that address key shortcomings in the literature. I therefore introduce an improved ‘location-sensitive residual income’ (LSRI) measure - which accounts for the nuances of household composition, financial circumstances, and residential location - and demonstrate how more typical measures are likely to under-estimate the challenges faced by low- and moderate-income households as they seek affordable housing. I then employ LSRI measures to investigate current landscapes of accessibility and affordability experienced by low- and moderate-income renters in eight U.S. metros. I first examine the extent to which supplies of affordable rental housing are located in transit-accessible neighborhoods. I then isolate the complex relationship between transit accessibility and affordability using a series of spatial error and geographically-weighted regression models that control for key characteristics of the built


and social environments, as well as for spatial dependence. Results indicate that geographies of opportunity as shaped by accessibility and affordability are surprisingly strong in several metros - Denver and Los Angeles most notably - but are quite weak others. While findings for some metros are largely consistent with a location efficiency narrative, results for a larger number challenge it, underscoring that high housing costs in transit-accessible areas cannot be assumed to be offset by lower transportation costs. Further implications for transportation justice and potential policy prescriptions to promote transit-accessible affordable housing are also discussed.
The form and content of this abstract are approved. I recommend its publication.
Approved: Kevin J. Krizek
IV


This dissertation is dedicated with gratitude to Steve, Olin, and Thea for helping me to live every day with purpose, determination, and joy; to my parents Kathrine and Gregory for encouraging curiosity and wonderment; and to my committee members, particularly my advisor Professor Kevin Krizek, for their unending support and guidance.
v


ACKNOWLEDGEM ENTS
This dissertation was supported through a National Science Foundation Integrative Graduate Education and Research Traineeship (IGERT) Fellowship in Sustainable Urban Infrastructure (IGERT Award No. DGE-0654378), as well as through a U.S. Department of Transportation Dwight D. Eisenhower Transportation Graduate Fellowship.
VI


TABLE OF CONTENTS
CHAPTER
I. SUMMARY..........................................................1
CONCEPTUAL BASIS...................................................1
EXISTING KNOWLEDGE.................................................2
ANALYTICAL APPROACH................................................3
RESULTS: GEOGRAPHIES OF TRANSIT ACCESSIBILITY AND HOUSING AFFORDABILITY......................................................6
RESULTS: THE RELATIONSHIP BETWEEN TRANSIT ACCESSIBILITY AND HOUSING AFFORDABILITY, ACCOUNTING FOR OTHER KEY FACTORS............7
CONCLUSIONS AND IMPLICATIONS.......................................9
II. GEOGRAPHIES OF OPPORTUNITY, TRANSIT ACCESSIBILITY, AND
HOUSING AFFORDABILITY: THEORETICAL AND PRACTICAL FOUNDATIONS.......................................................13
CONSIDERING SOCIAL JUSTICE IN THE CONTEXT OF U.S. METROPOLITAN TRANSPORTATION PLANNING AND POLICY................................13
Contemporary Perspectives on Social Justice.................14
The ‘Capabilities Approach’ Framework.......................20
Applying a Capabilities Approach Framework to Conceptualize Transportation Justice......................................22
The Role of Transit in Shaping Geographies of Opportunity for Low-
and Moderate-Income Households..............................27
EMPIRICAL RESEARCH ON THE AFFORDABILITY OF HOUSING IN TRANSIT-ACCESSIBLE NEIGHBORHOODS IN THE U.S.......................28
Effects of Transit Accessibility on Housing Costs...........29
Displacement Effects Associated with Transit Accessibility..31
The Location Efficiency Narrative: An Antidote to Concerns about Transit-Induced Displacement?...............................34
III. RESEARCH QUESTIONS AND APPROACH.................................40
RESEARCH QUESTIONS................................................40
vii


RESEARCH APPROACH.....................................................42
Case Selection..................................................42
Key Variables...................................................47
Overview of Methods.............................................49
IV. EVALUATING TYPICAL MEASURES OF HOUSING AFFORDABILITY AND INTRODUCING THE IMPROVED ‘LOCATION-SENSITIVE RESIDUAL
INCOME’ MEASURE.......................................................54
INTRODUCTION..........................................................54
The Growing Housing Affordability ‘Crisis’......................54
Defining and Measuring ‘Affordable Housing’.....................58
TYPICAL APPROACHES TO MEASURING HOUSING AFFORDABILITY.................59
A ‘Ratio’ Approach to Measuring Housing Affordability...........61
A ‘Location Affordability’ Approach to Measuring Housing Affordability.64
A ‘Residual Income’ Approach to Measuring Housing Affordability.66
Conclusions.....................................................69
A NEW APPROACH TO MEASURING HOUSING AFFORDABILITY: ‘LOCATION-SENSITIVE RESIDUAL INCOME’..............................70
V. METHODOLOGY FOR CONSTRUCTING A LOCATION-SENSITIVE
RESIDUAL INCOME MEASURE OF HOUSING AFFORDABILITY......................74
STEP 1: SPECIFY ASSUMPTIONS...........................................77
Geographic Extent...............................................78
Unit of Analysis................................................78
Housing Tenure..................................................79
STEP 2: DEFINE HOUSEHOLD PROFILES.....................................80
Define Household Composition(s).................................80
Specify Household Income Level(s)...............................81
STEP 3: CALCULATE ESTIMATED NON-HOUSING AND NONTRANSPORTATION COSTS..............................................83
viii


Estimated Childcare Costs.....................................85
Estimated Food Costs..........................................86
Estimated Medical Costs.......................................87
Estimated Costs for Other Basic Necessities...................88
Estimated Costs of Taxes......................................89
Total Estimated Non-Housing and Non-Transportation Costs...90
STEP 4: CALCULATE HOUSING AND TRANSPORTATION BUDGETS................91
STEP 5: IDENTIFY ESTIMATED TRANSPORTATION COSTS.....................92
Data Sources..................................................93
Summary of Estimated Transportation Costs.....................99
STEP 6: CALCULATE ESTIMATED HOUSING BUDGETS........................103
STEP 7: CALCULATE ESTIMATED SUPPLIES OF AFFORDABLE HOUSING .... 107
Calculate the Estimated Number of Units Available within Household Housing Budgets..............................................111
Calculate the Estimated Percent of Regional Housing Units that are Affordable within Household Housing Budgets..................112
CONTRIBUTIONS AND LIMITATIONS OF A LSRI APPROACH...................116
VI. COMPARING FOUR MEASURES OF HOUSING AFFORDABILITY: THE CASE OF LOW- AND MODERATE-INCOME HOUSEHOLDS IN THE DENVER METRO........................................................119
INTRODUCTION.......................................................119
DEFINING A SUBSET OF LOW-AND MODERATE-INCOME HOUSEHOLDS ....120
WHAT CAN LOW- AND MODERATE-INCOME HOUSEHOLDS AFFORD TO PAY FOR HOUSING IN DENVER?..................................121
Estimated Housing Budgets Calculated Using a LSRI Approach.122
Estimated Housing Budgets: A Comparison of the Ratio, Location Affordability, Standard Residual Income, and LSRI Approaches.126
WHAT IS THE METRO-WIDE SUPPLY OF HOUSING UNITS AFFORDABLE TO LOW-AND MODERATE-INCOME RENTERS IN DENVER?...............131
IX


Estimated Metro-Wide Supplies of Affordable Rental Housing
Calculated Using a LSRI Approach..............................131
Estimated Metro-Wide Supplies of Affordable Rental Housing: A Comparison of the Ratio, Location Affordability, Standard Residual Income and LSRI Approaches....................................133
HOW ARE SUPPLIES OF LOW- AND MODERATE-INCOME AFFORDABLE RENTAL UNITS SPATIALLY-DISTRIBUTED?............................136
Examining the Spatial Distribution of Affordable Rental Housing Using a LSRI Approach...............................................137
Identifying Affordability Clusters and Outliers...............139
CONCLUSIONS.........................................................146
VII. EXAMINING LANDSCAPES OF TRANSIT ACCESSIBILITY AND HOUSING
AFFORDABILITY IN EIGHT U.S. METROS..................................153
INTRODUCTION........................................................153
DATA AND METHODS....................................................155
Data.............................................................155
Methods..........................................................164
RESULTS AND DISCUSSION..............................................165
Supplies of Affordable Rental Units, by Accessibility Level...165
Accessibility Ratios..........................................167
SUMMARY OF KEY FINDINGS.............................................172
VIII. EXAMINING THE COMPLEX RELATIONSHIP BETWEEN TRANSIT
ACCESSIBILITY AND HOUSING AFFORDABILITY IN EIGHT U.S. METROS.......176
INTRODUCTION........................................................176
DATA AND METHODS....................................................177
Data..........................................................177
Methods.......................................................178
RESULTS AND DISCUSSION..............................................184
Examining Global Relationships between Transit Accessibility and Housing Affordability: Spatial Error Models...................185
x


Examining Local Relationships between Transit Accessibility and
Housing Affordability: Geographically-Weighted Regression Models.196
SUMMARY OF KEY FINDINGS.........................................200
IX. GEOGRAPHIES OF OPPORTUNITY FOR LOW- AND MODERATE-INCOME
HOUSEHOLDS IN EIGHT U.S. METROS: A SYNTHESIS OF FINDINGS........205
INTRODUCTION....................................................205
Conceptual Basis..........................................205
Existing Literature.......................................207
Research Questions and Approach...........................209
THE LSRI MEASURE OF HOUSING AFFORDABILITY.......................212
SYNTHESIS OF FINDINGS: CURRENT GEOGRAPHIES OF OPPORTUNITY FOR LOW- AND MODERATE-INCOME HOUSEHOLDS.........................215
Geographies of Opportunity: A Typology....................215
Metro-wide Geographies of Opportunity.....................216
SUMMARY OF CONTRIBUTIONS AND LIMITATIONS........................222
Key Contributions.........................................223
Limitations...............................................228
Future Research...........................................230
REFERENCES...................................................................232
APPENDIX
A. SUMMARY OF NON-HOUSING AND NON-TRANSPORTATION
(‘NON-H+T’) COSTS BY METRO......................................243
B. SUMMARY OF TRANSPORTATION COSTS BY METRO.......................245
C. LSRI MEASURES OF HOUSING AFFORDABILITY (DENVER)................247
D. SAMPLE R-CODE (DENVER).........................................249
E. FULL OLS AND SPATIAL ERROR REGRESSION RESULTS..................264
xi


LIST OF ABBREVIATIONS
ACS American Community Survey
AIC Akaike information criterion
AMI Area median income
BLS Bureau of Labor Statistics
CBSA Core-based statistical area
CE Consumer Expenditure [Survey]
CNT Center for Neighborhood Technology
CPI Consumer Price Index
CTOD Center for Transit-Oriented Development
EPA [United States] Environmental Protection Agency
GIS Geographic Information System
GTFS General Transit Feed Specification
GWR Geographically-weighted regression
H+T Housing and Transportation
HUD [United States] Department of Housing and Urban Development
ISTEA Intermodal Surface Transportation Efficiency Act
JCHS [Harvard University] Joint Center for Housing Studies
LAI Location Affordability Index
LAP Location Affordability Portal
LEHD Longitudinal Employer-Household Dynamics
LISA Local Indicators of Spatial Autocorrelation
LM Lagrange Multiplier
LODES Longitudinal Origin-Destination Employment Statistics LSRI Location-sensitive residual income
MLS Multiple Listing Survey
XII


MPO Metropolitan planning organization
MSA Metropolitan statistical area
OLS Ordinary Least Squares
SEM Structural equation modelling
SLD Smart Location Database
USDA United States Department of Agriculture
VIF
Variance Inflation Factor


CHAPTER I
SUMMARY
CONCEPTUAL BASIS
This dissertation begins by considering how several contemporary theoretical lenses relevant to social justice in the context of U.S. metropolitan planning and policy help in understanding what constitutes a ‘just’ transportation system (Chapter 2). Of these, I adopt Sen and Nussbaum’s ‘capabilities approach’ to argue that transportation justice requires that all individuals are able to access the opportunities required for them to reach their full potential. I then develop a conceptual framework that guides the present study by integrating principles of a capabilities approach with the concept of ‘geographies of opportunity,’ which is commonly used among practitioners and advocates around issues of spatial and social justice.
In this conceptual framework (Figure 1.1), an individual’s ‘geography of opportunity’ (or in the language of the capabilities approach, her/his set of ‘capabilities‘) represents the opportunities that are available to a person in their pursuit of well-being. Three components (‘primary goods1) related to physical planning and policy shape geographies of opportunity: 1) the quantity and qualities of the opportunities themselves; 2) the home location from which an individual seeks to access opportunities; and 3) the transportation options that enable their ability to access them. A multitude of other ‘personal and social conversion factors’ also influence geographies of opportunity. For the purposes of the present study, the most important of these is a household’s ‘housing budget,’ defined as the amount a household can afford to spend on housing.
Given the costs associated with car ownership, and given that low-income households are much less likely to have access to a private vehicles than more affluent households, public transit often plays a vital role in providing access to opportunities for those with limited means. The present study therefore conceptualizes geographies of
Page 1


opportunity for low- and moderate-income households as being bounded by two circumstances: 1) the ability to access employment opportunities via modes other than private auto (‘transit accessibility’) and 2) the ability to afford housing in transit-accessible areas, and thus benefit from the advantages conferred by access to transit (‘housing affordability’).
personal choice
achieved functionings
O
well-being
Figure 1.1. Basic conceptual framework
EXISTING KNOWLEDGE
The role of transit in maximizing geographies of opportunity for low- and moderate-income individuals is well-established. However, not until recently has the affordability of housing in transit-accessible areas been recognized as being equally integral. Two areas of concern around housing affordability in transit-rich neighborhoods have emerged in the existing literature. The first relates to direct displacement effects associated with property value increases in areas with high-frequency transit that render long-standing residents no longer able to afford housing in transit-accessible neighborhoods (often referred to as
Page 2


‘transit-induced gentrification’). The second area of concern relates to increased demand for transit-accessible locations on a regional scale, resulting in exclusionary displacement effects whereby newly-formed and relocating households with lower incomes are unable to afford housing in these neighborhoods and instead locate to more auto-oriented areas of the metro.
In recent years, a strand of literature focused on a ‘location efficiency’ approach to thinking about issues of affordability has emerged to suggest that local and regional displacement in transit-rich areas may be less of a threat when housing and transportation (‘H+T’) costs are considered in combination. A ‘location efficiency narrative’ therefore acknowledges that housing costs may be higher in transit-accessible areas, but counters that reduced transportation expenditures are likely to offset these costs resulting in better overall H+T affordability. While the location efficiency perspective has gained prominence in policy conversations, it remains unclear whether it is supported by on-the-ground empirics.
A critical review of the existing literature around transit-induced gentrification and location efficiency reveals four significant shortcomings in our understanding of the relationship between transit accessibility and housing affordability in U.S. metros (Chapter 2). First, the literature focuses predominately on effects associated with fixed-rail transit, thus neglecting the large role buses play in providing access across U.S. metros. Second, existing research has little to say about landscapes of affordability for market-rate renters, who are arguably the group most vulnerable to displacement. Third, only a handful of studies account for spatial error, despite the clear presence of spatial dependence associated with these phenomenon and well-documented evidence that ignoring these effects may lead to unreliable findings. Finally, and perhaps most seriously, all but one study rely upon inherently flawed ratio-based measures of housing affordability.
ANALYTICAL APPROACH
The present dissertation takes as its starting point a puzzle about whether transit-rich
Page 3


neighborhoods are indeed more affordable, as a location efficiency approach would suggest, when affordability is examined using measures and methods that address the four key gaps in the literature. I address this puzzle in two analytical parts. In Part 1, I discuss the ways in which typical measures of housing affordability are likely to mischaracterize the opportunities and challenges low- and moderate- income households experience in securing affordable housing, a topic which has received surprisingly little critical attention in both scholarly and public discourses (Chapter 4). I then introduce and provide a detailed methodology for constructing a ‘location-sensitive residual income’ (LSRI) measure of affordability which improves upon typical measures to more accurately reflect the financial realities faced by households as they seek affordable housing (Chapter 5). The LSRI approach defines housing as ‘affordable’ when a household is able to pay for its housing costs while still meeting its basic non-housing needs within the bounds of its income. Two LSRI measures are developed for a set of theoretical low- and moderate-income households that are specified to vary based on composition (size, presence of children), financial circumstances (income, childcare requirements) and location within the region (which determines transportation costs).
The first measure identifies a household’s ‘housing budget,’ or the amount of monthly income that remains available for housing after the household covers the costs of the goods and services that are required to sustain a basic standard of living (Figure 1.2). A second ‘supply’ measure is calculated using data from the U.S. Census American Community Survey to identify the quantity of rental units that are affordable within a particular household’s housing budget. The two LSRI measures are calculated for six household profiles at the block group level. Analyses specifically focus on the conditions experienced by households who are likely to earn too much to qualify for subsidy, but not enough that securing stable affordable rental housing is a foregone conclusion. These households are highly vulnerable to displacement effects since they are subject to the whims of rental
Page 4


markets while possessing little ability to cover higher premiums. Market-rate rental housing is also important to study because the vast majority of eligible households are unable to secure public assistance and must instead rely on unsubsidized housing.
‘non-H+T’ costs
Housing _ Household budget "" income
Child-
care
Food - Medical
Other ____V
T ransportation
Varies on household composition
Varies on Varies on
household household income composition & residential location
Figure 1.2. Location-sensitive residual income housing budget calculation
Comparisons between results of an analysis undertaken for the Denver metro using LSRI measures and results for the same metro generated using more typical measures
demonstrate how standard approaches mischaracterize - and likely overestimate - how much households with limited means can afford for housing (Chapter 6). As a consequence,
analyses relying on typical measures, including those related to the location efficiency perspective, may underestimate the challenges facing low- and moderate-income
households and overestimate the supply of rental units affordable to them. Results of this comparison point to the importance of accounting for the effects of household composition and financial circumstances in measuring housing affordability. By directly incorporating these factors, as well as those related to variations in transportation costs, a LSRI measure equips practitioners and policymakers with robust tools for exploring and developing
targeted interventions that account for nuances in landscapes of affordability.
In Part 2 of the dissertation, I employ LSRI measures to examine the current geographies of transit accessibility and housing affordability that low- and moderate-income renters confront as they seek housing in eight U.S. metros. I specifically address two research questions:
Page 5


• To what extent are supplies of rental housing that are affordable for low- and moderate-income households located in areas with high transit accessibility? (Research Question 1) (Chapter 7)
• And second, what is the relationship between transit accessibility and supplies of affordable rental housing, when controlling for key characteristics of the built and social environments that are likely to influence that relationship, as well as for spatial dependence effects? (Research Question 2) (Chapter 8)
These investigations are conducted for the universe of U.S. metros with ‘second-generation’ regional rail, which are likely to experience a specific set of challenges that speak both theoretically and practically to issues of transportation justice. These metros (defined as core-based statistical areas and identified by their core cities) are: Dallas, Denver, Houston, Los Angeles, Minneapolis, Portland, Salt Lake City, and Seattle. RESULTS: GEOGRAPHIES OF TRANSIT ACCESSIBILITY AND HOUSING AFFORDABILITY
After constructing LSRI measures for each metro, I address Research Question 1 by calculating the supply of rental units that are both affordable to a defined set of low- and moderate-income households and located in areas with high transit accessibility. I compare this analysis to the supply of affordable units located in areas with zero or low transit accessibility. Transit accessibility is defined as the percent of regional jobs that can be reached within a 45-minute transit commute. Areas with accessibility levels above the nonzero average accessibility are considered ‘high’ accessibility while those below the non-zero average are identified as ‘low’ accessibility. ‘Zero’ accessibility areas are those in which no jobs are reachable by transit within 45-minutes. ‘Accessibility ratios’ - the ratio of the number of affordable units located in zero/low accessibility areas to the number of affordable units located in high accessibility areas - are constructed for each of the household profiles. These accessibility ratios are then compared to the ratios for metro-wide supplies of rental
Page 6


units (regardless of their affordability) to detect deviations from metro-wide distributions.
Results indicate that the extent to which affordable rental housing is located in areas with high transit accessibility varies between metros, and in some cases, by household profile within the same metro. Findings for Denver and Los Angeles point to strong geographies of opportunity: All low- and moderate-income households are expected to find larger supplies of affordable rental housing in high accessibility areas, despite the fact that the majority of metro-wide rental units are located in zero/low accessibility areas. Patterns in Dallas and Houston, however, point to relatively weak geographies of opportunity, with larger supplies of affordable rental units in areas with zero or low transit accessibility. Results for the remaining four metros - Minneapolis, Portland, Salt Lake City, and Seattle -are mixed across household profiles. While the majority of rental units affordable to low housing budget households in these metros are located in high accessibility areas (suggesting strong geographies of opportunity), the majority of supplies affordable to more moderate housing budgets are located in areas with zero or low access (pointing to weak geographies).
RESULTS: THE RELATIONSHIP BETWEEN TRANSIT ACCESSIBILITY AND HOUSING AFFORDABILITY, ACCOUNTING FOR OTHER KEY FACTORS
Research Question 2 delves deeper into the complex relationship between transit accessibility and housing affordability by accounting for key factors that are likely to influence both phenomena. For this analysis, I first use multivariate spatial error regression to model the global relationship between transit accessibility (the primary explanatory variable) and supplies of rental units that are affordable within the housing budgets of two theoretical households (the outcome variables). These models control for the effects of various aspects of density, land use mix, housing tenure, and socio-economic conditions that have been shown to influence affordability. The presence of spatial dependence is also modelled through inclusion of a spatially-weighted error term. This effort results in two
Page 7


models for each metro: One for a ‘low housing budget’ household (one adult earning 50% AMI with one child who does not require childcare) and another for a ‘moderate housing budget household’ (two adults earning 100% AMI and two children, one of whom requires childcare). I then use the same model specifications in geographically-weighted regression (GWR) to explore how local relationships between accessibility and affordability vary across space. This analysis does not intend to draw causal conclusions about the relative effects of specific factors on supplies of affordable housing. Rather, the models are intended to isolate the relationship between the level of transit accessibility of a neighborhood (block group) and the supply of housing that is affordable to households with limited means located within it.
Results of global (spatial error) models demonstrate that in five metros - Dallas, Denver, Los Angeles, and Minneapolis - higher levels of accessibility are associated with larger supplies of affordable rental housing holding all else constant, thus pointing to strong geographies of opportunity. A positive (although not statistically-significant) relationship between accessibility and affordability also exists in Houston. These positive effects are quite substantial in some cases. For example, holding all other variables at mean values, block groups in Dallas with 10-percent higher transit accessibility are associated with an average of 36 additional rental units that are affordable to moderate housing budget households. However, these promising findings are tempered somewhat by local (GWR) results, which indicate that positive global coefficients mask the presence of negative local relationships for some metros.
In global models for the remaining three metros, higher levels of accessibility are associated with fewer affordable units, pointing to weak geographies of opportunity. In Portland and Seattle, results indicate a statistically-significant and negative relationship, controlling for other factors. Salt Lake City also demonstrates a negative, although not statistically-significant, relationship. These effects can be rather large: In Seattle, for
Page 8


example, 10-percent higher accessibility is associated with an average of 21 fewer affordable units, holding all other factors at mean values. However, GWR results suggest that pockets of positive local relationships may exist in some metros.
CONCLUSIONS AND IMPLICATIONS
Results from these investigations are synthesized into a typology that describes the geographies of opportunities experienced by low- and moderate-income households in the eight U.S. metros analyzed. The horizontal axis of the typology identifies whether a majority of affordable rental units are located in zero/low accessibility areas (weak geographies) or high accessibility areas (strong geographies). The vertical axis describes whether higher levels of accessibility are associated with additional affordable rental units (strong geographies) or fewer affordable units (weak geographies) when controlling for key factors and spatial error. These axes form four general typologies, each of which calls for a unique set of policy prescriptions (Figure 1.3).
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Minneapolis
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Salt Lake City
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Portland
(moderate)
very weak

very strong
Denver
(low & moderate)
Los Angeles
(low & moderate)
Minneapolis
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Salt Lake City
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higher accessibility associated with decreases in supply of affordable units
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Figure 1.3. Geographies of opportunity: A typology
Page 9


Households with low and moderate housing budgets are likely to encounter ‘very strong’ geographies of opportunity in Denver and Los Angeles. In these metros, supplies of affordable units are larger in high accessibility areas, and global models indicate a positive relationship between accessibility and affordability. Low and moderate housing budget households in Seattle are not as fortunate. Results indicate households in these metros face ‘very weak’ geographies of opportunity, with larger supplies of affordable units in zero/low accessibility areas, and negative relationships between the variables.
Households in Dallas and Houston demonstrate ‘somewhat weak’ geographies of opportunity. In these metros, higher accessibility is associated with larger supplies of affordable housing, holding other factors constant. Yet analysis indicates that the majority of affordable rental units are located in areas with zero/low accessibility areas. Geographies of opportunity for the remaining three metros differ by household. In Salt Lake City and Portland, low housing budget households have ‘somewhat strong’ geographies of opportunity. However moderate housing budget households in the same region experience ‘very weak’ geographies. Similarly, low housing budget households in Minneapolis enjoy ‘very strong’ geographies of opportunity while moderate housing budget households face ‘somewhat weak’ geographies. These findings point to a ‘barbell’ effect whereby geographies of opportunity are relatively strong for the very low income and more affluent, but are very weak for more moderate income households.
In addition to generating important insights into the complex relationships between accessibility and affordability across the U.S., results also contribute to an understanding about the ways in which current geographies are consistent with - and challenge - a location efficiency narrative. Taken together, analyses conducted using the robust LSRI measures lend mixed support. In some cases - Denver and Los Angeles, most notably -the majority of affordable housing is indeed located in transit-accessible areas and the relationship between accessibility and affordability is positive, as a location efficiency
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approach would predict. However, findings in other metros - Seattle, Dallas, and Houston in particular - are less supportive, with higher levels of accessibility associated with fewer affordable rental units. In fact, low- and moderate-households in many metros are more likely to encounter larger supplies of affordable rental units in areas with little or no transit accessibility (and consequently, higher levels of auto-dependency) despite the likelihood of lower transportation costs. These findings underscore that while the location efficiency approach offers a useful perspective, policymakers cannot assume that high housing costs will be offset by lower transportation costs.
Results also support a number of methodological conclusions. First, findings from the spatial error regression models demonstrate that failing to account for spatial dependence is likely to lead to biased results and conclusions thereby underscoring the importance of accounting for spatial error, particularly given the policy relevance of investigations around accessibility, affordability, and related phenomena. Model results also point to the large influence that elements of the built and social environments can have on the relationship between accessibility and affordability and highlight the need to fully account for mediating factors. Finally, GWR results demonstrate that global models may hide variations in neighborhood-level dynamics in ways that may have large policy implications. For example, results indicating positive global relationships may mask the need to address weaker geographies of opportunity that could exist at the neighborhood level. In other cases, global relationships that point to weak metro-wide geographies of opportunity may obscure the need for interventions that preserve strong local geographies. Finally, the largest methodological contribution of this work is the LSRI measure itself, which equips policymakers and practitioners with a set of tools to support targeted interventions aimed at maximizing affordability in transit-accessible locations.
Findings shed light on the varying conditions that exist across U.S. metros with ‘second-generation’ regional rail transit, and thus provide insights for metros with similar
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characteristics that are currently undertaking or considering large transit expansion projects. For example, results for some metros suggest that threats of exclusionary displacement in transit-accessible areas may be cause for less concern than current discourse might suggest. This is not to say that issues of transit-induced gentrification and displacement should be ignored, but rather that conditions may require a particular set of policy interventions aimed at preserving current affordability. At the same time, results for other metros demonstrate evidence of considerable exclusionary displacement in transit-accessible areas. If there is a generalized finding that holds true across all cases, it is therefore that geographies of affordability and accessibility are complex, and should be the subject of continued scholarly and practical research that delves deeper into the mechanisms at play and the social, institutional, and environmental factors that explain variations in the geographies of opportunity that exist across metros.
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CHAPTER II
GEOGRAPHIES OF OPPORTUNITY, TRANSIT ACCESSIBILITY, AND HOUSING AFFORDABILITY: THEORETICAL AND PRACTICAL FOUNDATIONS CONSIDERING SOCIAL JUSTICE IN THE CONTEXT OF U.S. METROPOLITAN TRANSPORTATION PLANNING AND POLICY
This dissertation takes as its starting point the question, what does it mean fora transportation system to be ‘just’? I begin this investigation with a brief overview of six contemporary frameworks that are commonly used in exploring issues of social justice in the context of U.S. metropolitan planning and policy. I focus particular attention to how these frameworks can help in understanding issues of transportation justice. I then provide a deeper discussion of one of these perspectives - Sen and Nussbaum’s ‘capabilities approach’ - which I use as the basis for a conceptual framework that guides the present research.
After introducing the capabilities approach, its constituent components, and its applicability to the transportation justice arena, I next describe how I combine this approach with the concept of ‘geographies of opportunity’ in order to form the conceptual framework guiding the dissertation. This conceptual framework focuses on exploring geographies of opportunity for low- and moderate-income households in terms of two aspects of transportation justice: the ability to access employment opportunities by public transit (‘transit accessibility’) and the ability to afford housing in transit-accessible areas (‘housing affordability’). It is important to acknowledge that there are many more issues that bear upon transportation justice than the two defined by this framework. For examples, issues related to environmental and racial justice are particularly important to consider in future research, but remain outside of the bounds of the present study.
The sections that follow synthesize existing empirical research on the affordability of housing in transit-accessible neighborhoods, including a summary of a substantial body of
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literature that investigates property value effects related to transit investments, as well as local gentrification and regional exclusionary displacement thought to be associated with these effects. I then discuss a ‘location efficiency’ thread of the literature, which suggests that concerns about direct and exclusionary displacement in transit-accessible locations may be less of a threat than often thought when housing and transportation costs are considered in combination. I conclude by outlining four significant shortcomings in our understanding of current geographies of transit accessibility and housing affordability in general, and more specifically, of the extent to which the location efficiency narrative plays out empirically.
Contemporary Perspectives on Social Justice
Since the 1970s, liberal political philosophies, particularly as embodied in John Rawls’ A Theory of Justice, have served as the foundation for contemporary discussions of social justice. This approach, which is rooted in the modern welfare state and notions of social democracy, sets forth a series of rules - the ‘Principles of Social Justice’ - that define the “distribution of benefits and burdens of social cooperation required for a “well-ordered society” (Rawls, 1971:4). These principles do not outline a specific notion of morality or define how individuals should live, but rather set forth basic rules which allow individuals to pursue their own vision of the ‘good life’ (Gutman, 1985) and guide how goods should be allocated so that all people - most importantly, the least advantaged - can achieve their particular vision. Of these, Rawls’ ‘Difference Principle’ is commonly cited when assessing the extent to which the distribution of benefits and burdens across populations in a metropolitan context is ‘just.’ This principle recognizes that in modern society, some people are born into more advantage than others, and therefore states that primary goods should be distributed unequally only when such a distribution benefits the least advantaged in society (Rawls, 1971).
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Following Rawls, achieving transportation justice requires that access to transportation infrastructure is distributed such that the groups and individuals who are least transportation-advantaged - low-income and zero-vehicle households among them - are ensured the highest levels of access. Although a Rawlsian approach has gained considerable support among transportation scholars and practitioners, it is not without its problems. First, it is not clear if transport can be understood as a primary good. While there is no evidence that Rawls would have included accessibility within the realm of primary goods, some scholars argue that access to important destinations (e.g. employment, schools, health care, and groceries) can be considered such (Van Wee & Geurs, 2011). However, others argue convincingly that transportation accessibility carries different social meanings for different people, and thus cannot be considered a primary good (Martens, 2012; Martens et al., 2012). It is also difficult to identify the ‘least advantaged’ in a Rawlsian approach since different people require different levels of access to fulfill their needs (Beatley, 1988). For instance, the elderly are likely to have much less need to access employment opportunities, but may require a higher level of access to health care facilities. Rawls’ focus on the individual is also problematic, since it is the nature of transportation infrastructure to provide access to collective groups, not specific individuals (Martens, et al., 2012).
A communitarian perspective on social justice offers an alternative to liberal political approaches by downplaying the importance of equality among individuals, and instead emphasizing the importance of understanding equity among groups of people (Buchanan, 1989; Gutman, 1985; Young, 1990). This emphasis on the community-level is generally useful in assessing social justice in the context of transportation planning and policy, since transportation access is provided to groups, not individuals (Martens, et al., 2012). Perhaps the most useful element of the communitarian approach in terms of its application to transportation justice is its challenge of the Rawlsian conception of ‘primary goods.’ Michael
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Walzer argues in his Spheres of Justice (1983) that primary goods are socially-constructed, carrying vastly different meanings for different people. Therefore, no single distribution criteria can be applied to all goods, as Rawls would suggest. So while it may be appropriate to exchange certain goods according to free market principles, it is entirely inappropriate to do so with goods that have different meanings to different people. According to Walzer, these goods should be exchanged within different ‘distributive spheres’ according to principles which correspond with the good’s social meaning (Walzer, 1983). It follows that because the transportation is a socially-constructed ‘good’ with vastly different meanings for different people, it is not appropriate to assess the ‘just’ distribution of transportation access through a simple market exchange that assumes it holds the same value for all people. The communitarian perspective, however, does not suggest an alternative means of assessing the just distribution of transportation access, leaving little guidance for practical application to transportation planning and policy.
A critical political economy approach critiques Rawls and liberal political philosophy for both its widespread acceptance of market-based capitalist approaches that ignore the structural factors that perpetuate injustice (Fainstein, 2010; Harvey, 1973) and for its exclusive focus on outcomes (distributive justice) to the exclusion of procedural justice (Harvey, 1973; Young, 1990). Critical political economists thus argue that in failing to address the structural processes that produce and reinforce injustices, a liberal approach leaves true justice unattainable. In this view, justice can only be achieved when we address the underlying power structures and institutions that give rise to inequities. In other words, just metropolitan planning and policymaking must go beyond specific cases of injustice to “challenge the legitimacy of the use of power itself” (Marcuse, 2009: 95).
While the critical economy approach does not offer a complete evaluative framework, several aspects of its argument are useful to understanding transportation justice. The emphasis on attending to larger structural processes that perpetuate injustice is particularly
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important to a transportation policy arena in which institutions built long-ago on discriminatory foundations - for example, the citing of urban highways in predominately African-American neighborhoods - may render current decisions unjust, even if the current policies have no discriminatory intent. Since decision-making around transportation infrastructure is often made based on current travel patterns and without regard to latent demand (Martens, 2012), past decisions may continue to perpetuate injustices borne by disadvantaged populations. A critical political economy approach thus reminds us that past decisions should be considered when aiming to equitably distribute transportation access through current decision-making around infrastructure.
This approach’s recognition of policy framing as an exercise of power is also important to understanding transportation justice. As Flyvbjerg (1998) notes, “one of the privileges of power... is the freedom to define reality” (322). Transportation justice thus requires daylighting the interests that lie behind the framing pf claims around who will benefit from -and who will be impacted by - specific transportation policies and projects.
The communicative approach, which has emerged in recent decades drawing from the work of Habermas and his Communicative Rationality, is also instructive in understanding aspects of transportation justice. This perspective argues that the best decisions are those reached through genuinely democratic deliberation and communication between parties resulting in mutual understanding and consensus (Fischer & Forester,
1993; Healey, 1996, 1997). The communicative approach therefore suggests that the primary means of assessing the justness of policy and planning decisions is to evaluate the inclusiveness of their decision-making process (Healey, 2003). A related perspective, the discursive approach, takes a more critical tact by evaluating how discourse - defined as a specific set of ideas and concepts conveyed through language - is used by policy actors to advance, interpret, and manipulate a particular set of interests and values (Hajer, 1993). Once they become dominant, specific discourses becomes codified within institutional
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structures, which then serve to reproduce the dominant discourse. This approach therefore argues that because all planning and policy decisions are rooted in the ideological assumptions embedded within these institutions, understanding discourse is “basic to the understanding and functioning of the system, including understandings of social justice” (Fischer, 2009: 57).
It is particularly important to understand how discourses in transportation planning and policy are deployed given that powerful interests attracted to land development opportunities associated with large capital investments, often seek to influence discourse to their advantage (Willson, 2001). It is also important to understand how dominant discourses are codified in institutions governing transportation planning and policy, and how those institutions reproduce ideas embedded within the discourse. A final approach, the Just City Model (Fainstein, 2010), integrates many of the principles of the frameworks reviewed above to offer a hybrid approach to understanding justice in the context of U.S. metropolitan planning and policy. In recent years, the Just City model has gained considerable prominence among urban policy and planning, and is proving to be one the most cohesive contemporary approaches to understanding justice in the city (Garcia & Judd, 2012). The model attends to both distributive and procedural aspects by adopting a critical political economy definition of social justice as ‘just distribution, justly arrived at’ (Harvey, 1973:357). However, the Just City emphasizes that while inclusive processes are a worthy goal, they do not guarantee just outcomes and in many cases may instead reflect power imbalances that work against just outcomes (Fainstein, 2001, 2010). Therefore, justice is ultimately achieved through substantive outcomes.
The result of the Just City model is a set of three principles intended to serve as an evaluative framework against which specific policy and planning interventions can be judged. The first principle, ‘equity,’ requires that the policy does not reinforce inequity, but allocates outcomes so that the condition of the least advantaged is improved. The second
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principle, ‘diversity,’ judges the policy based on the extent to which it promotes social inclusion and diminishes social exclusion. The final principle, ‘democracy,’ recognizes the existence of open, democratic processes that empower and educate non-elite groups as being necessary, but not sufficient, for justice to be achieved through policy and planning interventions.
Rather than relying on Rawlsian notions of ‘primary goods’, the Just City models follows a capabilities approach that instead evaluates justice based on whether individuals have access to the resources and opportunities necessary to fulfill their full potential (Fainstein, 2000). The capability approach framework is rooted in the work of economist Amartya Sen and philosopher Martha Nussbaum, who argue that justice is realized only when all individuals have the opportunity to achieve their full range of capabilities, defined as what people have the potential to do, regardless of whether individuals take advantage of those opportunities (Nussbaum, 2000; Sen, 1999). This framework thus constitutes a critical strand of the liberal political philosophy tradition. While it remains rooted in the idea that that individuals should have the freedom to define their own conception of the ‘good life’ in keeping with the norms of democratic and pluralistic society, it evaluates justice not in terms of how many goods (or how much income) a person possesses, but instead focuses on the extent to which the goods enable people to achieve the lives they want to lead (Robeyns, 2005). In other words, a capabilities approach does not consider primary goods to be ends in and of themselves, as Rawls does, but instead asks what the goods can do for people as they seek their conception of a ‘good life’ (Hananel & Berechman, 2016).
This framework is useful in thinking about transportation - which does not fit neatly within the Rawlsian notion of ‘primary goods’ - because it addresses not only the distribution of transportation infrastructure itself, but also the extent to which that infrastructure enables access to the opportunities that allow individuals to reach their full potential. In the sections
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that follow, I first outline the capabilities approach in more depth, then discuss how I deploy to conceptualize transportation justice in the present study.
The ‘Capabilities Approach’ Framework
The capabilities approach is quite complex, with many inter-related components that continue to undergo scholarly debate. However, the basic building blocks of the approach -and the relationships between those building blocks - are stable across the literature.
Figure 2.1 provides a basic model describing these basic components and how they relate to one another.
There are three primary components of a capability approach: ‘Primary goods,’ ‘capabilities,’ and ‘functionings.’ In this framework primary goods are the material and nonmaterial resources that people need in order to sustain a basic standard of living and in order to pursue their conception of the ‘good life’ (Sen, 1999). While a Rawlsian approach considers social justice to ultimately be defined as the just distribution of goods, a capability approach instead specifies the end goal as what can be achieved with the primary goods in terms of a person’s pursuit of well-being.
Capabilities represent the set of opportunities that are available to a person as they seek to achieve the various things (s)he values in leading her/his life. For Sen, social justice requires that all people possess a basic set of capabilities: the ability to be well-nourished, to have shelter, to move freely, and to participate in the political, civic, and social life of a community (Sen, 1980). Nussbaum takes the idea of a minimum threshold for social justice farther by specifying a list of 10 required capabilities which include basic functions like being able to have good health and nutrition, being secure from violence, being able to form attachments to other people, and being able to participate in political choices (Nussbaum, 2006).
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Figure 2.1. Capabilities approach framework
The capabilities approach recognizes that different people will take advantage of the same set of capabilities to greater and lesser extents. The approach therefore makes a distinction between capabilities, which constitute a set of opportunities, and the things people actually achieve using those capabilities, or their achieved functionings. This distinction recognizes that people with identical sets of capabilities are likely to make different choices about whether or not to take advantage of those capabilities, depending on their particular personal characteristics, circumstances, values, and conceptions of wellbeing. For this reason, a capability approach advocates that policies should ultimately be judged on the capabilities (i.e. opportunities) they provide, rather than the achieved
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functions that people choose to catalyze (or not) in order to transform those opportunities into action (Robeyns, 2005).
A number of factors shape the relationship between a primary good, the capabilities it enables, and a person’s achieved functionings. These material and non-material conditions are referred to in the capability approach as conversion factors. Personal conversion factors are individual-level characteristics and circumstances that influence how a person is able to convert resources (primary goods) into opportunities (capabilities). These might include cognitive and physical abilities, financial circumstances, and the presence of children or other individuals dependent on the person for their care.
Social and environmental conversion factors describe the overall background within which primary goods are converted into capabilities - factors such as public policies, institutions, social norms, power relations, and contextual features. These background factors influence the primary goods themselves, the capabilities that can be derived from them, and a person’s own ability to take advantage of those capabilities. Finally, capabilities are transformed into achieved functionings only when an individual makes a personal choice to take advantage of them. The choices people make to either catalyze an opportunity (capability) into an actual achievement (functioning) are influenced in large part by their individual value systems, personal circumstances, and social and environmental factors.
Applying a Capabilities Approach Framework to Conceptualize Transportation Justice
The capabilities approach offers a useful framework for evaluating the extent to which a broad range of policies and planning interventions promote individual well-being and social justice, including those related to transportation. The approach does not purport to be a complete theory of social justice, and thus cannot be used to explain transport disadvantage or inequalities (Robeyns, 2005). I therefore adopt the capabilities approach
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not as a predictive or explanatory model, but as a framework through which to conceptualize and evaluate issues of transportation as they relate to social justice.
The transportation justice literature has shown growing interest in the capabilities approach in recent years, with a small number of studies seeking to apply the approach to questions around the distribution of benefits and burdens associated with transportation infrastructure investments both theoretically (Beyazit, 2011; Hananel & Berechman, 2016) and empirically (Baumgartner et al., 2009; Gossling, 2016; Mullen et al., 2014; Smith et al., 2012). In this literature, primary goods are generally conceived of as the transportation infrastructure and service itself (for example, private vehicles, public transportation, bicycle lanes, etc.). Capabilities are typically framed as the ability of people to get to the places they need to go (in other words, accessibility) that is provided by the transportation infrastructure. A person’s choice to take advantage of the accessibility created by this infrastructure (or not) then determines her/his achieved functionings, or travel patterns. A large number of personal, social, and environmental conversion factors bear on this process.
A capabilities approach framework therefore acknowledges that different people will have different travel patterns (achieved functionings) depending on the transportation infrastructure and service available to them, the destinations they need to reach, their personal and financial circumstances, and any number of social and institutional factors. However, in this framework, what matters in terms of transportation justice is not these ultimate travel patterns (functionings), but the extent to which an individual has the opportunity (capability) to get where (s)he needs to go in order to achieve the functionings that support her/his preferences and well-being. In other words, the capabilities approach suggests that transportation justice should ultimately be evaluated based on the extent to which a transportation system grants individuals and groups the opportunity to access the places they need to go in order to reach their full potential.
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The capabilities approach thus dovetails well with the ‘geographies of opportunity’ frame introduced by Galster & Killen (1995), which has gained prominence in recent decades among practitioners and advocates working on issues of spatial and social justice in metropolitan areas (‘metros’). In this frame, ‘opportunities’ constitute the resources - jobs, education, child care, health services, healthy foods, social and civic activities - that enable individuals and families with limited means to improve their financial and social circumstances (Briggs, 2006). An individual’s ‘geography of opportunity’ is thus the extent to which (s)he is able to access these resources.
The conceptual framework developed to guide the present study (shown in Figure 2.2) reflects an integration of the ‘geographies of opportunity’ frame with a capabilities approach. When viewed through the lens of a capabilities approach, an individual’s ‘geography of opportunity’ is analogous to her/his set of capabilities. Three components related to physical planning and policy shape geographies of opportunity: 1) the quantity and qualities of the opportunities themselves; 2) the home location from which an individual seeks to access opportunities; and 3) the transportation options that enable their ability to access them. In a capabilities approach framework, these three components - opportunities, housing stock, and transportation infrastructure - can be thought of as the primary goods that are then transformed into capabilities. A multitude of other personal and social conversion factors also influence an individual’s geography of opportunity. For the purposes of the present study, the most of important of these conversion factors is a household’s ‘housing budget,’ defined as the amount a household can afford to spend on housing while still fulfilling its other basic non-housing needs.
Geographies of opportunity (capabilities) are thus defined as being shaped by the configuration of the three primary goods - opportunities, transportation, and housing - as mediated by the household’s housing budget (one of many conversion factors). Given the costs associated with car ownership and operations, and given that low-income households
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are much less likely to have access to a private vehicles as compared to more affluent households, public transit often plays a vital role in providing access to opportunities for individuals and families with limited resources (Giuliano, 2005; Taylor & Morris, 2015; Tomer, 2011). The ability to access employment opportunities by transit is specifically evaluated in the present study because of the importance of income generation in supporting financial, physical, and social well-being. I therefore conceptualize geographies of opportunity for low- and moderate-income households as being bounded by two circumstances: 1) the ability to access employment opportunities via modes other than private autos (‘transit accessibility’) and 2) the ability to afford housing in transit-accessible areas (‘housing affordability’).
Consistent with the capabilities approach, this framework acknowledges that ‘geographies of opportunities’ must be activated by personal choice in order to convert them to ‘achieved functionings.’ For example, choices around residential locations (i.e. the decision to live in a transit-accessible neighborhood) and mode choice (i.e. the decision to use available transit service as opposed to other modes) determine whether a household will benefit from the opportunities that affordable transit-accessible housing confers. However, the framework guiding the present research leaves issues of personal choice and resulting travel patterns to future research and instead focuses on exploring the capabilities (geographies of opportunity) of low- and moderate-income households in terms of transit accessibility and housing affordability, as determined by the supply of housing available within a household’s housing budget.
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-> primary goods - transit infrastructure and service - housing stock - opportunities -jobs, education, health services, child care, social activities, etc.
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Figure 2.2. Conceptual framework
The operationalization of both transit accessibility and housing affordability are discussed in considerable depth in the chapters that follow. Briefly, ‘accessibility,’ defined as the ease of reaching desired destinations, is bounded by two factors: the availability and qualities of transportation choices, and the distribution of destinations across space (Geurs & van Wee, 2004; Krizek & Levinson, 2012). Accessibility is one of the most well-established social outcomes of transportation (Jones & Lucas, 2012). It is particularly useful
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in assessing equity outcomes because it captures the relationship between people and the places that are important to them, accounting for both dimensions of transportation infrastructure as well as the distribution of important destinations across space and opportunities to access them (Grengs, 2012; Martens & Golub, 2012; Wachs & Kumagai, 1973). Following this conception, ‘transit accessibility’ is defined in the present study as the ease of reaching desired destinations by bus, rail, or other transit mode operated by a public transit agency.
The operationalization of housing affordability is less straightforward. Concerns about housing affordability have become a dominate theme in the public discourse around cities and regions in recent years. For example, a recent report authored by the National League of Cities found that a lack of affordable housing is identified by mayors nationwide in their ‘state of the city’ speeches as one of the top five issues that have a serious impact on the health of their cities (Langan et al., 2016). Yet, despite the ubiquity and importance of these issues, it remains unclear exactly what it means for housing to be ‘affordable.’ Furthermore, as I demonstrate in Chapter 4, typical measures of housing affordability often do not adequately reflect the financial circumstance of low- and moderate-income households, possibly resulting in misleading conclusions. In the present study, I introduce an improved measure of housing affordability that is reflective of a capabilities approach. A detailed discussion of this improved measure is provided in Chapter 5.
The Role of Transit in Shaping Geographies of Opportunity for Low- and Moderate-income Households
Access to transit among less advantaged populations is linked to numerous benefits, particularly in regards to securing and maintaining employment. Studies have found, for example, that transit-based job accessibility increases the probability of being employed among car-less households (Kawabata, 2003), among women welfare recipients (Ong & Houston, 2002) and among bus riders (Yi, 2005). Research also suggests that higher levels
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of transit accessibility are associated with higher numbers of hours worked per week (Kawabata, 2003) and the average annual weeks worked (Sanchez, 1999).
Beyond access to jobs, the availability of transit has far-reaching effects on people’s ability to access a wider range of opportunities that contribute to well-being including education, medical services, childcare, and other necessities (Bullard, 2003; Wachs, 2010). Research indicates that transit access is associated with improved physical well-being related to the ability to obtain regular health care and increased opportunities for physical activity (Delbosc, 2012). Transit accessibility is also linked to psychological well-being through the alleviation of social exclusion, which refers to a condition where residents living in areas with long-standing and concentrated poverty are unable to access employment, housing, and other services due to lack of transport and/or other barriers that severely limit their ability to fully participate in society and civic life (Dodson et al., 2010; Wells & Thill, 2012). Furthermore, transit accessibility is associated with financial well-being in the form of decreased household expenditures on transportation. The Center for Transit-Oriented Development (CTOD) reports that the average family spends approximately 19-percent of their income on transportation while households with access to transit spend only nine-percent (Center for Transit-Oriented Development, 2007), thus allowing for income to be spent on other life necessities (Jones & Lucas, 2012).
EMPIRICAL RESEARCH ON THE AFFORDABILITY OF HOUSING IN TRANSIT-ACCESSIBLE NEIGHBORHOODS IN THE U.S.
The role of transit access in shaping geographies of opportunity for low- and moderate-income households is well-established. However, not until recently has the affordability of housing in transit-accessible areas been recognized as being equally integral to the overall well-being of households with limited means. This recognition has been largely driven by growing demand for transit-accessible locations, which according to a study commissioned by the Federal Transit Administration is expected to double by 2030, calling
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into question the ability of lower-income households to afford housing in transit-rich neighborhoods and thus their ability to take advantage of the accessibility these locations confer (Thorne-Lyman et al., 2008).
Two areas of concern have emerged in regards to the affordability of housing in transit-rich neighborhoods. The first relates to property value increases in areas proximate to high-frequency transit and associated direct displacement effects in which long-standing residents can no longer afford to remain in highly-accessible neighborhoods. The second area of concern relates to increased demand for transit-accessible locations on a regional scale, resulting in exclusionary displacement effects whereby newly-formed and relocating households with lower incomes are unable to afford housing in these neighborhoods and instead locate in more auto-oriented areas of the metro.
In the below sections, I first review evidence from the existing literature related to property value effects in transit-accessible neighborhoods, as well as to local gentrification and regional exclusionary displacement thought to be associated with these effects. I then discuss the location efficiency narrative, a perspective that has emerged in recent years to suggest that local and regional displacement in transit-rich areas may be less of a threat than commonly thought when the cost of housing and transportation are considered in tandem. Finally, I review existing empirical research that sheds light on the relationship between housing affordability and transit accessibility in general, and on the location efficiency paradigm more specifically. Through this review, I conclude that our limited understanding of current geographies of housing affordability and transit accessibility in U.S. metros, including the extent to which the location efficiency narrative plays out empirically, is insufficient in a number of ways.
Effects of Transit Accessibility on Housing Costs
As with any amenity in a market economy, the value ascribed to transit accessibility would be expected to be capitalized in the value of land with access to transit service.
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Indeed, a substantial body of literature examining the effects of transit - and fixed-rail transit in particular - on the value of properties within station areas demonstrates that rail investments are generally, but not always, associated with higher premiums as compared to areas not served by rail. Research suggests that while properties located adjacent or very close to rail stations may experience slight reduction in values due to nuisance effects (Bartholomew & Ewing, 2011; Chatman et al., 2011; Golub et al., 2012), those outside the nuisance-zone but still within walking distance are likely to see a boost in values (Bartholomew & Ewing, 2011; Cervero et al., 2002; Cervero et al., 2004; Yan et al., 2012). These effects have been estimated to range from relatively small to rather large. A metaanalysis of 60 studies found that residential properties within one-quarter mile experienced a four-percent increase in value as compared to properties outside of station areas, controlling for other housing and neighborhood characteristics (Debrezion et al., 2007). However, another recent study found much larger effects - up to 42-percent increases - in areas within one-half mile of fixed-guideway bus and rail (Center for Neighborhood Technology, 2013). A smaller number of less recent studies have found decreases in property values in rail station areas (Bowes & Ihlanfeldt, 2001; Gatzlaff & Smith, 1993; Hess & Almeida, 2007).
Taken together, existing research suggests that property value effects of fixed-rail transit are largely dependent on a range of contextual factors1. The quality of the rail transit in terms of its frequency, geographic extent, service intensity, and the extent of congestion on parallel road systems has a large bearing on property values (Bartholomew & Ewing, 2011). In general, properties near commuter rail are likely to see greater increases than those near light rail, likely due to faster speeds, higher frequency service and more extensive geographical coverage (Bartholomew & Ewing, 2011; Debrezion, et al., 2007;
Hess & Almeida, 2007). Additionally, rail stations closer to the central business district and
1 For a thorough review of these factors, see Wardrip, 2011
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other activity centers are likely to see larger effects than those located farther away (Bartholomew & Ewing, 2011). Finally, the extent to which supporting policies, land use and zoning controls, and other developer incentives are offered by local jurisdictions can have a large effect property value outcomes (Cambridge Systematics, 1996; Cervero, et al., 2002; Cervero, et al., 2004).
The vast majority of research on the property values effects of transit accessibility has focused exclusively on fixed-rail transit, with very little attention paid to the effects of accessibility to non-rail transit. The few studies that exist in the western context focus on bus rapid transit (BRT), and find neutral to modest increases in property value premiums associated with investments in BRT (Government Accountability Office, 2012; Mulley, 2013; Mulley & Tsai, 2016). The lack of research on the relationship between transit accessibility regardless of mode constitutes a substantial gap in the literature given that buses often play a much larger role in U.S. transit networks than rail.
Comparatively little research has been conducted on the effects of transit accessibility on rental housing premiums. The few studies that exist demonstrate higher rental premiums in areas served by rail transit (Cervero, et al., 2004; Pollack et al., 2010; Wang et al., 2016). The lack of attention to the relationship between transit accessibility and rental housing costs is curious given that renters are more likely than home owners to use transit (Taylor & Morris, 2015) and that rail station areas are home to a disproportionate share of rental housing stock (Center for Transit-Oriented Development, 2006). Displacement Effects Associated with Transit Accessibility
While property value premiums in transit-accessible areas can be considered to be positive in some contexts, there is clearly potential for negative implications for low- and moderate-income households at both the local (station area) and regional geographies as rising housing costs leave households with limited means ‘priced-out’ of their existing housing and/or unable to afford new housing in transit-rich neighborhoods. Advocates and
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scholars have long-voiced concerns about so-called ‘transit-induced displacement’ effects in which increased housing costs in transit-accessible neighborhoods result in affluent households outbidding lower-income households (Chappie, 2009; Pollack, etal., 2010; Zuk & Chappie, 2015). These concerns have increased as the desirability of transit-oriented development (TOD) has grown among higher-income populations (Renne et al., 2016) and as evidence that demonstrates a growing demand for transit-accessible locations outstrips supply continues to mount (Dawkins & Rolf, 2016). Low-income renters in unsubsidized housing are particularly vulnerable to transit-induced displacement since they are subject to the whims of the housing market but have little available income to afford rising premiums. Although low-income residents living in subsidized rental units have greater security, they remain vulnerable to displacement as affordability requirements of units reach their sunset date, which is expected to occur in record numbers in the coming years (Mueller & Steiner, 2011). Indeed, many advocating on behalf of the interests of low-income populations view market-rate development in areas served by rail with skepticism, and in some cases have mounted challenges to TOD on the basis of social justice concerns (Rayle, 2014).
Evidence of gentrification effects in neighborhoods served by fixed-rail continues to grow, with a number of studies demonstrating disproportionately larger increases in home values and rents in areas served by rail transit as compared to areas in the same region not served by rail, as well as demographic changes in station areas indicative of patterns of gentrification and displacement. For example, Kahn (2007) identifies gentrification effects associated with rail transit investments, as marked by increases in home prices, increases in the share of college graduates, and increases in household income. These effects were found to be more pronounced in neighborhoods with ‘walk and ride’ stations as compared to those with ‘park and ride stations,’ although both show measurable effects. Using a survival analysis approach, Grube-Cavers & Patterson (2014) identified the presence of similar gentrification effects (as measured by changes in median income and education levels of
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station area residents) in their examination of commuter rail transit. In an analysis of rail transit systems across the U.S., Pollack et al. (2010) also identified shifts in the demographic and economic characteristics of rail transit station areas as compared to areas not served by rail in the same metros, with station areas residents generally becoming wealthier, housing becoming more expensive, and vehicle ownership becoming more prevalent. Recent research employing increasingly sophisticated methods to study transit-induced gentrification, including various spatial regression and geographically-weighted regression techniques, generally confirm earlier findings (Bardaka et al., 2015; Wang, et al., 2016; Zhong & Li, 2016).
Aggregated across an entire metro area, higher property values within individual transit-accessible neighborhoods contribute to dynamics at the regional level. In particular, localized gentrification effects occurring at a large enough scale are likely to lead to patterns of ‘exclusionary’ displacement (Marcuse, 1986) whereby more affluent groups are attracted to transit-rich neighborhoods in the urban core, thus resulting in a tightened housing market that makes it difficult for newly-formed and relocating households to compete for limited supplies of affordable housing near transit (Cervero, 2007; Chappie, 2009). Regional exclusionary displacement therefore shifts the ‘landscape’ of affordability for households, particularly those with limited means (and therefore, the fewest choices) (Pendall et al., 2012).
One likely result of these shifting landscapes is a circumstance where low-income residents living in transit-accessible areas of the urban core relocate to suburban areas as housing costs rise, requiring greater reliance on auto travel. This dynamic is captured in well-documented ‘suburbanization of poverty’ trends in which lower-income households are increasingly locating in auto-dependent suburban areas that are difficult to serve by transit and are lacking in supportive social services (Kneebone & Berube, 2013). Although there continues to be debate as to whether this characterization accurately reflects current
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geographies of poverty (Cooke & Denton, 2015), empirical evidence suggests that lower-income households are indeed commuting increasingly longer distances to reach jobs and are spending a larger portion of their income on transportation as a result when compared to more affluent households (Kneebone & Holmes, 2015; Roberto, 2008).
Perhaps a more fruitful characterization of these trends - and the one of primary concern in the present research - is the low-accessibility-ization” of poverty. The relocation of low-income households to suburban areas is not a problem in and of its self, and may in fact reflect changing preferences among these populations towards the set of resources and amenities available in suburban settings. However, the relocation of households with limited means to areas with low transit accessibility that require dependency on private vehicles is a problem given the inherent financial and social costs associated with car ownership, particularly among vulnerable populations.
The Location Efficiency Narrative: An Antidote to Concerns about Transit-Induced Displacement?
Another strand of literature focused on a ‘location efficiency’ approach to thinking about issues of affordability suggests that threats of displacement in transit-accessible areas may be less of a cause for concern than commonly thought when housing costs are considered alongside transportation costs. This perspective aims to make the interdependent relationship between transportation and housing costs more transparent to policymakers and the general public in the face of a growing ‘drive ‘til you qualify’ mentality among households attracted to inexpensive housing in far-flung suburban locations. Advocates of this approach argue that because transportation costs are not fully-capitalized into housing costs, housing and transportation (“H+T”) costs should be considered in combination to arrive at a more comprehensive understanding of ‘location affordability.’ The Center for Neighborhood Technology (CNT), an early advocate for this approach, first developed a measure of combined H+T costs across the U.S. (the “H+T Index”) with the
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clear intention of calling attention to the hidden high costs of commuting to more ‘affordable’ suburban areas (and the hidden low costs of transportation in more expensive urban areas) (Center for Housing Policy and Center for Neighborhood Technology, 2012).
A specific narrative is therefore implicit in the location efficiency approach: That while housing costs may be lowest in auto-dependent areas of the suburban fringe, transportation costs are likely be high in these areas, thus offsetting any affordability gains achieved through less expensive housing. Conversely, this perspective posits that although housing may be more costly in neighborhoods with close proximity to jobs, the ability to walk or bike to retail districts, and the availability of transit and non-motorized transportation options, lower transportation costs are likely to offset higher housing costs. This location efficiency narrative’ therefore acknowledges that housing may be more expensive in areas with high levels of non-auto accessibility, but counters that reduced transportation expenditures are likely to offset these costs resulting in better overall H+T affordability in these locations. This narrative has become increasingly embedded in the work of policymakers and advocates, including by federal agencies who have integrated it widely into transportation and housing programs and policies. One notable example of this is the joint effort by the U.S. Department of Transportation (DOT), Department of Housing and Urban Development (HUD), and Environmental Protection Agency (EPA) to develop the Location Affordability Index (LAI), a publicly-available dataset that estimates combined H+T costs for a series of theoretical household profiles at the block group level.
However, despite its widespread adoption, it remains unclear whether the location efficiency narrative is supported by on-the-ground empirics, particularly in light of the dynamics of local transit-induced displacement and regional exclusionary displacement in transit-accessible locations discussed above. A large body of research authored by the advocacy community has yielded results that are largely supportive of the claim that higher housing costs in transit-accessible locations are likely to be offset by lower transportation
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costs (for a recent example, see CNT, 2011). Findings from the few academic studies that explicitly examine the location efficiency narrative in the context of transit accessibility also demonstrate general support for this claim, with some exceptions. In their study of redevelopment projects in ‘shrinking’ cities, Tighe & Ganning (2016) find that lower transportation costs in areas that require less auto-dependency appear to offset higher housing costs. Another study of Auckland, New Zealand finds that while H+T costs are highest for commuters residing within transit-accessible employment centers where housing costs are exceptionally high, lower transportation costs offset higher housing costs in other transit-accessible areas (Mattingly & Morrissey, 2014). In an earlier study of the tradeoffs between housing costs and commute times (a proxy for transportation costs) among working families in seven metros, Cervero et al. (2006) find mixed support for the location efficiency narrative: High housing costs are offset by high levels of transit accessibility in some, but not all, regions. Hartell (2016) uses spatial lag regression models to demonstrate that transportation costs help to explain housing foreclosure rates (which she identifies as an observable measure of housing affordability), thus lending support for the location efficiency narrative.
Findings from several studies related to location efficiency also underscore that H+T affordability is associated with a variety of characteristics of the built and social environment beyond transit accessibility. For example, Renne et al.’s (2016) study of the areas within1/2-mile of over 4,000 fixed-rail transit stations finds that although station areas with characteristics embodying TOD (defined, broadly speaking, as dense, mixed-use development with pedestrian-oriented streets) have higher housing costs, households living in TODs spend four-percent less on combined H+T due to lower transportation costs. Hartell (2016) also finds that characteristics of urban form (e.g. housing and job density and land use mix) are important to consider alongside transit accessibility in explaining the relationship between H+T (un)affordability. A vast body of literature - the review of which is
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outside of the scope of this paper - affirms the relationship of urban form on transportation costs and behavior (for a comprehensive review of this literature, see Ewing & Cervero, 2010).
While existing research directly examining the location efficiency narrative offers some insight into the robustness of its claims, the literature is limited by its nearly-universal use of blunt ratio-based measures of affordability whereby housing is considered ‘affordable’ if combined H+T costs account for 45-percent or less of household income. The threshold used in the H+T approach (45% of income) is based in part upon a 30-percent threshold used for assessing housing affordability alone that has little theoretical or empirical basis and does not account for the ways in which a household’s characteristics and financial circumstances, particularly those related to the presence of children and associated childcare costs, affect the amount of income a household is able to afford for housing.
Issues associated with this, and other typical measures of affordability are discussed in detail in Chapter 4.
A single study relevant to issues of location efficiency recognizes the limitations of the typical ratio-based measure of H+T affordability by employing an alternate approach -the residual income measure - to explore the extent to which supplies of housing that are affordable to low-income renters both with and without children are located in rail-accessible areas of Montreal and Vancouver (Revington & Townsend, 2016). Use of this more nuanced measure of housing affordability yields findings that are less supportive of the location efficiency narrative. In particular, the authors find that housing affordable to low-income households is less plentiful in areas served by rail transit, particularly in central city locations. The authors also find that households with children face much more challenging circumstances in securing affordable rental housing due to the fact that a lower proportion of their income is available for housing. These findings suggest that the use of reductive ratio-based measures of affordability may misrepresent geographies of opportunity by obscuring
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the substantial differences that exist between the financial realities of households with the
same income, but with different characteristics and circumstances.
Gaps in the Literature around Transit-Induced Displacement and Location Efficiency
The above review of existing research around transit-induced displacement and location efficiency reveals four significant shortcomings in our current understanding of the geography of transit accessibility and housing affordability in U.S. metros. First, much of the literature - including the numerous studies examining transit-induced gentrification and displacement - focuses exclusively on affordability in the context of fixed-rail, neglecting the large role local buses serve in providing access across U.S. metros and therefore potentially mischaracterizing the relationship between housing costs and transit accessibility in general.
Second, most existing research examines home values, as opposed to rental premiums, despite the fact that market-rate rents are arguably more relevant to understanding affordability for low- and moderate-income households and certainly more important from a social justice perspective. Market-rate renters with limited means are much more vulnerable to both local transit-induced displacement and regional exclusionary displacement, since they are less resilient to unpredictable changes in market conditions and unlike low-income homeowners, do not benefit from increased property values.
Third, the majority of research around transit accessibility and H+T affordability fails to account for the spatial dependence and error inherent to these phenomena both independently and in relation to one other, despite well-documented evidence that doing so may lead to unreliable findings (Jun, 2016). In particular, investigations of H+T affordability often suffer from spatial error when boundaries of the spatial unit used in the analysis do not accurately reflect the true geography of the area of interest, as is the case with much of the literature that uses Census tracts or block groups to conceptualize neighborhoods that are not likely to fall neatly into census boundaries.
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Finally, all but one study rely on ratio-based measures of affordability, which - as I argue in subsequent chapters - do not accurately reflect the financial circumstances of low-and moderate-income households and are thus likely to misrepresent the opportunities and challenges experienced by these households.
These four gaps result in insufficient knowledge about the geographies of opportunity households with limited means confront as they seek market-rate rental housing in transit-accessible areas. As described in Chapter 3, I address these gaps in the literature through a comprehensive examination of current geographies of transit accessibility and housing affordability for low- and moderate-income renters in eight U.S. metros. Findings from these examinations contribute practical knowledge around the geographies of opportunity experienced by low- and moderate-income households, as well as equip practitioners and advocates with tools to support policy interventions that strengthen the capabilities of these households by maximizing the availability of transit-accessible affordable rental housing.
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CHAPTER III
RESEARCH QUESTIONS AND APPROACH RESEARCH QUESTIONS
In Chapter 2, I introduced a conceptual framework rooted in a capabilities approach that calls attention to how landscapes of transit accessibility and housing affordability to shape the geographies of opportunity of low- and moderate-income households. I also synthesized empirical research from several threads of literature that speak to the relationship between transit accessibility and housing affordability. This critical review points to four substantial gaps in our understanding of the geographies of transit accessibility and housing affordability that confront households as they seek market-rate housing. First, the literature focuses predominately on effects associated with fixed-rail transit, thus neglecting the large role buses play in providing access across U.S. metros. Second, existing research has little to say about landscapes of affordability and transit accessibility for market-rate renters, arguably the most vulnerable of all households. Third, only a handful of studies account for spatial error, despite clear evidence of its manifestation in urban phenomenon, including transit accessibility and housing affordability. Fourth, nearly all the existing research in this arena relies on flawed measures of housing affordability, thereby producing unreliable results.
I address these gaps by developing an improved measure of housing affordability that I then use to examine current geographies of transit accessibility (regardless of mode) and housing affordability for low- and moderate-income renters in eight U.S. metropolitan areas (‘metros’) while accounting for spatial error. In Part 1, I unpack the three most typical approaches to measuring housing affordability - the ratio, location affordability, and standard residual income approaches - and discuss the ways in which their shortcomings are likely to mischaracterize affordability for low- and moderate-income households (Chapter 4). I then introduce the location-sensitive residual income (LSRI) approach, a set of
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measures that address many of the flaws inherent to more typical measures of affordability, and provide a detailed methodology for constructing the LSRI measures (Chapter 5).
A LSRI approach first identifies the amount of monthly income a household can afford to pay for housing (its ‘housing budget’) after covering the necessities required to sustain a basic standard of living which vary depending on its composition (size, presence of children), financial circumstances (childcare costs, income) and its location within the region (and thus, transportation costs). A second ‘supply’ measure is then calculated using data from the Census ACS to identify the quantity of rental housing units that are affordable within the housing budgets of a defined set of low- and moderate-income households. A subsequent chapter applies the LSRI measure empirically by exploring housing affordability for households with limited means living in the Denver metro, and comparing these results to those generated using the three more typical measures of affordability (Chapter 6). This empirical application highlights the ways in which the LSRI measures are likely to more accurately reflect the financial realities faced by low- and moderate-income households as compared to more typical approaches, and to demonstrate how a LSRI approach can be used to understand nuanced landscapes of affordability and thus to support targeted policy interventions.
In Part 2, I employ the LSRI measure to examine geographies of transit accessibility and housing affordability for low- and moderate-income households in eight U.S. metros by addressing two research questions. First, I describe current landscapes of accessibility and affordability by asking: To what extent are supplies of rental housing that are affordable for low- and moderate-income households located in areas with high transit accessibility? (Research Question 1). Analysis supporting Research Question 1 does not attempt to account for the multitude of factors beyond transit accessibility that may also influence housing affordability. Rather, results presented in Chapter 7 provide an account of the conditions households with limited means are likely to confront as they seek transit-
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accessible affordable housing. Findings therefore offer insights into the lived experiences of low- and moderate-income households, who are unlikely to be care about the factors driving affordability, but instead are likely to be primarily concerned about the availability of rental housing that they are able to afford within their housing budget.
A second research question addressed in Part 2 extends the investigations presented in Chapter 7 by isolating the relationship between transit accessibility and housing affordability through a series of global and local regression analyses. This second question asks: What is the relationship between transit accessibility and supplies of affordable rental housing, when controlling for key characteristics of the built and social environments that are likely to influence that relationship, as well as for spatial dependence? (Research Question 2). Results of this analysis summarized in Chapter 8 shed light on the relationship that exists between transit accessibility and housing affordability across different metros, among households with different characteristics within the same metro, and across space within a single metro.
A final section (Part 3) synthesizes findings from Parts 1 and 2 to lend insights into the complex relationship between affordability and accessibility across U.S. metros, and into the ways in which current geographies are consistent with - and challenge - a location efficiency narrative. The result of this synthesis is a typology describing the geographies of opportunity generally experienced by low- and moderate-income households in eight U.S. metros, each of which calls for specific types of policy and planning interventions. RESEARCH APPROACH Case Selection
These investigations are conducted for all U.S. metros with ‘second-generation’ regional rail, defined as those in which fixed-rail transit systems that serve more than one contiguous county were established after the passage of the Intermodal Surface Transportation Efficiency Act (ISTEA) of 1991, which instituted significant changes in
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prioritizing regional (as opposed to singular metropolitan) transit investments (Weir et al., 2008). Specifically, ISTEA empowered metropolitan planning organizations (MPOs) with a strong institutional role in planning, funding, and implementing transportation, thus changing the inventive structure towards regional investments. The present research focuses specifically on metros with ‘second generation’ rail because they (as opposed to metros with older ‘legacy’ rail systems) are likely to face a set of challenges which are of particular theoretical and practical relevance to transportation justice and urban social justice more generally including the presence of a dispersed suburbanized population, the existence of rapid population and employment growth, and limited availability of federal funding for the capital and operating costs of transit (Griffin & Sener, 2015). Although this study is concerned with transit accessibility regardless of mode, the presence of fixed-rail transit is specified as a criterion because it serves as an indicator of the strength of a region’s commitment to transit in general given that rail requires significant capital and operating investments, and given that it is typically operated alongside bus and possibly other modes as part of an integrated transit system.
Metropolitan areas serve as the analytical focus of the present study because they are typically the scale at which interconnected urban and suburban transportation and other large-scale networks operate, and are increasingly recognized as the appropriate scale to consider issues of urban sustainability, including transportation (Keil & Whitehead, 2012). Metros are defined here as U.S. Census core-based statistical areas (CBSAs), clusters of counties that center around at least one ‘core’ of 10,000 people or more and include all counties that have a high degree of social and economic connection to that core, as measured by commuting activity (U.S. Census Bureau, 2010b). Any additional counties not included in the CBSA, but served by the regional transit agency are also included. The study area therefore roughly constitutes the reasonable ‘commute-shed’ of the metro.
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Nine U.S. metros were identified as having second-generation regional rail transit system. One of these (Phoenix) was eliminated from analysis due to data availability issues, leaving the eight cases outlined in Table 3.1. The eight metros are located primarily in the western U.S., with the exception of Minneapolis. Three of the metros are located on the west coast (Los Angeles, Portland, and Seattle), two are located in Texas (Dallas and Houston), and two are located in the mountain west (Denver and Salt Lake). This geographic distribution reflects the fact that regional rail systems in older East coast and Midwestern U.S. metros were established much earlier (so called ‘legacy systems’), and that most metros in the south and central U.S. have not established robust regional rail systems.
The eight case metros range in population size: Three metros have populations under three million (Denver, Portland, and Salt Lake City), two metros have populations of between three and six million (Minneapolis and Seattle), just over six million people live in two metros (Dallas and Houston), and a single metro (Los Angeles) has a population of nearly 13 million. The total housing units within the metros follows a similar distribution. Salt Lake City and Portland have the fewest units, while Houston, Dallas, and Los Angeles contain the largest housing stocks. The percent of housing units that are occupied by renters ranges from approximately 30-percent in Minneapolis and Salt Lake to over 60-percent in Los Angeles. Area median income (AMI) differs by over $10,000 across the metros. Households in Dallas, Houston, and Portland have an annual income of just under $60,000, with the lowest AMI in Houston ($58,589). Households in Seattle enjoy the highest annual incomes at approximately $69,000.
The robustness of the transit systems also vary substantially. Annual vehicle revenue-miles, a measure of the miles that the metro’s bus and rail vehicles are scheduled to travel while in revenue service, ranges from just over 39,000 miles in Portland to 193,000 in Los Angeles. Portland and Salt Lake City have the smallest systems, with under 40,000 vehicle-miles. Dallas, Denver, Houston, and Minneapolis have more moderately-sized
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systems (revenue-miles of roughly 60,000 to 80,000). The Seattle metro has the second-largest transit system by this measure with nearly 93,000 revenue-miles, although this is far eclipsed by the over 193,000 revenue-miles traveled in Los Angeles. While results are not widely-generalizable, findings shed light on varying conditions that are faced across U.S. metros with regional rail transit, and provide particular insights for metros that have recently undertaken or are currently embarking upon large transit expansion projects. Findings are particularly relevant to relatively dispersed metros in the western U.S. with that are experiencing high levels of population and employment growth.
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Table 3.1. Selected cases (metropolitan areas)
Metro (identified by its core city) Counties included in study area Regional transit agency(ies) Total population Total housing units1 % renter-occupied units Area median income Annual transit vehicle revenue miles2 (2014)
Dallas (TX) Collin, Dallas, Denton, Ellis, Hood, Hunt, Johnson, Kaufman, Parker, Rockwall, Somervell, Tarrant, Wise Dallas Area Rapid Transit 6,596,127 2,536,487 40.4% $59,175 58,987
Denver (CO) Adams, Arapahoe, Boulder, Broomfield, Clear Creek, Denver, Douglas, Elbert, Gilpin, Jefferson, Park Regional Transportation District 2,915,986 1,205,179 36.9% $64,206 68,887
Houston (TX) Austin, Brazoria, Chambers, Fort Ben, Galveston, Harris, Liberty, Montgomery, Waller Metropolitan Transit Authority of Harris County 6,191,773 2,362,346 39.9% $58,689 80,009
Los Angeles (CA) Los Angeles, Orange LA County Metro; Metrolink; other county agencies 12,991,225 4,504,858 51.2% $60,337 193,426
Minneapolis (MN, Wl) Anoka, Carver, Chisago, Dakota, Hennepin, Isanti, Ramsey, Scott, Sherburne, Washington, Wright, Pierce (Wl), St. Croix (Wl) Metro Transit 3,352,758 1,368,689 30.0% $68,019 73,703
Portland (OR, WA) Clackamas, Columbia, Multnomah, Washington, Yamhill, Clark (WA), Skamania (WA) TriMet; City of Portland 2,288,795 933,888 39.3% $58,832 39,125
Salt Lake City (UT) Davis, Salt Lake, Tooele, Utah, Weber Utah Transit Authority 2,209,204 728,314 31.3% $61,529 39,679
Seattle (WA) King, Pierce, Snohomish King County Metro; Community Transit; Pierce Transit Sound Transit 3,537,402 1,477,750 40.2% $68,969 92,606
Sources: U.S. Census American Community Survey 2010-14 Five-Year Estimates; Federal Transit Administration National Transit Database includes both renter- and owner-occupied includes bus and rail vehicle-miles


Key Variables
The research questions explored in the present study involve understanding the relationship between two primary variables of interest: Transit accessibility and housing affordability. Another set of variables are used in addressing Research Question in order to control for key characteristics of the built and social environment that are likely to influence affordability. Table 3.2 outlines these variables, and briefly identifies the measures used to operationalize them. The methodology used to develop the LSRI measure of housing affordability is described in detail in Chapter 5. Details about the measure of transit accessibility used in the analysis are provided in Chapter 7. The control variables both considered for and included in the analysis supporting Research Question 2 are discussed in Chapter 8.
All variables are measured at the Census block group level, which serves as the unit of analysis. Block groups are composed of clusters of contiguous blocks within the same census tract typically containing between 600 and 3,000 people and are therefore commonly used as a proxy for neighborhood units, as is intended in the present study (U.S. Census Bureau, 2010a).
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Table 3.2. Final set of variables included in the analysis
Variable Definition Measure(s)
Primary variables of interest
Transit accessibility The ability to reach desired destinations from a home location within a reasonable travel time using public transportation. Accessibility to employment destinations is used as a proxy for general transit accessibility. The percent of a region’s jobs that can be reached from a block group within a 45-minute commute by transit
Housing affordability The ability of a household to afford housing within its housing budget, defined as the amount of income remaining after paying for essential non-housing needs. The number of rental housing units within a block group that are affordable to six household profiles, as a percent of the total rental units within the metro
Key characteristics of the built and social environment
Household density The concentration of households across a geographic area Gross household density: The number of households per acre of developable land
Pedestrian- orientation The characteristics of a geographic unit in terms of the extent to which it is easily and safely traversed by people travelling by foot Pedestrian-oriented intersection density: The number of intersections that can be traversed by pedestrians per acre
Land use The characteristics of a geographic unit in terms of the activities that occur within it Employment-housing entropy: The mix of five employment categories (retail, office, industrial, service, entertainment) and occupied housing
Access to retail amenities: The number of retail jobs within half-mile of block group centroid divided by land area
Housing mix The characteristics of a geographic unit in terms of the types of housing that exist within it Proportion renters: The number of occupied rental units as a percent of the total number of occupied units
Total housing units The total number of units within a geographic unit that are habitable Total housing units: Total number of occupied and vacant housing units located within the block group
Socio- economic conditions The social and economic characteristics of the people living within a geographic unit Median household income Proportion non-Hispanic white population: The percent of population that identifies as non-Hispanic and white
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Overview of Methods
The present study examines affordability for unsubsidized, market-rate renters for two primary reasons. First, low-income renters in market-rate housing have little available income with which to respond to increased housing prices, leaving them particularly vulnerable to local direct and regional exclusionary displacement. Unsubsidized rental units also provide the vast majority of the nation’s affordable housing given that only 25-percent of eligible households are able to secure public assistance (Ault et al., 2015). Despite this fact, the availability of ‘naturally-occurring,’ market-rate affordable housing remains understudied.
In order to contribute to filling this gap, I analyze affordability for six household profiles specified based on their ability to shed light on the challenges faced by low- and moderate-income renters who are likely to earn too much to qualify for subsidy, but not enough that the availability of stable affordable housing is a foregone conclusions. The households examined vary on composition (number of adults, number of children) and financial circumstances (income and number of children who require childcare). The six profiles analyzed are:
• Profile A: Single adult, no children - 30% AMI
• Profile B-1 (0): Single adult, one child (not in childcare) - 50% AMI
• Profile B-2(1): Single adult, two children (one in childcare) - 80% AMI
• Profile C: Two adults, no children - 50% AMI
• Profile D-1 (0): Two adults, one child (not in childcare) - 80% AMI
• Profile D-2(1): Two adults, two children (one in childcare) - 100% AMI
In Part 1, LSRI ‘housing budgets’ - the upper limit of what a household can afford to pay for housing after covering its essential non-housing needs - were first calculated for these six profiles following the methodology described in Chapter 5. Housing budgets were calculated at the block group level for each of the eight metros and vary based on
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household composition, income, and residential location (which determines transportation costs). A second LSRI ‘supply’ measure was then calculated using U.S. Census American Community Survey data to identify the number of rental units within each block group that are affordable to the six household profiles. The result of this effort is a comprehensive dataset of the number of units that are estimated to be affordable to a theoretical household seeking housing in each block group of a metro, accounting for the characteristics of the household and the estimated transportation costs associated with the block group. Chapter 5 provides a comprehensive description of the methodology used to develop the two LSRI measures. Comparisons between results of an analysis undertaken for the Denver metro using LSRI measures and results for the same metro generated using more typical measures is presented in Chapter 6 to demonstrate how standard approaches mischaracterize - and likely overestimate - how much households with limited means can afford to spend on housing.
In Part 2, the LSRI measures of housing affordability were first overlaid with data on transit accessibility to calculate the supply of rental units that are both affordable to the six low- and moderate-income households and located in areas with high transit accessibility. Supplies of affordable high accessibility housing are then compared to supplies of affordable rental units located in areas with no or low transit accessibility. In this analysis, a block group’s accessibility level is defined by whether the percent of regional jobs that are accessible within a 45-minute transit commute is above the average accessibility of all block groups that have non-zero accessibility values (‘high’ accessibility) or below the non-zero average (‘low’ accessibility). The supply of affordable housing located in block groups in which no jobs are accessible within a 45-minute transit commute are reported separately (‘zero’ accessibility). Thresholds therefore reflect each metro’s individual landscape of accessibility, with high accessibility thresholds ranging from 5.9-percent of regional jobs in Los Angeles to 17.5-percent of jobs in Portland.
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In addition to observing differences in the supplies of affordable housing located in high vs. zero/low accessibility, ‘accessibility ratios’ are also constructed for each of the household profiles. These ratios divide the number of affordable units located in zero/low accessibility areas by the number of affordable units located in high accessibility areas to arrive. Each household profile’s accessibility ratio is then compared to the accessibility ratio of the metro’s overall supply of rental units (regardless of affordability) in order to detect deviations from metro-wide distributions of rental housing across high and zero/low accessibility areas. Chapter 7 provides additional details about the methods used in addressing Research Question 1, including the thresholds used to define high and low accessibility, and the accessibility ratios developed to support the analysis.
I then use multivariate spatial regression modeling to address Research Question 2, with the goal of investigating the complex relationship between supplies of affordable rental housing and transit accessibility while controlling for key characteristics of the built and social environment, as well as for spatial dependence. Two spatial methods are used to support the analysis presented in Chapter 8. First, a series of multivariate spatial error regression models are developed in order to investigate global (metro-wide) relationships between transit accessibility and housing affordability. The same model specifications are then used in geographically-weighted regression (GWR) models in order to explore how these relationships vary across block groups within a single metro.
Two spatial error models and two GWR models are developed per metro: One set examining the supply of rental units that are affordable to a theoretical household with relatively little income available for housing and a second set examining affordability for households with more moderate housing budgets. Models were specified with the intention of capturing the key factors that are likely to influence accessibility and affordability directly (as well as factors that may mediate the relationship between the two variables), while also maximizing parsimony and avoiding issues of multi-collinearity. R open-source software
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(v3.3.1) was used to specify models following the iterative model-building process described in detail in Chapter 8.
Because statistical tests indicate the presence of spatial autocorrelation in both the variables and regression residuals, spatial error regression estimated using the maximum likelihood method is employed. Spatial autocorrelation may be due to any number of issues. Given the nature of the present investigation, spatial error due to the use of units of analysis (block groups) that do not accurately reflect the actual geography of the unit of interest (neighborhoods) is likely to be present. It is also likely that the variables are distributed across space in a way that does not coincide with the units of analysis, further perpetuating spatial error. Spatial error regression account for these issues by including a spatially-weighted error term in the model alongside the usual random error term. Additional details about the final model specifications are provided in Chapter 8.
Spatial error regression is used in this analysis to identify global relationships between transit accessibility and housing affordability, holding all else constant. While these models provide important insights into the overall relationship between accessibility and affordability, global statistics may mask variations in the relationship that occur on a local basis. I therefore turn to a final analytical tool - GWR - in order to understand the relationship between these variables at the neighborhood (block group) level, controlling for other key factors. Geographically-weighted regression estimates models for each block group in a metro, therefore allowing the relationships between variables to vary across space. The GWR models are specified using the same sets of variables as are included in the spatial error models, thus enabling comparisons between global and local coefficients. Details about the GWR model specifications are provided in Chapter 8.
The analyses undertaken in Part 2 are not intended for use in drawing causal conclusions about the relative effects of specific factors on supplies of affordable housing. Rather, the models are intended to isolate and closely examine the complex relationship
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between accessibility and affordability. Results deepen our understanding of the geographies of opportunity experienced by low- and moderate-income households across the U.S., and shed further light on the robustness of a location efficiency narrative when affordability is assessed using more nuanced measures and analytical approaches.
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CHAPTER IV
EVALUATING TYPICAL MEASURES OF HOUSING AFFORDABILITY AND INTRODUCING THE IMPROVED ‘LOCATION-SENSITIVE RESIDUAL INCOME’
MEASURE
INTRODUCTION
The Growing Housing Affordability ‘Crisis’
Following the recovery from the Great Recession of 2008, unprecedented increases in housing costs across many U.S. cities and regions has generated growing concern about housing affordability among policymakers and the public. According to the National Association of Realtors and Harvard University’s Joint Center for Housing Studies (JCHS), the median price for existing homes nationally increased four-percent between 2013 and 2015 (JCHS, 2015). Renters face similar challenges: Nationally, rents increased an average of 3.2-percent between 2014 and 2015, with the ‘hottest’ metropolitan areas increasing 10-percent or more. With vacancy rates at their lowest in 20 years (7.6%), pressures on rental markets across the U.S. are expected to continue mounting, particularly as demand for housing grows among the millennial population (Ellen & Karfunkel, 2016). These trends have led to calls of a housing affordability ‘crisis’ among U.S. mayors, particularly those in cities located in large high-growth metropolitan areas (Langan et al., 2016).
Not surprisingly, rising housing costs, and rents in particular, are felt most acutely by the over 10 million ‘extremely low-income’ renters, defined as those with an annual household income of less than 30-percent of area median income (AMI). The National Low-Income Housing Coalition reports that the supply of housing affordable to these households, who constitute 25-percent of the nation’s renters, is becoming increasingly limited: Only three affordable units are available for every 10 extremely low-income household (Bravve et al., 2013). The dearth of affordable rental housing left nearly 80-percent of extremely low-income households ‘severely cost-burdened’ in 2014, a term used to indicate that a
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household’s housing expenditures consumed more than half of the its income (Ault et al., 2015).
Research by the Center for Housing Policy suggests that ‘working’ renters -households with members who work at least 20 hours per week and make no more than 120-percent AMI also face increasing challenges in securing affordable housing. Over 70-percent of workers earning the federal minimum wage for 40 hours of work per week (approximately $15,000 per year) are left severely cost-burdened (JCHS, 2015). Indeed, working renters experienced a six-percent increase in housing costs between 2011 and 2014. These trends are true not only for low-income working households but also for more moderate-income households, particularly those living in high-cost metropolitan areas. In its research on the ten highest-cost regions (a cohort that includes Boston, Los Angeles, New York, San Francisco, and Seattle),the JCHS reports that nearly 50-percent of moderate-income renters (those earning $45,000 to $75,000) are severely cost-burdened (JCHS, 2015).
Many policymakers at the state and local level are seeking to address housing affordability through legislation encouraging increases in the supply of both new market-rate housing and new affordable units created through inclusionary zoning and similar policies. Although helpful to some extent, these measures are not likely to be a panacea. While the market is beginning to respond to increased demand for rental housing, only one-tenth of new multi-family units are affordable to the 50-percent of rental households that make less than $34,000 per year (JCHS, 2015). Inclusionary zoning and other policies designed to increase production of affordable housing are positive developments, but cannot begin to meet demand alone. Meanwhile, wages remain persistently low. Nationally, the hourly wage required to afford a two-bedroom apartment at Fair Market Rent (referred to as the ‘housing wage’) is $18.79. Among the case regions focused on in the present study, the ‘housing wage’ varies from $16.13 (Salt Lake City) to $27.33 (Los Angeles) (Bravve, et al., 2013).
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Meanwhile, the average hourly wage of renters is only $14.32, and nearly 60-percent of jobs created since the Great Recession pay no more than $13.84 per hour. Recent efforts undertaken in many cities to increase the minimum wage are a promising step in closing the gap between housing costs and wages, yet even the $15 per hour minimum wage that is commonly advocated is far too low to cover market-rate housing in most large U.S. cities.
Although subsidized housing at the federal, state, and local level plays a critical role in addressing housing affordability for low-income households, demand for rental housing assistance far exceeds demand. In 2014, only one-quarter of eligible low-income households were able to secure rental assistance through the federal government (Ault, et al., 2015). State and local rental assistance remains minimal in the majority of U.S. regions (Belsky & Drew, 2007). Unsubsidized, market-rate rentals therefore provide the vast majority of housing for low- and moderate income households. Reliance on market-rate housing is only likely to grow as 50-percent of the 4.8 million rental units subsidized through federal programs expire in the coming decade and as federal subsidies continue to decline (JCHS, 2015).
The inability of subsidized and unsubsidized housing to meet demand among low-and moderate-income households is responsible for a host of deleterious effects. A lack of affordable housing contributes to the homelessness of an estimated 600,000 people in the U.S., over a third of whom are people in families (JCHS, 2015). Nearly one in four households on waiting lists for federally-subsidized rental assistance report periods of homelessness and another 40-percent report ‘doubling-up’ with family or friends, a condition often leading to homelessness (Leopold, 2012). Even when low-income households are able to secure stable housing, they are likely to make concessions in terms of the condition of the units: A reported 17 million households currently live in housing that is sub-standard in terms of pests, leaks, broken windows, plumbing issues, electrical hazards, or structural problems (Jacob et al., 2014).
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Furthermore, many rental units affordable to low-income households are also located in areas of concentrated poverty. A large body of research on ‘neighborhood effects’ demonstrates that low-income households living in high-poverty neighborhoods face many more challenges in terms of economic, educational, physical and mental health, and subjective well-being as compared to low-income households living in low-poverty areas (Chetty et al., 2015; Ludwig et al., 2012). These effects appear to have a particularly large effect on children. For example, children in low-income households living in high-poverty neighborhoods generally exhibit significantly lower levels of school readiness and achievement as compared to children in similar households living in low-poverty areas (Leventhal & Brooks-Gunn, 2000). Furthermore, evidence suggests that children in low-income households that move from a high-poverty area to a low-poverty area are likely to complete college at higher rates and earn higher incomes as adults when compared to children from similar households who remained in high-poverty neighborhoods (Chetty & Hendren, 2015).
Low-income households that spend a disproportionate amount of their income on housing also have much less disposable income available to meet the basic necessities of daily living, not to mention the ability to save for the future. The JCHS reports that severely-cost burdened households in the bottom expenditure quartile spent 70-percent less on healthcare and 40-percent less on food than similar households in more affordable housing (JCHS, 2015). Spending less on these necessities leaves low-income renters at higher risk for health-related crises, and may lead to reduced worker productivity and increased reliance on publicly-subsidized health care programs. High housing costs also reduce a household’s ability to save for the future (including for retirement), further heightening financial strains on individual households and the social welfare system (Belsky & Drew, 2007). The impacts of this circumstance are especially harsh for children since households with severe housing cost burdens have little disposable income available to spend on their
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children’s care and enrichment (Brooks-Gunn & Duncan, 1997; Newman & Holupka, 2014). Indeed, evidence suggests that higher percentages of income spent on housing are associated with lower levels of cognitive achievement in children (Newman & Holupka, 2013). Conversely, secure and stable affordable housing allows families to spend resources on food and health care expenditures, thereby positively effecting the physical and mental health of children and their caretakers (Maqbool et al., 2016).
Defining and Measuring ‘Affordable Housing’
Existing research clearly demonstrates the large role that affordable housing plays in promoting social and economic well-being. The literature also points to mounting challenges among low- and moderate-income households in securing affordable places to live. Yet despite the ubiquity and importance of these issues in public and scholarly conversations, there has been surprisingly little critical examination in both the academic and public spheres about how to define and operationalize the concept of ‘affordable’ housing
I contribute to addressing this gap in the present chapter by unpacking the three most commonly-used approaches to measuring affordable housing, and introducing a fourth approach that addresses many of their shortcomings. This fourth approach considers housing to be ‘affordable’ when a household is able to pay for housing while still meeting its essential non-housing needs within the bounds of its income. Conversely, housing is ‘unaffordable’ when housing costs require reduced spending on other non-housing expenditures such that a household is not able to afford its most basic necessities.
Under this definition, housing affordability is not a static characteristic as it is often treated; Rather, it is a dynamic relationship between housing costs on the one hand and the specific features, composition, and financial circumstances of individual households on the other (Stone, 2006). Different households clearly experience housing affordability differently. It is therefore obvious that when assessing housing affordability one must always ask the question ‘affordable for whom’? However, the most typical approaches to measuring
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housing affordability do not address this crucial question and instead rely on blunt measures that assume a homogeneity of circumstances among households that is not likely to exist in reality.
In the sections that follow, I first provide an overview of the three most typical measures of housing affordability - the ratio, location affordability, and residual income approaches - and outline the shortcomings of each. I then introduce an innovative fourth approach - the location-sensitive residual income’ (LSRI) measures - that corrects for many of the shortcomings inherent to standard approaches. A subsequent chapter (Chapter 5) provides a detailed methodology intended to guide practitioners in constructing the LSRI measures. In Chapter 6, I demonstrate how the LSRI approach can be applied empirically by investigating the spatial distribution of housing that is affordable to low- and moderate-income renters in the Denver metro area. Results derived using LSRI measures are then compared to those generated using the three more typical approaches. Findings from this comparison highlight how LSRI measures account for the nuanced financial circumstances of households with different compositions and residential locations, thus offering a more robust alternative to more typical measures. Furthermore, findings generate a more refined understanding of current landscapes of affordability in the Denver metro area, thus equipping planners and policymakers with knowledge to support policy interventions targeted specifically to local conditions. In the remaining chapters, I employ LSRI measures in combination with measures of transit accessibility to examine the complex relationship between accessibility and housing through two research questions.
TYPICAL APPROACHES TO MEASURING HOUSING AFFORDABILITY
Housing affordability is measured in myriad ways in the existing empirical literature. Measures may focus exclusively on housing costs - for example, the minimum, average, or total costs of owning or a renting a particular type of housing might be specified. Or, the average price per square foot for housing in a specific geographic area may be used. Most
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commonly, measures attempt to account for the relationship between housing costs and household income. For example, affordability may be measured as the minimum income or wage required to rent or purchase a particular type of housing. Or the median housing cost divided by the median household income may be calculated for a particular geographic area (Litman, 2015). Reported housing expenditures may also be examined, often as a share of household income. Still other measures focus on the supply of vacant units with certain characteristics available at a specific cost. More sophisticated measures may also incorporate housing quality to account for the adequacy of living conditions (Li, 2014).
This wide array of measures underscores the complex layers of household-level factors and decisions that underlie the ambiguous concept of housing affordability, as well as the multitude of geographic scales at which it can be measured. The number of possible measures also reflects tradeoffs associated with the robustness of a measure on the one hand and the ease with which data can be collected, analyzed, and interpreted on the other. Indeed, measures of housing affordability must optimize many objectives. They are expected to reflect “individual experiences [mediated] through analytical indicators and normative standards” and enable conclusions to be drawn about the where and the extent to which affordability is a problem, all while employing readily-available data and easily-interpretable analytical techniques (Stone, 2006: 151-152).
The three most commonly-used measures of housing affordability - the ‘ratio,’ ‘location affordability,’ and ‘residual income’ approaches - achieve some of these objectives with varying degrees of success. The ‘ratio’ measure considers housing to be affordable if it consumes less than a defined threshold (typically 30%) of income. A second ‘location affordability’ measure also uses a ratio-based approach, but accounts for the combined effects of housing and transportation costs such that housing is considered to be affordable if combined costs consume less than 45-percent of income. The third ‘residual income’ measure is less widely-used among practitioners, but is generally recognized among
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scholars as offering a more precise measure of affordability (Newman & Holupka, 2014). A residual income approach defines housing as affordable when a particular household is able to cover the costs of all its essential, non-housing needs after paying for housing.
In the sections that follow, I outline each of these approaches, including assessments of both the benefits and shortcomings associated with each. I then introduce the LSRI approach, which integrates the location affordability and residual income approaches to more accurately reflect the financial realities low- and moderate-income households face in securing affordable housing.
A ‘Ratio’ Approach to Measuring Housing Affordability
The most common measure of housing affordability sets a threshold calculated as a percent of household income (typically 30%) whereby housing that costs less than the threshold is considered affordable, and housing costs exceeding the threshold are considered ‘unaffordable.’ Under this ratio approach, households spending more than 30-percent of their income on rent or ownership costs are considered ‘cost-burdened.’ Those spending more than 50-percent of household income on housing are identified as ‘severely cost-burdened.’
There is no particular theoretical or empirical basis for the use of a 30-percent threshold (Stone, 2006). Rather, the threshold is rooted in a normative ‘rule of thumb’ first adopted by banks in the 1920s based on the idea that no more than one week’s income should go to housing (Newman & Holupka, 2014). This threshold approach was codified into federal policy in the 1969 “Brooke Amendment” which limited rent in public housing to 25-percent of residents’ income. The threshold, subsequently raised to 30-percent in the 1980s by Congress, has been widely adopted as the primary measure of housing affordability by federal, state, and local agencies responsible for setting housing policy. Most notably, the U.S. Department of Housing and Urban Development (HUD) uses the 30-percent threshold to determine eligibility for publicly-subsidized rental housing and ownership programs (U.S.
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Department of Housing and Urban Development Office of Policy Development and Research, 2014).
The ratio approach is also widely-used among organizations advocating for affordable housing, in part due to its prevalence in federal policy and also because it is computationally-straightforward and intuitive for both policymakers and the general public (Benner & Karner, 2016). In particular, the household income and housing expenditure data required for calculating a ratio measure is easily retrievable from the U.S. Census Bureau and Bureau of Labor Statistics. The ratio measure is also comparable across geographies and time, making it particularly useful for national-level analyses.
Despite its widespread use, the ratio approach is subject to much criticism from both scholars and advocates (see, for example, Belsky & Drew, 2007; Bogdon & Can, 1997; Hulchanski, 1995; Hertz, 2015b; Stone, 2006; Kutty, 2005). The first, and perhaps most significant shortcoming of the ratio measure, is its insensitivity to differences in household income. For instance, a low-income household making $1,800 a month and spending 45-percent ($810) of its monthly income on housing has only $990 remaining for food, healthcare, taxes, childcare, and other necessities. A more affluent household also spending 45-percent of its income on housing, but with monthly earnings of $6,000 has much more disposable income ($3,300). Yet, based on the ratio measure of affordable housing, both households are considered ‘cost-burdened’ even though the former has far more challenging circumstances than the latter.
Ratio measures also often fail to account for differences between households with characteristics and financial circumstances. Ratio measures are often insensitive to household size and the presence of children, both of which have a large impact on the nonhousing costs incurred. For example, a two adult, moderate-income (80-percent AMI) household with no children will have vastly different financial circumstances as compared to a single-parent of two children with the same income. The latter household is likely to spend
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a much larger portion of its income meeting its basic non-housing needs, and thus will feel the crunch of high housing costs to a much greater degree than the former. Ratio measures also do not account for the cost of childcare, which often exceed housing costs for many families with young children (Glasmeier, 2014). HUD-adjusted median family income (HAMFI) classifications used in awarding housing subsidies to low-income households address this shortcoming to some extent by adjusting AMI values up or down based on a household’s size (Bogdon & Can, 1997). However, HAMFI measures are not commonly used in analyzing housing affordability, nor do they address issues related to childcare requirements.
Furthermore, a ratio measure alone does not reflect the tradeoffs that exist between housing costs and residential locations, amenities, and housing quality. While affluent households may have the disposable income to spend far more than 30-percent of their income on housing in order to enjoy more desirable location or amenities without sacrificing on other necessities, low-income households do not. A ratio measure also does not account for the challenges low-income households may face when affordable housing is primarily located in neighborhoods suffering under high crime rates, poor school quality, low transportation connectivity and other consequences of concentrated poverty (U.S. Department of Housing and Urban Development Office of Policy Development and Research, 2014).
A final criticism of the ratio approach is its inattention to variations in transportation costs associated with the extent to which a household must rely on a single-occupancy vehicle to access employment opportunities and other basic necessities of daily life (Revington & Townsend, 2016). A household living in a neighborhood well-served by public transit is likely able to minimize transportation costs by owning a single (or no) car and limiting its use, thus freeing up income that can instead be spent on housing. Conversely, a household living in a neighborhood in which there is limited or no transit service and where
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basic services are located a distance away may require significantly more spending to maintain and operate multiple cars, thus reducing the income available for housing. This shortcoming is addressed by a second approach - the ‘location affordability’ measure -discussed below.
A ‘Location Affordability’ Approach to Measuring Housing Affordability
The location affordability measure also follows a threshold-based approach, but accounts for variation in transportation expenditures by considering housing and transportation costs in combination. A location affordability measure thus defines housing as ‘affordable’ when combined housing and transportation (‘H+T’) costs do not exceed 45-percent of income. Housing that requires households to spend more than 45-percent of their income on H+T costs is thus considered ‘unaffordable.’ The location affordability approach has its origins in efforts by the Center for Neighborhood Technology (CNT) to encourage a more comprehensive view of housing affordability through documentation of transportation costs associated with different housing locations. In many regions, housing costs tend to be lowest in the auto-oriented suburban fringe, yet these same areas are likely to lack employment opportunities, amenities, and non-auto transportation options - all factors which contribute to higher transportation costs. Proponents of the location affordability (or ‘location efficiency’) approach therefore argue that although housing in neighborhoods with close proximity to jobs, the ability to walk or bike to shopping districts, and the availability of transit and non-motorized transportation options may be more costly, high housing costs are likely to be offset by lower transportation costs. The adage ‘drive until you qualify’ describes this theoretical tradeoff: While housing, and single-family homes in particular, may be cheapest in far-flung areas of the region, reliance on auto modes are likely to render transportation costs much higher as compared to more central areas with higher housing costs. For instance, CNT found that in some heavily auto-dependent neighborhoods of Washington,
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D.C., transportation costs comprise as much as 32-percent of income, while in more accessible areas they are as low as 10-percent (CNT, 2011).
Tradeoffs between housing and transportation costs are also clear at an aggregate level: Some metropolitan areas that appear to be quite affordable in terms of housing alone are much less affordable when considering housing and transportation in combination. For example, research from the Center for Housing Policy and CNT indicates that while Houston is the eighth most affordable region for housing costs alone, it ranks 17th when considering combined H+T costs. On the other end of the spectrum, this research suggests that many dense, highly-accessible regions are among the least affordable regions in terms of housing, but are considerably more affordable when accounting for transportation (Center for Housing Policy and Center for Neighborhood Technology, 2012).
The interplay between housing and transportation costs is particularly stark for the working poor. While higher-income households have the luxury of being able to choose to live in more accessible areas of the region, low-income households are likely to be much more constrained in their choices. In many cases, low- and moderate-income households may only be able to secure housing in less accessible areas of the region that require long and costly commutes. Not only does this burden lower-income households with the high costs of auto- dependence, but it also exposes these households to financial uncertainties related to the fluctuating price of gas and car maintenance. Indeed, low-income households living in housing that does not exceed 30-percent of their income spend $100 more a month on transportation (Belsky & Drew, 2007). Research also indicates that nationally, the combined costs of housing and transportation consume much more of a low-income household’s income as compared to more affluent households (Roberto, 2008).
The original CNT “H+T Index” has gained considerable traction since its inception in 2006. The U.S. HUD launched its own ‘Location Affordability Index’ (LAI) based on the CNT model in 2013 and have subsequently incorporated a much more sophisticated
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methodology to predict housing and transportation costs for eight different household profiles (Haas et al., 2016; U.S. Department of Housing and Urban Development, 2015).
The resulting data is publicly-available through HUD’s Location Affordability Portal1, which promotes the use of a Location Affordability Index (LAI) among planners, policymakers, developers, and the general public.
Despite its laudatory emphasis on the interplay between housing and transportation costs, location affordability measures perpetuate two key shortcomings of the ratio approach upon which it is based. First, the location affordability approach continues to rely on an arbitrary threshold (45-percent of income) that has little theoretical basis and is insensitive to differences in household income. The location affordability approach also does not account for nuanced differences in household characteristics or financial circumstances, particularly those related to the presence of children and associated childcare costs.
A ‘Residual Income’ Approach to Measuring Housing Affordability
A third approach that is increasingly popular among advocates improves upon many of the shortcoming of the ratio and location affordability measures of housing affordability (Hertz, 2015a; Weise, 2014). First originated by Michael Stone in the 1975 and continually refined since, the residual income approach subtracts the total non-housing costs required to maintain a minimum standard of living from household income, thus identifying the remaining ‘residual’ income that is available for housing (Stone, 2006). Stated differently, housing is affordable if income (I) less housing expenditures (H) is greater than or equal to the minimum necessary non-housing expenditures (NH), such that:
I - H > NH (Thalmann, 2003)
Stone’s concept provides the basis for the definition of ‘housing affordability’ adopted by the present study: A condition in which a household is able to afford all housing-related costs while still being able to meet its essential non-housing needs within the bounds of its
1 http://www.locationaffordability.info/lai.aspx
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income. This approach can be applied to either a ‘real’ household, or to a ‘hypothetical’ household defined to represent a particular set of household characteristics.
By recognizing that housing affordability is entirely dependent on a household’s composition and financial circumstances, the residual income approach corrects for the most critical shortcomings of the ratio and location affordability approaches. A residual income measure provides a ‘sliding scale’ of affordability, with the maximum affordable amount varying with household size, the presence of children, and specific financial circumstance. Depending on these factors, some affluent households are able to afford far more than 30-percent of their income on housing (or 45-percent on housing and transportation combined) while lower-income households may be unable to afford housing at all without heavy subsidy. The residual income measure is therefore consistent with the ‘capabilities approach’ framework adopted in the present study in that it accounts not only for income (as the more Rawlsian ratio and location affordability measures do), but also for what a household is able to Wo’with that income given the full set of its circumstances.
The first step in developing a residual income measure of affordability is to identify the non-housing costs that are required to sustain a basic standard of living. Defining what constitutes a ‘basic’ standard of living requires normative judgement about the conditions that are acceptable to a particular society at a specific point in time (Stone, 2006). Most empirical research employing a residual income approach in the U.S. context uses the ‘lower-budget’ standards defined by U.S. Bureau of Labor Statistics (BLS) to identify the ‘basket’ of non-housing goods and services required to maintain a basic standard of living, which include: Food; Medical expenses; Childcare (if applicable); Transportation; Clothing; Other goods required for basic household operations; and Local, state, and federal taxes.
A small number of studies using residual income measures have also employed large-scale surveys and/or focus groups to define a basic standard of living (Stone, 2006).
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Data on non-housing expenditures are most often sourced from U.S. BLS Consumer Expenditure (CE) Survey, a dataset released annually based on findings from interviews and diary surveys that ask American consumers about details related to their household characteristics, expenditures, and income (U.S. Bureau of Labor Statistics, 2016). A number of resources that collate and present BLS CE Survey and other household expenditure data in a user-friendly format have recently become available for most U.S cities and regions, rendering the residual income approach more accessible to practitioners, policymakers, and the general public. The ‘Living Wage Calculator’ (LWC) developed by Dr. Amy Glasmeier at the Massachusetts Institute of Technology is perhaps the most well-developed of these resources2. The ‘Self-Sufficiency Standard’ available through the University of Washington’s Center for Women’s Welfare3 and the Economic Policy Institute’s ‘Family Budget Calculator’4 provide similar data, although they are less comprehensive than the LWC. All three of these resources report the cost of basic necessities by region, and are therefore sensitive to variations in costs of livings across different geographies.
Empirical research using BLS CE data to compare the residual income approach to the more typical ratio approach demonstrate that the two measures tell very different stories about affordability. In particular, findings derived from residual income measures indicate that housing affordability is much more problematic for families with children than ratio measures would suggest (Newman & Holupka, 2014; Stone, 2006).
While the residual income approach provides the most robust measure discussed thus far, is not without shortcomings. Residual income measures require more data and are more computationally-intensive than the ratio and location affordability approaches, rendering them somewhat less accessible to practitioners. This issue is becoming less important as data portals like the ones noted above - The Living Wage Calculator, the Self-
2 http://livingwage.mit.edu/
3 http://www.selfsufficiencystandard.org/
4 http://www.epi.org/resources/budget/
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Sufficiency Standard, and the Family Budget Calculator - bring consumer expenditure data to the mainstream public in a user-friendly interface. A residual income approach is also rooted in a particular time and place, making them more difficult (although not impossible) to compare across time periods and geographies. Furthermore, like the ratio and location affordability approaches, residual income approaches do not account for housing quality. Finally, and perhaps most importantly, residual income measures view transportation costs as static and are therefore not sensitive to the wide variations in auto-dependence, and thus transportation costs that exist across a region. Because transportation costs vary quite widely depending on a household’s residential location, it is imperative that any measure of affordability account for these variations.
Conclusions
Affordable housing is becoming a dominant concern in high-growth metropolitan areas across the U.S. It is therefore more important than ever that we clearly define what ‘affordable’ means, and develop measures that accurately reflect that definition. The three ‘typical’ approaches described above tell vastly different stories of affordability, to varying levels of robustness. In the section that follows, I introduce a fourth approach that addresses many of the collective shortcomings of more typical approaches. In doing so, this fourth ‘location-sensitive residual income’ approach more accurately reflects on-the-ground conditions related to affordable housing while offering a relatively straightforward and computationally-manageable method. This methodology thus equips practitioners and policymakers with tools to explore nuanced landscapes of affordability and thus to support the development of policy prescriptions that target the specific challenges faced by areas with different affordability dynamic.
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A NEW APPROACH TO MEASURING HOUSING AFFORDABILITY: ‘LOCATION-SENSITIVE RESIDUAL INCOME’
Despite criticism, ratio measures continue to enjoy hegemonic use, which is primarily justified by a perceived lack of alternative measures that “can be computed and understood with equal facility” (Thalmann, 2003:292). However, alternatives do exist and are increasingly being used by practitioners and researchers. In particular, the location affordability measure has recently gained acceptance as an intuitive - but more robust -alternative to ratio measures. Yet, while location affordability measures address shortcomings associated with the treatment of transportation costs, they perpetuate many of the same issues of the ratio approach - namely, the use of arbitrary normative thresholds that are entirely insensitive to differences in household income and composition. A third measure - residual income - is also gaining attention as a viable alternative, although it remains infrequently used. However, the utility and accuracy of the standard residual income approach continues to be limited by its failure to account for the variation of transportation costs across space.
I therefore propose a fourth alternative - the location-sensitive residual income (LSRI) approach - that incorporates elements of the location affordability and residual income approaches to arrive at a measure that addresses many of the shortcomings detailed above. Under the LSRI approach, affordability is assessed by calculating the amount a theoretical household is able to pay for housing after covering all of the other essential goods and services required to support a basic standard of living. The amount remaining for housing after all other essential expenses are paid is referred to as a household’s ‘housing budget’. Housing budgets vary widely depending on household composition (size, presence of children), financial circumstances (income, childcare requirements), and residential location (which determines transportation costs). As shown in Figure 4.1, housing budgets are calculated for a specified set of theoretical household
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profiles by subtracting six categories of household expenditures - childcare, food, medical, other basic necessities, taxes, and transportation - from household income.
Housing _ Household budget ” income
‘non-H+T’ costs
Child-
care
Food - Medical - Other - Taxes
Varies on household composition
Varies on household income
Transportation
Varies on household composition & residential location
Figure 4.1. Housing budget components
Costs associated with childcare, food, medical expenses, other basic necessities, and taxes are referred to as non-housing and transportation (‘non-H+T’) costs. The five non-H+T costs are calculated separately for each theoretical household profile based on its composition and financial circumstance. The first four of the costs vary as a function of household composition: Larger households are expected to consume more food, incur additional medical costs, and require higher spending on other basic necessities than smaller households. Childcare costs are dependent on another aspect of household composition - the presence and number of children under school-age - which is incorporated into the defined household profiles. Cost associated with state and federal income taxes vary as a function of household income. There are likely innumerable circumstances that may affect a household’s non-H+T costs - for example, it is possible that a grandparent or other relative provides free childcare - yet it would be impossible to account for all of these. The LSRI measures developed here instead aims to account for circumstances that are likely to exist across a wide swatch of U.S. households.
Transportation costs vary not only based on household size, but also on a household’s residential location. Transportation costs are thus calculated for each theoretical household profile at the block group level. The resulting dataset provides a
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comprehensive understanding of the amount a theoretical household with a particular set of characteristics can afford to pay for housing if it were to locate in a specific block group. For example, the LSRI approach enables an analyst to identify the housing budget of a household with one adult and no children earning 50-percent AMI and residing in a particular block group located in an outer suburb. Or, an analyst could identify the housing budget of a median-income household with two adults and two children (one of whom requires childcare) residing in a block group located in the central city.
After calculating housing budgets for each theoretical household profile by block group, the analyst is then able to assess the supply of housing that is both located within that block group and is affordable within the household’s housing budget. This calculation is completed for every block group within a region, for each theoretical household profile. The number of units affordable to a particular household profile can then be summed across a set of block groups in any number of ways depending on the aims of the analysis. For example, the number of housing units affordable to a single-adult household with no children earning 80-percent AMI could be summed across all block groups within a region, or across all block groups located within a specified distance of a particular amenity.
The LSRI approach to measuring housing affordability improves upon the ratio, location affordability, and standard residual incomes approaches in several respects. First, LSRI measures provide for a much more robust accounting of the financial realities faced by households with different characteristics than is possible through ratio and location affordability measures. In particular, the LSRI approach addresses circumstances around the need for childcare, which often constitutes a household’s largest expense when young children are present. The LSRI measure also avoids the use of the arbitrary and reductive thresholds that are inherent to the ratio and location affordability approaches, and corrects for a key shortcoming of the standard residual income approach by accounting for variations in transportation costs related to a household’s location within the region. The LSRI
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approach achieves all of these improvements through the use of publicly-available data and a relatively straightforward methodology, rendering it useful across many different policy arenas and among a broad range of users. Furthermore, the LSRI method is flexible: It can utilize various household expenditure and housing supply datasets available across multiple scales, and can easily incorporate improved data as it becomes available. The LSRI methodology provided in the following chapter is therefore able to support meaningful discussions around housing affordability at the neighborhood, local, and regional levels, as well as around the intersection of affordability with other policy issues the provision of transit services as is done in Chapters 7 and 8.
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CHAPTER V
METHODOLOGY FOR CONSTRUCTING A LOCATION-SENSITIVE RESIDUAL INCOME
MEASURE OF HOUSING AFFORDABILITY
As detailed in Chapter 4, the LSRI measure of housing affordability improves upon standard measures by more fully accounting for the financial realities faced by households in securing affordable housing, including issues related to household composition and childcare requirements, income, and residential location. LSRI measures are relevant to any application that aims to assess housing affordability at a range of geographies, from the neighborhood up. The utility of LSRI measures and the ease with which they can be constructed using publicly-available data render them highly accessible to practice. The methodology outlined below provides practitioners with details on the data and operations involved in constructing the LSRI measures.
Two LSRI measures are developed in the present chapter. The first measure identifies a household’s ‘housing budget,’ or the amount of monthly income that remains available for housing after the household covers costs associated with the goods and services required to sustain a basic standard of living. A second ‘supply’ measure quantifies the number of rental units that are affordable within a particular household’s housing budget. There are seven steps involved in constructing these two measures, as outlined in Figure 5.1.
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STEPS FOR CONSTRUCTING A LSRI MEASURE
RESULTING LSRI MEASURE
Step"!: Specify assumptions
Step 2: Define household profiles
Step 3: Calculate estimated non-H+T costs
by household profile
Step 4: Calculate H+T budgets
by household profile
Step 5: Calculate estimated transportation costs
by household profile
Step 6: Calculate housing budgets
by household profile
Step 7: Calculate the supply of affordable housing units by household profile
Figure 5.1. Steps for constructing a LSRI measure of housing affordability In Step 1, the analyst specifies a series of assumptions about the geographic extent of the analysis, the unit of analysis for which affordability will be assessed, and whether the analysis will evaluate affordability for homeowners, renters, or both. Step 2 involves defining a set of theoretical household profiles that vary on household composition (the number of adults, number of children, and number of those children that require childcare) and household income. Next, costs associated with the essential goods and services required to meet a basic standard of living, except for those associated with housing and transportation, are summed to identify the total ‘non-H+T’ costs (Step 3). Non-H+T costs vary depending on household composition and financial circumstance, and are therefore calculated for each household profile separately. In Step 4, non-H+T costs are subtracted from household income to arrive at the total remaining amount available for housing and transportation costs, referred to as the ‘H+T budget.’ H+T budgets are calculated for all specified
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household profiles. In Step 5, transportation costs are then estimated for each household profile based on their theoretical location within the region. The result of this step is a comprehensive dataset of estimated transportation costs for every Census block group in the region, by household profile.
After establishing estimated transportation costs, the analyst is then able to calculate the total funds that remain available for housing costs for all block groups in the metro (Step 6). This housing budget represents the upper limit of what a household can afford to pay for housing while still covering the necessities associated with maintaining a basic standard of living. It therefore varies by household characteristics, and by location in the region, such that a housing budget is calculated for each of the defined household profiles theoretically residing in each block group within a region. In the final step (Step 7), the analyst calculates the supply of housing units that are affordable within a particular household’s housing budget for every theoretical residential location (block group). The key components generated by these seven steps are summarized in Figure 5.2.
The remainder of the present chapter provides a detailed account of the operations involved in each of the seven steps. These operations are demonstrated by calculating a LSRI measure of housing affordability for an example metropolitan area (Denver). The same methodology was followed to develop LSRI measure the remaining seven case metros to support the analysis present in Chapters 7 and 8.
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LSRI component
Household
profile
Non-H+T costs
H+T budget
Definition
A theoretical household for which affordability is assessed; Each household profile varies based on:
• Number of adults in household
• Number of children in household
• Number of children requiring childcare
• Household income
Total costs associated with the goods and services required to support a basic standard of living, except for those related to housing and transportation The amount of income that remains available for housing and transportation costs after non-H+T costs are subtracted
Transportation
costs
Housing budget
Supply of affordable housing
Costs associated with transportation, depending on a household’s residential location within the region The amount of income that remains available for housing after non-H+T costs and transportation costs are subtracted;
Represents the upper limit of what a household can afford to pay for housing while still covering its other basic necessities
The number (or percent) of housing units that are affordable to a theoretical household given its composition and income
Varies by
household
profile
Varies by household profile, and by block group
Figure 5.2. LSRI components STEP 1: SPECIFY ASSUMPTIONS
A number of analytic choices that define the bounds and assumptions of the analysis are required as the first step in developing the LSRI measures. This involves: 1) Identifying the geographic extent of the analysis (e.g. neighborhood, municipality, region, etc.); 2) Defining the unit of analysis for which affordability will be assessed (e.g. block group, tract, municipal, etc.); and 3) Specifying whether the analysis will assess affordability for homeowners, renters, or both, and whether the analysis will include unsubsidized market-rate housing and/or subsidized housing. Assumptions made in the present analysis are outlined below.
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Geographic Extent
For the purposes of this study, LSRI measures are developed for all block groups in a metro. However, the methodology can easily be adapted to evaluate housing affordability at multiple other scales, from the neighborhood to the national level. As described in Chapter 3, the present study defines the ‘metro’ (also referred to interchangeably as the ‘region’) as the core-based statistical area (CBSA),1 a cluster of counties that centers around at least one ‘core’ of 10,000 people or more and includes all counties that have a high degree of social and economic connection to that core (U.S. Census Bureau, 2010), as well as any additional counties served by the regional transit agency. Many other datasets relevant to this study use the CBSA as the unit of analysis, including HUD’s Location Affordability Index and various measures of transit accessibility discussed.
Unit of Analysis
The defined unit of analysis, or the geography at which affordability is assessed, will vary depending on the aims of the particular analysis and the level of error that can be tolerated. The present study assesses affordability at the Census block group level. Housing supply and demand vary considerably across, and even within, neighborhoods. It is therefore important to use the smallest unit of analysis possible to account for this variation. Block groups are commonly used as a proxy for neighborhoods and are the smallest geography at which much of the data employed by the LSRI approach are available. It is important to recognize, however, the tradeoff that exists between the granularity of an analysis and the level of error associated with small-geography datasets: The smaller the unit of analysis, the larger the error. Much of the data for the present analysis is derived from the U.S. Census American Community Survey (ACS), which often has substantial margins of error. The downsides of using a dataset with such high levels of error are well-documented (for a recent review, see Spielman & Singleton, 2015). While the margin of
1 CBSAs defined by the U.S. Census Bureau in 2014 are used in the present analysis.
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error inherent to ACS data is certainly a concern of which analysts should be aware, it is considered to be tolerable when weighed against the utility of the findings generated for small geographies.
Housing Tenure
The LSRI approach can be used to assess affordability for both homeowners and renters depending on the data used to build the measure. However, the present study focuses exclusively on renters for several reasons. First, renters face the largest affordability challenges in U.S. metropolitan areas. In 2014, 24-percent of all renter households spent more than half of their income on housing as compared to 10-percent of homeowners (Ault et al., 2015). Second, low-income households are much more likely to rent their homes as compared to higher-income households (Schwartz, 2010). Third, rising housing costs faced by home owners, while certainly a problem for those with fixed or declining incomes, may be mitigated by longer-term gains in the equity of the home. This is not the case for renters, who see no financial gains from increasing housing costs (Revington & Townsend, 2016). Finally, assessing housing costs associated with owner-occupied housing is much more complex than for renters and requires many assumptions about a household’s ability to secure a mortgage, the amount provided as a down payment, mortgage interest rates, and property tax deductions (Joice, 2014).
The methodology presented in this chapter focuses exclusively on unsubsidized, market-rate rental units for several reasons. Low-income renters in market-rate housing are the group most vulnerable to transit-induced displacement since they are subject to the whims of the housing market with little available income to afford rising premiums. Unsubsidized rental housing also provides the vast majority of the nation’s affordable housing, since only one-quarter of eligible households are able to secure public rental assistance (Ault, et al., 2015). The reliance of low- and moderate-income households on market-rate rental housing is only likely to grow as many subsidized units reach their sunset
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dates, which is expected to occur in record numbers in the coming years (Mueller & Steiner, 2011). Analysts wishing to include subsidized units in future analyses could do so by integrating additional data in Step 7.
STEP 2: DEFINE HOUSEHOLD PROFILES
As with the standard residual income approach, developing a LSRI measure requires defining the set of household profiles for which affordability will be assessed. There are two dimensions involved in defining these household profiles: Household composition and household income.
Define Household Composition(s)
Household composition is defined based on the three key variables that have the largest influence on household expenditures: The number of adults, number of children, and number of children who require childcare (if any). The goals of a particular analysis should drive how these variables are combined to create a specified set of household composition types. For example, an analyst interested in understanding the landscape of housing affordability for single parent households with one child would focus exclusively on households of that type. Another analyst might choose to focus on households with young children, and would thus define a set of households based on those parameters.
The goal of the present analysis is to broadly explore housing affordability across a wide swath of low- and moderate-income households. I therefore define a set of 12 theoretical household compositions, each with either one or two adults, and with zero, one, or two children. The number of children requiring childcare (if any) is also specified. Combining these characteristics results in the 12 household composition types identified in Table 5.1. Of course, households with more than two adults and/or more than two children could also be included if an analyst wished to understand housing affordability for larger families.
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Table 5.1. Household compositions included in the present analysis
children
Household composition types adult(s) in childcare not in childcare
Single adult, no children 1 0 -
Single adult, 1 child (1 in childcare) 1 0 1
Single adult, 1 child (not in childcare) 1 1 0
Single adult, 2 children (both in childcare) 1 2 0
Single adult, 2 children (1 in childcare) 1 1 1
Single adult, 2 children (not in childcare) 1 0 2
Two adults, no children 2 - -
Two adults, 1 child (1 in childcare) 2 1 0
Two adults, 1 child (not in childcare) 2 0 1
Two adults, 2 children (both in childcare) 2 2 0
Two adults, 2 children (1 in childcare) 2 1 1
Two adults, 2 children (not in childcare) 2 0 2
Specify Household Income Level(s)
Defining household profiles also requires specifying the income level(s) at which affordability will be assessed. The goals of the analysis again drive this decision. Income levels could be defined as a percent of area median income (AMI), as is commonly done in affordability analyses (e.g. 60% AMI). Area median income is calculated by the U.S. Census Bureau for Metropolitan Statistical Area (MSA) geographies, which are comprised of a collection of counties that have a high degree of social and economic integration (U.S. Census Bureau, 2010). An analyst might also elect to focus on specific thresholds of income (e.g. $40,000 to $60,000). Or, an analyst might define income levels based on details about a theoretical household in a specific line of work (e.g. a two-adult household headed by a nursing assistant making $12.50/hourfor 40 hours/week and a unionized welder making $25/hour for 35 hours/week).
Because the present analysis aims to understand landscapes of affordability for a broad spectrum of low- and moderate-income households, LSRI measures are constructed for five income levels, each roughly corresponding to particular HUD designations. HUD defines low-income households based on a percent of AMI adjusted up or down based on
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household size. Less than 50-percent of AMI is considered “very low income.” Between 50-percent and 80-percent AMI is defined as “low income.” “Middle income” households are those earning between 80- and 100-percent of AMI, while those earning more than 100-percent are considered “high income” (U.S. Department of Housing and Urban Development, 2014). Based on these thresholds, I develop LSRI measures that assess affordability at 30-, 50-, 80-, and 100-percent of AMI. I also develop measures of affordability for households earning 120-percent AMI in order to address the circumstances of ‘workforce’ households, which are commonly defined as those earning 120-percent AMI or less (Ault, et al., 2015). Table 5.2 summarizes the five household income levels as they apply to the Denver metro, which in 2014 had an AMI of $64,2062.
Table 5.2. Household income levels analyzed (Denver)
Household income as percent of AMI Annual household income Monthly household income*
30% AMI $19,262 $1,610
50% AMI $32,103 $2,680
80% AMI $51,365 $4,280
100% AMI $64,206 $5,350
120% AMI $77,047 $6,420
*Rounded to nearest tenth
Combining each of the 12 household composition types defined in the above section with the five income levels results in a total of 60 household profiles. While this extensive number of profiles is appropriate for the present analysis given the goal of broadly understanding affordability among low- and moderate-income households, practitioners wishing to employ the LSRI approach could define far fewer (or more) as is necessary for the specific aims of their research.
2 For this analysis, data on area median income is collected for each Metropolitan Statistical Area (MSA) from Table B19013 of the 2010-2014 American Community Survey (ACS) Five-Year Estimates. Reported values are in 2014 adjusted dollars.
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STEP 3: CALCULATE ESTIMATED NON-HOUSING AND NON-TRANSPORTATION COSTS
Once assumptions have been specified and household profiles have been defined, the analyst proceeds to constructing the LSRI measure. The initial step in this process involves specifying costs for all the essential goods and services required to meet a basic standard of living, except for those associated with housing and transportation. These are referred to as ‘non-H+T costs.’ Defining what constitutes a ‘basic’ standard of living requires normative judgement about the conditions that are acceptable to a particular society at a specific point in time (Stone, 2006). Most empirical research employing a residual income approach in the U.S. context uses the ‘lower-budget’ standards defined by U.S. Bureau of Labor Statistics (BLS) to identify the ‘basket’ of non-housing goods and services required to maintain a basic standard of living, including: Food; Medical expenses; Childcare (if applicable); Transportation; Clothing; Other goods required for basic household operations; and Local, state, and federal taxes.
A variety of data sources are available to identify non-H+T costs. Three primary resources provide data for non-H+T costs: The Massachusetts Institute of Technology (MIT) Living Wage Calculator3, the University of Washington (UW) Center for Women’s Welfare Self-Sufficiency Standard4, and the Economic Policy Institute (EPI) Family Budget Calculator.5 All three of these present household-level expenditure data for a range of household types in a user-friendly interface that is easily accessible for researchers,
3 The Living Wage Calculator was created and is maintained by Dr. Amy K. Glasmeier, Professor of Economic Geography and Regional Planning at Massachusetts Institute of Technology (MIT). It is available for all 50 states and is updated annually and can be found at: http://livinqwaqe.mit.edu/.
4 The Self-Sufficiency Standard was created by Dr. Diana Pearce, Director of the Center for Women’s Welfare at the University of Washington. Data is available for 38 states and is current to 2014 for most, but not all, states It can be found at: http://www.selfsufficiencvstandard.org/.
5 The Family Budget Calculator is maintained by the Economic Policy Institute, a not-for-profit, nonpartisan think tank focused on research related to economic policies that address the needs of low-and middle-income workers. The Family Budget Calculator is available for all 50 states and can be found here: http://www.epi.org/resources/budqet/.
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practitioners, and members of the public. Data on non-housing expenditures are most often sourced from U.S. BLS Consumer Expenditure (CE) Survey, a dataset released annually based on findings from interviews and diary surveys that ask American consumers about details related to their household characteristics, expenditures, and income (U.S. Bureau of Labor Statistics, 2016).
Of the three resources that aggregate data on household expenditures, the MIT Living Wage Calculator (LWC) offers the most robust dataset that is available for all case metros and was therefore selected for primary use in the present analysis. While the UW Self-Sufficiency Standard also offers a comprehensive dataset, it does not provide standardized data across all case metros and so is not appropriate for cross-case comparisons. The EPI Family Budget Calculator provides consistent data across all U.S. metros, but is less robust than the other two sources. Analysts may find each of these resources to have different advantages depending on the specific aims of the research.
The MIT LWC is designed to be used in identifying the minimum hourly wage required to sustain a basic standard of living across all metros of the U.S., assuming a standard 40 hours per week of work. The resulting ‘living wage’ calculation therefore “draws a very fine line between the financial independence of the working poor and the need to seek out public assistance or suffer consistent and severe housing and food insecurity” (Glasmeier, 2014:2). The LWC does not include any luxuries that moderate- and high-income households may be accustomed to - for example, meals in restaurants, entertainment, and travel, nor does it allow for any savings for retirement or for large capital expenses like homes or cars. As a result, the LWC is well-suited for the present analysis, which aims to identify the costs associated with a basic standard of living. Details associated with each of the five non-H+T costs - childcare, food, medical, other basic necessities, and taxes - are discussed below.
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Estimate Childcare Costs
Data obtained from Child Care Aware6, a national association of child care resource agencies, is used to compute childcare costs for each of the case metros. Childcare costs are also reported in the LWC from the same source, although computations are simplified to a greater extent than is done in the present study. Child Care Aware documents the average costs of legally-operating childcare centers and family home care on an annual basis, as reported by market surveys conducted by child care resources and referral state networks (Child Care Aware of America, 2014). The data used in the present analysis represents 2013 costs, which are then adjusted to 2014 dollars using the U.S. BLS Consumer Price Index (CPI) inflation calculator7. Child Care Aware reports childcare costs for children in three age groups: Infants and toddlers (0 to 36 months), pre-school (4-year olds), and school age (after-school care for children 5-years and older). The organization reports costs separately for licensed ‘childcare centers’ (traditional daycare centers) and for smaller-scale childcare centers operated from an individual’s home (‘home care’), which tend to be less expensive than daycare centers.
Several operations were conducted to compute childcare costs in the present study. First, the least expensive option (childcare center or home care) is employed for each state based on the assumption that low- and moderate-income households are likely to seek the least costly childcare as possible. The least expensive childcare costs for the two youngest age groups - infants/toddlers and preschoolers - are then averaged and inflated to 2014 dollars to arrive at an estimated cost per child. Total childcare costs for each household type are calculated based on the number of children requiring childcare.
Childcare costs vary quite significantly across the case metros, with the annual cost ranging from $5,700 per child in Salt Lake City to $8,660 per child in Seattle. As shown in
6 http://childcareaware.org/
7 http://www.bls.gov/data/inflation calculator.htm
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Table 5.3, childcare costs are nearly as high in the Denver metro ($8,640 per child) as they
are in Seattle. Appendix A outlines the estimated cost of childcare per child for each of the
states in which the eight case metros are located.
Table 5.3. Estimated childcare costs by number of children requiring childcare
(Denver)
Number of children Childcare costs
requiring childcare Annual Monthly*
1 child $8,638 $720
2 children $17,276 $1,440
*Rounded to nearest tenth Source: Childcare Aware of America, 2014
Estimated Food Costs
Food costs are sourced directly from the LWC, which reports regionally-adjusted data from the United States Department of Agriculture’s (USDA) official low-cost food plan for the period of July 2013 through June 2014. The second least expensive food plan (of four) is used, which assumes that households prepare all meals and snacks in the home using lower-cost foods.8 9 Food cost estimates vary by household type, with the assumption that adults consume more than older children and that older children consume more than younger children (Glasmeier, 2014).9 Table 5.4 summarizes these costs for each the 12 household types for the Denver metro. Appendix A provides the same data for all eight case metros.
8 Values from the USDA low-cost food plan used in LWC’s food cost estimates are available here: http://www.cnpp.usda.gov/sites/default/files/usda food plans cost of food/CostofFoodJun2014.pdf.
9 Additional details about the LWC food cost estimates can be found in the Living Wage Calculator User’s Guide /Technical Notes (2014 Update) (Glasmeier, 2014)
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Table 5.4. Estimated food costs by household composition type (Denver)
Household type Food costs
Annual Monthly*
Single adult, no children $3,607 $300
Single adult, 1 child $5,319 $440
Single adult, 2 children $8,002 $670
Two adults, no children $6,612 $550
Two adults, 1 child $8,234 $690
Two adults, 2 children $10,627 $890
*Rounded to nearest tenth
Source: MIT Living Wage Calculator (Glasmeier, 2014)
Estimated Medical Costs
As with food costs, medical and health-related expenses are sourced directly from the LWC. Medical costs reported by the LWC represent the sum of four expenses: Health insurance costs associated with employer-sponsored plans; Medical services; Pharmaceutical drugs; and Medical supplies. Data for these expenses come from two primary sources. First, the Health Insurance Component Analytical Tool (MESPnet/IC)10 developed by the Agency for Healthcare Research and Quality is used to compute employer-sponsored health insurance costs. Health care costs are very difficult to estimate due to a range of individual- and household variables that influence the need for health care expenditures and the extent to which those expenditures are covered by a household’s insurance. Specifying medical expenses thus requires making assumptions about the general health of household members and the presence of employer-provided health insurance, which may not reflect reality. However, these assumptions are justified since it allows for standardized data that can be applied across households and across metros.I 11
Data for the remaining three medical expenses - medical services, pharmaceutical drugs, and medical supplies - are sourced by the LWC from the 2014 U.S. BLS CE Survey then adjusted for regional differences and inflated to 2014 dollars using the CPI inflation
I n
Available at http://meps.ahrq.gov/mepsweb/data stats/MEPSnetIC.isp.
II See Glasmeier (2014) for more details about the assumptions and methods underlying the LWC medical cost estimates.
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Full Text

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EXAMINING GEOGRAPHIES OF OPPORTUNITY FOR HOUSEHOLDS WITH LIMITED MEANS: AN INVESTIGATION OF TRANSIT ACCESSIBILITY AN D HOUSING AFFORDABILITY IN EIGHT U.S. METROPOLITAN AREAS by KARA S. LUCKEY B.S.C.E., The Cooper Union for the Advancement of A rt and Science, 2003 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Design and Planning Program 2017

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ii This thesis for the Doctor of Philosophy degree by Kara S. Luckey has been approved for the Design and Planning Program by Jeremy Nemeth, Chair Kevin J. Krizek, Advisor Wesley Marshall Tanya Heikkila Date: May 13, 2017

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iii Luckey, Kara S. (PhD, Design and Planning) Examining Geographies of Opportunity for Households with Limited Means: An Investigation of Transit Accessibility and Housing Affordability in Eight U.S. Metropolitan Areas Thesis directed by Professor Kevin J. Krizek ABSTRACT The role of transit in maximizing geographies of op portunity for lowand moderateincome individuals is well-established, although em erging concerns about direct and exclusionary displacement in transit-rich neighborh oods call into question the ability of those with limited means to benefit from transit access. In the face of these questions, a ‘location efficiency narrative’ suggests that displacement ma y be less of a threat than commonly thought because lower transportation costs in trans it-accessible neighborhoods are likely to offset higher housing costs. Yet it remains unclear whether this narrative is supported by onthe-ground empirics, especially given concerns abou t the robustness of typical measures of affordability. This study takes as its starting poi nt a puzzle about whether transit-rich neighborhoods are indeed more affordable, as a loca tion efficiency approach would suggest, when affordability is examined using measu res and methods that address key shortcomings in the literature. I therefore introdu ce an improved ‘location-sensitive residual income’ (LSRI) measure – which accounts for the nua nces of household composition, financial circumstances, and residential location – and demonstrate how more typical measures are likely to under -estimate the challenges faced by lowand moderate -income households as they seek affordable housing. I then employ LSRI measures to investigate current landscapes of accessibility and affordabili ty experienced by lowand moderateincome renters in eight U.S. metros. I first examin e the extent to which supplies of affordable rental housing are located in transit-accessible ne ighborhoods. I then isolate the complex relationship between transit accessibility and affo rdability using a series of spatial error and geographically-weighted regression models that cont rol for key characteristics of the built

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iv and social environments, as well as for spatial dep endence. Results indicate that geographies of opportunity as shaped by accessibili ty and affordability are surprisingly strong in several metros – Denver and Los Angeles m ost notably – but are quite weak others. While findings for some metros are largely consistent with a location efficiency narrative, results for a larger number challenge it , underscoring that high housing costs in transit-accessible areas cannot be assumed to be of fset by lower transportation costs. Further implications for transportation justice and potential policy prescriptions to promote transit-accessible affordable housing are also disc ussed. The form and content of this abstract are approved. I recommend its publication. Approved: Kevin J. Krizek

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v This dissertation is dedicated with gratitude to St eve, Olin, and Thea for helping me to live every day with purpose, determination, and joy; to my parents Kathrine and Gregory for encouraging curiosity and wonderment; and to my com mittee members, particularly my advisor Professor Kevin Krizek, for their unending support and guidance.

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vi ACKNOWLEDGEMENTS This dissertation was supported through a National Science Foundation Integrative Graduate Education and Research Traineeship (IGERT) Fellowship in Sustainable Urban Infrastructure (IGERT Award No. DGE-0654378), as we ll as through a U.S. Department of Transportation Dwight D. Eisenhower Transportation Graduate Fellowship.

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vii TABLE OF CONTENTS CHAPTER I. SUMMARY ........................................ ................................................... ..................... 1 CONCEPTUAL BASIS .................................. ................................................... .......... 1 EXISTING KNOWLEDGE ................................ ................................................... ....... 2 ANALYTICAL APPROACH ............................... ................................................... ...... 3 RESULTS: GEOGRAPHIES OF TRANSIT ACCESSIBILITY AND H OUSING AFFORDABILITY...................................... ................................................... .............. 6 RESULTS: THE RELATIONSHIP BETWEEN TRANSIT ACCESSIBI LITY AND HOUSING AFFORDABILITY, ACCOUNTING FOR OTHER KEY FAC TORS ............ 7 CONCLUSIONS AND IMPLICATIONS ...................... ................................................ 9 II. GEOGRAPHIES OF OPPORTUNITY, TRANSIT ACCESSIBILI TY, AND HOUSING AFFORDABILITY: THEORETICAL AND PRACTICAL FOUNDATIONS ....................................... ................................................... ............ 13 CONSIDERING SOCIAL JUSTICE IN THE CONTEXT OF U.S. M ETROPOLITAN TRANSPORTATION PLANNING AND POLICY ................ ...................................... 13 Contemporary Perspectives on Social Justice ....... ....................................... 14 The ‘Capabilities Approach’ Framework ............. .......................................... 20 Applying a Capabilities Approach Framework to Conce ptualize Transportation Justice ............................ ................................................... ... 22 The Role of Transit in Shaping Geographies of Oppor tunity for Lowand Moderate-Income Households .................... .......................................... 27 EMPIRICAL RESEARCH ON THE AFFORDABILITY OF HOUSING IN TRANSIT-ACCESSIBLE NEIGHBORHOODS IN THE U.S. ...... ............................... 28 Effects of Transit Accessibility on Housing Costs . ........................................ 29 Displacement Effects Associated with Transit Access ibility .......................... 31 The Location Efficiency Narrative: An Antidote to C oncerns about Transit-Induced Displacement? ..................... ............................................... 34 III. RESEARCH QUESTIONS AND APPROACH .............. ............................................ 40 RESEARCH QUESTIONS ................................ ................................................... .... 40

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viii RESEARCH APPROACH ................................. ................................................... .... 42 Case Selection .................................... ................................................... ...... 42 Key Variables ..................................... ................................................... ....... 47 Overview of Methods ............................... ................................................... . 49 IV. EVALUATING TYPICAL MEASURES OF HOUSING AFFORDAB ILITY AND INTRODUCING THE IMPROVED ‘LOCATION-SENSITIVE RESIDU AL INCOME’ MEASURE ................................... ................................................... ......... 54 INTRODUCTION ...................................... ................................................... ............ 54 The Growing Housing Affordability ‘Crisis’ ........ ............................................ 54 Defining and Measuring ‘Affordable Housing’ ....... ........................................ 58 TYPICAL APPROACHES TO MEASURING HOUSING AFFORDABILI TY .............. 59 A ‘Ratio’ Approach to Measuring Housing Affordabili ty ................................. 61 A ‘Location Affordability’ Approach to Measuring Ho using Affordability ........ 64 A ‘Residual Income’ Approach to Measuring Housing A ffordability ............... 66 Conclusions ....................................... ................................................... ....... 69 A NEW APPROACH TO MEASURING HOUSING AFFORDABILITY: ‘LOCATION-SENSITIVE RESIDUAL INCOME’ .............. ......................................... 70 V. METHODOLOGY FOR CONSTRUCTING A LOCATION-SENSITIV E RESIDUAL INCOME MEASURE OF HOUSING AFFORDABILITY .. ....................... 74 STEP 1: SPECIFY ASSUMPTIONS ....................... ................................................. 7 7 Geographic Extent ................................. ................................................... ... 78 Unit of Analysis .................................. ................................................... ....... 78 Housing Tenure..................................... ................................................... .... 79 STEP 2: DEFINE HOUSEHOLD PROFILES ................. .......................................... 80 Define Household Composition(s) ................... ............................................. 80 Specify Household Income Level(s) ................. ............................................ 81 STEP 3: CALCULATE ESTIMATED NON-HOUSING AND NON-TRANSPORTATION COSTS............................... ................................................... . 83

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ix Estimated Childcare Costs ......................... .................................................. 85 Estimated Food Costs .............................. ................................................... . 86 Estimated Medical Costs ........................... ................................................... 87 Estimated Costs for Other Basic Necessities ....... ........................................ 88 Estimated Costs of Taxes .......................... .................................................. 89 Total Estimated Non-Housing and Non-Transportation Costs ...................... 90 STEP 4: CALCULATE HOUSING AND TRANSPORTATION BUDGET S ................ 91 STEP 5: IDENTIFY ESTIMATED TRANSPORTATION COSTS ... ........................... 92 Data Sources ...................................... ................................................... ...... 93 Summary of Estimated Transportation Costs ......... ...................................... 99 STEP 6: CALCULATE ESTIMATED HOUSING BUDGETS ....... ............................ 103 STEP 7: CALCULATE ESTIMATED SUPPLIES OF AFFORDABLE HOUSING .... 107 Calculate the Estimated Number of Units Available w ithin Household Housing Budgets ................................... ................................................... .. 111 Calculate the Estimated Percent of Regional Housing Units that are Affordable within Household Housing Budgets ....... .................................... 112 CONTRIBUTIONS AND LIMITATIONS OF A LSRI APPROACH .. ......................... 116 VI. COMPARING FOUR MEASURES OF HOUSING AFFORDABILIT Y: THE CASE OF LOWAND MODERATE-INCOME HOUSEHOLDS IN THE DENVER METRO ...................................... ................................................... ......... 119 INTRODUCTION ...................................... ................................................... .......... 119 DEFINING A SUBSET OF LOWAND MODERATE-INCOME HOUSE HOLDS .... 120 WHAT CAN LOWAND MODERATE-INCOME HOUSEHOLDS AFFORD TO PAY FOR HOUSING IN DENVER? ........................ ............................................... 121 Estimated Housing Budgets Calculated Using a LSRI A pproach ................ 122 Estimated Housing Budgets: A Comparison of the Rati o, Location Affordability, Standard Residual Income, and LSRI A pproaches ................ 126 WHAT IS THE METRO-WIDE SUPPLY OF HOUSING UNITS AFFO RDABLE TO LOWAND MODERATE-INCOME RENTERS IN DENVER? .... ...................... 131

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x Estimated Metro-Wide Supplies of Affordable Rental Housing Calculated Using a LSRI Approach .................. .......................................... 131 Estimated Metro-Wide Supplies of Affordable Rental Housing: A Comparison of the Ratio, Location Affordability, St andard Residual Income and LSRI Approaches ........................ ............................................ 133 HOW ARE SUPPLIES OF LOWAND MODERATE-INCOME AFFORD ABLE RENTAL UNITS SPATIALLY-DISTRIBUTED? ............... ....................................... 136 Examining the Spatial Distribution of Affordable Re ntal Housing Using a LSRI Approach ................................... ................................................... .. 137 Identifying Affordability Clusters and Outliers ... .......................................... 139 CONCLUSIONS ....................................... ................................................... .......... 146 VII. EXAMINING LANDSCAPES OF TRANSIT ACCESSIBILITY AND HOUSING AFFORDABILITY IN EIGHT U.S. METROS ................ .......................................... 153 INTRODUCTION ...................................... ................................................... .......... 153 DATA AND METHODS .................................. ................................................... ..... 155 Data .............................................. ................................................... ................ 155 Methods ........................................... ................................................... ............. 164 RESULTS AND DISCUSSION............................. .................................................. 165 Supplies of Affordable Rental Units, by Accessibili ty Level ......................... 165 Accessibility Ratios .............................. ................................................... ... 167 SUMMARY OF KEY FINDINGS ........................... ................................................. 1 72 VIII. EXAMINING THE COMPLEX RELATIONSHIP BETWEEN TR ANSIT ACCESSIBILITY AND HOUSING AFFORDABILITY IN EIGHT U. S. METROS ..... 176 INTRODUCTION ...................................... ................................................... .......... 176 DATA AND METHODS .................................. ................................................... ..... 177 Data .............................................. ................................................... .......... 177 Methods ........................................... ................................................... ....... 178 RESULTS AND DISCUSSION............................. .................................................. 184 Examining Global Relationships between Transit Acce ssibility and Housing Affordability: Spatial Error Models ....... ......................................... 185

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xi Examining Local Relationships between Transit Acces sibility and Housing Affordability: Geographically-Weighted Regr ession Models .......... 196 SUMMARY OF KEY FINDINGS ........................... ................................................. 2 00 IX. GEOGRAPHIES OF OPPORTUNITY FOR LOWAND MODERAT E-INCOME HOUSEHOLDS IN EIGHT U.S. METROS: A SYNTHESIS OF FIN DINGS ............ 205 INTRODUCTION ...................................... ................................................... .......... 205 Conceptual Basis .................................. ................................................... .. 205 Existing Literature ............................... ................................................... .... 207 Research Questions and Approach ................... ......................................... 209 THE LSRI MEASURE OF HOUSING AFFORDABILITY ......... ............................... 212 SYNTHESIS OF FINDINGS: CURRENT GEOGRAPHIES OF OPPOR TUNITY FOR LOWAND MODERATE-INCOME HOUSEHOLDS ........... ........................... 215 Geographies of Opportunity: A Typology ............ ........................................ 215 Metro-wide Geographies of Opportunity ............. ........................................ 216 SUMMARY OF CONTRIBUTIONS AND LIMITATIONS .......... ............................... 222 Key Contributions ................................. ................................................... ... 223 Limitations ....................................... ................................................... ........ 228 Future Research ................................... ................................................... .. 230 REFERENCES .................................................. ................................................... ............. 232 APPENDIX A. SUMMARY OF NON-HOUSING AND NON-TRANSPORTATION (‘NON-H+T’) COSTS BY METRO ........................ .................................................. 243 B. SUMMARY OF TRANSPORTATION COSTS BY METRO ....... ............................. 245 C. LSRI MEASURES OF HOUSING AFFORDABILITY (DENVER) ............................ 247 D. SAMPLE R-CODE (DENVER) ......................... ................................................... ... 249 E. FULL OLS AND SPATIAL ERROR REGRESSION RESULTS .. ............................ 264

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xii LIST OF ABBREVIATIONS ACS American Community Survey AIC Akaike information criterion AMI Area median income BLS Bureau of Labor Statistics CBSA Core-based statistical area CE Consumer Expenditure [Survey] CNT Center for Neighborhood Technology CPI Consumer Price Index CTOD Center for Transit-Oriented Development EPA [United States] Environmental Protection Agency GIS Geographic Information System GTFS General Transit Feed Specification GWR Geographically-weighted regression H+T Housing and Transportation HUD [United States] Department of Housing and Urban Development ISTEA Intermodal Surface Transportation Efficiency Act JCHS [Harvard University] Joint Center for Housing Studies LAI Location Affordability Index LAP Location Affordability Portal LEHD Longitudinal Employer-Household Dynamics LISA Local Indicators of Spatial Autocorrelation LM Lagrange Multiplier LODES Longitudinal Origin-Destination Employment St atistics LSRI Location-sensitive residual income MLS Multiple Listing Survey

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xiii MPO Metropolitan planning organization MSA Metropolitan statistical area OLS Ordinary Least Squares SEM Structural equation modelling SLD Smart Location Database USDA United States Department of Agriculture VIF Variance Inflation Factor

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Page 1 CHAPTER I SUMMARY CONCEPTUAL BASIS This dissertation begins by considering how several contemporary theoretical lenses relevant to social justice in the context of U.S. m etropolitan planning and policy help in understanding what constitutes a ‘just’ transportat ion system (Chapter 2). Of these, I adopt Sen and Nussbaum’s ‘capabilities approach’ to argue that transportation justice requires that all individuals are able to access the opportunitie s required for them to reach their full potential. I then develop a conceptual framework that guides t he present study by integrating principles of a capabilities approach w ith the concept of ‘geographies of opportunity,’ which is commonly used among practiti oners and advocates around issues of spatial and social justice. In this conceptual framework ( Figure 1.1 ), an individual’s ‘geography of opportunity’ (or in the language of the capabilities approach, h er/his set of ‘ capabilities ‘) represents the opportunities that are available to a person in the ir pursuit of well-being. Three components (‘ primary goods ‘) related to physical planning and policy shape ge ographies of opportunity: 1) the quantity and qualities of the opportunities themselves; 2) the home location from which an individual seeks to access opportunities; and 3) the transportation options that enable their ability to access them. A multitude of other ‘ personal and social conversion factors’ also influence geographies of opportunity. For the purposes of the present study, the most important of these is a household’s ‘housing b udget,’ defined as the amount a household can afford to spend on housing. Given the costs associated with car ownership, and given that low-income households are much less likely to have access to a private vehicles than more affluent households, public transit often plays a vital role in providing access to opportunities for those with limited means. The present study therefo re conceptualizes geographies of

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Page 2 opportunity for lowand moderate-income households as being bounded by two circumstances: 1) the ability to access employment opportunities via modes other than private auto (‘transit accessibility’) and 2) the a bility to afford housing in transit-accessible areas, and thus benefit from the advantages conferr ed by access to transit (‘housing affordability’). Figure 1.1. Basic conceptual framework EXISTING KNOWLEDGE The role of transit in maximizing geographies of op portunity for lowand moderateincome individuals is well-established. However, no t until recently has the affordability of housing in transit-accessible areas been recognized as being equally integral. Two areas of concern around housing affordability in transit-ric h neighborhoods have emerged in the existing literature. The first relates to direct di splacement effects associated with property value increases in areas with high-frequency transi t that render long-standing residents no longer able to afford housing in transit-accessible neighborhoods (often referred to as

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Page 3 ‘transit-induced gentrification’). The second area of concern relates to increased demand for transit-accessible locations on a regional scale, r esulting in exclusionary displacement effects whereby newly-formed and relocating househo lds with lower incomes are unable to afford housing in these neighborhoods and instead l ocate to more auto-oriented areas of the metro. In recent years, a strand of literature focused on a ‘location efficiency’ approach to thinking about issues of affordability has emerged to suggest that local and regional displacement in transit-rich areas may be less of a threat when housing and transportation (‘H+T’) costs are considered in combination. A ‘loc ation efficiency narrative’ therefore acknowledges that housing costs may be higher in tr ansit-accessible areas, but counters that reduced transportation expenditures are likely to offset these costs resulting in better overall H+T affordability. While the location effic iency perspective has gained prominence in policy conversations, it remains unclear whether it is supported by on-the-ground empirics. A critical review of the existing literature around transit-induced gentrification and location efficiency reveals four significant shortc omings in our understanding of the relationship between transit accessibility and hous ing affordability in U.S. metros (Chapter 2). First, the literature focuses predominately on effects associated with fixed-rail transit, thus neglecting the large role buses play in provid ing access across U.S. metros. Second, existing research has little to say about landscape s of affordability for market-rate renters, who are arguably the group most vulnerable to displ acement. Third, only a handful of studies account for spatial error, despite the clea r presence of spatial dependence associated with these phenomenon and well-documente d evidence that ignoring these effects may lead to unreliable findings. Finally, a nd perhaps most seriously, all but one study rely upon inherently flawed ratio-based measures of housing affordability. ANALYTICAL APPROACH The present dissertation takes as its starting poin t a puzzle about whether transit-rich

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Page 4 neighborhoods are indeed more affordable, as a loca tion efficiency approach would suggest, when affordability is examined using measu res and methods that address the four key gaps in the literature. I address this puzzle i n two analytical parts. In Part 1, I discuss the ways in which typical measures of housing affordabi lity are likely to mischaracterize the opportunities and challenges lowand moderateinc ome households experience in securing affordable housing, a topic which has received surp risingly little critical attention in both scholarly and public discourses (Chapter 4). I the n introduce and provide a detailed methodology for constructing a ‘location-sensitive residual income’ (LSRI) measure of affordability which improves upon typical measures to more accurately reflect the financial realities faced by households as they seek affordab le housing (Chapter 5). The LSRI approach defines housing as ‘affordable’ when a hou sehold is able to pay for its housing costs while still meeting its basic non-housing nee ds within the bounds of its income. Two LSRI measures are developed for a set of theoretica l lowand moderate-income households that are specified to vary based on comp osition (size, presence of children), financial circumstances (income, childcare requirem ents) and location within the region (which determines transportation costs). The first measure identifies a household’s ‘housing budget,’ or the amount of monthly income that remains available for housing after the household covers the costs of the goods and services that are required to sustain a basic s tandard of living ( Figure 1.2 ). A second ‘supply’ measure is calculated using data from the U.S. Census American Community Survey to identify the quantity of rental units tha t are affordable within a particular household’s housing budget. The two LSRI measures a re calculated for six household profiles at the block group level. Analyses specifi cally focus on the conditions experienced by households who are likely to earn too much to qu alify for subsidy, but not enough that securing stable affordable rental housing is a fore gone conclusion. These households are highly vulnerable to displacement effects since the y are subject to the whims of rental

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Page 5 markets while possessing little ability to cover hi gher premiums. Market-rate rental housing is also important to study because the vast majorit y of eligible households are unable to secure public assistance and must instead rely on u nsubsidized housing. Figure 1.2. Location-sensitive residual income hous ing budget calculation Comparisons between results of an analysis undertak en for the Denver metro using LSRI measures and results for the same metro genera ted using more typical measures demonstrate how standard approaches mischaracterize – and likely overestimate – how much households with limited means can afford for h ousing (Chapter 6). As a consequence, analyses relying on typical measures, including tho se related to the location efficiency perspective, may under estimate the challenges facing lowand moderate-in come households and over estimate the supply of rental units affordable to t hem. Results of this comparison point to the importance of accounting fo r the effects of household composition and financial circumstances in measuring housing af fordability. By directly incorporating these factors, as well as those related to variatio ns in transportation costs, a LSRI measure equips practitioners and policymakers with robust t ools for exploring and developing targeted interventions that account for nuances in landscapes of affordability. In Part 2 of the dissertation, I employ LSRI measur es to examine the current geographies of transit accessibility and housing af fordability that lowand moderate-income renters confront as they seek housing in eight U.S. metros. I specifically address two research questions:

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Page 6 · To what extent are supplies of rental housing that are affordable for lowand moderateincome households located in areas with high transi t accessibility? (Research Question 1) (Chapter 7) · And second, what is the relationship between transit accessibil ity and supplies of affordable rental housing, when controlling for key characteristics of the built and social environments that are likely to influence that rela tionship, as well as for spatial dependence effects? (Research Question 2) (Chapter 8) These investigations are conducted for the universe of U.S. metros with ‘secondgeneration’ regional rail, which are likely to expe rience a specific set of challenges that speak both theoretically and practically to issues of transportation justice. These metros (defined as core-based statistical areas and identi fied by their core cities) are: Dallas, Denver, Houston, Los Angeles, Minneapolis, Portland , Salt Lake City, and Seattle. RESULTS: GEOGRAPHIES OF TRANSIT ACCESSIBILITY AND H OUSING AFFORDABILITY After constructing LSRI measures for each metro, I address Research Question 1 by calculating the supply of rental units that are bot h affordable to a defined set of lowand moderate-income households and located in areas wit h high transit accessibility. I compare this analysis to the supply of affordable units loc ated in areas with zero or low transit accessibility. Transit accessibility is defined as the percent of regional jobs that can be reached within a 45-minute transit commute. Areas w ith accessibility levels above the nonzero average accessibility are considered ‘high’ ac cessibility while those below the non-zero average are identified as ‘low’ accessibility. ‘Zer o’ accessibility areas are those in which no jobs are reachable by transit within 45-minutes. ‘A ccessibility ratios’ – the ratio of the number of affordable units located in zero/low acce ssibility areas to the number of affordable units located in high accessibility areas – are con structed for each of the household profiles. These accessibility ratios are then compared to the ratios for metro-wide supplies of rental

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Page 7 units (regardless of their affordability) to detect deviations from metro-wide distributions. Results indicate that the extent to which affordabl e rental housing is located in areas with high transit accessibility varies between metr os, and in some cases, by household profile within the same metro. Findings for Denver and Los Angeles point to strong geographies of opportunity: All lowand moderate-i ncome households are expected to find larger supplies of affordable rental housing in hig h accessibility areas, despite the fact that the majority of metro-wide rental units are located in zero/low accessibility areas. Patterns in Dallas and Houston, however, point to relatively we ak geographies of opportunity, with larger supplies of affordable rental units in areas with zero or low transit accessibility. Results for the remaining four metros – Minneapolis , Portland, Salt Lake City, and Seattle – are mixed across household profiles. While the majo rity of rental units affordable to low housing budget households in these metros are locat ed in high accessibility areas (suggesting strong geographies of opportunity), the majority of suppl ies affordable to more moderate housing budgets are located in areas with zero or low access (pointing to weak geographies). RESULTS: THE RELATIONSHIP BETWEEN TRANSIT ACCESSIBI LITY AND HOUSING AFFORDABILITY, ACCOUNTING FOR OTHER KEY FACTORS Research Question 2 delves deeper into the complex relationship between transit accessibility and housing affordability by accounti ng for key factors that are likely to influence both phenomena. For this analysis, I firs t use multivariate spatial error regression to model the global relationship between transit ac cessibility (the primary explanatory variable) and supplies of rental units that are aff ordable within the housing budgets of two theoretical households (the outcome variables). The se models control for the effects of various aspects of density, land use mix, housing t enure, and socio-economic conditions that have been shown to influence affordability. Th e presence of spatial dependence is also modelled through inclusion of a spatially-weighted error term. This effort results in two

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Page 8 models for each metro: One for a ‘low housing budge t’ household (one adult earning 50% AMI with one child who does not require childcare) and another for a ‘moderate housing budget household’ (two adults earning 100% AMI and two children, one of whom requires childcare). I then use the same model specification s in geographically-weighted regression (GWR) to explore how local relationships between accessibility and affordabili ty vary across space. This analysis does not intend to draw causal conclusions about the relative effects of specific factors on supplies of affordable housing. Rather, the models are intended to isolate the relationship between the level of transit acces sibility of a neighborhood (block group) and the supply of housing that is affordable to hou seholds with limited means located within it. Results of global (spatial error) models demonstrat e that in five metros – Dallas, Denver, Los Angeles, and Minneapolis – higher level s of accessibility are associated with larger supplies of affordable rental housing holding all else constant, thus pointing to strong geographies of opportunity. A positive (although no t statistically-significant) relationship between accessibility and affordability also exists in Houston. These positive effects are quite substantial in some cases. For example, holdi ng all other variables at mean values, block groups in Dallas with 10-percent higher trans it accessibility are associated with an average of 36 additional rental units that are affo rdable to moderate housing budget households. However, these promising findings are t empered somewhat by local (GWR) results, which indicate that positive global coeffi cients mask the presence of negative local relationships for some metros. In global models for the remaining three metros, hi gher levels of accessibility are associated with fewer affordable units, pointing to weak geographies of opportunity. In Portland and Seattle, results indicate a statistica lly-significant and negative relationship, controlling for other factors. Salt Lake City also demonstrates a negative, although not statistically-significant, relationship. These effe cts can be rather large: In Seattle, for

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Page 9 example, 10-percent higher accessibility is associa ted with an average of 21 fewer affordable units, holding all other factors at mean values. However, GWR results suggest that pockets of positive local relationships may exist in some metros. CONCLUSIONS AND IMPLICATIONS Results from these investigations are synthesized i nto a typology that describes the geographies of opportunities experienced by lowan d moderate-income households in the eight U.S. metros analyzed. The horizontal axis of the typology identifies whether a majority of affordable rental units are located in zero/low accessibility areas (weak geographies) or high accessibility areas (strong geographies). The vertical axis describes whether higher levels of accessibility are associated with additio nal affordable rental units (strong geographies) or fewer affordable units (weak geogra phies) when controlling for key factors and spatial error. These axes form four general typ ologies, each of which calls for a unique set of policy prescriptions ( Figure 1.3 ). Figure 1.3. Geographies of opportunity: A typology

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Page 10 Households with low and moderate housing budgets ar e likely to encounter ‘very strong’ geographies of opportunity in Denver and Lo s Angeles. In these metros, supplies of affordable units are larger in high accessibility a reas, and global models indicate a positive relationship between accessibility and affordabilit y. Low and moderate housing budget households in Seattle are not as fortunate. Results indicate households in these metros face ‘very weak’ geographies of opportunity, with larger supplies of affordable units in zero/low accessibility areas, and negative relationships bet ween the variables. Households in Dallas and Houston demonstrate ‘somew hat weak’ geographies of opportunity. In these metros, higher accessibility is associated with larger supplies of affordable housing, holding other factors constant. Yet analysis indicates that the majority of affordable rental units are located in areas with z ero/low accessibility areas. Geographies of opportunity for the remaining three metros differ b y household. In Salt Lake City and Portland, low housing budget households have ‘somew hat strong’ geographies of opportunity. However moderate housing budget househ olds in the same region experience ‘very weak’ geographies. Similarly, low housing bud get households in Minneapolis enjoy ‘very strong’ geographies of opportunity while mode rate housing budget households face ‘somewhat weak’ geographies. These findings point t o a ‘barbell’ effect whereby geographies of opportunity are relatively strong fo r the very low income and more affluent, but are very weak for more moderate income househol ds. In addition to generating important insights into t he complex relationships between accessibility and affordability across the U.S., re sults also contribute to an understanding about the ways in which current geographies are con sistent with – and challenge – a location efficiency narrative. Taken together, anal yses conducted using the robust LSRI measures lend mixed support. In some cases – Denver and Los Angeles, most notably – the majority of affordable housing is indeed locate d in transit-accessible areas and the relationship between accessibility and affordabilit y is positive, as a location efficiency

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Page 11 approach would predict. However, findings in other metros – Seattle, Dallas, and Houston in particular – are less supportive, with higher level s of accessibility associated with fewer affordable rental units. In fact, lowand moderate -households in many metros are more likely to encounter larger supplies of affordable r ental units in areas with little or no transit accessibility (and consequently, higher levels of a uto-dependency) despite the likelihood of lower transportation costs. These findings undersco re that while the location efficiency approach offers a useful perspective, policymakers cannot assume that high housing costs will be offset by lower transportation costs. Results also support a number of methodological con clusions. First, findings from the spatial error regression models demonstrate that fa iling to account for spatial dependence is likely to lead to biased results and conclusions th ereby underscoring the importance of accounting for spatial error, particularly given th e policy relevance of investigations around accessibility, affordability, and related phenomena . Model results also point to the large influence that elements of the built and social env ironments can have on the relationship between accessibility and affordability and highlig ht the need to fully account for mediating factors. Finally, GWR results demonstrate that global models may hide variations in neighborhood-level dynamics in ways that may have l arge policy implications. For example, results indicating positive global relationships ma y mask the need to address weaker geographies of opportunity that could exist at the neighborhood level. In other cases, global relationships that point to weak metro-wide geograp hies of opportunity may obscure the need for interventions that preserve strong local geographies. Finally, the largest methodological contribution of this work is the LSR I measure itself, which equips policymakers and practitioners with a set of tools to support targeted interventions aimed at maximizing affordability in transit-accessible loca tions. Findings shed light on the varying conditions that exist across U.S. metros with ‘second-generation’ regional rail transit, and thus provide insights for metros with similar

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Page 12 characteristics that are currently undertaking or c onsidering large transit expansion projects. For example, results for some metros suggest that t hreats of exclusionary displacement in transit-accessible areas may be cause for less conc ern than current discourse might suggest. This is not to say that issues of transitinduced gentrification and displacement should be ignored, but rather that conditions may r equire a particular set of policy interventions aimed at preserving current affordabi lity. At the same time, results for other metros demonstrate evidence of considerable exclusi onary displacement in transitaccessible areas. If there is a generalized finding that holds true across all cases, it is therefore that geographies of affordability and acc essibility are complex, and should be the subject of continued scholarly and practical resear ch that delves deeper into the mechanisms at play and the social, institutional, a nd environmental factors that explain variations in the geographies of opportunity that e xist across metros.

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Page 13 CHAPTER II GEOGRAPHIES OF OPPORTUNITY, TRANSIT ACCESSIBILITY, AND HOUSING AFFORDABILITY: THEORETICAL AND PRACTICAL FOUNDATION S CONSIDERING SOCIAL JUSTICE IN THE CONTEXT OF U.S. M ETROPOLITAN TRANSPORTATION PLANNING AND POLICY This dissertation takes as its starting point the q uestion, what does it mean for a transportation system to be ‘just’? I begin this investigation with a brief overview of six contemporary frameworks that are commonly used in e xploring issues of social justice in the context of U.S. metropolitan planning and policy. I focus particular attention to how these frameworks can help in understanding issues of tran sportation justice. I then provide a deeper discussion of one of these perspectives – Se n and Nussbaum’s ‘capabilities approach’ – which I use as the basis for a conceptu al framework that guides the present research. After introducing the capabilities approach, its co nstituent components, and its applicability to the transportation justice arena, I next describe how I combine this approach with the concept of ‘geographies of opportunity’ in order to form the conceptual framework guiding the dissertation. This conceptual framework focuses on exploring geog raphies of opportunity for lowand moderate-income households in terms of two aspects of transportation justice: the ability to access emplo yment opportunities by public transit (‘transit accessibility’) and the ability to afford housing in transit-accessible areas (‘housing affordability’). It is important to acknowledge that there are many more issues that bear upon transportation justice than the two defined by this framework. For examples, issues related to environmental and racial justice are particularl y important to consider in future research, but remain outside of the bounds of the present stu dy. The sections that follow synthesize existing empiri cal research on the affordability of housing in transit-accessible neighborhoods, includ ing a summary of a substantial body of

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Page 14 literature that investigates property value effects related to transit investments, as well as local gentrification and regional exclusionary disp lacement thought to be associated with these effects. I then discuss a ‘location efficiency’ thread of th e literature, which suggests that concerns about direct and exclusionary displac ement in transit-accessible locations may be less of a threat than often thought when hou sing and transportation costs are considered in combination. I conclude by outlining four significant shortcomin gs in our understanding of current geographies of transit acc essibility and housing affordability in general, and more specifically, of the extent to wh ich the location efficiency narrative plays out empirically. Contemporary Perspectives on Social Justice Since the 1970s, liberal political philosophies, particularly as embodied in John Rawls’ A Theory of Justice, have served as the foundation for contemporary disc ussions of social justice. This approach, which is rooted in t he modern welfare state and notions of social democracy, sets forth a series of rules – th e ‘Principles of Social Justice’ – that define the “distribution of benefits and burdens of social cooperation required for a “well-ordered society” (Rawls, 1971:4). These principles do not o utline a specific notion of morality or define how individuals should live, but rather set forth basic rules which allow individuals to pursue their own vision of the ‘good life’ (Gutman, 1985) and guide how goods should be allocated so that all people – most importantly, th e least advantaged – can achieve their particular vision. Of these, Rawls’ ‘Difference Pri nciple’ is commonly cited when assessing the extent to which the distribution of benefits an d burdens across populations in a metropolitan context is ‘just.’ This principle reco gnizes that in modern society, some people are born into more advantage than others, and there fore states that primary goods should be distributed unequally only when such a distribut ion benefits the least advantaged in society (Rawls, 1971).

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Page 15 Following Rawls, achieving transportation justice r equires that access to transportation infrastructure is distributed such t hat the groups and individuals who are least transportation-advantaged – low-income and zero-veh icle households among them – are ensured the highest levels of access. Although a Ra wlsian approach has gained considerable support among transportation scholars and practitioners, it is not without its problems. First, it is not clear if transport can b e understood as a primary good. While there is no evidence that Rawls would have included acces sibility within the realm of primary goods, some scholars argue that access to important destinations (e.g. employment, schools, health care, and groceries) can be conside red such (Van Wee & Geurs, 2011). However, others argue convincingly that transportat ion accessibility carries different social meanings for different people, and thus cannot be c onsidered a primary good (Martens, 2012; Martens et al., 2012). It is also difficult t o identify the ‘least advantaged’ in a Rawlsian approach since different people require different l evels of access to fulfill their needs (Beatley, 1988). For instance, the elderly are like ly to have much less need to access employment opportunities, but may require a higher level of access to health care facilities. Rawls’ focus on the individual is also problematic, since it is the nature of transportation infrastructure to provide access to collective grou ps, not specific individuals (Martens, et al., 2012). A communitarian perspective on social justice offers an alternative to liberal political approaches by downplaying the importance of equalit y among individuals , and instead emphasizing the importance of understanding equity among groups of people (Buchanan, 1989; Gutman, 1985; Young, 1990). This emphasis on the community-level is generally useful in assessing social justice in the context o f transportation planning and policy, since transportation access is provided to groups, not in dividuals (Martens, et al., 2012). Perhaps the most useful element of the communitarian approa ch in terms of its application to transportation justice is its challenge of the Rawl sian conception of ‘primary goods.’ Michael

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Page 16 Walzer argues in his Spheres of Justice (1983) that primary goods are socially-constructed , carrying vastly different meanings for different pe ople. Therefore, no single distribution criteria can be applied to all goods, as Rawls woul d suggest. So while it may be appropriate to exchange certain goods according to free market principles, it is entirely inappropriate to do so with goods that have different meanings to di fferent people. According to Walzer, these goods should be exchanged within different ‘d istributive spheres’ according to principles which correspond with the good’s social meaning (Walzer, 1983). It follows that because the transportation is a socially-constructe d ‘good’ with vastly different meanings for different people, it is not appropriate to assess t he ‘just’ distribution of transportation access through a simple market exchange that assumes it ho lds the same value for all people. The communitarian perspective, however, does not sugges t an alternative means of assessing the just distribution of transportation access, lea ving little guidance for practical application to transportation planning and policy. A critical political economy approach critiques Rawls and liberal political phil osophy for both its widespread acceptance of market-based capitalist approaches that ignore the structural factors that perpetuate injustice (Fains tein, 2010; Harvey, 1973) and for its exclusive focus on outcomes ( distributive justice) to the exclusion of procedural justice (Harvey, 1973; Young, 1990). Critical political eco nomists thus argue that in failing to address the structural processes that produce and r einforce injustices, a liberal approach leaves true justice unattainable. In this view, jus tice can only be achieved when we address the underlying power structures and institutions th at give rise to inequities. In other words, just metropolitan planning and policymaking must go beyond specific cases of injustice to “challenge the legitimacy of the use of power itsel f” (Marcuse, 2009: 95). While the critical economy approach does not offer a complete evaluative framework, several aspects of its argument are useful to under standing transportation justice. The emphasis on attending to larger structural processe s that perpetuate injustice is particularly

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Page 17 important to a transportation policy arena in which institutions built long-ago on discriminatory foundations – for example, the citin g of urban highways in predominately African-American neighborhoods – may render current decisions unjust, even if the current policies have no discriminatory intent. Since decis ion-making around transportation infrastructure is often made based on current trave l patterns and without regard to latent demand (Martens, 2012), past decisions may continue to perpetuate injustices borne by disadvantaged populations. A critical political eco nomy approach thus reminds us that past decisions should be considered when aiming to equit ably distribute transportation access through current decision-making around infrastructu re. This approach’s recognition of policy framing as an exercise of power is also important to understanding transportation justice. As Flyvbje rg (1998) notes, “one of the privileges of power … is the freedom to define reality” (322). Tr ansportation justice thus requires daylighting the interests that lie behind the frami ng pf claims around who will benefit from – and who will be impacted by – specific transportati on policies and projects. The communicative approach , which has emerged in recent decades drawing from the work of Habermas and his Communicative Rational ity, is also instructive in understanding aspects of transportation justice. Th is perspective argues that the best decisions are those reached through genuinely democ ratic deliberation and communication between parties resulting in mutual understanding a nd consensus (Fischer & Forester, 1993; Healey, 1996, 1997). The communicative approa ch therefore suggests that the primary means of assessing the justness of policy a nd planning decisions is to evaluate the inclusiveness of their decision-making process (Hea ley, 2003). A related perspective, the discursive approach , takes a more critical tact by evaluating how disc ourse – defined as a specific set of ideas and concepts conveyed through language – is used by policy actors to advance, interpret, and manipulate a particular set of interests and values (Hajer, 1993). Once they become dominant, specific discourses beco mes codified within institutional

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Page 18 structures, which then serve to reproduce the domin ant discourse. This approach therefore argues that because all planning and policy decisio ns are rooted in the ideological assumptions embedded within these institutions, und erstanding discourse is “basic to the understanding and functioning of the system, includ ing understandings of social justice” (Fischer, 2009: 57). It is particularly important to understand how disc ourses in transportation planning and policy are deployed given that powerful interests a ttracted to land development opportunities associated with large capital investments, often se ek to influence discourse to their advantage (Willson, 2001). It is also important to understand how dominant discourses are codified in institutions governing transportation p lanning and policy, and how those institutions reproduce ideas embedded within the di scourse. A final approach, the Just City Model (Fainstein, 2010), integrates many of the principle s of the frameworks reviewed above to offer a hybrid approach to understanding j ustice in the context of U.S. metropolitan planning and policy. In recent years, the Just City model has gained considerable prominence among urban policy and planning, and is proving to be one the most cohesive contemporary approaches to understanding justice in the city (Garcia & Judd, 2012). The model attends to both distributive and procedural a spects by adopting a critical political economy definition of social justice as ‘just distr ibution, justly arrived at’ (Harvey, 1973:357). However, the Just City emphasizes that while inclus ive processes are a worthy goal, they do not guarantee just outcomes and in many cases may i nstead reflect power imbalances that work against just outcomes (Fainstein, 2001, 2010). Therefore, justice is ultimately achieved through substantive outcomes. The result of the Just City model is a set of three principles intended to serve as an evaluative framework against which specific policy and planning interventions can be judged. The first principle, ‘equity,’ requires tha t the policy does not reinforce inequity, but allocates outcomes so that the condition of the lea st advantaged is improved. The second

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Page 19 principle, ‘diversity,’ judges the policy based on the extent to which it promotes social inclusion and diminishes social exclusion. The fina l principle, ‘democracy,’ recognizes the existence of open, democratic processes that empowe r and educate non-elite groups as being necessary, but not sufficient, for justice to be achieved through policy and planning interventions. Rather than relying on Rawlsian notions of ‘primary goods’, the Just City models follows a capabilities approach that instead evaluates justice based on whether in dividuals have access to the resources and opportunities nece ssary to fulfill their full potential (Fainstein, 2000). The capability approach framewor k is rooted in the work of economist Amartya Sen and philosopher Martha Nussbaum, who ar gue that justice is realized only when all individuals have the opportunity to achiev e their full range of capabilities, defined as what people have the potential to do, regardless of whether individuals take advantage of those opportunities (Nussbaum, 2000; Sen, 1999). Th is framework thus constitutes a critical strand of the liberal political philosophy traditio n. While it remains rooted in the idea that that individuals should have the freedom to define their own conception of the ‘good life’ in keeping with the norms of democratic and pluralisti c society, it evaluates justice not in terms of how many goods (or how much income) a person pos sesses, but instead focuses on the extent to which the goods enable people to achieve the lives they want to lead (Robeyns, 2005). In other words, a capabilities approach does not consider primary goods to be ends in and of themselves, as Rawls does, but instead as ks what the goods can do for people as they seek their conception of a ‘good life’ (Hanane l & Berechman, 2016). This framework is useful in thinking about transpor tation – which does not fit neatly within the Rawlsian notion of ‘primary goods’ – bec ause it addresses not only the distribution of transportation infrastructure itself, but also t he extent to which that infrastructure enables access to the opportunities that allow individuals to reach their full potential. In the sections

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Page 20 that follow, I first outline the capabilities appro ach in more depth, then discuss how I deploy to conceptualize transportation justice in the pres ent study. The ‘Capabilities Approach’ Framework The capabilities approach is quite complex, with ma ny inter-related components that continue to undergo scholarly debate. However, the basic building blocks of the approach – and the relationships between those building blocks – are stable across the literature. Figure 2.1 provides a basic model describing these basic compo nents and how they relate to one another. There are three primary components of a capability approach: ‘Primary goods,’ ‘capabilities,’ and ‘functionings.’ In this framewo rk primary goods are the material and nonmaterial resources that people need in order to sus tain a basic standard of living and in order to pursue their conception of the ‘good life’ (Sen, 1999). While a Rawlsian approach considers social justice to ultimately be defined a s the just distribution of goods, a capability approach instead specifies the end goal as what can be achieved with the primary goods in terms of a person’s pursuit of well-being. Capabilities represent the set of opportunities that are availab le to a person as they seek to achieve the various things (s)he values in leading her/his life. For Sen, social justice requires that all people possess a basic set of cap abilities: the ability to be well-nourished, to have shelter, to move freely, and to participate in the political, civic, and social life of a community (Sen, 1980). Nussbaum takes the idea of a minimum threshold for social justice farther by specifying a list of 10 required capabil ities which include basic functions like being able to have good health and nutrition, being secur e from violence, being able to form attachments to other people, and being able to part icipate in political choices (Nussbaum, 2006).

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Page 21 Loosely adapted from Robeyns 2005 Figure 2.1. Capabilities approach framework The capabilities approach recognizes that different people will take advantage of the same set of capabilities to greater and lesser exte nts. The approach therefore makes a distinction between capabilities , which constitute a set of opportunities, and the things people actually achieve using those capabilities, o r their achieved functionings . This distinction recognizes that people with identical s ets of capabilities are likely to make different choices about whether or not to take adva ntage of those capabilities, depending on their particular personal characteristics, circumst ances, values, and conceptions of wellbeing. For this reason, a capability approach advoc ates that policies should ultimately be judged on the capabilities (i.e. opportunities) the y provide, rather than the achieved

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Page 22 functions that people choose to catalyze (or not) i n order to transform those opportunities into action (Robeyns, 2005). A number of factors shape the relationship between a primary good, the capabilities it enables, and a person’s achieved functionings. T hese material and non-material conditions are referred to in the capability approa ch as conversion factors . Personal conversion factors are individual-level characteristics and circumsta nces that influence how a person is able to convert resources ( primary goods ) into opportunities ( capabilities ). These might include cognitive and physical abilitie s, financial circumstances, and the presence of children or other individuals dependent on the person for their care. Social and environmental conversion factors describe the overall background within which primary goods are converted into capab ilities – factors such as public policies, institutions, social norms, power relations, and co ntextual features. These background factors influence the primary goods themselves, the capabilities that can be derived from them, and a person’s own ability to take advantage of those capabilities. Finally, capabilities are transformed into achieved functionings only whe n an individual makes a personal choice to take advantage of them. The choices people make to either catalyze an opportunity ( capability ) into an actual achievement ( functioning ) are influenced in large part by their individual value systems, personal circums tances, and social and environmental factors. Applying a Capabilities Approach Framework to Conce ptualize Transportation Justice The capabilities approach offers a useful framework for evaluating the extent to which a broad range of policies and planning interv entions promote individual well-being and social justice, including those related to transpor tation. The approach does not purport to be a complete theory of social justice, and thus canno t be used to explain transport disadvantage or inequalities (Robeyns, 2005). I the refore adopt the capabilities approach

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Page 23 not as a predictive or explanatory model, but as a framework through which to conceptualize and evaluate issues of transportation as they relat e to social justice. The transportation justice literature has shown gro wing interest in the capabilities approach in recent years, with a small number of st udies seeking to apply the approach to questions around the distribution of benefits and b urdens associated with transportation infrastructure investments both theoretically (Beya zit, 2011; Hananel & Berechman, 2016) and empirically (Baumgartner et al., 2009; Gössling , 2016; Mullen et al., 2014; Smith et al., 2012). In this literature, primary goods are generally conceived of as the transportation infrastructure and service itself (for example, pri vate vehicles, public transportation, bicycle lanes, etc.). Capabilities are typically framed as the ability of people to g et to the places they need to go (in other words, accessibility) tha t is provided by the transportation infrastructure. A person’s choice to take advantage of the accessibility created by this infrastructure (or not) then determines her/his achieved functionings , or travel patterns. A large number of personal, social, and environmental conversion fact ors bear on this process. A capabilities approach framework therefore acknowl edges that different people will have different travel patterns ( achieved functionings ) depending on the transportation infrastructure and service available to them, the d estinations they need to reach, their personal and financial circumstances, and any numbe r of social and institutional factors. However, in this framework, what matters in terms o f transportation justice is not these ultimate travel patterns ( functionings ), but the extent to which an individual has the opportunity ( capability ) to get where (s)he needs to go in order to achiev e the functionings that support her/his preferences and well-being. In other words, the capabilities approach suggests that transportation justice should ultimat ely be evaluated based on the extent to which a transportation system grants individuals an d groups the opportunity to access the places they need to go in order to reach their full potential.

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Page 24 The capabilities approach thus dovetails well with the ‘geographies of opportunity’ frame introduced by Galster & Killen (1995), which has gained prominence in recent decades among practitioners and advocates working o n issues of spatial and social justice in metropolitan areas (‘metros’). In this frame, ‘o pportunities’ constitute the resources – jobs, education, child care, health services, healthy foo ds, social and civic activities – that enable individuals and families with limited means to impr ove their financial and social circumstances (Briggs, 2006). An individual’s ‘geog raphy of opportunity’ is thus the extent to which (s)he is able to access these resources. The conceptual framework developed to guide the pre sent study (shown in Figure 2.2 ) reflects an integration of the ‘geographies of op portunity’ frame with a capabilities approach. When viewed through the lens of a capabil ities approach, an individual’s ‘geography of opportunity’ is analogous to her/his set of capabilities . Three components related to physical planning and policy shape geogr aphies of opportunity: 1) the quantity and qualities of the opportunities themselves; 2) the h ome location from which an individual seeks to access opportunities; and 3) the transport ation options that enable their ability to access them. In a capabilities approach framework, these three components – opportunities, housing stock, and transportation infrastructure – can be thought of as the primary goods that are then transformed into capabilities . A multitude of other personal and social conversion factors also influence an individual’s geography of opport unity. For the purposes of the present study, the most of important of thes e conversion factors is a household’s ‘housing budget,’ defined as the amount a household can afford to spend on housing while still fulfilling its other basic non-housing needs. Geographies of opportunity ( capabilities ) are thus defined as being shaped by the configuration of the three primary goods – opportunities, transportation, and housing – as mediated by the household’s housing budget (one of many conversion factors ). Given the costs associated with car ownership and operations, and given that low-income households

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Page 25 are much less likely to have access to a private ve hicles as compared to more affluent households, public transit often plays a vital role in providing access to opportunities for individuals and families with limited resources (Gi uliano, 2005; Taylor & Morris, 2015; Tomer, 2011). The ability to access employment oppo rtunities by transit is specifically evaluated in the present study because of the impor tance of income generation in supporting financial, physical, and social well-bei ng. I therefore conceptualize geographies of opportunity for lowand moderate-income househo lds as being bounded by two circumstances: 1) the ability to access employment opportunities via modes other than private autos (‘transit accessibility’) and 2) the ability to afford housing in transit-accessible areas (‘housing affordability’). Consistent with the capabilities approach, this fra mework acknowledges that ‘geographies of opportunities’ must be activated by personal choice in order to convert them to ‘ achieved functionings .’ For example, choices around residential location s (i.e. the decision to live in a transit-accessible neighborho od) and mode choice (i.e. the decision to use available transit service as opposed to other m odes) determine whether a household will benefit from the opportunities that affordable transit-accessible housing confers. However, the framework guiding the present research leaves issues of personal choice and resulting travel patterns to future research and in stead focuses on exploring the capabilities (geographies of opportunity) of lowand moderate-i ncome households in terms of transit accessibility and housing affordability, as determi ned by the supply of housing available within a household’s housing budget.

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Page 26 Figure 2.2. Conceptual framework The operationalization of both transit accessibilit y and housing affordability are discussed in considerable depth in the chapters tha t follow. Briefly, ‘accessibility,’ defined as the ease of reaching desired destinations, is bound ed by two factors: the availability and qualities of transportation choices, and the distri bution of destinations across space (Geurs & van Wee, 2004; Krizek & Levinson, 2012). Accessib ility is one of the most wellestablished social outcomes of transportation (Jone s & Lucas, 2012). It is particularly useful

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Page 27 in assessing equity outcomes because it captures th e relationship between people and the places that are important to them, accounting for b oth dimensions of transportation infrastructure as well as the distribution of impor tant destinations across space and opportunities to access them (Grengs, 2012; Martens & Golub, 2012; Wachs & Kumagai, 1973). Following this conception, ‘transit accessib ility’ is defined in the present study as the ease of reaching desired destinations by bus, rail, or other transit mode operated by a public transit agency. The operationalization of housing affordability is less straightforward. Concerns about housing affordability have become a dominate theme in the public discourse around cities and regions in recent years. For example, a recent report authored by the National League of Cities found that a lack of affordable housing i s identified by mayors nationwide in their ‘state of the city’ speeches as one of the top five issues that have a serious impact on the health of their cities (Langan et al., 2016). Yet, despite the ubiquity and importance of these issues, it remains unclear exactly what it means for housing to be ‘affordable.’ Furthermore, as I demonstrate in Chapter 4, typical measures of housing affordability often do not adequately reflect the financial circumstance of lo wand moderate-income households, possibly resulting in misleading conclusions. In th e present study, I introduce an improved measure of housing affordability that is reflective of a capabilities approach. A detailed discussion of this improved measure is provided in Chapter 5. The Role of Transit in Shaping Geographies of Oppor tunity for Lowand Moderateincome Households Access to transit among less advantaged populations is linked to numerous benefits, particularly in regards to securing and maintaining employment. Studies have found, for example, that transit-based job accessibility incre ases the probability of being employed among car-less households (Kawabata, 2003), among w omen welfare recipients (Ong & Houston, 2002) and among bus riders (Yi, 2005). Res earch also suggests that higher levels

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Page 28 of transit accessibility are associated with higher numbers of hours worked per week (Kawabata, 2003) and the average annual weeks worke d (Sanchez, 1999). Beyond access to jobs, the availability of transit has far-reaching effects on peopleÂ’s ability to access a wider range of opportunities th at contribute to well-being including education, medical services, childcare, and other n ecessities (Bullard, 2003; Wachs, 2010). Research indicates that transit access is associate d with improved physical well-being related to the ability to obtain regular health car e and increased opportunities for physical activity (Delbosc, 2012). Transit accessibility is also linked to psychological well-being through the alleviation of social exclusion, which refers to a condition where residents living in areas with long-standing and concentrated povert y are unable to access employment, housing, and other services due to lack of transpor t and/or other barriers that severely limit their ability to fully participate in society and c ivic life (Dodson et al., 2010; Wells & Thill, 2012). Furthermore, transit accessibility is associ ated with financial well-being in the form of decreased household expenditures on transportation. The Center for Transit-Oriented Development (CTOD) reports that the average family spends approximately 19-percent of their income on transportation while households wit h access to transit spend only ninepercent (Center for Transit-Oriented Development, 2 007), thus allowing for income to be spent on other life necessities (Jones & Lucas, 201 2). EMPIRICAL RESEARCH ON THE AFFORDABILITY OF HOUSING IN TRANSITACCESSIBLE NEIGHBORHOODS IN THE U.S. The role of transit access in shaping geographies o f opportunity for lowand moderate-income households is well-established. How ever, not until recently has the affordability of housing in transit-accessible area s been recognized as being equally integral to the overall well-being of households with limite d means. This recognition has been largely driven by growing demand for transit-accessible loc ations, which according to a study commissioned by the Federal Transit Administration is expected to double by 2030, calling

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Page 29 into question the ability of lower-income household s to afford housing in transit-rich neighborhoods and thus their ability to take advant age of the accessibility these locations confer (Thorne-Lyman et al., 2008). Two areas of concern have emerged in regards to the affordability of housing in transit-rich neighborhoods. The first relates to pr operty value increases in areas proximate to high-frequency transit and associated direct displa cement effects in which long-standing residents can no longer afford to remain in highlyaccessible neighborhoods. The second area of concern relates to increased demand for tra nsit-accessible locations on a regional scale, resulting in exclusionary displacement effec ts whereby newly-formed and relocating households with lower incomes are unable to afford housing in these neighborhoods and instead locate in more auto-oriented areas of the m etro. In the below sections, I first review evidence from the existing literature related to property value effects in transit-accessible neighb orhoods, as well as to local gentrification and regional exclusionary displacement thought to be associated with these effects. I then discuss the location efficiency narrative, a perspe ctive that has emerged in recent years to suggest that local and regional displacement in tra nsit-rich areas may be less of a threat than commonly thought when the cost of housing and transportation are considered in tandem. Finally, I review existing empirical resear ch that sheds light on the relationship between housing affordability and transit accessibi lity in general, and on the location efficiency paradigm more specifically. Through this review, I conclude that our limited understanding of current geographies of housing aff ordability and transit accessibility in U.S. metros, including the extent to which the location efficiency narrative plays out empirically, is insufficient in a number of ways. Effects of Transit Accessibility on Housing Costs As with any amenity in a market economy, the value ascribed to transit accessibility would be expected to be capitalized in the value of land with access to transit service.

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Page 30 Indeed, a substantial body of literature examining the effects of transit – and fixed-rail transit in particular – on the value of properties within s tation areas demonstrates that rail investments are generally, but not always, associat ed with higher premiums as compared to areas not served by rail. Research suggests that while properties located adj acent or very close to rail stations may experience slight reduct ion in values due to nuisance effects (Bartholomew & Ewing, 2011; Chatman et al., 2011; G olub et al., 2012), those outside the nuisance-zone but still within walking distance are likely to see a boost in values (Bartholomew & Ewing, 2011; Cervero et al., 2002; C ervero et al., 2004; Yan et al., 2012). These effects have been estimated to range from rel atively small to rather large. A metaanalysis of 60 studies found that residential prope rties within one-quarter mile experienced a four-percent increase in value as compared to prope rties outside of station areas, controlling for other housing and neighborhood characteristics (Debrezion et al., 2007). However, another recent study found much larger effects – up to 42-percent increases – in areas within one-half mile of fixed-guideway bus and rail (Center for Neighborhood Technology, 2013). A smaller number of less recent studies have found decreases in property values in rail station areas (Bowes & Ihlanfeldt, 2001; Gatzl aff & Smith, 1993; Hess & Almeida, 2007). Taken together, existing research suggests that pro perty value effects of fixed-rail transit are largely dependent on a range of context ual factors1. The quality of the rail transit in terms of its frequency, geographic extent, servi ce intensity, and the extent of congestion on parallel road systems has a large bearing on pro perty values (Bartholomew & Ewing, 2011). In general, properties near commuter rail ar e likely to see greater increases than those near light rail, likely due to faster speeds, higher frequency service and more extensive geographical coverage (Bartholomew & Ewin g, 2011; Debrezion, et al., 2007; Hess & Almeida, 2007). Additionally, rail stations closer to the central business district and 1 For a thorough review of these factors, see Wardri p, 2011

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Page 31 other activity centers are likely to see larger eff ects than those located farther away (Bartholomew & Ewing, 2011). Finally, the extent to which supporting policies, land use and zoning controls, and other developer incentives are offered by local jurisdictions can have a large effect property value outcomes (Cambridge Sys tematics, 1996; Cervero, et al., 2002; Cervero, et al., 2004). The vast majority of research on the property value s effects of transit accessibility has focused exclusively on fixed-rail transit, with very little attention paid to the effects of accessibility to non-rail transit. The few studies that exist in the western context focus on bus rapid transit (BRT), and find neutral to modest inc reases in property value premiums associated with investments in BRT (Government Acco untability Office, 2012; Mulley, 2013; Mulley & Tsai, 2016). The lack of research on the relationship between tr ansit accessibility regardless of mode constitutes a substantial gap in the literature given that buses often play a much larger role in U.S. transit networks than ra il. Comparatively little research has been conducted on the effects of transit accessibility on rental housing premiums. The few studies that exist demonstrate higher rental premiums in areas served by rail transit (Ce rvero, et al., 2004; Pollack et al., 2010; Wang et al., 2016). The lack of attention to the relationship between t ransit accessibility and rental housing costs is curious given that renters are more likely than home owners to use transit (Taylor & Morris, 2015) and that rail stati on areas are home to a disproportionate share of rental housing stock (Center for Transit-O riented Development, 2006). Displacement Effects Associated with Transit Access ibility While property value premiums in transit-accessible areas can be considered to be positive in some contexts, there is clearly potenti al for negative implications for lowand moderate-income households at both the local (stati on area) and regional geographies as rising housing costs leave households with limited means ‘priced-out’ of their existing housing and/or unable to afford new housing in tran sit-rich neighborhoods. Advocates and

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Page 32 scholars have long-voiced concerns about so-called ‘transit-induced displacement’ effects in which increased housing costs in transit-accessible neighborhoods result in affluent households outbidding lower-income households (Chap ple, 2009; Pollack, et al., 2010; Zuk & Chapple, 2015). These concerns have increased as the desirability of transit-oriented development (TOD) has grown among higher-income pop ulations (Renne et al., 2016) and as evidence that demonstrates a growing demand for transit-accessible locations outstrips supply continues to mount (Dawkins & Rolf, 2016). L ow-income renters in unsubsidized housing are particularly vulnerable to transit-indu ced displacement since they are subject to the whims of the housing market but have little ava ilable income to afford rising premiums. Although low-income residents living in subsidized rental units have greater security, they remain vulnerable to displacement as affordability requirements of units reach their sunset date, which is expected to occur in record numbers in the coming years (Mueller & Steiner, 2011). Indeed, many advocating on behalf of the int erests of low-income populations view market-rate development in areas served by rail wit h skepticism, and in some cases have mounted challenges to TOD on the basis of social ju stice concerns (Rayle, 2014). Evidence of gentrification effects in neighborhoods served by fixed-rail continues to grow, with a number of studies demonstrating dispro portionately larger increases in home values and rents in areas served by rail transit as compared to areas in the same region not served by rail, as well as demographic changes in s tation areas indicative of patterns of gentrification and displacement. For example, Kahn (2007) identifies gentrification effects associated with rail transit investments, as marked by increases in home prices, increases in the share of college graduates, and increases in ho usehold income. These effects were found to be more pronounced in neighborhoods with ‘ walk and ride’ stations as compared to those with ‘park and ride stations,’ although both show measurable effects. Using a survival analysis approach, Grube-Cavers & Patterson (2014) identified the presence of similar gentrification effects (as measured by changes in m edian income and education levels of

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Page 33 station area residents) in their examination of com muter rail transit. In an analysis of rail transit systems across the U.S., Pollack et al. (20 10) also identified shifts in the demographic and economic characteristics of rail tr ansit station areas as compared to areas not served by rail in the same metros, with station areas residents generally becoming wealthier, housing becoming more expensive, and veh icle ownership becoming more prevalent. Recent research employing increasingly s ophisticated methods to study transitinduced gentrification, including various spatial r egression and geographically-weighted regression techniques, generally confirm earlier fi ndings (Bardaka et al., 2015; Wang, et al., 2016; Zhong & Li, 2016). Aggregated across an entire metro area, higher prop erty values within individual transit-accessible neighborhoods contribute to dyna mics at the regional level. In particular, localized gentrification effects occurring at a lar ge enough scale are likely to lead to patterns of ‘exclusionary’ displacement (Marcuse, 1986) wher eby more affluent groups are attracted to transit-rich neighborhoods in the urban core, th us resulting in a tightened housing market that makes it difficult for newly-formed and reloca ting households to compete for limited supplies of affordable housing near transit (Cerver o, 2007; Chapple, 2009). Regional exclusionary displacement therefore shifts the ‘lan dscape’ of affordability for households, particularly those with limited means (and therefor e, the fewest choices) (Pendall et al., 2012). One likely result of these shifting landscapes is a circumstance where low-income residents living in transit-accessible areas of the urban core relocate to suburban areas as housing costs rise, requiring greater reliance on a uto travel. This dynamic is captured in well-documented ‘suburbanization of poverty’ trends in which lower-income households are increasingly locating in auto-dependent suburban ar eas that are difficult to serve by transit and are lacking in supportive social services (Knee bone & Berube, 2013). Although there continues to be debate as to whether this character ization accurately reflects current

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Page 34 geographies of poverty (Cooke & Denton, 2015), empi rical evidence suggests that lowerincome households are indeed commuting increasingly longer distances to reach jobs and are spending a larger portion of their income on tr ansportation as a result when compared to more affluent households (Kneebone & Holmes, 2015; Roberto, 2008). Perhaps a more fruitful characterization of these t rends – and the one of primary concern in the present research – is the ‘low-acces sibility-ization” of poverty. The relocation of low-income households to suburban areas is not a problem in and of its self, and may in fact reflect changing preferences among these popul ations towards the set of resources and amenities available in suburban settings. However, the relocation of households with limited means to areas with low transit accessibility that require dependency on private vehicles is a problem given the inherent financial and social cos ts associated with car ownership, particularly among vulnerable populations. The Location Efficiency Narrative: An Antidote to C oncerns about Transit-Induced Displacement? Another strand of literature focused on a ‘location efficiency’ approach to thinking about issues of affordability suggests that threats of displacement in transit-accessible areas may be less of a cause for concern than commonly th ought when housing costs are considered alongside transportation costs. This per spective aims to make the interdependent relationship between transportation and housing costs more transparent to policymakers and the general public in the face of a growing ‘drive ‘til you qualify’ mentality among households attracted to inexpensive housing i n far-flung suburban locations. Advocates of this approach argue that because trans portation costs are not fully-capitalized into housing costs, housing and transportation (“H+ T”) costs should be considered in combination to arrive at a more comprehensive understanding of ‘location affordability.’ The Center for Neighborhood Technology (CNT), an early advocate for this approach, first developed a measure of combined H+T costs across th e U.S. (the “H+T Index”) with the

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Page 35 clear intention of calling attention to the hidden high costs of commuting to more ‘affordable’ suburban areas (and the hidden low costs of transpo rtation in more expensive urban areas) (Center for Housing Policy and Center for Neighborh ood Technology, 2012). A specific narrative is therefore implicit in the l ocation efficiency approach: That while housing costs may be lowest in auto-dependent areas of the suburban fringe, transportation costs are likely be high in these areas, thus offse tting any affordability gains achieved through less expensive housing. Conversely, this pe rspective posits that although housing may be more costly in neighborhoods with close prox imity to jobs, the ability to walk or bike to retail districts, and the availability of transi t and non-motorized transportation options, lower transportation costs are likely to offset hig her housing costs. This location efficiency narrative’ therefore acknowledges that housing may be more expensive in areas with high levels of non-auto accessibility, but counters that reduced transportation expenditures are likely to offset these costs resulting in better ov erall H+T affordability in these locations. This narrative has become increasingly embedded in the w ork of policymakers and advocates, including by federal agencies who have integrated i t widely into transportation and housing programs and policies. One notable example of this is the joint effort by the U.S. Department of Transportation (DOT), Department of Housing and Urban Development (HUD), and Environmental Protection Agency (EPA) to develop th e Location Affordability Index (LAI), a publicly-available dataset that estimates combined H+T costs for a series of theoretical household profiles at the block group level. However, despite its widespread adoption, it remain s unclear whether the location efficiency narrative is supported by on-the-ground empirics, particularly in light of the dynamics of local transit-induced displacement and regional exclusionary displacement in transit-accessible locations discussed above. A lar ge body of research authored by the advocacy community has yielded results that are lar gely supportive of the claim that higher housing costs in transit-accessible locations are l ikely to be offset by lower transportation

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Page 36 costs (for a recent example, see CNT, 2011). Findin gs from the few academic studies that explicitly examine the location efficiency narrativ e in the context of transit accessibility also demonstrate general support for this claim, with so me exceptions. In their study of redevelopment projects in ‘shrinking’ cities, Tighe & Ganning (2016) find that lower transportation costs in areas that require less aut o-dependency appear to offset higher housing costs. Another study of Auckland, New Zeala nd finds that while H+T costs are highest for commuters residing within transit-acces sible employment centers where housing costs are exceptionally high, lower transportation costs offset higher housing costs in other transit-accessible areas (Mattingly & Morrissey, 20 14). In an earlier study of the tradeoffs between housing costs and commute times (a proxy fo r transportation costs) among working families in seven metros, Cervero et al. (2006) fi nd mixed support for the location efficiency narrative: High housing costs are offset by high le vels of transit accessibility in some, but not all, regions. Hartell (2016) uses spatial lag regre ssion models to demonstrate that transportation costs help to explain housing forecl osure rates (which she identifies as an observable measure of housing affordability), thus lending support for the location efficiency narrative. Findings from several studies related to location e fficiency also underscore that H+T affordability is associated with a variety of chara cteristics of the built and social environment beyond transit accessibility. For example, Renne et al.’s (2016) study of the areas within1/2mile of over 4,000 fixed-rail transit stations find s that although station areas with characteristics embodying TOD (defined, broadly spe aking, as dense, mixed-use development with pedestrian-oriented streets) have higher housing costs, households living in TODs spend four-percent less on combined H+T due to lower transportation costs. Hartell (2016) also finds that characteristics of urban for m (e.g. housing and job density and land use mix) are important to consider alongside transi t accessibility in explaining the relationship between H+T (un)affordability. A vast body of literature – the review of which is

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Page 37 outside of the scope of this paper – affirms the re lationship of urban form on transportation costs and behavior (for a comprehensive review of t his literature, see Ewing & Cervero, 2010). While existing research directly examining the loca tion efficiency narrative offers some insight into the robustness of its claims, the literature is limited by its nearly-universal use of blunt ratio-based measures of affordability whereby housing is considered ‘affordable’ if combined H+T costs account for 45-percent or les s of household income. The threshold used in the H+T approach (45% of income) is based i n part upon a 30-percent threshold used for assessing housing affordability alone that has little theoretical or empirical basis and does not account for the ways in which a househ old’s characteristics and financial circumstances, particularly those related to the pr esence of children and associated childcare costs, affect the amount of income a hous ehold is able to afford for housing. Issues associated with this, and other typical meas ures of affordability are discussed in detail in Chapter 4. A single study relevant to issues of location effic iency recognizes the limitations of the typical ratio-based measure of H+T affordabilit y by employing an alternate approach – the residual income measure – to explore the extent to which supplies of housing that are affordable to low-income renters both with and with out children are located in rail-accessible areas of Montreal and Vancouver (Revington & Towns end, 2016). Use of this more nuanced measure of housing affordability yields fin dings that are less supportive of the location efficiency narrative. In particular, the a uthors find that housing affordable to lowincome households is less plentiful in areas served by rail transit, particularly in central city locations. The authors also find that households wi th children face much more challenging circumstances in securing affordable rental housing due to the fact that a lower proportion of their income is available for housing. These findin gs suggest that the use of reductive ratiobased measures of affordability may misrepresent ge ographies of opportunity by obscuring

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Page 38 the substantial differences that exist between the financial realities of households with the same income, but with different characteristics and circumstances. Gaps in the Literature around Transit-Induced Displ acement and Location Efficiency The above review of existing research around transi t-induced displacement and location efficiency reveals four significant shortc omings in our current understanding of the geography of transit accessibility and housing affo rdability in U.S. metros. First, much of the literature – including the numerous studies examini ng transit-induced gentrification and displacement – focuses exclusively on affordability in the context of fixed-rail, neglecting the large role local buses serve in providing access ac ross U.S. metros and therefore potentially mischaracterizing the relationship between housing costs and transit accessibility in general . Second, most existing research examines home values , as opposed to rental premiums, despite the fact that market-rate rents a re arguably more relevant to understanding affordability for lowand moderate-i ncome households and certainly more important from a social justice perspective. Market-rate renters with limited means are much more vulnerable to both local transit-induced displ acement and regional exclusionary displacement, since they are less resilient to unpr edictable changes in market conditions and unlike low-income homeowners, do not benefit fr om increased property values. Third, the majority of research around transit acce ssibility and H+T affordability fails to account for the spatial dependence and error inh erent to these phenomena both independently and in relation to one other, despite well-documented evidence that doing so may lead to unreliable findings (Jun, 2016). In particular, investigations of H+T affordability often suffer from spatial error when boundaries of the spatial unit used in the analysis do not accurately reflect the true geography of the area o f interest, as is the case with much of the literature that uses Census tracts or block groups to conceptualize neighborhoods that are not likely to fall neatly into census boundaries.

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Page 39 Finally, all but one study rely on ratio-based meas ures of affordability, which – as I argue in subsequent chapters – do not accurately re flect the financial circumstances of lowand moderate-income households and are thus likely to misrepresent the opportunities and challenges experienced by these households. These four gaps result in insufficient knowledge ab out the geographies of opportunity households with limited means confront as they seek market-rate rental housing in transitaccessible areas. As described in Chapter 3, I address these gaps in the literature through a comprehensive examination of current geographies of transit accessibility and housing affordability for lowand moderate-income renters in eight U.S. metros. Findings from these examinations contribute practical knowledge around the geographies of opportunity experienced by lowand moderate-income households, as well as equip practitioners and advocates with tools to support policy intervention s that strengthen the capabilities of these households by maximizing the availability of transi t-accessible affordable rental housing.

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Page 40 CHAPTER III RESEARCH QUESTIONS AND APPROACH RESEARCH QUESTIONS In Chapter 2, I introduced a conceptual framework r ooted in a capabilities approach that calls attention to how landscapes of transit a ccessibility and housing affordability to shape the geographies of opportunity of lowand mo derate-income households. I also synthesized empirical research from several threads of literature that speak to the relationship between transit accessibility and hous ing affordability. This critical review points to four substantial gaps in our understanding of th e geographies of transit accessibility and housing affordability that confront households as t hey seek market-rate housing. First, the literature focuses predominately on effects associa ted with fixed-rail transit, thus neglecting the large role buses play in providing access acros s U.S. metros. Second, existing research has little to say about landscapes of affordability and transit accessibility for market-rate renters, arguably the most vulnerable of all househ olds. Third, only a handful of studies account for spatial error, despite clear evidence o f its manifestation in urban phenomenon, including transit accessibility and housing afforda bility. Fourth, nearly all the existing research in this arena relies on flawed measures of housing affordability, thereby producing unreliable results. I address these gaps by developing an improved meas ure of housing affordability that I then use to examine current geographies of t ransit accessibility (regardless of mode) and housing affordability for lowand moderate-inc ome renters in eight U.S. metropolitan areas (‘metros’) while accounting for spatial error . In Part 1 , I unpack the three most typical approaches to measuring housing affordability – the ratio, location affordability, and standard residual income approaches – and discuss t he ways in which their shortcomings are likely to mischaracterize affordability for low and moderate-income households (Chapter 4). I then introduce the location-sensitive residua l income (LSRI) approach, a set of

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Page 41 measures that address many of the flaws inherent to more typical measures of affordability, and provide a detailed methodology for constructing the LSRI measures (Chapter 5). A LSRI approach first identifies the amount of mont hly income a household can afford to pay for housing (its ‘housing budget’) af ter covering the necessities required to sustain a basic standard of living which vary depen ding on its composition (size, presence of children), financial circumstances (childcare costs , income) and its location within the region (and thus, transportation costs). A second ‘supply’ measure is then calculated using data from the Census ACS to identify the quantity of ren tal housing units that are affordable within the housing budgets of a defined set of lowand moderate-income households. A subsequent chapter applies the LSRI measure empiric ally by exploring housing affordability for households with limited means living in the Den ver metro, and comparing these results to those generated using the three more typical mea sures of affordability (Chapter 6). This empirical application highlights the ways in which the LSRI measures are likely to more accurately reflect the financial realities faced by lowand moderate-income households as compared to more typical approaches, and to demonst rate how a LSRI approach can be used to understand nuanced landscapes of affordabil ity and thus to support targeted policy interventions. In Part 2 , I employ the LSRI measure to examine geographies of transit accessibility and housing affordability for lowand moderate-inc ome households in eight U.S. metros by addressing two research questions. First, I describ e current landscapes of accessibility and affordability by asking: To what extent are supplies of rental housing that are affordable for lowand moderate-income households located in areas with high transit accessibility? (Research Question 1). Analysis supporting Research Question 1 does not attempt to account for the multitude of factors bey ond transit accessibility that may also influence housing affordability. Rather, results pr esented in Chapter 7 provide an account of the conditions households with limited means are li kely to confront as they seek transit-

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Page 42 accessible affordable housing. Findings therefore o ffer insights into the lived experiences of lowand moderate-income households, who are unlike ly to be care about the factors driving affordability, but instead are likely to be primari ly concerned about the availability of rental housing that they are able to afford within their h ousing budget. A second research question addressed in Part 2 exte nds the investigations presented in Chapter 7 by isolating the relationshi p between transit accessibility and housing affordability through a series of global an d local regression analyses. This second question asks: What is the relationship between transit accessibil ity and supplies of affordable rental housing, when controlling for key characteristics of the built and social environments that are likely to influence th at relationship, as well as for spatial dependence? (Research Question 2). Results of this analysis sum marized in Chapter 8 shed light on the relationship that exists between transit accessibility and housing affordability across different metros, among househ olds with different characteristics within the same metro, and across space within a single me tro. A final section ( Part 3 ) synthesizes findings from Parts 1 and 2 to lend i nsights into the complex relationship between affordability and accessibility across U.S. metros, and into the ways in which current geographies are consisten t with – and challenge – a location efficiency narrative. The result of this synthesis is a typology describing the geographies of opportunity generally experienced by lowand moder ate-income households in eight U.S. metros, each of which calls for specific types of p olicy and planning interventions. RESEARCH APPROACH Case Selection These investigations are conducted for all U.S. met ros with ‘second-generation’ regional rail, defined as those in which fixed-rail transit systems that serve more than one contiguous county were established after the passag e of the Intermodal Surface Transportation Efficiency Act (ISTEA) of 1991, whic h instituted significant changes in

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Page 43 prioritizing regional (as opposed to singular metro politan) transit investments (Weir et al., 2008) . Specifically, ISTEA empowered metropolitan planning organizations (MPOs) with a strong institutional role in planning, funding, and implementing transportation, thus changing the inventive structure towards regional investment s. The present research focuses specifically on metros with ‘second generation’ rai l because they (as opposed to metros with older ‘legacy’ rail systems) are likely to face a s et of challenges which are of particular theoretical and practical relevance to transportati on justice and urban social justice more generally including the presence of a dispersed sub urbanized population, the existence of rapid population and employment growth, and limited availability of federal funding for the capital and operating costs of transit (Griffin & S ener, 2015). Although this study is concerned with transit accessibility regardless of mode, the presence of fixed-rail transit is specified as a criterion because it serves as an in dicator of the strength of a region’s commitment to transit in general given that rail requires significant capital and o perating investments, and given that it is typically operate d alongside bus and possibly other modes as part of an integrated transit system. Metropolitan areas serve as the analytical focus of the present study because they are typically the scale at which interconnected urb an and suburban transportation and other large-scale networks operate, and are increasingly recognized as the appropriate scale to consider issues of urban sustainability, including transportation (Keil & Whitehead, 2012). Metros are defined here as U.S. Census core-based s tatistical areas (CBSAs), clusters of counties that center around at least one ‘core’ of 10,000 people or more and include all counties that have a high degree of social and econ omic connection to that core, as measured by commuting activity (U.S. Census Bureau, 2010b). Any additional counties not included in the CBSA, but served by the regional tr ansit agency are also included. The study area therefore roughly constitutes the reasonable ‘ commute-shed’ of the metro.

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Page 44 Nine U.S. metros were identified as having second-g eneration regional rail transit system. One of these (Phoenix) was eliminated from analysis due to data availability issues, leaving the eight cases outlined in Table 3.1 . The eight metros are located primarily in the western U.S., with the exception of Minneapolis. Th ree of the metros are located on the west coast (Los Angeles, Portland, and Seattle), tw o are located in Texas (Dallas and Houston), and two are located in the mountain west (Denver and Salt Lake). This geographic distribution reflects the fact that regi onal rail systems in older East coast and Midwestern U.S. metros were established much earlie r (so called ‘legacy systems’), and that most metros in the south and central U.S. have not established robust regional rail systems. The eight case metros range in population size: Thr ee metros have populations under three million (Denver, Portland, and Salt Lak e City), two metros have populations of between three and six million (Minneapolis and Seat tle), just over six million people live in two metros (Dallas and Houston), and a single metro (Los Angeles) has a population of nearly 13 million. The total housing units within t he metros follows a similar distribution. Salt Lake City and Portland have the fewest units, while Houston, Dallas, and Los Angeles contain the largest housing stocks. The percent of housing units that are occupied by renters ranges from approximately 30-percent in Min neapolis and Salt Lake to over 60percent in Los Angeles. Area median income (AMI) di ffers by over $10,000 across the metros. Households in Dallas, Houston, and Portland have an annual income of just under $60,000, with the lowest AMI in Houston ($58,589). Households in Seattle enjoy the highest annual incomes at approximately $69,000. The robustness of the transit systems also vary sub stantially. Annual vehicle revenue-miles, a measure of the miles that the metr o’s bus and rail vehicles are scheduled to travel while in revenue service, ranges from jus t over 39,000 miles in Portland to 193,000 in Los Angeles. Portland and Salt Lake City have th e smallest systems, with under 40,000 vehicle-miles. Dallas, Denver, Houston, and Minneap olis have more moderately-sized

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Page 45 systems (revenue-miles of roughly 60,000 to 80,000) . The Seattle metro has the secondlargest transit system by this measure with nearly 93,000 revenue-miles, although this is far eclipsed by the over 193,000 revenue-miles traveled in Los Angeles. While results are not widely-generalizable, findings shed light on varyin g conditions that are faced across U.S. metros with regional rail transit, and provide part icular insights for metros that have recently undertaken or are currently embarking upon large tr ansit expansion projects. Findings are particularly relevant to relatively dispersed metro s in the western U.S. with that are experiencing high levels of population and employme nt growth.

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Page 46 Table 3.1. Selected cases (metropolitan areas) Metro (identified by its core city) Counties included in study area Regional transit agency(ies) Total population Total housing units1 % renter occupied units Area median income Annual transit vehicle revenue miles2 (2014) Dallas (TX) Collin, Dallas, Denton, Ellis, Hood, Hunt, Johnson, Kaufman, Parker, Rockwall, Somervell, Tarrant, Wise Dallas Area Rapid Transit 6,596,127 2,536,487 40.4% $59,175 58,987 Denver (CO) Adams, Arapahoe, Boulder, Broomfield, Clear Creek, Denver, Douglas, Elbert, Gilpin, Jefferson, Park Regional Transportation District 2,915,986 1,205,179 36.9% $64,206 68,887 Houston (TX) Austin, Brazoria, Chambers, Fort Ben, Galveston, Harris, Liberty, Montgomery, Waller Metropolitan Transit Authority of Harris County 6,191,773 2,362,346 39.9% $58,689 80,009 Los Angeles (CA) Los Angeles, Orange LA County Metro; Metrolink; other county agencies 12,991,225 4,504,858 51.2% $60,337 193,426 Minneapolis (MN, WI) Anoka, Carver, Chisago, Dakota, Hennepin, Isanti, Ramsey, Scott, Sherburne, Washington, Wright, Pierce (WI), St. Croix (WI) Metro Transit 3,352,758 1,368,689 30.0% $68,019 73, 703 Portland (OR, WA) Clackamas, Columbia, Multnomah, Washington, Yamhill, Clark (WA), Skamania (WA) TriMet; City of Portland 2,288,795 933,888 39.3% $58,832 39,125 Salt Lake City (UT) Davis, Salt Lake, Tooele, Utah, Weber Utah Transit Authority 2,209,204 728,314 31.3% $61,529 39,679 Seattle (WA) King, Pierce, Snohomish King County Metro; Community Transit; Pierce Transit Sound Transit 3,537,402 1,477,750 40.2% $68,969 92,606 Sources: U.S. Census American Community Survey 2010 -14 Five-Year Estimates; Federal Transit Administra tion National Transit Database 1Includes both renterand owner-occupied 2Includes bus and rail vehicle-miles

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Page 47 Key Variables The research questions explored in the present stud y involve understanding the relationship between two primary variables of inter est: Transit accessibility and housing affordability. Another set of variables are used in addressing Research Question in order to control for key characteristics of the built and so cial environment that are likely to influence affordability. Table 3.2 outlines these variables, and briefly identifies t he measures used to operationalize them. The methodology used to develo p the LSRI measure of housing affordability is described in detail in Chapter 5. Details about the measure of transit accessibility used in the analysis are provided in Chapter 7. The control variables both considered for and included in the analysis support ing Research Question 2 are discussed in Chapter 8. All variables are measured at the Census block grou p level, which serves as the unit of analysis. Block groups are composed of clusters of contiguous blocks within the same census tract typically containing between 600 and 3 ,000 people and are therefore commonly used as a proxy for neighborhood units, as is inten ded in the present study (U.S. Census Bureau, 2010a).

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Page 48 Table 3.2. Final set of variables included in the a nalysis Variable Definition Measure(s) Primary variables of interest Transit accessibility The ability to reach desired destinations from a home location within a reasonable travel time using public transportation. Accessibility to employment destinations is used as a proxy for general transit accessibility. The percent of a regionÂ’s jobs that can be reached from a block group within a 45-minute commute by transit Housing affordability The ability of a household to afford housing within its housing budget, defined as the amount of income remaining after paying for essential non-housing needs. The number of rental housing units within a block group that are affordable to six household profiles, as a percent of the total rental units within the metro Key characteristics of the built and social environ ment Household density The concentration of households across a geographic area Gross household density: The number of households per acre of developable land Pedestrianorientation The characteristics of a geographic unit in terms of the extent to which it is easily and safely traversed by people travelling by foot Pedestrian-oriented intersection density: The number of intersections that can be traversed by pedestrians per acre Land use The characteristics of a geographic unit in terms of the activities that occur within it Employment-housing entropy: The mix of five employment categories (retail, office, industrial, service, entertainment) and occupied housing Access to retail amenities: The number of retail jobs within half-mile of block group centroid divided by land area Housing mix The characteristics of a geographic unit in terms of the types of housing that exist within it Proportion renters: The number of occupied rental units as a percent of the total number of occupied units Total housing units The total number of units within a geographic unit that are habitable Total housing units: Total number of occupied and vacant housing units located within the block group Socio-economic conditions The social and economic characteristics of the people living within a geographic unit Median household income Proportion non-Hispanic white population: The percent of population that identifies as non-Hispanic and white

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Page 49 Overview of Methods The present study examines affordability for unsubs idized, market-rate renters for two primary reasons. First, low-income renters in m arket-rate housing have little available income with which to respond to increased housing p rices, leaving them particularly vulnerable to local direct and regional exclusionar y displacement. Unsubsidized rental units also provide the vast majority of the nation’s affo rdable housing given that only 25-percent of eligible households are able to secure public assis tance (Ault et al., 2015). Despite this fact, the availability of ‘naturally-occurring,’ market-r ate affordable housing remains understudied. In order to contribute to filling this gap, I analy ze affordability for six household profiles specified based on their ability to shed l ight on the challenges faced by lowand moderate-income renters who are likely to earn too much to qualify for subsidy, but not enough that the availability of stable affordable h ousing is a foregone conclusions. The households examined vary on composition (number of adults, number of children) and financial circumstances (income and number of child ren who require childcare). The six profiles analyzed are: · Profile A: Single adult, no children – 30% AMI · Profile B-1(0): Single adult, one child (not in ch ildcare) – 50% AMI · Profile B-2(1): Single adult, two children (one in childcare) – 80% AMI · Profile C: Two adults, no children – 50% AMI · Profile D-1(0): Two adults, one child (not in chil dcare) – 80% AMI · Profile D-2(1): Two adults, two children (one in c hildcare) – 100% AMI In Part 1, LSRI ‘housing budgets’ – the upper limit of what a household can afford to pay for housing after covering its essential non-ho using needs – were first calculated for these six profiles following the methodology descri bed in Chapter 5. Housing budgets were calculated at the block group level for each of the eight metros and vary based on

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Page 50 household composition, income, and residential loca tion (which determines transportation costs). A second LSRI ‘supply’ measure was then cal culated using U.S. Census American Community Survey data to identify the number of ren tal units within each block group that are affordable to the six household profiles. The r esult of this effort is a comprehensive dataset of the number of units that are estimated t o be affordable to a theoretical household seeking housing in each block group of a metro, acc ounting for the characteristics of the household and the estimated transportation costs as sociated with the block group. Chapter 5 provides a comprehensive description of the metho dology used to develop the two LSRI measures. Comparisons between results of an analysi s undertaken for the Denver metro using LSRI measures and results for the same metro generated using more typical measures is presented in Chapter 6 to demonstrate h ow standard approaches mischaracterize – and likely overestimate – how muc h households with limited means can afford to spend on housing. In Part 2, the LSRI measures of housing affordabili ty were first overlaid with data on transit accessibility to calculate the supply of re ntal units that are both affordable to the six lowand moderate-income households and located in areas with high transit accessibility. Supplies of affordable high accessibility housing a re then compared to supplies of affordable rental units located in areas with no or low transi t accessibility. In this analysis, a block group’s accessibility level is defined by whether t he percent of regional jobs that are accessible within a 45-minute transit commute is ab ove the average accessibility of all block groups that have non-zero accessibility values (‘hi gh’ accessibility) or below the non-zero average (‘low’ accessibility). The supply of afford able housing located in block groups in which no jobs are accessible within a 45-minute tra nsit commute are reported separately (‘zero’ accessibility). Thresholds therefore reflec t each metro’s individual landscape of accessibility, with high accessibility thresholds r anging from 5.9-percent of regional jobs in Los Angeles to 17.5-percent of jobs in Portland.

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Page 51 In addition to observing differences in the supplie s of affordable housing located in high vs. zero/low accessibility, ‘accessibility rat ios’ are also constructed for each of the household profiles. These ratios divide the number of affordable units located in zero/low accessibility areas by the number of affordable uni ts located in high accessibility areas to arrive. Each household profile’s accessibility rati o is then compared to the accessibility ratio of the metro’s overall supply of rental units (rega rdless of affordability) in order to detect deviations from metro-wide distributions of rental housing across high and zero/low accessibility areas. Chapter 7 provides additional details about the methods used in addressing Research Question 1, including the thres holds used to define high and low accessibility, and the accessibility ratios develop ed to support the analysis. I then use multivariate spatial regression modeling to address Research Question 2, with the goal of investigating the complex relation ship between supplies of affordable rental housing and transit accessibility while controlling for key characteristics of the built and social environment, as well as for spatial dependen ce. Two spatial methods are used to support the analysis presented in Chapter 8. First, a series of multivariate spatial error regression models are developed in order to investi gate global (metro-wide) relationships between transit accessibility and housing affordabi lity. The same model specifications are then used in geographically-weighted regression (GW R) models in order to explore how these relationships vary across block groups within a single metro. Two spatial error models and two GWR models are dev eloped per metro: One set examining the supply of rental units that are affor dable to a theoretical household with relatively little income available for housing and a second set examining affordability for households with more moderate housing budgets. Mode ls were specified with the intention of capturing the key factors that are likely to inf luence accessibility and affordability directly (as well as factors that may mediate the relationsh ip between the two variables), while also maximizing parsimony and avoiding issues of multi-c ollinearity. R open-source software

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Page 52 (v3.3.1) was used to specify models following the i terative model-building process described in detail in Chapter 8. Because statistical tests indicate the presence of spatial autocorrelation in both the variables and regression residuals, spatial error r egression estimated using the maximum likelihood method is employed. Spatial autocorrelat ion may be due to any number of issues. Given the nature of the present investigation, spat ial error due to the use of units of analysis (block groups) that do not accurately reflect the a ctual geography of the unit of interest (neighborhoods) is likely to be present. It is also likely that the variables are distributed across space in a way that does not coincide with t he units of analysis, further perpetuating spatial error. Spatial error regression account for these issues by including a spatiallyweighted error term in the model alongside the usua l random error term. Additional details about the final model specifications are provided i n Chapter 8. Spatial error regression is used in this analysis t o identify global relationships between transit accessibility and housing affordabi lity, holding all else constant. While these models provide important insights into the overall relationship between accessibility and affordability, global statistics may mask variation s in the relationship that occur on a local basis. I therefore turn to a final analytical tool – GWR – in order to understand the relationship between these variables at the neighbo rhood (block group) level, controlling for other key factors. Geographically-weighted regressi on estimates models for each block group in a metro, therefore allowing the relationsh ips between variables to vary across space. The GWR models are specified using the same sets of variables as are included in the spatial error models, thus enabling comparisons between global and local coefficients. Details about the GWR model specifications are prov ided in Chapter 8. The analyses undertaken in Part 2 are not intended for use in drawing causal conclusions about the relative effects of specific factors on supplies of affordable housing. Rather, the models are intended to isolate and clos ely examine the complex relationship

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Page 53 between accessibility and affordability. Results de epen our understanding of the geographies of opportunity experienced by lowand moderate-income households across the U.S., and shed further light on the robustness of a location efficiency narrative when affordability is assessed using more nuanced measur es and analytical approaches.

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Page 54 CHAPTER IV EVALUATING TYPICAL MEASURES OF HOUSING AFFORDABILIT Y AND INTRODUCING THE IMPROVED ‘LOCATION-SENSITIVE RESIDU AL INCOME’ MEASURE INTRODUCTION The Growing Housing Affordability ‘Crisis’ Following the recovery from the Great Recession of 2008, unprecedented increases in housing costs across many U.S. cities and region s has generated growing concern about housing affordability among policymakers and the pu blic. According to the National Association of Realtors and Harvard University’s Jo int Center for Housing Studies (JCHS), the median price for existing homes nationally incr eased four-percent between 2013 and 2015 (JCHS, 2015). Renters face similar challenges: Nationally, rents increased an average of 3.2-percent between 2014 and 2015, with the ‘hot test’ metropolitan areas increasing 10percent or more. With vacancy rates at their lowest in 20 years (7.6%), pressures on rental markets across the U.S. are expected to continue mo unting, particularly as demand for housing grows among the millennial population (Elle n & Karfunkel, 2016). These trends have led to calls of a housing affordability ‘crisi s’ among U.S. mayors, particularly those in cities located in large high-growth metropolitan ar eas (Langan et al., 2016). Not surprisingly, rising housing costs, and rents i n particular, are felt most acutely by the over 10 million ‘extremely low-income’ renters, defined as those with an annual household income of less than 30-percent of area me dian income (AMI). The National LowIncome Housing Coalition reports that the supply of housing affordable to these households, who constitute 25-percent of the nation’s renters, is becoming increasingly limited: Only three affordable units are available for every 10 e xtremely low-income household (Bravve et al., 2013). The dearth of affordable rental housing left nearly 80-percent of extremely lowincome households ‘severely cost-burdened’ in 2014, a term used to indicate that a

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Page 55 household’s housing expenditures consumed more than half of the its income (Ault et al., 2015). Research by the Center for Housing Policy suggests that ‘working’ renters – households with members who work at least 20 hours per week and make no more than 120-percent AMI also face increasing challenges in securing affordable housing. Over 70percent of workers earning the federal minimum wage for 40 hours of work per week (approximately $15,000 per year) are left severely cost-burdened (JCHS, 2015). Indeed, working renters experienced a six-percent increase in housing costs between 2011 and 2014. These trends are true not only for low-income working households but also for more moderate-income households, particularly those livi ng in high-cost metropolitan areas. In its research on the ten highest-cost regions (a cohort that includes Boston, Los Angeles, New York, San Francisco, and Seattle),the JCHS reports that nearly 50-percent of moderateincome renters (those earning $45,000 to $75,000) a re severely cost-burdened (JCHS, 2015). Many policymakers at the state and local level are seeking to address housing affordability through legislation encouraging incre ases in the supply of both new market-rate housing and new affordable units created through in clusionary zoning and similar policies. Although helpful to some extent, these measures are not likely to be a panacea. While the market is beginning to respond to increased demand for rental housing, only one-tenth of new multi-family units are affordable to the 50-per cent of rental households that make less than $34,000 per year (JCHS, 2015). Inclusionary zo ning and other policies designed to increase production of affordable housing are posit ive developments, but cannot begin to meet demand alone. Meanwhile, wages remain persiste ntly low. Nationally, the hourly wage required to afford a two-bedroom apartment at Fair Market Rent (referred to as the ‘housing wage’) is $18.79. Among the case regions focused on in the present study, the ‘housing wage’ varies from $16.13 (Salt Lake City) to $27.33 (Los Angeles) (Bravve, et al., 2013).

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Page 56 Meanwhile, the average hourly wage of renters is on ly $14.32, and nearly 60-percent of jobs created since the Great Recession pay no more than $13.84 per hour. Recent efforts undertaken in many cities to increase the minimum w age are a promising step in closing the gap between housing costs and wages, yet even the $ 15 per hour minimum wage that is commonly advocated is far too low to cover market-r ate housing in most large U.S. cities. Although subsidized housing at the federal, state, and local level plays a critical role in addressing housing affordability for low-income households, demand for rental housing assistance far exceeds demand. In 2014, only one-qu arter of eligible low-income households were able to secure rental assistance th rough the federal government (Ault, et al., 2015). State and local rental assistance remai ns minimal in the majority of U.S. regions (Belsky & Drew, 2007). Unsubsidized, market-rate re ntals therefore provide the vast majority of housing for lowand moderate income households. Reliance on market-rate housing is only likely to grow as 50-percent of the 4.8 millio n rental units subsidized through federal programs expire in the coming decade and as federal subsidies continue to decline (JCHS, 2015). The inability of subsidized and unsubsidized housin g to meet demand among lowand moderate-income households is responsible for a host of deleterious effects. A lack of affordable housing contributes to the homelessness of an estimated 600,000 people in the U.S., over a third of whom are people in families ( JCHS, 2015). Nearly one in four households on waiting lists for federally-subsidize d rental assistance report periods of homelessness and another 40-percent report ‘doublin g-up’ with family or friends, a condition often leading to homelessness (Leopold, 2012). Even when low-income households are able to secure stable housing, they are likely to m ake concessions in terms of the condition of the units: A reported 17 million households curr ently live in housing that is sub-standard in terms of pests, leaks, broken windows, plumbing iss ues, electrical hazards, or structural problems (Jacob et al., 2014).

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Page 57 Furthermore, many rental units affordable to low-in come households are also located in areas of concentrated poverty. A large body of r esearch on ‘neighborhood effects’ demonstrates that low-income households living in h igh-poverty neighborhoods face many more challenges in terms of economic, educational, physical and mental health, and subjective well-being as compared to low-income hou seholds living in low-poverty areas (Chetty et al., 2015; Ludwig et al., 2012). These e ffects appear to have a particularly large effect on children. For example, children in low-in come households living in high-poverty neighborhoods generally exhibit significantly lower levels of school readiness and achievement as compared to children in similar hous eholds living in low-poverty areas (Leventhal & Brooks-Gunn, 2000). Furthermore, evide nce suggests that children in lowincome households that move from a high-poverty are a to a low-poverty area are likely to complete college at higher rates and earn higher in comes as adults when compared to children from similar households who remained in hi gh-poverty neighborhoods (Chetty & Hendren, 2015). Low-income households that spend a disproportionate amount of their income on housing also have much less disposable income avail able to meet the basic necessities of daily living, not to mention the ability to save fo r the future. The JCHS reports that severelycost burdened households in the bottom expenditure quartile spent 70-percent less on healthcare and 40-percent less on food than similar households in more affordable housing (JCHS, 2015). Spending less on these necessities le aves low-income renters at higher risk for health-related crises, and may lead to reduced worker productivity and increased reliance on publicly-subsidized health care program s. High housing costs also reduce a household’s ability to save for the future (includi ng for retirement), further heightening financial strains on individual households and the social welfare system (Belsky & Drew, 2007). The impacts of this circumstance are especia lly harsh for children since households with severe housing cost burdens have little dispos able income available to spend on their

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Page 58 children’s care and enrichment (Brooks-Gunn & Dunca n, 1997; Newman & Holupka, 2014). Indeed, evidence suggests that higher percentages o f income spent on housing are associated with lower levels of cognitive achieveme nt in children (Newman & Holupka, 2013). Conversely, secure and stable affordable hou sing allows families to spend resources on food and health care expenditures, thereby posit ively effecting the physical and mental health of children and their caretakers (Maqbool et al., 2016). Defining and Measuring ‘Affordable Housing’ Existing research clearly demonstrates the large ro le that affordable housing plays in promoting social and economic well-being. The liter ature also points to mounting challenges among lowand moderate-income households in securi ng affordable places to live. Yet despite the ubiquity and importance of these issues in public and scholarly conversations, there has been surprisingly little critical examina tion in both the academic and public spheres about how to define and operationalize the concept of ‘affordable’ housing I contribute to addressing this gap in the present chapter by unpacking the three most commonly-used approaches to measuring affordab le housing, and introducing a fourth approach that addresses many of their shortcomings. This fourth approach considers housing to be ‘affordable’ when a household is able to pay for housing while still meeting its essential non-housing needs within the bounds of it s income. Conversely, housing is ‘unaffordable’ when housing costs require reduced s pending on other non-housing expenditures such that a household is not able to a fford its most basic necessities. Under this definition, housing affordability is not a static characteristic as it is often treated; Rather, it is a dynamic relationship betwe en housing costs on the one hand and the specific features, composition, and financial circu mstances of individual households on the other (Stone, 2006). Different households clearly e xperience housing affordability differently. It is therefore obvious that when assessing housing affordability one must always ask the question ‘affordable for whom ’? However, the most typical approaches to measurin g

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Page 59 housing affordability do not address this crucial q uestion and instead rely on blunt measures that assume a homogeneity of circumstances among ho useholds that is not likely to exist in reality. In the sections that follow, I first provide an ove rview of the three most typical measures of housing affordability – the ratio, loca tion affordability, and residual income approaches – and outline the shortcomings of each. I then introduce an innovative fourth approach – the location-sensitive residual income’ (LSRI) measures – that corrects for many of the shortcomings inherent to standard approaches . A subsequent chapter (Chapter 5) provides a detailed methodology intended to guide p ractitioners in constructing the LSRI measures. In Chapter 6, I demonstrate how the LSRI approach can be applied empirically by investigating the spatial distribution of housin g that is affordable to lowand moderateincome renters in the Denver metro area. Results de rived using LSRI measures are then compared to those generated using the three more ty pical approaches. Findings from this comparison highlight how LSRI measures account for the nuanced financial circumstances of households with different compositions and resid ential locations, thus offering a more robust alternative to more typical measures. Furthe rmore, findings generate a more refined understanding of current landscapes of affordabilit y in the Denver metro area, thus equipping planners and policymakers with knowledge to support policy interventions targeted specifically to local conditions. In the r emaining chapters, I employ LSRI measures in combination with measures of transit accessibili ty to examine the complex relationship between accessibility and housing through two resea rch questions. TYPICAL APPROACHES TO MEASURING HOUSING AFFORDABILI TY Housing affordability is measured in myriad ways in the existing empirical literature. Measures may focus exclusively on housing costs – f or example, the minimum, average, or total costs of owning or a renting a particular typ e of housing might be specified. Or, the average price per square foot for housing in a spec ific geographic area may be used. Most

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Page 60 commonly, measures attempt to account for the relat ionship between housing costs and household income. For example, affordability may be measured as the minimum income or wage required to rent or purchase a particular type of housing. Or the median housing cost divided by the median household income may be calcu lated for a particular geographic area (Litman, 2015). Reported housing expenditures may a lso be examined, often as a share of household income. Still other measures focus on the supply of vacant units with certain characteristics available at a specific cost. More sophisticated measures may also incorporate housing quality to account for the adeq uacy of living conditions (Li, 2014). This wide array of measures underscores the complex layers of household-level factors and decisions that underlie the ambiguous c oncept of housing affordability, as well as the multitude of geographic scales at which it c an be measured. The number of possible measures also reflects tradeoffs associated with th e robustness of a measure on the one hand and the ease with which data can be collected, analyzed, and interpreted on the other. Indeed, measures of housing affordability must opti mize many objectives. They are expected to reflect “individual experiences [mediat ed] through analytical indicators and normative standards” and enable conclusions to be d rawn about the where and the extent to which affordability is a problem, all while employi ng readily-available data and easilyinterpretable analytical techniques (Stone, 2006: 1 51-152). The three most commonly-used measures of housing af fordability – the ‘ratio,’ ‘location affordability,’ and ‘residual income’ app roaches – achieve some of these objectives with varying degrees of success. The ‘ratio’ measur e considers housing to be affordable if it consumes less than a defined threshold (typically 3 0%) of income. A second ‘location affordability’ measure also uses a ratio-based appr oach, but accounts for the combined effects of housing and transportation costs such that housing is consider ed to be affordable if combined costs consume less than 45-percent of i ncome. The third ‘residual income’ measure is less widely-used among practitioners, bu t is generally recognized among

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Page 61 scholars as offering a more precise measure of affo rdability (Newman & Holupka, 2014). A residual income approach defines housing as afforda ble when a particular household is able to cover the costs of all its essential, non-housin g needs after paying for housing. In the sections that follow, I outline each of thes e approaches, including assessments of both the benefits and shortcomings a ssociated with each. I then introduce the LSRI approach, which integrates the location af fordability and residual income approaches to more accurately reflect the financial realities lowand moderate-income households face in securing affordable housing. A ‘Ratio’ Approach to Measuring Housing Affordabili ty The most common measure of housing affordability se ts a threshold calculated as a percent of household income (typically 30%) whereby housing that costs less than the threshold is considered affordable, and housing cos ts exceeding the threshold are considered ‘unaffordable.’ Under this ratio approac h, households spending more than 30percent of their income on rent or ownership costs are considered ‘cost-burdened.’ Those spending more than 50-percent of household income o n housing are identified as ‘severely cost-burdened.’ There is no particular theoretical or empirical bas is for the use of a 30-percent threshold (Stone, 2006). Rather, the threshold is r ooted in a normative ‘rule of thumb’ first adopted by banks in the 1920s based on the idea tha t no more than one week’s income should go to housing (Newman & Holupka, 2014). This threshold approach was codified into federal policy in the 1969 “Brooke Amendment” which limited rent in public housing to 25percent of residents’ income. The threshold, subseq uently raised to 30-percent in the 1980s by Congress, has been widely adopted as the primary measure of housing affordability by federal, state, and local agencies responsible for setting housing policy. Most notably, the U.S. Department of Housing and Urban Development (H UD) uses the 30-percent threshold to determine eligibility for publicly-subsidized re ntal housing and ownership programs (U.S.

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Page 62 Department of Housing and Urban Development Office of Policy Development and Research, 2014). The ratio approach is also widely-used among organi zations advocating for affordable housing, in part due to its prevalence i n federal policy and also because it is computationally-straightforward and intuitive for b oth policymakers and the general public (Benner & Karner, 2016). In particular, the househo ld income and housing expenditure data required for calculating a ratio measure is easily retrievable from the U.S. Census Bureau and Bureau of Labor Statistics. The ratio measure i s also comparable across geographies and time, making it particularly useful for nationa l-level analyses. Despite its widespread use, the ratio approach is s ubject to much criticism from both scholars and advocates (see, for example, Belsky & Drew, 2007; Bogdon & Can, 1997; Hulchanski, 1995; Hertz, 2015b; Stone, 2006; Kutty, 2005). The first, and perhaps most significant shortcoming of the ratio measure, is it s insensitivity to differences in household income. For instance, a low-income household making $1,800 a month and spending 45percent ($810) of its monthly income on housing has only $990 remaining for food, healthcare, taxes, childcare, and other necessities . A more affluent household also spending 45-percent of its income on housing, but with month ly earnings of $6,000 has much more disposable income ($3,300). Yet, based on the ratio measure of affordable housing, both households are considered ‘cost-burdened’ even thou gh the former has far more challenging circumstances than the latter. Ratio measures also often fail to account for diffe rences between households with characteristics and financial circumstances. Ratio measures are often insensitive to household size and the presence of children, both o f which have a large impact on the nonhousing costs incurred. For example, a two adult, m oderate-income (80-percent AMI) household with no children will have vastly differe nt financial circumstances as compared to a single-parent of two children with the same incom e. The latter household is likely to spend

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Page 63 a much larger portion of its income meeting its bas ic non-housing needs, and thus will feel the crunch of high housing costs to a much greater degree than the former. Ratio measures also do not account for the cost of childcare, whic h often exceed housing costs for many families with young children (Glasmeier, 2014). HUD -adjusted median family income (HAMFI) classifications used in awarding housing su bsidies to low-income households address this shortcoming to some extent by adjustin g AMI values up or down based on a householdÂ’s size (Bogdon & Can, 1997). However, HAM FI measures are not commonly used in analyzing housing affordability, nor do they address issues related to childcare requirements. Furthermore, a ratio measure alone does not reflect the tradeoffs that exist between housing costs and residential locations, amenities, and housing quality. While affluent households may have the disposable income to spend far more than 30-percent of their income on housing in order to enjoy more desirable location or amenities without sacrificing on other necessities, low-income households do not. A ratio measure also does not account for the challenges low-income households may face w hen affordable housing is primarily located in neighborhoods suffering under high crime rates, poor school quality, low transportation connectivity and other consequences of concentrated poverty (U.S. Department of Housing and Urban Development Office of Policy Development and Research, 2014). A final criticism of the ratio approach is its inat tention to variations in transportation costs associated with the extent to which a househo ld must rely on a single-occupancy vehicle to access employment opportunities and othe r basic necessities of daily life (Revington & Townsend, 2016). A household living in a neighborhood well-served by public transit is likely able to minimize transportation c osts by owning a single (or no) car and limiting its use, thus freeing up income that can i nstead be spent on housing. Conversely, a household living in a neighborhood in which there i s limited or no transit service and where

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Page 64 basic services are located a distance away may requ ire significantly more spending to maintain and operate multiple cars, thus reducing t he income available for housing. This shortcoming is addressed by a second approach – the ‘location affordability’ measure – discussed below. A ‘Location Affordability’ Approach to Measuring Ho using Affordability The location affordability measure also follows a t hreshold-based approach, but accounts for variation in transportation expenditur es by considering housing and transportation costs in combination . A location affordability measure thus defines hou sing as ‘affordable’ when combined housing and transportati on (‘H+T’) costs do not exceed 45percent of income. Housing that requires households to spend more than 45-percent of their income on H+T costs is thus considered ‘unaffordabl e.’ The location affordability approach has its origins in efforts by the Center for Neighb orhood Technology (CNT) to encourage a more comprehensive view of housing affordability th rough documentation of transportation costs associated with different housing locations. In many regions, housing costs tend to be lowest in the auto-oriented suburban fringe, yet th ese same areas are likely to lack employment opportunities, amenities, and non-auto t ransportation options – all factors which contribute to higher transportation costs. Proponen ts of the location affordability (or ‘location efficiency’) approach therefore argue that although housing in neighborhoods with close proximity to jobs, the ability to walk or bike to s hopping districts, and the availability of transit and non-motorized transportation options may be mor e costly, high housing costs are likely to be offset by lower transportation costs. The adage ‘drive until you q ualify’ describes this theoretical tradeoff: While housing, and single-fam ily homes in particular, may be cheapest in far-flung areas of the region, reliance on auto modes are likely to render transportation costs much higher as compared to more central areas with higher housing costs. For instance, CNT found that in some heavily auto-depen dent neighborhoods of Washington,

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Page 65 D.C., transportation costs comprise as much as 32-p ercent of income, while in more accessible areas they are as low as 10-percent (CNT , 2011). Tradeoffs between housing and transportation costs are also clear at an aggregate level: Some metropolitan areas that appear to be qu ite affordable in terms of housing alone are much less affordable when considering housing a nd transportation in combination. For example, research from the Center for Housing Polic y and CNT indicates that while Houston is the eighth most affordable region for housing co sts alone, it ranks 17th when considering combined H+T costs. On the other end of the spectru m, this research suggests that many dense, highly-accessible regions are among the leas t affordable regions in terms of housing, but are considerably more affordable when accountin g for transportation (Center for Housing Policy and Center for Neighborhood Technolo gy, 2012). The interplay between housing and transportation co sts is particularly stark for the working poor. While higher-income households have t he luxury of being able to choose to live in more accessible areas of the region, low-in come households are likely to be much more constrained in their choices. In many cases, l owand moderate-income households may only be able to secure housing in less accessib le areas of the region that require long and costly commutes. Not only does this burden lowe r-income households with the high costs of autodependence, but it also exposes thes e households to financial uncertainties related to the fluctuating price of gas and car mai ntenance. Indeed, low-income households living in housing that does not exceed 30-percent o f their income spend $100 more a month on transportation (Belsky & Drew, 2007). Research a lso indicates that nationally, the combined costs of housing and transportation consum e much more of a low-income household’s income as compared to more affluent hou seholds (Roberto, 2008). The original CNT “H+T Index” has gained considerabl e traction since its inception in 2006. The U.S. HUD launched its own ‘Location Affor dability Index’ (LAI) based on the CNT model in 2013 and have subsequently incorporated a much more sophisticated

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Page 66 methodology to predict housing and transportation c osts for eight different household profiles (Haas et al., 2016; U.S. Department of Hou sing and Urban Development, 2015). The resulting data is publicly-available through HU D’s Location Affordability Portal1, which promotes the use of a Location Affordability Index (LAI) among planners, policymakers, developers, and the general public. Despite its laudatory emphasis on the interplay bet ween housing and transportation costs, location affordability measures perpetuate t wo key shortcomings of the ratio approach upon which it is based. First, the location afforda bility approach continues to rely on an arbitrary threshold (45-percent of income) that has little theoretical basis and is insensitive to differences in household income. The location affor dability approach also does not account for nuanced differences in household characteristic s or financial circumstances, particularly those related to the presence of children and assoc iated childcare costs. A ‘Residual Income’ Approach to Measuring Housing A ffordability A third approach that is increasingly popular among advocates improves upon many of the shortcoming of the ratio and location afford ability measures of housing affordability (Hertz, 2015a; Weise, 2014). First originated by Mi chael Stone in the 1975 and continually refined since, the residual income approach subtrac ts the total non-housing costs required to maintain a minimum standard of living from house hold income, thus identifying the remaining ‘residual’ income that is available for h ousing (Stone, 2006). Stated differently, housing is affordable if income (I) less housing ex penditures (H) is greater than or equal to the minimum necessary non-housing expenditures (NH) , such that: I – H NH (Thalmann, 2003) Stone’s concept provides the basis for the definiti on of ‘housing affordability’ adopted by the present study: A condition in which a househ old is able to afford all housing-related costs while still being able to meet its essential non-housing needs within the bounds of its 1 http://www.locationaffordability.info/lai.aspx

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Page 67 income. This approach can be applied to either a ‘r eal’ household, or to a ‘hypothetical’ household defined to represent a particular set of household characteristics. By recognizing that housing affordability is entire ly dependent on a household’s composition and financial circumstances, the residu al income approach corrects for the most critical shortcomings of the ratio and locatio n affordability approaches. A residual income measure provides a ‘sliding scale’ of afford ability, with the maximum affordable amount varying with household size, the presence of children, and specific financial circumstance. Depending on these factors, some affl uent households are able to afford far more than 30-percent of their income on housing (or 45-percent on housing and transportation combined) while lower-income househo lds may be unable to afford housing at all without heavy subsidy. The residual income m easure is therefore consistent with the ‘capabilities approach’ framework adopted in the pr esent study in that it accounts not only for income (as the more Rawlsian ratio and location affordability measures do), but also for what a household is able to ‘do’ with that income given the full set of its circums tances. The first step in developing a residual income meas ure of affordability is to identify the non-housing costs that are required to sustain a basic standard of living. Defining what constitutes a ‘basic’ standard of living requires n ormative judgement about the conditions that are acceptable to a particular society at a sp ecific point in time (Stone, 2006). Most empirical research employing a residual income appr oach in the U.S. context uses the ‘lower-budget’ standards defined by U.S. Bureau of Labor Statistics (BLS) to identify the ‘basket’ of non-housing goods and services required to maintain a basic standard of living, which include: Food; Medical expenses; Childcare (i f applicable); Transportation; Clothing; Other goods required for basic household operations ; and Local, state, and federal taxes. A small number of studies using residual income mea sures have also employed large-scale surveys and/or focus groups to define a basic standard of living (Stone, 2006).

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Page 68 Data on non-housing expenditures are most often sou rced from U.S. BLS Consumer Expenditure (CE) Survey, a dataset released annuall y based on findings from interviews and diary surveys that ask American consumers about details related to their household characteristics, expenditures, and income (U.S. Bur eau of Labor Statistics, 2016). A number of resources that collate and present BLS CE Survey and other household expenditure data in a user-friendly format have recently become avai lable for most U.S cities and regions, rendering the residual income approach more accessi ble to practitioners, policymakers, and the general public. The ‘Living Wage Calculator’ (L WC) developed by Dr. Amy Glasmeier at the Massachusetts Institute of Technology is perhap s the most well-developed of these resources2. The ‘Self-Sufficiency Standard’ available through the University of Washington’s Center for Women’s Welfare3 and the Economic Policy Institute’s ‘Family Budget Calculator’4 provide similar data, although they are less compr ehensive than the LWC. All three of these resources report the cost of basic n ecessities by region, and are therefore sensitive to variations in costs of livings across different geographies. Empirical research using BLS CE data to compare the residual income approach to the more typical ratio approach demonstrate that th e two measures tell very different stories about affordability. In particular, findings derive d from residual income measures indicate that housing affordability is much more problematic for families with children than ratio measures would suggest (Newman & Holupka, 2014; Sto ne, 2006). While the residual income approach provides the mos t robust measure discussed thus far, is not without shortcomings. Residual inc ome measures require more data and are more computationally-intensive than the ratio and l ocation affordability approaches, rendering them somewhat less accessible to practiti oners. This issue is becoming less important as data portals like the ones noted above – The Living Wage Calculator, the Self2 http://livingwage.mit.edu/ 3 http://www.selfsufficiencystandard.org/ 4 http://www.epi.org/resources/budget/

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Page 69 Sufficiency Standard, and the Family Budget Calcula tor – bring consumer expenditure data to the mainstream public in a user-friendly interfa ce. A residual income approach is also rooted in a particular time and place, making them more difficult (although not impossible) to compare across time periods and geographies. Furthe rmore, like the ratio and location affordability approaches, residual income approache s do not account for housing quality. Finally, and perhaps most importantly, residual inc ome measures view transportation costs as static and are therefore not sensitive to the wi de variations in auto-dependence, and thus transportation costs that exist across a region. Be cause transportation costs vary quite widely depending on a household’s residential locat ion, it is imperative that any measure of affordability account for these variations. Conclusions Affordable housing is becoming a dominant concern i n high-growth metropolitan areas across the U.S. It is therefore more importan t than ever that we clearly define what ‘affordable’ means, and develop measures that accur ately reflect that definition. The three ‘typical’ approaches described above tell vastly di fferent stories of affordability, to varying levels of robustness. In the section that follows, I introduce a fourth approach that addresses many of the collective shortcomings of more typical approaches. In doing so, this fourth ‘location-sensitive residual income’ approach more accurately reflects on-the-ground conditions related to affordable housing while offe ring a relatively straightforward and computationally-manageable method. This methodology thus equips practitioners and policymakers with tools to explore nuanced landscap es of affordability and thus to support the development of policy prescriptions that target the specific challenges faced by areas with different affordability dynamic.

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Page 70 A NEW APPROACH TO MEASURING HOUSING AFFORDABILITY: ‘LOCATIONSENSITIVE RESIDUAL INCOME’ Despite criticism, ratio measures continue to enjoy hegemonic use, which is primarily justified by a perceived lack of alternative measur es that “can be computed and understood with equal facility” (Thalmann, 2003:292). However, alternatives do exist and are increasingly being used by practitioners and resear chers. In particular, the location affordability measure has recently gained acceptanc e as an intuitive – but more robust – alternative to ratio measures. Yet, while location affordability measures address shortcomings associated with the treatment of trans portation costs, they perpetuate many of the same issues of the ratio approach – namely, the use of arbitrary normative thresholds that are entirely insensitive to differences in hou sehold income and composition. A third measure – residual income – is also gaining attenti on as a viable alternative, although it remains infrequently used. However, the utility and accuracy of the standard residual income approach continues to be limited by its fail ure to account for the variation of transportation costs across space. I therefore propose a fourth alternative – the loca tion-sensitive residual income (LSRI) approach – that incorporates elements of the location affordability and residual income approaches to arrive at a measure that addre sses many of the shortcomings detailed above. Under the LSRI approach, affordabil ity is assessed by calculating the amount a theoretical household is able to pay for h ousing after covering all of the other essential goods and services required to support a basic standard of living. The amount remaining for housing after all other essential exp enses are paid is referred to as a household’s ‘housing budget’. Housing budgets vary widely depending on household composition (size, presence of children), financial circumstances (income, childcare requirements), and residential location (which dete rmines transportation costs). As shown in Figure 4.1 , housing budgets are calculated for a specified se t of theoretical household

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Page 71 profiles by subtracting six categories of household expenditures – childcare, food, medical, other basic necessities, taxes, and transportation – from household income. Figure 4.1. Housing budget components Costs associated with childcare, food, medical expe nses, other basic necessities, and taxes are referred to as non-housing and transp ortation (‘non-H+T’) costs. The five nonH+T costs are calculated separately for each theore tical household profile based on its composition and financial circumstance. The first f our of the costs vary as a function of household composition: Larger households are expect ed to consume more food, incur additional medical costs, and require higher spendi ng on other basic necessities than smaller households. Childcare costs are dependent o n another aspect of household composition – the presence and number of children u nder school-age – which is incorporated into the defined household profiles. C ost associated with state and federal income taxes vary as a function of household income . There are likely innumerable circumstances that may affect a household’s non-H+T costs – for example, it is possible that a grandparent or other relative provides free child care – yet it would be impossible to account for all of these. The LSRI measures develop ed here instead aims to account for circumstances that are likely to exist across a wid e swatch of U.S. households. Transportation costs vary not only based on househo ld size, but also on a household’s residential location. Transportation co sts are thus calculated for each theoretical household profile at the block group le vel. The resulting dataset provides a

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Page 72 comprehensive understanding of the amount a theoret ical household with a particular set of characteristics can afford to pay for housing if it were to locate in a specific block group. For example, the LSRI approach enables an analyst to id entify the housing budget of a household with one adult and no children earning 50 -percent AMI and residing in a particular block group located in an outer suburb. Or, an analyst could identify the housing budget of a median-income household with two adults and two children (one of whom requires childcare) residing in a block group locat ed in the central city. After calculating housing budgets for each theoreti cal household profile by block group, the analyst is then able to assess the suppl y of housing that is both located within that block group and is affordable within the householdÂ’s housing budge t. This calculation is completed for every block group within a region, fo r each theoretical household profile. The number of units affordable to a particular househol d profile can then be summed across a set of block groups in any number of ways depending on the aims of the analysis. For example, the number of housing units affordable to a single-adult household with no children earning 80-percent AMI could be summed across all b lock groups within a region, or across all block groups located within a specified distanc e of a particular amenity. The LSRI approach to measuring housing affordabilit y improves upon the ratio, location affordability, and standard residual incom es approaches in several respects. First, LSRI measures provide for a much more robust accoun ting of the financial realities faced by households with different characteristics than is p ossible through ratio and location affordability measures. In particular, the LSRI app roach addresses circumstances around the need for childcare, which often constitutes a h ouseholdÂ’s largest expense when young children are present. The LSRI measure also avoids the use of the arbitrary and reductive thresholds that are inherent to the ratio and locat ion affordability approaches, and corrects for a key shortcoming of the standard residual inco me approach by accounting for variations in transportation costs related to a householdÂ’s lo cation within the region. The LSRI

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Page 73 approach achieves all of these improvements through the use of publicly-available data and a relatively straightforward methodology, rendering it useful across many different policy arenas and among a broad range of users. Furthermor e, the LSRI method is flexible: It can utilize various household expenditure and housing s upply datasets available across multiple scales, and can easily incorporate improved data as it becomes available. The LSRI methodology provided in the following chapter is th erefore able to support meaningful discussions around housing affordability at the nei ghborhood, local, and regional levels, as well as around the intersection of affordability wi th other policy issues the provision of transit services as is done in Chapters 7 and 8.

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Page 74 CHAPTER V METHODOLOGY FOR CONSTRUCTING A LOCATION-SENSITIVE R ESIDUAL INCOME MEASURE OF HOUSING AFFORDABILITY As detailed in Chapter 4, the LSRI measure of housi ng affordability improves upon standard measures by more fully accounting for the financial realities faced by households in securing affordable housing, including issues re lated to household composition and childcare requirements, income, and residential loc ation. LSRI measures are relevant to any application that aims to assess housing affordabili ty at a range of geographies, from the neighborhood up. The utility of LSRI measures and t he ease with which they can be constructed using publicly-available data render th em highly accessible to practice. The methodology outlined below provides practitioners w ith details on the data and operations involved in constructing the LSRI measures. Two LSRI measures are developed in the present chap ter. The first measure identifies a household’s ‘housing budget,’ or the a mount of monthly income that remains available for housing after the household covers co sts associated with the goods and services required to sustain a basic standard of li ving. A second ‘supply’ measure quantifies the number of rental units that are affordable with in a particular household’s housing budget. There are seven steps involved in constructing thes e two measures, as outlined in Figure 5.1 .

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Page 75 Figure 5.1. Steps for constructing a LSRI measure o f housing affordability In Step 1 , the analyst specifies a series of assumptions abo ut the geographic extent of the analysis, the unit of analysis for which aff ordability will be assessed, and whether the analysis will evaluate affordability for homeowners , renters, or both. Step 2 involves defining a set of theoretical household profiles that vary o n household composition (the number of adults, number of children, and number of those chi ldren that require childcare) and household income. Next, costs associated with the e ssential goods and services required to meet a basic standard of living, except for those a ssociated with housing and transportation, are summed to identify the total ‘non-H+T’ costs ( Step 3 ). Non-H+T costs vary depending on household composition and financial circumstance, a nd are therefore calculated for each household profile separately. In Step 4 , non-H+T costs are subtracted from household income to arrive at the total remaining amount avai lable for housing and transportation costs, referred to as the ‘H+T budget.’ H+T budgets are calculated for all specified

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Page 76 household profiles. In Step 5 , transportation costs are then estimated for each household profile based on their theoretical location within the region. The result of this step is a comprehensive dataset of estimated transportation c osts for every Census block group in the region, by household profile. After establishing estimated transportation costs, the analyst is then able to calculate the total funds that remain available for housing c osts for all block groups in the metro ( Step 6 ). This housing budget represents the upper limit o f what a household can afford to pay for housing while still covering the necessities associ ated with maintaining a basic standard of living. It therefore varies by household characteri stics, and by location in the region, such that a housing budget is calculated for each of the defined household profiles theoretically residing in each block group within a region. In th e final step ( Step 7 ), the analyst calculates the supply of housing units that are affordable wit hin a particular householdÂ’s housing budget for every theoretical residential location ( block group). The key components generated by these seven steps are summarized in Figure 5.2 . The remainder of the present chapter provides a det ailed account of the operations involved in each of the seven steps. These operatio ns are demonstrated by calculating a LSRI measure of housing affordability for an exampl e metropolitan area (Denver). The same methodology was followed to develop LSRI measure th e remaining seven case metros to support the analysis present in Chapters 7 and 8.

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Page 77 LSRI component Definition Household profile A theoretical household for which affordability is assessed; Each household profile varies based on: · Number of adults in household · Number of children in household · Number of children requiring childcare · Household income Non H+T costs Total costs associated with the goods and services required to support a basic standard of living, exc ept for those related to housing and transportation Varies by household profile H+T budget The amount of income that remains available for housing and transportation costs after non-H+T cost s are subtracted Transportation costs Costs associated with transportation, depending on a household’s residential location within the region Varies by household profile, and by block group Housing budget The amount of income that remains available for housing after non-H+T costs and transportation cost s are subtracted; Represents the upper limit of what a household can afford to pay for housing while still covering its other basic necessities Supply of affordable housing The number (or percent) of housing units that are affordable to a theoretical household given its composition and income Figure 5.2. LSRI components STEP 1: SPECIFY ASSUMPTIONS A number of analytic choices that define the bounds and assumptions of the analysis are required as the first step in developing the LS RI measures. This involves: 1) Identifying the geographic extent of the analysis (e.g. neighbo rhood, municipality, region, etc.); 2) Defining the unit of analysis for which affordabili ty will be assessed (e.g. block group, tract, municipal, etc.); and 3) Specifying whether the ana lysis will assess affordability for homeowners, renters, or both, and whether the analy sis will include unsubsidized marketrate housing and/or subsidized housing. Assumptions made in the present analysis are outlined below.

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Page 78 Geographic Extent For the purposes of this study, LSRI measures are d eveloped for all block groups in a metro. However, the methodology can easily be ada pted to evaluate housing affordability at multiple other scales, from the neighborhood to the national level. As described in Chapter 3, the present study defines the ‘metro’ (a lso referred to interchangeably as the ‘region’) as the core-based statistical area (CBSA) ,1 a cluster of counties that centers around at least one ‘core’ of 10,000 people or more and in cludes all counties that have a high degree of social and economic connection to that co re (U.S. Census Bureau, 2010), as well as any additional counties served by the regional t ransit agency. Many other datasets relevant to this study use the CBSA as the unit of analysis, including HUD’s Location Affordability Index and various measures of transit accessibility discussed. Unit of Analysis The defined unit of analysis, or the geography at w hich affordability is assessed, will vary depending on the aims of the particular analys is and the level of error that can be tolerated. The present study assesses affordability at the Census block group level. Housing supply and demand vary considerably across, and eve n within, neighborhoods. It is therefore important to use the smallest unit of ana lysis possible to account for this variation. Block groups are commonly used as a proxy for neigh borhoods and are the smallest geography at which much of the data employed by the LSRI approach are available. It is important to recognize, however, the tradeoff that exists between the granularity of an analysis and the level of error associated with sma ll-geography datasets: The smaller the unit of analysis, the larger the error. Much of the data for the present analysis is derived from the U.S. Census American Community Survey (ACS ), which often has substantial margins of error. The downsides of using a dataset with such high levels of error are welldocumented (for a recent review, see Spielman & Sin gleton, 2015). While the margin of 1 CBSAs defined by the U.S. Census Bureau in 2014 ar e used in the present analysis.

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Page 79 error inherent to ACS data is certainly a concern o f which analysts should be aware, it is considered to be tolerable when weighed against the utility of the findings generated for small geographies. Housing Tenure The LSRI approach can be used to assess affordabili ty for both homeowners and renters depending on the data used to build the mea sure. However, the present study focuses exclusively on renters for several reasons. First, renters face the largest affordability challenges in U.S. metropolitan areas. In 2014, 24percent of all renter households spent more than half of their income on housing as compar ed to 10-percent of homeowners (Ault et al., 2015). Second, low-income households are mu ch more likely to rent their homes as compared to higher-income households (Schwartz, 201 0). Third, rising housing costs faced by home owners, while certainly a problem for those with fixed or declining incomes, may be mitigated by longer-term gains in the equity of the home. This is not the case for renters, who see no financial gains from increasing housing costs (Revington & Townsend, 2016). Finally, assessing housing costs associated with ow ner-occupied housing is much more complex than for renters and requires many assumpti ons about a householdÂ’s ability to secure a mortgage, the amount provided as a down pa yment, mortgage interest rates, and property tax deductions (Joice, 2014). The methodology presented in this chapter focuses e xclusively on unsubsidized, market-rate rental units for several reasons. Low-i ncome renters in market-rate housing are the group most vulnerable to transit-induced displa cement since they are subject to the whims of the housing market with little available i ncome to afford rising premiums. Unsubsidized rental housing also provides the vast majority of the nationÂ’s affordable housing, since only one-quarter of eligible househo lds are able to secure public rental assistance (Ault, et al., 2015). The reliance of lo wand moderate-income households on market-rate rental housing is only likely to grow a s many subsidized units reach their sunset

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Page 80 dates, which is expected to occur in record numbers in the coming years (Mueller & Steiner, 2011). Analysts wishing to include subsidized units in future analyses could do so by integrating additional data in Step 7. STEP 2: DEFINE HOUSEHOLD PROFILES As with the standard residual income approach, deve loping a LSRI measure requires defining the set of household profiles for which af fordability will be assessed. There are two dimensions involved in defining these household pro files: Household composition and household income. Define Household Composition(s) Household composition is defined based on the three key variables that have the largest influence on household expenditures: The nu mber of adults, number of children, and number of children who require childcare (if any). The goals of a particular analysis should drive how these variables are combined to create a specified set of household composition types. For example, an analyst interested in unders tanding the landscape of housing affordability for single parent households with one child would focus exclusively on households of that type. Another analyst might choo se to focus on households with young children, and would thus define a set of households based on those parameters. The goal of the present analysis is to broadly expl ore housing affordability across a wide swath of lowand moderate-income households. I therefore define a set of 12 theoretical household compositions, each with eithe r one or two adults, and with zero, one, or two children. The number of children requiring c hildcare (if any) is also specified. Combining these characteristics results in the 12 h ousehold composition types identified in Table 5.1 . Of course, households with more than two adults a nd/or more than two children could also be included if an analyst wished to unde rstand housing affordability for larger families.

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Page 81 Table 5.1. Household compositions included in the p resent analysis Household composition types children adult(s) in childcare not in childcare Single adult, no children 1 0 Single adult, 1 child (1 in childcare) 1 0 1 Single adult, 1 child (not in childcare) 1 1 0 Single adult, 2 children (both in childcare) 1 2 0 Single adult, 2 children (1 in childcare) 1 1 1 Single adult, 2 children (not in childcare) 1 0 2 Two adults, no children 2 Two adults, 1 child (1 in childcare) 2 1 0 Two adults, 1 child (not in childcare) 2 0 1 Two adults, 2 children (both in childcare) 2 2 0 Two adults, 2 children (1 in childcare) 2 1 1 Two adults, 2 children (not in childcare) 2 0 2 Specify Household Income Level(s) Defining household profiles also requires specifyin g the income level(s) at which affordability will be assessed. The goals of the an alysis again drive this decision. Income levels could be defined as a percent of area median income (AMI), as is commonly done in affordability analyses (e.g. 60% AMI). Area median income is calculated by the U.S. Census Bureau for Metropolitan Statistical Area (MSA) geog raphies, which are comprised of a collection of counties that have a high degree of s ocial and economic integration (U.S. Census Bureau, 2010). An analyst might also elect t o focus on specific thresholds of income (e.g. $40,000 to $60,000). Or, an analyst might def ine income levels based on details about a theoretical household in a specific line of work (e.g. a two-adult household headed by a nursing assistant making $12.50/hour for 40 hours/w eek and a unionized welder making $25/hour for 35 hours/week). Because the present analysis aims to understand lan dscapes of affordability for a broad spectrum of lowand moderate-income households, LS RI measures are constructed for five income levels, each roughly corresponding to partic ular HUD designations. HUD defines low-income households based on a percent of AMI adj usted up or down based on

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Page 82 household size. Less than 50-percent of AMI is cons idered “very low income.” Between 50percent and 80-percent AMI is defined as “low incom e.” “Middle income” households are those earning between 80and 100-percent of AMI, w hile those earning more than 100percent are considered “high income” (U.S. Departme nt of Housing and Urban Development, 2014). Based on these thresholds, I de velop LSRI measures that assess affordability at 30-, 50-, 80-, and 100-percent of AMI. I also develop measures of affordability for households earning 120-percent AMI in order to address the circumstances of ‘workforce’ households, which are commonly defined as those earning 120-percent AMI or less (Ault, et al., 2015). Table 5.2 summarizes the five household income levels as the y apply to the Denver metro, which in 2014 had an AMI of $64,2062. Table 5.2. Household income levels analyzed (Denver ) Household income as percent of AMI Annual household income Monthly household income* 30% AMI $19,262 $1,610 50% AMI $32,103 $2,680 80% AMI $51,365 $4,280 100% AMI $64,206 $5,350 120% AMI $77,047 $6,420 *Rounded to nearest tenth Combining each of the 12 household composition type s defined in the above section with the five income levels results in a total of 6 0 household profiles. While this extensive number of profiles is appropriate for the present a nalysis given the goal of broadly understanding affordability among lowand moderate -income households, practitioners wishing to employ the LSRI approach could define fa r fewer (or more) as is necessary for the specific aims of their research. 2 For this analysis, data on area median income is c ollected for each Metropolitan Statistical Area (MSA) from Table B19013 of the 2010-2014 American C ommunity Survey (ACS) Five-Year Estimates. Reported values are in 2014 adjusted dol lars.

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Page 83 STEP 3: CALCULATE ESTIMATED NON-HOUSING AND NON-TRA NSPORTATION COSTS Once assumptions have been specified and household profiles have been defined, the analyst proceeds to constructing the LSRI measu re. The initial step in this process involves specifying costs for all the essential goo ds and services required to meet a basic standard of living, except for those associated wit h housing and transportation. These are referred to as ‘non-H+T costs.’ Defining what const itutes a ‘basic’ standard of living requires normative judgement about the conditions that are a cceptable to a particular society at a specific point in time (Stone, 2006). Most empirica l research employing a residual income approach in the U.S. context uses the ‘lower-budget ’ standards defined by U.S. Bureau of Labor Statistics (BLS) to identify the ‘basket’ of non-housing goods and services required to maintain a basic standard of living, including: Foo d; Medical expenses; Childcare (if applicable); Transportation; Clothing; Other goods required for basic household operations; and Local, state, and federal taxes. A variety of data sources are available to identify non-H+T costs. Three primary resources provide data for non-H+T costs: The Massa chusetts Institute of Technology (MIT) Living Wage Calculator3, the University of Washington (UW) Center for Wome n’s Welfare Self-Sufficiency Standard4, and the Economic Policy Institute (EPI) Family Bu dget Calculator.5 All three of these present household-level expendi ture data for a range of household types in a user-friendly interface that i s easily accessible for researchers, 3 The Living Wage Calculator was created and is main tained by Dr. Amy K. Glasmeier, Professor of Economic Geography and Regional Planning at Massach usetts Institute of Technology (MIT). It is available for all 50 states and is updated annually and can be found at: http://livingwage.mit.edu/ . 4 The Self-Sufficiency Standard was created by Dr. D iana Pearce, Director of the Center for Women’s Welfare at the University of Washington. Data is av ailable for 38 states and is current to 2014 for most, but not all, states It can be found at: http://www.selfsufficiencystandard.org/ . 5 The Family Budget Calculator is maintained by the Economic Policy Institute, a not-for-profit, nonpartisan think tank focused on research related to economic policies that address the needs of lowand middle-income workers. The Family Budget Calcul ator is available for all 50 states and can be found here: http://www.epi.org/resources/budget/ .

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Page 84 practitioners, and members of the public. Data on n on-housing expenditures are most often sourced from U.S. BLS Consumer Expenditure (CE) Sur vey, a dataset released annually based on findings from interviews and diary surveys that ask American consumers about details related to their household characteristics, expenditures, and income (U.S. Bureau of Labor Statistics, 2016). Of the three resources that aggregate data on house hold expenditures, the MIT Living Wage Calculator (LWC) offers the most robust datase t that is available for all case metros and was therefore selected for primary use in the p resent analysis. While the UW SelfSufficiency Standard also offers a comprehensive da taset, it does not provide standardized data across all case metros and so is not appropria te for cross-case comparisons. The EPI Family Budget Calculator provides consistent data a cross all U.S. metros, but is less robust than the other two sources. Analysts may find each of these resources to have different advantages depending on the specific aims of the re search. The MIT LWC is designed to be used in identifying t he minimum hourly wage required to sustain a basic standard of living across all metro s of the U.S., assuming a standard 40 hours per week of work. The resulting ‘living wage’ calculation therefore “draws a very fine line between the financial independence of the work ing poor and the need to seek out public assistance or suffer consistent and severe housing and food insecurity” (Glasmeier, 2014:2). The LWC does not include any luxuries that moderate and high-income households may be accustomed to – for example, meals in restaurants, entertainment, and travel, nor does it allow for any savings for retirement or for large c apital expenses like homes or cars. As a result, the LWC is well-suited for the present anal ysis, which aims to identify the costs associated with a basic standard of living. Details associated with each of the five non-H+T costs – childcare, food, medical, other basic neces sities, and taxes – are discussed below.

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Page 85 Estimate Childcare Costs Data obtained from Child Care Aware6, a national association of child care resource agencies, is used to compute childcare costs for ea ch of the case metros. Childcare costs are also reported in the LWC from the same source, although computations are simplified to a greater extent than is done in the present study. Child Care Aware documents the average costs of legally-operating childcare centers and fa mily home care on an annual basis, as reported by market surveys conducted by child care resources and referral state networks (Child Care Aware of America, 2014). The data used in the present analysis represents 2013 costs, which are then adjusted to 2014 dollars using the U.S. BLS Consumer Price Index (CPI) inflation calculator7. Child Care Aware reports childcare costs for chil dren in three age groups: Infants and toddlers (0 to 36 mon ths), pre-school (4-year olds), and school age (after-school care for children 5-years and older). The organization reports costs separately for licensed ‘childcare centers’ (tradit ional daycare centers) and for smaller-scale childcare centers operated from an individual’s hom e (‘home care’), which tend to be less expensive than daycare centers. Several operations were conducted to compute childc are costs in the present study. First, the least expensive option (childcare center or home care) is employed for each state based on the assumption that lowand moderate-inco me households are likely to seek the least costly childcare as possible. The least expen sive childcare costs for the two youngest age groups – infants/toddlers and preschoolers – ar e then averaged and inflated to 2014 dollars to arrive at an estimated cost per child. T otal childcare costs for each household type are calculated based on the number of children requ iring childcare. Childcare costs vary quite significantly across the case metros, with the annual cost ranging from $5,700 per child in Salt Lake City to $8,660 per child in Seattle. As shown in 6 http://childcareaware.org/ 7 http://www.bls.gov/data/inflation_calculator.htm

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Page 86 Table 5.3 , childcare costs are nearly as high in the Denver metro ($8,640 per child) as they are in Seattle. Appendix A outlines the estimated cost of childcare per child for each of the states in which the eight case metros are located. Table 5.3. Estimated childcare costs by number of c hildren requiring childcare (Denver) Number of children requiring childcare Childcare costs Annual Monthly* 1 child $8,638 $720 2 children $17,276 $1,440 *Rounded to nearest tenth Source: Childcare Aware of America, 2014 Estimated Food Costs Food costs are sourced directly from the LWC, which reports regionally-adjusted data from the United States Department of Agricultu reÂ’s (USDA) official low-cost food plan for the period of July 2013 through June 2014. The second least expensive food plan (of four) is used, which assumes that households prepar e all meals and snacks in the home using lower-cost foods.8 Food cost estimates vary by household type, with t he assumption that adults consume more than older children and th at older children consume more than younger children (Glasmeier, 2014).9 Table 5.4 summarizes these costs for each the 12 household types for the Denver metro. Appendix A provides the same data for all eight case metros. 8 Values from the USDA low-cost food plan used in LW CÂ’s food cost estimates are available here: http://www.cnpp.usda.gov/sites/default/files/usda_f ood_plans_cost_of_food/CostofFoodJun2014.pdf . 9 Additional details about the LWC food cost estimat es can be found in the Living Wage Calculator UserÂ’s Guide / Technical Notes (2014 Update) (Glasmeier, 2014)

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Page 87 Table 5.4. Estimated food costs by household compos ition type (Denver) Household type Food costs Annual Monthly* Single adult, no children $3,607 $300 Single adult, 1 child $5,319 $440 Single adult, 2 children $8,002 $670 Two adults, no children $6,612 $550 Two adults, 1 child $8,234 $690 Two adults, 2 children $10,627 $890 *Rounded to nearest tenth Source: MIT Living Wage Calculator (Glasmeier, 2014 ) Estimated Medical Costs As with food costs, medical and health-related expe nses are sourced directly from the LWC. Medical costs reported by the LWC represen t the sum of four expenses: Health insurance costs associated with employer-sponsored plans; Medical services; Pharmaceutical drugs; and Medical supplies. Data fo r these expenses come from two primary sources. First, the Health Insurance Compon ent Analytical Tool (MESPnet/IC)10 developed by the Agency for Healthcare Research and Quality is used to compute employer-sponsored health insurance costs. Health c are costs are very difficult to estimate due to a range of individualand household variabl es that influence the need for health care expenditures and the extent to which those expendit ures are covered by a household’s insurance. Specifying medical expenses thus require s making assumptions about the general health of household members and the presenc e of employer-provided health insurance, which may not reflect reality. However, these assumptions are justified since it allows for standardized data that can be applied ac ross households and across metros.11 Data for the remaining three medical expenses – med ical services, pharmaceutical drugs, and medical supplies – are sourced by the LW C from the 2014 U.S. BLS CE Survey then adjusted for regional differences and inflated to 2014 dollars using the CPI inflation 10 Available at http://meps.ahrq.gov/mepsweb/data_stats/MEPSnetIC.j sp . 11 See Glasmeier (2014) for more details about the as sumptions and methods underlying the LWC medical cost estimates.

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Page 88 calculator. Table 5.5 summarizes estimated medical costs by household ty pe for the Denver metro. Appendix A provides the same data for all eight case metros. Table 5.5. Estimated medical costs by household com position type (Denver) Household type Medical costs Annual Monthly* Single adult, no children $2,172 $180 Single adult, 1 child $6,167 $510 Single adult, 2 children $5,956 $500 Two adults, no children $4,561 $380 Two adults, 1 child $5,956 $500 Two adults, 2 children $6,020 $500 *Rounded to nearest tenth Source: MIT Living Wage Calculator (Glasmeier, 2014 ) Estimated Costs for Other Basic Necessities In addition to food and medical costs, a LSRI appro ach accounts for other necessities required to sustain a basic standard of living. The present analysis again uses data sourced directly from the LWC to account for t hese expenses, which constitutes the sum of expenditures from five categories of goods i ncluded in the 2014 BLS CE Survey: Apparel, housekeeping supplies, personal care, read ing, and miscellaneous. The sum of these expenditures is then adjusted for regional di fferences and inflated to 2014 dollars using the CPI calculator. Table 5.6 summarizes estimated costs associated with other b asic necessities by household type for the Denver metro. Appendix A provides the same data for all eight case metros.

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Page 89 Table 5.6. Estimated costs associated with other ba sic necessities by household composition type (Denver) Household type Other basic necessities Annual Monthly* Single adult, no children $2,284 $190 Single adult, 1 child $3,971 $330 Single adult, 2 children $4,344 $360 Two adults, no children $3,971 $330 Two adults, 1 child $4,344 $360 Two adults, 2 children $5,250 $440 *Rounded to nearest tenth Source: MIT Living Wage Calculator (Glasmeier, 2014 ) Estimated Costs of Taxes Most ratio and location affordability approaches us e pre-tax income to assess housing affordability, resulting in a measure that does not accurately represent the financial circumstances of households (Stone, 2006). As with the standard residual income approach, a LSRI measure corrects for this shortcoming by cal culating state and federal payroll and income taxes as a percent of total income. The pres ent analysis employs several sources to do so, although other analysts could elect to use L WC data alone to similar effect. I first compute payroll taxes (combined Social Security and Medicare taxes) using the rate specified in the Federal Insurance Contributions Ac t for 2014 (6.2%). I then identify state income tax rates using a report of state individual income tax rates and brackets for 2014 published by the non-partisan Tax Foundation.12 In states with a graduated income tax, the appropriate tax rate is identified for each househo ld income level being analyzed (in the case of the present analysis, 30-, 50-, 80-, 100-, and 120-percent AMI). Finally, I apply the average federal income rate pa id by a median-income four-person family (5.32%, as specified by the Tax Policy Cente r of the Brookings Institution and Urban Institute13) which includes the effects of the Earned Income T ax Credit, Child Tax Credit, and Making Work Pay Credit enacted in the American Reco very and Reinvestment Act of 2009. 12 http://taxfoundation.org/article/state-individualincome-tax-rates-and-brackets-2015 13 http://www.taxpolicycenter.org/index.cfm

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Page 90 While these assumptions may not be representative o f the financial circumstances of smaller households, a 5.32-percent tax rate if anyt hing, under estimates taxes paid and therefore total non-H+T costs. Sales taxes are assu med to be included in costs estimated for other basic necessities. Table 5.7 summarizes taxes paid by household income level fo r the Denver metro. Appendix A outlines payroll, state income, and federal income tax rates for all eight case metros by household income. Table 5.7. Estimated cost of taxes by household inc ome (Denver) Household income (all household types) Taxes Annual Monthly* 30% AMI ($19,262/year) $3,111 $260 50% AMI ($32,103/year) $5,185 $430 80% AMI ($51,365/year) $8,295 $690 100% AMI ($64,206/year) $10,369 $860 120% AMI ($77,047/year) $12,443 $1,040 *Rounded to nearest tenth Source: Tax Policy Center of the Brookings Institut ion and Urban Institute Total Estimated Non-Housing and Non-Transportation Costs The final task under Step 3 is to sum the five elem ents outlined above – childcare, food, medical expenses, other basic necessities, an d taxes – to arrive at a total ‘non-H+T cost’ for each of household profiles. Non-H+T costs vary by household type and household income. Therefore, each of the 60 possible househol d profiles has unique non-H+T costs. Table 5.8 provides information on non-H+T costs for an examp le household profile (two adults and two children, one of whom childcare earn ing 100-percent AMI, or $64,206). As shown, households with this profile would be expect ed to pay $4,130 of their $5,350 monthly income on non-H+T costs.

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Page 91 Table 5.8. Total non-H+T costs for an example house hold type (Denver) Household type: Two adults, two children (one in ch ildcare) Household income: 100% AMI ($64,206) Non-H+T costs Costs (annual) Costs (monthly) Childcare $17,276 $1,440 Food $10,627 $890 Medical $6,020 $500 Other necessities $5,250 $440 Taxes $10,369 $860 Total non-H+T costs (estimated) $49,542 $4,130 *Rounded to nearest tenth STEP 4: CALCULATE HOUSING AND TRANSPORTATION BUDGET S Next, non-H+T costs are subtracted from household i ncome to arrive at the estimated amount of income that remains available f or housing and transportation costs (referred to as the ‘H+T budget’). This operation i s completed using monthly and/or annual income and the non-H+T costs associated with each h ousehold profile calculated in Step 3. Table 5.9 demonstrates this calculation for an example house hold profile (a median income household with two adults and two children, one of whom requires childcare). Table 5.9. Estimated H+T budget for an example hous ehold profile (Denver) Household type: Two adults, two children (one in ch ildcare) Household income: 100% AMI ($64,206) Monthly Expenses Monthly Budget Household income $5,350 Non-H+T costs (estimated) Childcare $720 Food $890 Medical $500 Other necessities $440 Taxes $860 Total non-H+T costs (estimated) $3,410 H+T budget (estimated) $1,940 *Rounded to nearest tenth

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Page 92 STEP 5: IDENTIFY ESTIMATED TRANSPORTATION COSTS In Step 5, transportation costs are estimated for a ll block groups in the metro, by household profile. It is here that the LSRI approac h breaks with a standard residual income approach, which assumes that transportation costs a re static for all households of a particular profile regardless of the householdÂ’s re sidential location. In other words, the standard residual income approach contends that a h ousehold residing in the central city is expected to spend an equal amount on transportation as a household with the same composition and income residing in a distant area o f the suburbs. In fact, ample research demonstrates that household s residing in areas that require heavy reliance on private autos are likely to incur much higher transportation costs as compared to households living in areas that support more limited car use. For example, the U.S. Department of Housing and Urban Development (H UD) Location Affordability Index (LAI)14 indicates that annual transportation costs for a r enter household with two adults and two children earning 100-percent AMI range from $7, 010 to $15,690 (in 2014 dollars) across Census block groups in the Denver metro. The LWC, w hich follows a standard residual income approach and therefore considers transportat ion costs to be static, estimates annual costs for the same household to be $9,970 (2014 dol lars). This suggests that use of the static LWC estimates would under estimate annual transportation costs for some block groups by up to $5,500 per year. Conversely, LWC da ta could also over estimate annual transportation costs by nearly $3,000 in some locat ions These figures make it clear that a more nuanced acc ounting of the spatial variations of transportation costs is required to ensure that housing affordability is accurately represented. This issue lies at the heart of the LS RI approach: By estimating transportation costs at the block group level across the region, t he LSRI provides a more accurate 14 Data available through the HUD Location Affordabil ity Portal at http://www.locationaffordability.info/lai.aspx

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Page 93 accounting of the financial realities households fa ce depending on where they live in the region, thus resulting in a more robust measure of housing affordability. In addition to varying across space, transportation costs also vary widely among households with different compositions. For example , HUD LAI data identifies the average annual transportation costs for a renter household with one adult and no children in the Denver CBSA to be $5,610, while the annual costs fo r a renter household with two adults and two children is reported to be nearly double th at ($10,610). The LSRI approach accounts for these differences by estimating transp ortation costs for each theoretical household profile separately. The resulting dataset estimates transportation costs for six household types – single adult with no children, si ngle adult with one child, single adult with two children, two adults with no children, two adul ts with one child, and two adults with two children – for each block group within the metro. W hile the present analysis calculates estimated costs at the block group level in order t o develop the most detailed data possible, other analysts might elect to use a less-granular l evel of analysis (for example, Census tracts). Data Sources The LSRI approach detailed below uses both HUD LAI data at the block group level and LWC data at the regional level to develop trans portation cost estimates that reflect variations across space, as well as variations acro ss household with different compositions. HUD’s Location Affordability Portal (which reports the LAI) was originally developed to encourage a comprehensive view of housing affordabi lity by making transparent the tradeoffs that exist between low housing costs and high transportation costs (and vice versa). The LAI does this by modeling housing and t ransportation costs for eight household profiles using a structural equation model that ass esses the effect of the built environment on a variety of dependent variables at the block gr oup level including vehicle miles traveled, auto ownership, the percent of residents using tran sit for their journey to work, and housing

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Page 94 costs (gross rent and selected monthly costs for ho me owners). Eighteen predictor variables are used to estimate the models, including various dimensions of residential and employment density, block density, employment acces sibility, proportion of renters, and household income. Transportation costs are then est imated based on the model outputs (autos per household, annual vehicle miles traveled , and percent of commute trips made by transit) and based on costs associated with both au to and transit travel (Haas et al., 2016). Estimated transportation costs reflect all dimensio ns of car ownership and operation including the purchase and financing of a vehicle(s ), regular maintenance, insurance coverage, and fuel.15 The HUD LAI reports the results of the model for ei ght household profiles (outlined in Table 5.10 ), which vary on household income (as percent of AM I for the metropolitan statistical area), household size, and the number o f commuters16. The resulting LAI data reports estimated H+T costs for each household prof ile, by block group. Raw LAI data is available for download at the HUD Location Affordab ility Portal at various levels of geography, from block group to CBSA17. The LAI data is missing data for a handful of blo ck groups in the case metros. In these instances, bloc k groups with missing data were eliminated from the analysis. 15 Detailed methodology about variables and model spe cification can be found in the document Data and Methodology: Location Affordability Index Version 2.0 available on the HUD Location Affordability Portal: http://www.locationaffordability.info/LAPMethodsV2. pdf 16 Ibid. 17 http://www.locationaffordability.info/lai.aspx?url= download.php

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Page 95 Table 5.10. HUD Location Affordability Index househ old profiles Location Affordability Index household profile Household income Household size Number of commuters “Median-income family” 100% AMI 4 2 “Very low-income individual” Federal poverty line 1 1 “Working individual” 50% AMI 1 1 “Single professional” 135% AMI 1 1 “Retired couple” 80% AMI 2 0 “Single-parent family” 50% AMI 3 1 “Moderate-income family” 80% AMI 3 1 “Dual-professional family” 150% AMI 4 2 Source: U.S. Department of Housing and Urban Develo pment, 2015 Despite its usefulness, the LAI is often criticized for its use of aggregate (versus household-level) data. Indeed, a recent study compa ring the LAI to address-level data in Los Angeles County, CA found the LAI consistently r eported higher housing and transportation costs than data modeled with the mor e-granular data (Salon et al., 2016). While the LSRI approach would certainly be improved by incorporating transportation cost estimates based on household-level data, such data is not available on a widespread basis. Another common criticism stems from the LAI’s relia nce on data from the U.S. Census ACS which suffers from considerable margins of error. T he LAI does not disclose the level of error associated with the model, thus making it imp ossible to assess the accuracy of the resulting data (Tighe & Ganning, 2016). Despite the se shortcomings, the LAI remains the most comprehensive and dataset estimating transport ation costs that is readily-available to practitioners. The LSRI approach could easily be up dated if more robust models are developed to address the shortcomings of the LAI. The LAI is also limited by its focus on just eight household profiles, which are not necessarily consistent with the household profiles selected for analysis as part of a LSRI approach. This is the case in the present analysis: Only seven of the 12 LSRI household types are roughly consistent with LAI household pro files. In order to address this issue, I use data from the LWC to develop a multiplier that I th en apply to LAI data such that estimated

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Page 96 transportation costs are ‘right-sized’ to the appro priate household characteristics. This process is described below for each of the househol d types defined in the present analysis. Table 5.11 summarizes the LAI household profiles and multipli ers used to estimate transportation costs for the Denver metro. The same information for each of the remaining case metros can be found in Appendix B . Table 5.11. LAI household profiles and multipliers used to calculate estimated transportation costs, by household type (Denver) LSRI household composition Corresponding HUD LAI ho usehold profile Multiplier* Single adult, no children “Working individual” Single adult, no children (50% AMI) 1.0 Single adult, 1 child “Single-parent family” Single adult, 2 children (50% AMI) 0.868 Single adult, 2 children “Single-parent family” Single adult, 2 children (50% AMI) 1.0 Two adults, no children “Moderate income family” Two adults, 1 child (80% AMI) 0.868 Two adults, 1 child “Median income family” Two adults, 2 children (100% AMI) 0.854 Two adults, 2 children “Median income family” Two adults, 2 children (100% AMI) 1.0 *Multiplier developed using LWC data, as described in below narrative Household type: Single adult, no children The LAI “working individual” household profile is r oughly consistent with this LSRI household type. Both households are composed of a single adult with no children. Therefore, the LAI estimates are used without any f urther calculation (i.e. a multiplier of 1.0 is used). Household type: Single adult, one child The LAI “single-parent family” household profile, c omposed of one adult and two children, is used as the basis for this LSRI househ old type. Because the LAI data assumes two children, there is a need to ‘right-size’ the d ata so that it is applicable to a single-parent family with only one child. To do so, estimated transportation costs fr om the LWC are identified for households with one adult and one ch ild, and households with one adult and

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Page 97 two children. The ratio of these estimates is then calculated to develop a ‘multiplier’ using the following formula: multiplier = LWC (1 adult, 1 child) LWC (1 adult, 2 children) The multiplier is then applied to the LAI estimates for the “single-parent family” household profile according to the below formula to arrive at estimated transportation costs for the LSRI measure: LSRI transportation costs for single adult, one child household = (multiplier)* (LAI transportation costs for “single-parent family”) For example, the LWC estimates annual transportatio n costs in the Denver metro for a household with one adult and one child to be $7,3 82 and $8,509 for a household with one adult and two children. The multiplier is therefore calculated t o be $7,382 divided by $8,509, or a value of 0.868. LAI estimates for the “singleparent family” profile (composed of one adult and two children) are then multiplied by 0.86 8 to estimate LSRI transportation costs for households with one adult and one child. This calculation is completed for every blo ck group within each of the eight case metros. Household type: Single adult, two children The LAI “single-parent family” household profile is roughly consistent with this LSRI household type: Both households are composed of a s ingle adult with two children. Therefore, the LAI estimates are used without any f urther calculation (i.e., a multiplier of 1.0 is used). Household type: Two adults, no children The LAI “moderate income family” household profile, composed of two adults and one child, is used as the basis for this LSRI house hold type. Because the LAI data assumes one child, there is a need to ‘right-size’ the data so that it is applicable to a two adult household with no children. To do so, estimated transportation costs from the LWC are

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Page 98 identified for households with two adults and no ch ildren, and for households with two adults and one child. The ‘multiplier’ is then calculated for the ratio of these estimates following the below formula: multiplier = LWC (2 adults, 0 children) LWC (2 adult, 1 child) The multiplier is then applied to the LAI estimates for the “moderate income family” household profile according to the below formula to arrive at estimated transportation costs for the LSRI measure: LSRI transportation costs for two adult, no children household = (multiplier)* (LAI transportation costs for “moderate income family”) For example, LWC data estimates annual transportati on costs in the Denver metro for a household with two adults and no children to be $7,382 and $8,509 for a household with two adults and one child. The multiplier is therefore calculated to b e $7,382 divided by $8,509, or a value of 0.868. LAI estimates for the “moderate income family” profile (composed of two adults and one child) are then mul tiplied by 0.868 to estimate LSRI transportation costs for households with two adults and no children. This calculation is completed for every block group within each of the eight case metros. Household type: Two adults, one child The LAI “median income family” household profile, c omposed of two adults and two children, is used as the basis for this LSRI househ old type. Because the LAI data assumes two children, there is a need to ‘right-size’ the d ata so that it is applicable to a two adult household with one child. To do so, estimated transportation costs fro m the LWC are identified for households with two adults and one c hild, and for households with two adults and two children. The ‘multiplier’ is then calculated for the ratio of these estimates following the below formula: multiplier = LWC (2 adults, 1 child) LWC (2 adults, 2 children)

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Page 99 The multiplier is then applied to the LAI estimates for the “median income family” household profile according to the below formula to arrive at estimated transportation costs for the LSRI measure: LSRI transportation costs for two adult, one child household = (multiplier)* (LAI transportation costs for “median income family”) For example, LWC data estimates annual transportati on costs in the Denver metro for a household with two adults and one child to be $8,509 and $9,970 for a household with two adults and two children. The multiplier is therefore calculated t o be $8,509 divided by $9,970, or a value of 0.8535. LAI estimates for the “median income family” profile (composed of two adults and two children) are then multiplied by 0.8535 to estimate LSRI transportation costs for households with two adults and one child. This calculation is completed for every block group within each of the eight case metros. Household type: Two adults, two children The LAI “median income family” household profile is roughly consistent with this LSRI household type: Both households are composed o f two adults with two children. Therefore, the LAI estimates are used without any f urther calculation (i.e., a multiplier of 1.0 is used). Summary of Estimated Transportation Costs The result of the above calculations is estimated t ransportation costs for each theoretical household profile, for every block grou p in the metro. Table 5.12 demonstrates this calculation for two example households, each w ith the same profile (a median income household with two adults and two children, one of whom requires childcare), but residing in two different block groups. In this example, “block group A” is located in an inner-ring suburb to the west of Denver. Estimated LSRI transportatio n costs for a household with two adults and two children living in this location are approx imately $920 per month. Meanwhile,

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Page 100 estimated LSRI transportation costs for “block grou p B” located in a central neighborhood of Denver are much lower ($380 per month) than those f or block group A. Calculations for these two block groups highlight the large range in estimated transportation costs that can exist for the same household profile depending on w here it resides within the metro. Table 5.12. Estimated monthly transportation costs for two example households residing in block groups A and B (Denver) Household type: Two adults, two children (one in ch ildcare) Household income: 100% AMI ($64,206) Monthly Budget* Block Group A Block Group B Household income $5,350 Same as A Non-H+T costs (estimated) Childcare ($720) Same as A Food ($890) Same as A Medical ($500) Same as A Other necessities ($440) Same as A Taxes ($860) Same as A H+T budget (estimated) $1,940 Same as A Transportation costs (estimated) ($920) ($380) *Rounded to nearest tenth Figure 5.3 below summarizes the minimum, median, and maximum estimated transportation costs for all household types, furth er underscoring the differences in transportation costs that exist between households with different compositions and residential locations. For example, a household wit h two adults and two children is expected to spend nearly double the amount of income on tran sportation as compared to household composed of a single adult with no children ($574 a nd $1,016, respectively). Appendix B contains the same data for household profiles in al l eight case metros.

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Page 101 Figure 5.3. Estimated monthly transportation costs by household type (Denver) It may also be useful to examine the spatial distri bution of estimated transportation costs across the metro. Figure 5.4 depicts estimated transportation costs across the D enver metro for a household with two adults and two children, calcula ted using a LSRI approach. As expected, estimated transportation costs are highest at the o uter-reaches of the metro and lowest in the city of DenverÂ’s central core. For example, blo ck group A located in a suburban county has estimated transportation costs in the highest q uartile (approximately $920/month), while estimated costs for the same household located in a n area of the central city (block group B) are in the lowest quartile (approximately $380/mont h).

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Page 102 Figure 5.4. Estimated monthly transportation costs for an example household profile (Denver)

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Page 103 STEP 6: CALCULATE ESTIMATED HOUSING BUDGETS After establishing estimated transportation costs f or all block groups (or other defined geographic unit) by household profile, the analyst is then able to calculate the total funds that remain available for housing. This ‘housing bu dget’ is one of two measures generated by a LSRI approach. A household’s housing budget re presents the upper limit it can afford to pay for housing while also covering its basic ne cessities. Housing budgets are calculated for each household profile given its particular com position, income, and residential location using the following formula: housing budget for household profile X located in block group Y = household income for household profile X non-H+T costs for household profile X estimated transportation costs for household profile X located in block group Y The result of the above calculation is a comprehens ive dataset of the estimated housing budgets for all 12 theoretical household pr ofiles, at each of the five household income levels, for each block group in the metro. Table 5.13 demonstrates this calculation for two households of the same profile, highlightin g the large variation in housing budgets for households with the same characteristics and financ ial circumstances, but residing in different areas of the metro. In this example, a me dian-income household with two adults and two children (one of whom requires childcare) l ocated in an inner-ring suburb (block group A) can afford $1,020 per month in housing cos ts. The same household residing in a central neighborhood of Denver (block group B) woul d have a housing budget of over $500 more than block group A ($1,560 per month).

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Page 104 Table 5.13. Estimated housing budgets for two examp le households with the same profile residing in block groups “A” and “B” (Denve r) Household type: Two adults, two children (one in ch ildcare) Household income: 100% AMI ($64,206) Monthly Budget* Block Group A Block Group B Household income $5,350 Same as A Non-H+T costs (estimated) Childcare ($720) Same as A Food ($890) Same as A Medical ($500) Same as A Other necessities ($440) Same as A Taxes ($860) Same as A H+T budget (estimated) $1,940 Same as A Transportation costs (estimated) ($920) ($380) Housing budget (estimated) $1,020 $1,560 *Rounded to nearest tenth A summary of the housing budget data resulting from calculations completed for all theoretical household profiles the Denver metro are displayed in Figure 5.5 . Many lowincome and some moderate-income households (those m arked by an “x”) have housing budgets at or below zero; that is, their income is consumed entirely by the non-housing expenditures required to maintain a basic standard of living, leaving no remaining funds available for housing. The figure also highlights t he effect of household composition, and in particular the number of children requiring childca re, on housing budgets. Table 7.1 (Chapter 7) provides the same data for selected hou sehold profiles in all eight case metros.

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Page 105 Single adult, no children Two adults, no children 30% 50% 80% 100% 120% Single adult, one child (in childcare) Two adults, one child (in childcare) 30% 50% 80% 100% 120% Single adult, one child ( not in childcare) Two adults, one child ( not in childcare) 30% 50% 80% 100% 120% Single adult, two children ( both in childcare) Two adults, two children ( both in childcare) 30% 50% 80% 100% 120% Single adult, two children (1 in childcare) Two adults, two children (1 in childcare) 30% 50% 80% 100% 120% Single adult, two children ( none in childcare) Two adults, two children ( none in childcare) 30% 50% 80% 100% 120% Range (minimum, median, maximum) of monthly housing budget (2014$) Figure 5.5. Estimated housing budgets by household profile (Denver)

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Page 106 Depending on the number of household profiles being analyzed, housing budget data may be too unwieldy to effectively present in tabular or chart form. Displaying housing budgets spatially, as is done in Figure 5.6 for an example household profile in the Denver metro, may therefore be most useful. The figure und erscores that a theoretical household of this profile living in central areas of the city of Denver generally has more income available for housing as compared to the same household livin g in farther-reaches of the metro. Whether housing units are actually available within the housing budgets of lowand moderate-income households in either of these locat ions remains an open question, which is addressed in the final step of the LSRI methodol ogy. Figure 5.6. Estimated monthly housing budget for ex ample household profile (Denver)

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Page 107 STEP 7: CALCULATE ESTIMATED SUPPLIES OF AFFORDABLE HOUSING The housing budgets calculated in Step 6 shed light on one element of the demand that exists for housing at particular price points. Because housing affordability is a market outcome, accurately assessing it also requires that we analyze the supply of housing at those same price points. The present section outlin es the steps involved in developing a LSRI measure of supply by calculating the number of housing units that are priced such that they are affordable within the housing budgets calc ulated in Step 6. Assessing the supply of affordable rental housing first requires identifyin g the total number of rental units that are affordable to each of the defined household profile s within a particular block group (or other geographic unit being analyzed). The number of affo rdable rental units can then be summed across a set of block groups – for example, all blo ck groups within a metro, or all block groups located within a specified distance of a par ticular amenity. The number of affordable rental units can also be calculated as the percent of a metro’s total rental units in order to provide a standardized measure that can be compared to other household profiles, and to other metros. This latter approach is taken in the present analysis. Data Sources A variety of data sources can be used in identifyin g the number of housing units available at particular prices points within a spec ified geographic unit. The U.S. Census American Community Survey (ACS), which releases two datasets annually based on sample data (the One-Year and Five-Year Estimates), is the most common and accessible of these sources. American Community Survey B25056 (Contract Rent), B025061 (Rent Asked), and Tables B25093 (Gross Rent) all report housing costs for renter-occupied units down to the block group level. ‘Contract Rent’ is the monthly a greed-upon rent that is paid for occupied units, not including any utilities, furnishings, fe es, or services that may be provided. ‘Rent Asked’ provides the same information for vacant uni ts. ‘Gross Rent’ is the contract rent for occupied units, plus the estimated average monthly cost of utilities. The present analysis

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Page 108 combines data from Tables B25056 (Contract Rent) an d B025061 (Rent Asked) in order to account for both occupied and vacant rental units. Housing costs for owner-occupied units are reported in Table B25094 (“Selected Monthly Own er Costs”). Five-Year Estimate data is the most reliable of the two ACS datasets, and is m ost appropriate for use with very small populations (such as block groups).18 The present study therefore uses data from the ACS 2010-14 Five-Year Estimates, which represent data c ollected between 2010 and 2014 reported in 2014 dollars. Several other sources provide data on the number of renterand/or owner-occupied housing units available at particular price points, including local Multiple Listing Service (MLS) data, on-line real estate resources such as Z illow19 and Trulia,20 and on-line rental listings such as Craigslist21 and Adobo.22 Although data from these sources may be appropriate depending on the goals of a particular analysis, all present challenges. For instance, Zillow and MLS data are not publicly-avai lable, and can be quite expensive. MLS data is also difficult to obtain in many states. Da ta from Craigslist and other on-line listings are typically available to the general public free of charge, but are likely to be difficult to gather and clean. In addition, these on-line resour ces are typically oriented towards a particular demographic – usually young single adult s or couples – and are therefore likely to over-represent some types of housing while under-re presenting others. Data from these sources therefore may not accurately reflect on-the -ground realities of the rental housing market. Although ACS data is often the most appropriate sou rce for renter-occupied data, it is not without its problems. The most challenging i ssue relates to the large margin of errors inherent to ACS data, particularly at small geograp hies. While this error is certainly a 18 For more details, see http://www.census.gov/programs-surveys/acs/guidance /estimates.html 19 www.zillow.com 20 www.truilia.com 21 www.craigslist.com 22 www.adobo.com

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Page 109 concern, aggregating data across larger geographies (such as the metro) helps to balance errors and minimize their effects (Spielman & Singl eton, 2015). ACS data is also limited by the rolling nature of its collection. For example, the Five-Year Estimates used in the present analysis reflect conditions that exist across five years (2010 to 2014). The resulting data therefore does not necessarily represent current co nditions accurately. Furthermore, data on Contract Rent is likely to include rents for units that have been occupied for long periods and thus may not represent going market rates. Contract Rent and Rent Asked data also do not include the cost of utilities, which may be conside rable. Taken together, these issues may result in measure that overestimate the number of a ffordable units that are available, thus understating the challenges lowand moderate-incom e households face. Data reported by the ACS is also limited by the fac t that it does not report the number of bedrooms in a rental unit, thereby making it impossible to identify the number of people who could comfortably be housed in the same unit. Furthermore, the highest rent reported in the tables is $2,000 per month, thus li miting the conclusions that can be drawn about units with gross rents higher than that amoun t. While this limitation may impede the ability to study housing affordability among higher -income household, it does not present much of an issue for the present analysis since hou sing budgets for lowand moderateincome households are likely to be lower than $2,00 0 per month in most metros. Table 5.14 outlines the categories of gross rent that are repo rted by Tables B25056 (Contract Rent) and 25061 (Rent Asked), along with the median annua l gross rent of each category.

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Page 110 Table 5.14. ACS Tables B25056 (Contract Rent) and 2 5061 (Rent Asked) categories Category Monthly gross rent (2014$)* Annual gross rent (2014$) Median annual gross rent (2014$) Lower limit Upper limit Lower limit Upper limit A $0 $99 $0 $1,188 $594 B $100 $149 $1,200 $1,788 $1,494 C $150 $199 $1,800 $2,388 $2,094 D $200 $249 $2,400 $2,988 $2,694 E $250 $299 $3,000 $3,588 $3,294 F $300 $349 $3,600 $4,188 $3,894 G $350 $399 $4,200 $4,788 $4,494 H $400 $449 $4,800 $5,388 $5,094 I $450 $499 $5,400 $5,988 $5,694 J $500 $549 $6,000 $6,588 $6,294 K $550 $599 $6,600 $7,188 $6,894 L $600 $649 $7,200 $7,788 $7,494 M $650 $699 $7,800 $8,388 $8,094 N $700 $749 $8,400 $8,988 $8,694 O $750 $799 $9,000 $9,588 $9,294 P $800 $899 $9,600 $10,788 $10,194 Q $900 $999 $10,800 $11,988 $11,394 R $1,000 $1,249 $12,000 $14,988 $13,494 S $1,250 $1,499 $15,000 $17,988 $16,494 T $1,500 $1,999 $18,000 $23,988 $20,994 U $2,000 n/a $24,000 n/a $24,000 *Tables B25056 and B25061 report monthly gross rent . All other columns are calculated by the author

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Page 111 Calculate the Estimated Number of Units Available w ithin Household Housing Budgets The present analysis uses the median value of the g ross rent categories reported in Tables B25056 and B25061 as the threshold for deter mining the number of rental units available at particular price points. To do so, the total number of units within a block group that have annual rents at or below a particular hou sing budget are summed following the below protocol: IF annual housing budget calculated in Step 6 isÂ… THEN, the number of rental units is calculated asÂ… Â…less than $594 Â…n/a (no units reported) Â…between $595 and $1,494 Â…Category A Â…between $1,495 and $2,094 Â…sum of Categories A and B Â…between $2,095 and $2,694 Â…sum of Categories A thr ough C Â…between $2,695 and $3,294 Â…sum of Categories A thr ough D Â….. Â….. Â…between $13,495 and $16,494 Â…sum of Category A thr ough R Â…between $16,495 and $20,994 Â…sum of Category A thr ough S Â…between $20,995 and $24,000 Â…sum of Category A thr ough T Â…greater than $24,001 Â…sum of Category A through U For example, if a particular household profileÂ’s an nual housing budget in a specific block group is $16,400, then the number of rental u nits that are affordable to the household is calculated as the sum of categories A through R. Similarly, the supply of housing affordable to a household with an estimated housing budget of $2,800 residing in a particular block group would be calculated as the s um of categories A through D. To further clarify this calculation, let us revisit two theoretical households, both earning median income and composed of two adults an d two children, one of whom requires childcare. We assume one of these households reside s in block group A located in an innerring suburban neighborhood and the other resides in block group B located in central Denver. Table 5.13 specifies that a household of this profile living in block group A can afford to pay $1,020 per month ($12,240 annually) f or housing while the same household

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Page 112 living in block group B can afford to pay $1,560 pe r month ($18,720 annually). We then sum the number of housing units in block groups A and B that are reported to have a gross rent that is at or below their respective housing budget s through a simple operation in a geographic information system (GIS) or spreadsheet program. Doing so indicates that a total of 170 rental units located in block group A have gross rents within the householdÂ’s monthly housing budget of $1,020, while 921 rental units located in block group B have gross rents at or below the householdÂ’s monthly hou sing budget of $1,560. The same analysis is completed for all block groups within t he metro, resulting in a comprehensive dataset containing the number of rental units that have gross rents at or below the housing budget specific to each block group, for each theor etical household profile. Calculate the Estimated Percent of Regional Housing Units that are Affordable within Household Housing Budgets Next, the raw number of affordable rental units is standardized in order to allow for comparisons of affordability both within, and acros s, metros. There is a multitude of ways an analyst might choose to standardize the number of a ffordable units depending on the aims of the analysis. Here I choose to calculate the num ber of rental units affordable to a particular household type as a percent of the metro Â’s total number of rental units. The first step in calculating the standardized supply of affo rdable housing is to identify the total number of rental units within the metro. This data is summed from Tables 25056 (Contract Rent) and 25061 (Rent Asked) of the ACS estimates.23 The number of affordable rental units in each of the metroÂ’s block groups is then divided by the total number of rental units in the metro. The resulting measure reflects the percent o f regional rental housing units that are both affordable to the particular household profile under investigation and located in the specified block group. Table 5.15 displays the resulting data for two theoretical ho useholds 23 For example, 2010-14 5-Year Estimates report the t otal number of rental units in the Denver region to be 428,050.

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Page 113 residing in block groups A and B. Results indicate that 0.04-percent of the metro’s rental housing (170 divided by 428,050) is both affordable to a median-income household with two adults and two children (one in childcare) and located in block group A. Meanwhile, 0.22percent of the Denver metro’s rental units (921 div ided by 428,050) are both affordable to a household of this type and located in block group B. Table 5.15. Supply of affordable housing for two ex ample households residing in two block groups “A” and “B” (Denver) Household type: Two adults, two children (one in ch ildcare) Household income: 100% AMI ($64,206) Block Group “A” Block Group “B” H+T budget $1,940 $1,940 Transportation costs ($920) ($380) Housing budget $1,020 $1,560 Affordable rental units: # of units in block group with gross rents at or below the household’s housing budget 170 units 921 units Affordable rental units in block group as percent o f the total rental units in the metro* 0.04% 0.22% *Total number of rental units in Denver metro=428,0 50 While it may be valuable to assess the availability of affordable housing for individual block groups or a collection of block groups as is done in Table 5.15 , it may be more helpful to sum the percent of units within block groups acr oss an entire metro, or some portion of the metro that is of particular interest. Table 5.16 provides an example of how a LSRI measure can be used to summarize region-wide afford ability for a household with two adults and two children (one of whom requires childcare) e arning 30-, 50-, 80-, 100-, and 120percent AMI. Here we observe that the minimum, medi an, and maximum housing budgets of households earning up to 50-percent AMI (approximat ely $30,000) are less than zero, indicating that these households consume all of the ir financial resources meeting their nonhousing needs, thus leaving no funds available for housing. These households are therefore unable to afford rental housing in any part of the metro and must instead rely upon some sort of assistance to secure housing. Households ea rning 80-percent of AMI ($51,365) fare

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Page 114 only slightly better: 1.6-percent of the metroÂ’s re ntal housing stock is affordable to households of this type and income level. Similar t o other lower-income households, households with two adults and two children earning 80-percent AMI are therefore likely to live with family or friends, or rely upon public su bsidy to secure housing. A household with the same composition earning 100-percent AMI ($64,2 06) are likely to experience greatly improved conditions: Approximately half of the metr oÂ’s rental units are affordable to them. Affordability looks even brighter for households ma king above median-income, with over 90percent of the metroÂ’s rental units affordable to a household making 120-percent AMI ($77,047). See Table 7.1 (Chapter 7) for a summary of the percent of regiona l rental units that are affordable to select household profiles in all eight case metros. Table 5.16. Percent of regional rental housing unit s available within the housing budgets of an example household type (Denver) Household type: Two adults, two children (one in ch ildcare) Annual Household Income Monthly housing budget, by block group (2014$) % of regional rental housing units affordable within housing budget Minimum Median Maximum $19,262 (30% AMI) -$2,547 -$2,214 -$1,802 n/a* $32,103 (50% AMI) -$1,650 -$1,317 -$904 n/a* $51,365 (80% AMI) -$304 $29 $442 1.6% $64,206 (100% AMI) $594 $926 $1,339 50.5% $77,047 (120% AMI) $1,491 $1,823 $2,236 92.7% *Maximum monthly housing budget is less than $0/mon th; thus, no rental units are affordable to this household profile at this income level While the summary data appearing in Table 5.16 is useful in understanding regionwide affordability, it gives us very little insight into how affordable housing is distributed across space. Mapping LSRI data, as is done in Figure 5.7 , offers the most fruitful means of exploring the spatial distribution of affordable ho using. By inspecting the patterns displayed on the map, one is able to roughly identify the loc ations in which a particular household would be most likely to secure affordable housing, and conversely, the areas of the metro in which there is little or no chance of securing affo rdable housing. In Figure 5.7 we see that

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Page 115 central areas of the metro contain the highest conc entration of rental units affordable to a median-income household with two adults and two chi ldren (one in childcare), along with portions of the outer-reaches of the metro that may be considered to be rural or semi-rural. A large ring-shaped swath just outside of the centr al city remains entirely unaffordable to households of this type (shown in white). It is imp ortant to remember that the LSRI approach accounts for variation in transportation costs. The landscape of affordability displayed in the map therefore reflects the combined effects of hous ing and transportation costs. This suggests, for example, that outer areas of the Denv er metro remain relatively affordable within the housing budgets of households of this ty pe despite high transportation costs. Figure 5.7. Percent of regional rental housing unit s that are affordable within the housing budgets of an example household type (Denve r)

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Page 116 CONTRIBUTIONS AND LIMITATIONS OF A LSRI APPROACH This section outlines each of the steps required to construct LSRI measures of housing affordability. By avoiding the use of arbit rary thresholds of affordability, accounting for the nuanced financial circumstances of househol ds with different compositions, and incorporating the effects of residential location o n transportation costs, the LSRI methodology offers an intuitive yet much more robus t alternative to more typical measures. The LSRI approach achieves all of these improvement s while employing publicly-available data, rendering it useful across many different pol icy and planning arenas and among a variety of users. It is also flexible: A LSRI metho d can utilize various household expenditure and housing supply datasets available across multip le scales, and can incorporate improved data as they become available. The LSRI methodology described above results in two measures that can be used to explore various dimensions of affordability. First, a LSRI approach generates data on the amount households can afford to pay for housing aft er covering their basic necessities (‘housing budgets’) for a defined set of theoretica l household profiles with different compositions, income levels, and residential locati ons. Exploring the housing budgets of different household profiles is helpful in understa nding demand for affordable housing at particular price points. The second output generated by the LSRI is a measur e of the supply of affordable housing. Resulting data can then be analyzed using spatial analysis techniques to understand various dimensions of the ‘landscape’ of affordability that exist in a metro. LSRI measures can also be used in exploring intersection s between affordability and other elements of the built and social environments. Subs equent chapters employ LSRI measures in both these ways, first by assessing the spatial distribution of affordable housing across the Denver metro (Chapter 6), and then by consideri ng housing affordability alongside transit accessibility (Chapters 7 and 8).

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Page 117 Despite the contributions of a LSRI approach, there exist several limitations, most having to do with qualities of the secondary data u sed in its construction. American Community Survey data which serves as the basis for data on supplies of rental units, as well as for the HUD LAI measure used in estimating transportation costs has substantial margins of error, particularly at small geographies . While this error is certainly a concern, it is considered to be tolerable when weighed against the utility of the granularity of findings that are generated for small geographies. Location Affordability Index data also poses limitations having to do with its use of aggregate (versus household-level) data, which a recent study attributes to the LAI reporting higher housing and transportation costs as compared to estimates modeled with more granular da ta (Salon, et al., 2016). Despite this shortcoming, the LAI remains the only comprehensive dataset of estimated transportation costs that is readily-available to practitioners. A LSRI approach can easily incorporate improved data on transportation costs as it becomes available. Finally, data sourced from the ACS on the rent of occupied housing units refle cts the rent of housing units paid by current residents, many of whom may be long-term re nters, and thus may not be fully representative of the amount of rent that would be asked from new renters. This likely has the effect of overestimating supplies of affordable rental housing, and may therefore under estimate the challenges lowand moderate-income ho usehold face in securing affordable rental housing. Because of these shortco mings, both the LSRI housing budget and supply measures should be interpreted as estima tes that are subject to measurement error originating with several data sources. Beyond issues with data sources, the detailed measu res that the LSRI approach generates may not be appropriate for every applicat ion. LSRI measures require numerous calculations. Although these calculations require n o sophisticated knowledge or software, they are considerably more complex than simple rati o-based approaches. The LSRI approach also requires a series of analytical choic es and normative judgments about which

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Page 118 households will be assessed, which goods and servic es should be accounted for in calculating non-housing costs, and what constitutes a ‘basic standard of living.’ While clear justifications can be made for all of these decisio ns (as is done in the present chapter), their subjective nature make it challenging to compare me asures across different geographies, time periods, and researchers. Finally, the depth o f information generated by a LSRI approach render it less universal than blunt ratiobased measures. Although I argue that this depth is generally a benefit, it is likely that pra ctitioners using a LSRI approach will need to make decisions about how to reduce data so that it is digestible to policymakers and the general public.

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Page 119 CHAPTER VI COMPARING FOUR MEASURES OF HOUSING AFFORDABILITY: T HE CASE OF LOWAND MODERATE-INCOME HOUSEHOLDS IN THE DENVER METRO INTRODUCTION There are two primary objectives in this chapter. F irst, I aim to demonstrate how the LSRI measures developed in Chapter 5 can be deploye d by exploring the landscapes of housing affordability that lowand moderate-income households in the Denver metro currently experience. Secondly, I aim to understand how results generated using a LSRI approach compare to those generated using the three standard measures of affordability. These comparisons are used to detect discrepancies between the ‘stories’ each approach tells about affordability, and to identify the cont ributions that the LSRI measures achieve beyond what is possible through more typical measur es. To achieve these objectives, I address three general questions: 1) What does the LSRI measure tell us about how muc h lowand moderate-income renters in the Denver area can afford to pay for ho using, and how do these results compare to those generated using the three typical measures of affordability? 2) What does the LSRI measure tell us about metro-w ide supplies of housing that are affordable to lowand moderate-income renters in D enver, and how do these results compare to those generated using the three typical measures of affordability? 3) How are supplies of affordable rental housing, a s measured using a LSRI approach, spatially-distributed across the Denver metro? The present analysis contributes to an existing lit erature on U.S. housing affordability that remains persistently (and surprisingly) a-spat ial (Revington & Townsend, 2016). Comparisons between the four measures highlight how a LSRI approach illuminates nuances in the landscape of affordability that is n ot possible through typical approaches. Furthermore, the present chapter demonstrates how t he LSRI measures can be applied in a

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Page 120 variety of spatial analyses to support planners and policymakers in developing policy interventions targeted towards the unique circumsta nces of small sub-areas of the region. DEFINING A SUBSET OF LOWAND MODERATE-INCOME HOUSE HOLDS The analysis presented in this chapter is concerned with exploring housing affordability for a range of lowand moderate-inco me households who are not likely to qualify for subsidies and must therefore rely upon ‘naturally-occurring’ market-rate housing. Because it would be onerous and perhaps unproductiv e to interpret findings for the 60 different permutations of household composition and income levels for which LSRI measures were generated following the methodology o utlined in Chapter 5, I instead focus on a subset of household profiles that reflect a re presentative range of characteristics. Household profiles were selected for inclusion base d on their ability to serve as a ‘canary in the coal mine’ – that is, profiles for which analys is provides a strong indication of affordability for other households with similar characteristics, but with lower incomes. The ‘canary’ household profiles are defined specifi cally to support investigations of affordability among households that earn too much t o qualify for subsidy, but not enough that the availability of stable housing is a forego ne conclusion. The extensive affordability challenges that exist among low-income households a re well-documented: It is clear that for many of these households, securing adequate and sta ble housing will only be possible through subsidies provided by the federal governmen t or other sources. Moderate-income households living in many U.S. metropolitan areas a lso face increasing difficulty in securing affordable housing (Ault, et al., 2015), although s ubsidies are typically not available to households earning more than 60-percent AMI (Belsky & Drew, 2007). However, despite these trends, there is currently very limited resea rch about affordability challenges among moderate-income households. The analysis presented in this chapter therefore ai ms to contribute to our understanding about affordability challenges among the households that

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Page 121 are most likely to rely on naturally-occurring affo rdable housing through the unsubsidized rental market. The subset of canary household profiles analyzed he re reflects a range of household compositions in terms of the number of adults and c hildren, and the number of those children who require childcare. The income levels of the canary households roughly correspond to the lowest income a household could e arn in order to have sufficient funds available for housing costs without relying upon su bsidy. Following these specifications, the present analysis focuses on the six household profi les outlined in Table 6.1 . Table 6.1. Characteristics of ‘canary’ household pr ofiles ‘Canary’ household profile # Adults # children (# requiring childcare) Household income Profile A 1 adult No children 30% AMI Profile B-1 1 adult 1 child (not in childcare) 50% AMI Profile B-2 1 adult 2 children (1 in childcare) 80% AMI Profile C 2 adults No children 50% AMI Profile D-1 2 adults 1 child (not in childcare) 80% AMI Profile D-2 2 adults 2 children (1 in childcare) 100% AMI WHAT CAN LOWAND MODERATE-INCOME HOUSEHOLDS AFFORD TO PAY FOR HOUSING IN DENVER? Understanding affordability using a LSRI approach b egins with analyzing how much households can afford to pay for housing given a pa rticular set of characteristics and financial circumstances. The results presented here explore this question by calculating housing budgets for the six lowand moderate-incom e canary household profiles, then analyzing how housing budgets vary depending on res idential location. The analysis is first conducted using a LSRI approach. Results are then c ompared to housing budgets calculated using the ratio, location affordability, and standard residual income approaches. Findings demonstrate how the four measures lead to widely-divergent conclusions about

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Page 122 how much lowand moderate-income households can af ford to pay for housing, thus highlighting how a LSRI measure more accurately ref lects the financial realities faced by households with limited means. Estimated Housing Budgets Calculated Using a LSRI A pproach In a LSRI approach, the ‘housing budget’ represents the upper limit of what a household can afford to pay for housing while still covering the goods and services necessary to maintain a basic standard of living. A household’s housing budget is a function of its composition (the number of adults and childr en), financial circumstances (household income and childcare requirements), and the transpo rtation costs associated with its residential location. As a result, housing budgets vary quite substantially depending on household characteristics as shown in Figure 6.1 , which provides the minimum, median, and maximum housing budgets for the six canary prof iles. Appendix C provides the same data for the complete set of Denver household profi les.

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Page 123 Figure 6.1. Estimated monthly housing budgets, as c alculated using an LSRI approach (Denver) Figure 6.1 demonstrates that the median amount a single adult household with no children earning 30-percent AMI ($19,262) (Profile A) can afford to pay for housing is just $100 per month. Canary households composed of a sin gle adult with children (Profiles B-1 and B-2) fare better because of their higher income s. However, as shown in Appendix C , households earning less than 50-percent AMI ($32,10 3) are often left with little to no available funds for housing after covering their ba sic necessities. In nearly all cases, households with one adult and children requiring ch ildcare must earn at least 80-percent AMI ($51,365) in order for any amount of income to remain for housing. Those earning less must therefore rely on subsidies or other support t o secure affordable housing.

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Page 124 Canary household profiles with two adults also high light how household composition and income impacts the amount of income available f or housing. The median housing budget for a two adult household with no children e arning 50-percent AMI (Profile C) is $328. Similar households earning less than 50-perce nt AMI are likely to have very little, if any, income left for housing after covering other b asic necessities. Two adult households with children require much higher incomes in order for any amount of funds to be available for housing, particularly when childcare is require d. For example, the median housing budget for Profile D-1 – a household with one adult and one child (not in childcare) earning 80-percent AMI – is approximately $1,180 per month. The median housing budget for the same household with one child who does require childcare is less than half of that ($460) , highlighting the large effect of childcare on a hou sehold’s budget. Most households with two adults and two children earning less than 80-percen t AMI are unlikely to retain any available funds for housing after covering their basic necess ities, particularly if childcare is required. Housing budgets also vary substantially across geog raphy. Maps of housing budgets by block group for each of the six canary household profiles appearing in Figure 6.2 suggest that households tend to be able to afford l arger sums for housing in central areas of Denver, as well as central portions of some smaller cities surrounding Denver. This is primarily an artefact of transportation costs, whic h are lowest in transit-accessible areas, thus increasing the amount of income that remains a vailable for housing. Theoretical households residing in inner-ring suburban areas ap pear to have the least amount of funds available for housing, a pattern which can be simil arly traced to high transportation costs in those areas. Interestingly, there appears to be a s light increase in housing budgets in the farthest reaches of the region.

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Page 125 Monthly housing budget (2014$) Profile A: 1 adult, no children – 30% AMI Profile C : 2 adults, no children – 50% AMI Profile B 1 : 1 adult, 1 child (not in childcare) – 50% AMI Profile D 1 : 2 adults, 1 child (not in childcare) – 80% AMI Profile B 2 : 1 adult, 2 children (1 in childcare) – 80% AMI Profile D 2 : 2 adults, 2 children (1 in childcare) – 100% AMI Figure 6.2. Estimated monthly housing budgets, by b lock group (Denver)

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Page 126 While housing budgets are useful in understanding h ow much theoretical households with different compositions and financial circumsta nces can afford to pay for housing depending on their residential location, they tell us nothing about whether housing units are actually available in those locations at correspond ing price points. To address this issue, we must assess the supply of housing affordable to lowand moderate-income households, as is done in the subsequent section. Estimated Housing Budgets: A Comparison of the Rati o, Location Affordability, Standard Residual Income, and LSRI Approaches Results of the previous section demonstrate that th e amount of income households in the Denver metro are able to allocate to housing varies substantially depending on household composition, financial circumstances, and residential location. Housing budgets also vary considerably depending on the measurement approach. In the present section, LSRI housing budgets calculated for the six canary profiles are compared to those analyzed using the three more typical approaches (ratio, loc ation affordability, and standard residual income) in order to understand how the four measure s may support different conclusions about affordability. Figure 6.3 displays the median values for housing budgets cal culated using each of the four measures. Minimum and maximum values are a lso shown for the location affordability and LSRI approaches (the only two mea sures that vary depending on a householdÂ’s residential location).

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Page 127 Measure Profile A: 1 adult, no children – 30% AMI Profile C: 2 adults, no children – 50% AMI Ratio Location Affordability Standard Residual LSRI Profile B-1: 1 adult, 1 child (not in childcare) – 50% AMI Profile D-1: 2 adults, 1 child (not in childcare) – 80% AMI Ratio Location Affordability Standard Residual LSRI Profile B-2: 1 adult, 2 children (1 in childcare) – 80% AMI Profile D-2: 2 adults, 2 children (1 in childcare) – 100% AMI Ratio Location Affordability Standard Residual LSRI Median monthly housing budget s (2014$) Figure 6.3. Estimated monthly housing budgets, as c alculated by four measures (Denver)

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Page 128 Ratio approach Median values for housing budgets calculated using the ratio approach are shown in Figure 6.3 as circles. Under a ratio approach, the maximum am ount a household is able to pay for ‘affordable’ housing is calculated as 30-pe rcent of household income. For nearly all canary profiles, a ratio approach generates the lar gest housing budget, indicating that households are expected to have more funds availabl e for housing under a ratio measure than other approaches would suggest. For example, t he ratio approach calculates that housing budgets for a household with two adults and two children (one in childcare) earning 100-percent AMI (Profile D-2) are approximately $20 0 to $680 per month higher than housing budgets calculated using the other approach es. Location affordability approach Median housing budgets calculated using the locatio n affordability approach are shown in Figure 6.3 as diamonds, with minimum and maximum values denot ed by bars at either end of the range. Under a location affordabi lity approach, housing is considered affordable when 45-percent of household income or l ess is spent on combined housing and transportation (‘H+T’) costs. Therefore, to calcula te location affordability housing budgets, the threshold for affordable H+T costs is first cal culated as 45-percent of income. Estimated transportation costs are then subtracted from this value, leaving the total amount that a household is able to pay for ‘affordable’ housing. Housing budgets generated through a location affordability approach for the six canary profiles are lower than those calculated using a ratio approach, with median values substant ially lower (up to $375 per month) for some households. A location affordability approach therefore indicates that most households would be expected to have less income available for housing than a ratio approach would suggest. However, maximum values of location affordability housing budgets also indicate that some households may have substantially more funds available for housing than suggested by a ratio approach. These r esults highlight the wide-ranging

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Page 129 effects of variations in transportation costs, as w ell as how the measures tell vastly different ‘stories’ about housing affordability. Standard residual income approach Median values for housing budgets calculated using a standard residual approach, shown as squares in Figure 6.3 , follow the same methodology as for the LSRI appro ach, except that transportation costs are assumed to be static across the region. In all but two of the six canary profiles, the standard residual inco me approach indicates that households have less income available for housing (up to $650 per month) than the ratio and location affordability approaches would suggest, but more than under the LSRI approach. LSRI approach Median values for housing budgets calculated using the LSRI approach are shown in Figure 6.3 as triangles, with the range denoted by bars at th e minimum and maximum values. For half of the canary profiles, the LSRI a pproach indicates that less income would be expected to be available for housing as compared to the three more typical approaches. For the remaining three canary profiles, the LSRI g enerates housing budgets that are substantially lower than those calculated using the ratio and location affordability approaches, but similar to the standard residual in come budgets. In some cases, the difference between the LSRI and other approaches is quite substantial. For example, the median LSRI housing budget for a household with two adults and two children (one of whom requires childcare) earning median income is $680 lower per month than the housing budget calculated through a ratio approach, and $400 and $ 190 lower per month than the location affordability and standard residual income measures (respectively). However, results from the LSRI approach also indicate that some household s located in some areas of the region may have substantially more funds available for housing than suggested by the other approaches. These non-trivial differences between t he LSRI and other approaches

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Page 130 underscore that the measure used to assess affordab ility greatly impacts the conclusions drawn. Summary The comparisons presented in Figure 6.3 and detailed above highlight the large inconsistencies that exist between measures of hous ing affordability generated by the four approaches. Because the LSRI approach offers the mo st robust and accurate measure of affordability, it serves as the ‘benchmark’ against which the other three approaches are evaluated. In particular, the most commonly-used ap proach (ratio) is likely to considerably over estimate the amount households are able to afford f or housing and therefore under estimate the affordability challenges facing lowa nd moderate-income households. A location affordability approach also tends to misch aracterize affordability, although in less predictable ways with housing budgets over estimated for some canary profiles and under estimated for others. These trends make reports of the affordability ‘crisis’ outlined in Chapter 4 all the more alarming, since nearly all o f the existing research on housing affordability uses either the ratio or location aff ordability approach. Findings from this analysis therefore have significant implications fo r the work of developing and implementing policies that establish the need for and direct res ources towards affordable housing. Meanwhile, results of the comparison between housin g affordability measures also suggest that some households living in particularly transit-accessible areas of the metro may have more funds available for housing than the three most typ ical approaches to measuring housing affordability would suggest. This is due to the fact that a LSRI measure accounts for the financial realities of households more accurate ly, and also incorporates variations in transportation costs across the metro based on the level of auto dependence required by a residential location. The LSRI therefore enables po licymakers and practitioners to more accurately assess the landscape of affordability wi thin a particular geography and develop interventions targeted to specific dynamics within different areas of the metro.

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Page 131 WHAT IS THE METRO-WIDE SUPPLY OF HOUSING UNITS AFFO RDABLE TO LOWAND MODERATE-INCOME RENTERS IN DENVER? The analysis of housing budgets undertaken in the p revious section helps in understanding demand for housing at particular price points; however, t he extent to which rental housing is actually available at those price points remains an open question. The next step in the analysis is therefore to assess the supply of housing that is affordable to lowand moderate-income renters within their respective hou sing budgets. In this section, metro-wide supplies of affordable rental housing are first cal culated using a LSRI approach. Results of the LSRI analysis are then compared to measures of supply calculated using the ratio, location affordability, and standard residual incom e approaches in order to explore discrepancies between the ‘stories’ of affordabilit y generated by each measure. Estimated Metro-Wide Supplies of Affordable Rental Housing Calculated Using a LSRI Approach Assessing the metro-wide supply of affordable housi ng involves three general steps. First, the total number of rental units that are af fordable within the housing budget of a particular household profile are calculated for eac h block group. The number of affordable units in each block group is then summed across the metro. Finally, the number of metrowide affordable rental units are calculated as a pe rcent of a metro’s total rental units to provide a standardized measure that can be compared to other household profiles, and to other metros. This analysis focuses exclusively on affordable rental units for several reasons. First, the existing literature indicates that renters face the largest affordability challenges in U.S. metropolitan areas, with 24-percent of all rental h ouseholds spending more than half of their income on housing in 2014, as compared to 10-percen t of homeowners (Ault, et al., 2015). Furthermore, rising housing costs are generally a m uch larger concern for renters than for homeowners (who are likely to benefit from increase d property values over the long-term).

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Page 132 Data from Tables 25056 (Contract Rent) and 25061 (R ent Asked) of the ACS 2010-14 FiveYear Estimates are used to identify the percent of the Denver metroÂ’s rental units that are available within the housing budget of each canary profile following the methodology described in Chapter 5. Results of this analysis are presented in Figure 6.4 . Profile A: 1 adult, no children 30% AMI Profile B 1: 1 adult, 1 child (not in childcare) 50% AMI Profile B 2: 1 adult, 2 children (1 childcare) 80% AMI Profile C: 2 adults, no children 50% AMI Profile D 1: 2 adults, 1 child (not childcare) 80% AMI Profile D 2: 2 adults, 2 children (1 childcare) 100% AMI Figure 6.4. Percent of the metro-wide rental housin g units that are estimated to be affordable to canary household profiles The results shown in Figure 6.4 underscore the challenges lowand moderateincome households face in securing affordable renta l housing in the Denver metro, particularly those earning 50-percent AMI and less, for whom only a fraction of the regionÂ’s housing is affordable. Even households earning median-income face challeng es, with only half of the regionÂ’s rental housing affordable to h ouseholds with two adults and two children, one of whom requires childcare (Profile D-2). This in part reflects the large impact of childcare costs on a householdÂ’s housing budget, ev en among those with moderateincomes. 2.2% 6.0% 25.7% 5.5% 69.4% 50.5%

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Page 133 Estimated Metro-Wide Supplies of Affordable Rental Housing: A Comparison of the Ratio, Location Affordability, Standard Residual In come, and LSRI Approaches Results of the previous section demonstrate that th e supply of housing affordable to lowand moderate-income households varies widely d epending on a householdÂ’s composition and financial circumstance. As with hou sing budgets, the supply of affordable housing also varies substantially depending on the measure used. In the present section, region-wide supplies of affordable housing calculat ed for the six canary profiles using a LSRI approach are compared to those calculated usin g the three more typical approaches (ratio, location affordability, and standard residu al income). Figure 6.5 summarizes the supply of affordable housing for th e six canary households, as calculated using the four approaches . Findings demonstrate that, overall, the ratio and location affordability approaches are likely to overestimate the supply of affordable housing as compared to the LSRI approach . These overestimates are quite substantial in some cases. For example, the ratio a nd location affordability approaches both suggest that approximately 70-percent of DenverÂ’s r ental housing is affordable to single adult households with two children (one of whom req uires childcare) earning 80-percent AMI (Profile B-2). However, a LSRI approach indicates t hat only one-quarter of the metroÂ’s rental housing is affordable to the same household profile . Similar differences exist for Profile C households (two adults and no children earning 50-p ercent AMI): The ratio and location affordability approaches suggest that 10and 25-pe rcent of rental housing is affordable (respectively) while a LSRI approach indicates only 5.5-percent is affordable. However, this pattern does not hold true for all households. For instance, the supply of rental housing affordable to households with two adults and one ch ild earning 80-percent AMI (Profile D-2) are relatively stable across all four approaches. S upplies calculated for Profile A households (single adults with no children earning 30-percent AMI) are also similar across all four approaches, likely due to the small housing budgets available to these very low-income

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Page 134 households. In most cases, the much less commonly-u sed standard residual income approach points to relatively similar region-wide a ffordability as compared to LSRI approach. Findings from the comparative analysis demonstrate that the four measures yield vastly different conclusions about housing affordab ility. In particular, because the ratio and location affordability measures currently dominate affordability analyses, the results presented here suggest that reports of the affordab ility ‘crisis’ may be more extreme than recently reported. Discrepancies are particularly s tark among households with children requiring childcare, pointing to the importance of accurately addressing the substantial effects of childcare costs on a household’s ability to secure affordable housing. More generally, results of this comparison point to the importance of accounting for the impact of household composition and financial circumstances i n measuring housing affordability. By directly incorporating these factors, as well as th ose related to variations in transportation cost based on residential location, a LSRI approach offers a robust measure of the realities faced by lowand moderate-income households in sec uring affordable housing, thus enabling policymakers and practitioners to accurate ly assess affordability conditions and develop interventions targeted at addressing them.

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Page 135 Measure Profile A: 1 adult, no children – 30% AMI Profile C: 2 adults, no children – 50% AMI Ratio Location Affordability Standard Residual LSRI Profile B-1: 1 adult, 1 child (not in childcare) – 50% AMI Profile D-1: 2 adults, 1 child (not in childcare) – 80% AMI Ratio Location Affordability Standard Residual LSRI Profile B-2: 1 adult, 2 children (1 in childcare) – 80% AMI Profile D-2: 2 adults, 2 children (1 in childcare) – 100% AMI Ratio Location Affordability Standard Residual LSRI Percent of regional rental units affordable within housing budget (2014) Figure 6.5. Estimated metro-wide supply of affordab le rental housing, as calculated by four measures ( Denver)

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Page 136 HOW ARE SUPPLIES OF LOWAND MODERATE-INCOME AFFORD ABLE RENTAL UNITS SPATIALLY-DISTRIBUTED? Housing affordability is fundamentally a spatial issue, with conditions likely varying considerably between different locations within a m etro. So while region-wide analyses provide an overall ‘snapshot’ of affordability that is useful in understanding broad conditions and comparing them across multiple metros, it is pe rhaps more important that practitioners and policymakers have access to tools to understand the nuances that exist across local conditions. In particular, the design and implement ation of policy interventions requires that we not only understand total supplies of affordable housing, but also how those supplies are distributed across space and the extent to which af fordability may be concentrated in some areas while lacking in others. Yet despite this cle ar need, most affordability analyses in the existing literature remain surprisingly a-spatial ( Revington & Townsend, 2016). The present section seeks to address this gap by us ing a LSRI approach to explore the spatial distribution of affordability in the De nver metro, with particular attention paid to the extent to which rental housing that is affordab le to lowand moderate-income households is concentrated (and/or dispersed) acros s the metro. To this end, supplies of affordable rental housing are first mapped in order to gain a general understanding of the distribution of affordability for each theoretical household profile. Next, a Global Moran’s I summary statistic is used to assess the degree to w hich observations are clustered across space. Finally, local indicators of spatial autocor relation analysis is undertaken to identify the specific locations of high affordability clusters ( ‘hot spots’) and high affordability ‘outliers.’ Taken together, these analyses provide a nuanced un derstanding of the landscape of affordability in Denver, and equip planners and pol icymakers with the tools to develop policy interventions targeted towards the circumstances un ique to specific sub-areas of the metro.

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Page 137 Examining the Spatial Distribution of Affordable Re ntal Housing Using a LSRI Approach The supply of rental housing affordable to each can ary household profile is mapped in Figure 6.6 in order to highlight general spatial patterns of affordability in the Denver metro. Here we see that the largest supplies of aff ordable rental housing are located in central areas of the city of Denver. Indeed, househ olds with the lowest levels of affordability (Profiles A, B-1, and C) are most likely to secure housing in the central city. Some pockets of affordability also exist in the smaller communities to the north and northwest of Denver. Interestingly, a large swath of housing affordable to moderate-income households (Profiles B-2, D-1, and D-2) also exists in the outer edges o f the metro. This suggests that despite the likelihood of higher transportation costs, the fart hest reaches of the Denver metro remain relatively affordable within the housing budgets of some moderate-income households. A large ring-shaped swath just outside of the central city remains entirely unaffordable to all the lowand moderate-income households assessed he re, likely reflecting a general lack of rental housing in these areas, as well as high hous ing costs for the rental units that do exist.

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Page 138 Percent of regional rental units that are affordabl e to household profile Profile A: 1 adult, no children – 30% AMI Profile C: 2 adults, no children – 50% AMI Profile B 1: 1 adult, 1 child (not in childcare) – 50% AMI Profile D 1: 2 adults, 1 child (not in childcare) – 80% AMI Profile B 2: 1 adult, 2 children (1 in childcare) – 80% AMI Profile D 2: 2 adults, 2 children (1 in childcare) – 100% AMI Figure 6.6. Estimated supply of affordable rental h ousing, by block group (Denver)

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Page 139 Identifying Affordability Clusters and Outliers The maps displayed in Figure 6.4 suggest that affordable housing is somewhat clustered across space. To test whether this is an accurate assessment, Global MoranÂ’s I, a statistic that summarizes how evenly observations w ith similar values are distributed across space, is computed for all household profiles. The resulting value identifies the extent to which affordable rental housing is clustered across the Denver metro. Values of Global MoranÂ’s I range from -1.0 to +1.0, with a positive and statistically-significant value indicating that block groups with similar levels of affordabil ity are clustered together. A statisticallysignificant and negative value indicates that dissi milar values tend to cluster. A Global MoranÂ’s I value of zero indicates a completely rand om distribution. As summarized in Table 6.2 , Global MoranÂ’s I statistics are statistically-sig nificant and positive for all six profiles suggesting that b lock groups with similar levels of affordability tend to cluster together, as would be expected. In other words, block groups with large supplies of affordable rental housing are likely to neighbor other high-affordability block groups, while block groups with low supplies of aff ordable rental housing are likely to neighbor one another. This finding confirms that, a s expected, affordable rental housing is not distributed evenly across space, but rather is clustered such that some areas have highconcentrations of affordability while others lack a ffordable housing entirely.

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Page 140 Table 6.2. Global Moran’s I statistic assessing the spatial distribution of affordable rental units (Denver) Household profile Global Moran’s I Profile A: Single adult, no children – 30% AMI 0.32** Profile B-1: Single adult, 1 child (not in childcare) – 50% AMI 0.32** Profile B-2: Single adult, 2 children (1 in childcare) – 80% AMI 0.37** Profile C: Two adults, no children – 50% AMI 0.29** Profile D-1: Two adults, 1 child (not in childcare) – 80% AMI 0.29** Profile D-2: Two adults, 2 children (1 in childcare) – 100% AMI 0.32** ** p 0.01 Global Moran’s I statistics indicate that some area s of the Denver metro have high concentrations of affordable housing while other ar eas have little. Another set of spatial statistics, Local indicators of spatial autocorrela tion (LISA), is next used to identify where these concentrations occur. The key LISA statistic is Local Moran’s I, which provides an indication of the extent to which a block group is surrounded by block groups with similar values of a key variable. While Global Moran’s I ge nerates a single value that reflects the extent to which block groups with similar values ar e located near to one another across the entire metro, Local Moran’s I calculates a value fo r each individual block group reflecting the degree to which it is similar or different from its neighbors.1 Values of Local Moran’s I are then mapped to highlight where statistically-signif icant clusters of similar values occur. Applied to the present analysis, Local Moran’s I de scribes the extent to which the percent of affordable rental housing within each bl ock group is similar to the percent within its neighboring block groups. LISA can thus be used to identify the locations of block groups with high affordability that are surrounded by bloc k groups with similarly high levels of 1 See Anselin (1995) for a comprehensive overview of LISA techniques

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Page 141 affordability (‘hot spots’). It is also possible to map clusters of low-affordability block groups (‘cold spots’), as well as high-affordability block groups that are surrounded by lowaffordability block groups (‘high-low outliers’) an d low-affordability block groups surrounded by high-affordability block groups (‘high-low outli ers’). LISA mapping is increasingly being used in a range of planning and policy arenas to id entify clusters of a specific population or particular amenity. For example, LISA has been rece ntly used to identify clusters of racial and ethnic minority populations (McKenzie, 2013), t o detect the presence of redeveloping and declining neighborhoods in U.S. cities (Tighe & Ganning, 2016), and to assess the availability of transit among different socioeconom ic groups (Bardaka et al., 2015; Griffin & Sener, 2015). However, despite its usefulness to ho using studies, LISA has rarely (if ever) been used to analyze the spatial distribution of af fordable housing. The present analysis therefore contributes the existing literature by de monstrating how this novel approach can be helpful in understanding landscapes of housing a ffordability. Local Moran’s I is calculated here using the “univa riate LISA” tool in open-source GeoDa software.2 Calculating Local Moran’s I requires specifying ho w ‘neighbor’ relationships are defined. A ‘distance-based’ defin ition specifies that a certain number (“k”) of the nearest observations are neighbors. The pres ent analysis estimates Local Moran’s I using a ‘contiguity-based’ approach (specifically, a row standardized, first order queen continuity weights matrix), which defines neighbors as observations that share a border. A 95-percent confidence level is used to assess stati stical significance. Because LISA results are derived from a randomization procedure, differe nt numbers of permutations may yield slightly different results. The present analysis ma ximizes the stability of results by using 9,999 permutations3. 2 https://geodacenter.asu.edu/ 3 GeoDa allows for permutations to be specified betw een 99 and 9,999.

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Page 142 As with Global Moran’s I, Local Moran’s I values ra nge between -1.0 and +1.0, with a positive, statistically-significant value indicatin g that the block group is surrounded by neighboring block groups with similarly high (or lo w) values. These spatial clusters are referred to as ‘high-high’ (hot spots) or ‘low-low’ (cold spots). A negative, statisticallysignificant value indicates that the block group is surrounded by block groups with dissimilar values, pointing to the presence of high (or low) o utliers. Block groups lacking statisticallysignificant values are neither significantly simila r, nor dissimilar, to neighboring block groups. Figure 6.7 presents results of the exploratory LISA analysis c onducted in the Denver metro for each of the household profiles. Areas in red are high affordability ‘hot spots,’ meaning they have statistically-significant and pos itive values of Local Moran’s I. These blocks group have a high percent of affordable rent al units, and are surrounded by block groups with similarly high levels of affordability. Block groups in pink indicate the presence of a statistically-significant high-low outlier. Th ese are block groups which themselves have high affordability, but are surrounded by block gro ups that have low affordability. The pink and red areas therefore highlight the areas of the metro in which lowand moderate-income households are most likely to secure affordable hou sing. Areas shown in dark blue are low affordability clus ters in which low affordability block groups cluster together. Light blue block groups ar e low affordability outliers – these areas have low affordability, but are surrounded by block groups with high affordability. Areas shown in white are neither statistically-significan t hot spots nor outliers. The patterns displayed in the maps shed light on th e Denver metro’s landscape of affordability by pointing to the locations with sig nificant concentrations of affordable rental housing for lowand moderate-income households, an d conversely, the areas of the region in which there is little or no chance of securing a ffordable housing. In particular, the maps suggest that clusters of rental housing affordable to lowand moderate-income households

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Page 143 are generally located within the city and county of Denver, and primarily located near the central core of the city. This pattern may be attributed to two general issue s. First, households living in central parts of Denver are likely to have much low er transportation costs than those living in more distant parts of the metro, thus providing the former with more available funds for housing. Indeed, as discussed earlier in this chapt er, households residing in the central city have much larger housing budgets as compared to hou seholds living in the suburban fringe. This finding lends support to arguments commonly ma de among advocates that areas of the metro requiring less reliance on private vehicles ( and thus, lower transportation costs) still offer lowand moderate-income households the best opportunities for securing affordable housing despite higher housing costs (see, for exam ple,Center for Housing Policy and Center for Neighborhood Technology, 2012). It shoul d be noted that these dynamics may change considerably in coming years due to rapid ch anges in property values, particularly in central city locations. Additionally, results of th e LISA analysis could simply reflect the existence of more plentiful rental housing (regardl ess of its cost) in central parts of the city as compared to more suburban areas. Conditions are also likely to change if the proportion of residents renting continues to grow and the mark et responds to the resulting increase in demand for rental housing. LISA mapping also points to a handful of areas in w hich high affordability block groups are surrounded by neighboring block groups w ith low supplies of affordable rental housing. These high affordability outliers are scat tered throughout the metro, both within the city of Denver and just outside of it. If low affor dability areas are inhabited by higher-income households as one might expect, this pattern could point to the existence of mixed-income neighborhoods, which existing research suggest may be associated with improved outcomes for lowand moderate-income households (f or a recent review, see Hyra, 2013).

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Page 144 Results generated by exploratory LISA mapping enabl e policymakers and practitioners to identify where in the region lowand moderate-income households are most likely to secure affordable housing, and develop ta rgeted policy interventions aimed at addressing nuanced location conditions. For instanc e, results outlined here indicate that despite a dominant narrative pointing to widespread gentrification and displacement in central cities, the metro’s most significant concen trations of affordable rental housing are still located within Denver’s urban core, suggesting cons iderable opportunities to implement preservation programs designed to maintain affordab ility. Results also reveal that the vast majority of the region, particularly areas outside of central Denver, contains no significant clusters of affordable housing at all, suggesting a n urgent need to promote the creation of affordable rental housing through market-based and/ or subsidized development. LISA analyses can also be used alongside other data to u nderstand the extent to which affordable housing co-exists with a particular set of amenitie s – for example, transit access.

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Page 145 Profile A: 1 adult, no children – 30% AMI Profile C: 2 adults, no children – 50% AMI Profile B 1: 1 adult, 1 child (not in childcare) – 50% AMI Profile D 1: 2 adults, 1 child (not in childcare) – 80% AMI Profile B 2: 1 adult, 2 children (1 in childcare) – 80% AMI Profile D 2: 2 adults, 2 children (1 in childcare) – 100% AMI Figure 6.7. Spatial distribution of high affordabil ity ‘clusters’ and ‘outliers’ (Denver)

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Page 146 CONCLUSIONS Concerns about housing affordability are mounting i n many metropolitan areas across the U.S., with even moderate-income househol ds facing challenges in securing affordable housing. Yet despite the importance of t his issue and its implications for the social and economic health of our communities, ther e has been surprisingly little critical examination in either the academic or public sphere s around how to define and measure the concept of ‘affordable housing.’ Chapter 4 introduc ed the three most typical approaches to measuring affordable housing – ratio, location affo rdability, and residual income – and outlined limitations of each. I then developed an i mproved approach – the location-sensitive residual income (LSRI) measure – which considers ho using to be affordable when its costs do not exceed the amount of income that remains ava ilable after a household has covered the goods and services required to maintain a basic standard of living. A detailed methodology for constructing LSRI measures of affor dability is provided in Chapter 5. The present chapter set out to demonstrate how the LSRI measures developed in Chapter 5 can be deployed towards understanding lan dscapes of housing affordability, and to compare results generated using a LSRI approach to those derived from the three typical measures of affordability. To do so, I addressed th ree research questions: 1) What does the LSRI measure tell us about how much lowand modera te-income renters in the Denver area can afford to pay for housing, and how do thes e results compare to those generated using the three typical measures of affordability?; 2) What does the LSRI measure tell us about metro-wide supplies of housing that are affor dable to lowand moderate-income renters in Denver, and how do these results compare to those generated using the three typical measures of affordability?; and 3) How are supplies of affordable rental housing, as measured using a LSRI approach, spatially-distribut ed across the Denver metro? Key conclusions drawn from these analyses are outlined below.

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Page 147 Different approaches to measuring affordability tel l vastly different stories about the demand for and supply of affordable housi ng. In particular, the most commonly-used measure of affordability (the ratio a pproach) appears to considerably overestimate the amount households are able to affo rd for housing and the number of rental units available within those housing budgets, thus under estimating the extent to which affordability is a problem for lowand moderate-in come households. A location affordability approach also tends to mischaracterize affordabilit y, although in less predictable ways with housing budgets overestimated for some canary profi les and underestimated for others. These trends make reports of the affordability ‘cri sis’ outlined in Chapter 4 all the more alarming, since nearly all of the existing research on housing affordability uses one of these two approaches. Discrepancies are particularly star k among households with children requiring childcare, pointing to the importance of accurately addressing the substantial effects of childcare costs on a household’s ability to secure affordable housing. More generally, results of this comparison also point to the importance of accounting for the impact of household composition and financial circu mstances in measuring housing affordability. A LSRI approach offers the most accurate account of realities faced by lowand moderate-income households in securing affordab le housing. Comparisons between the LSRI measure and the three more typical approaches clearly demonstrate the importance of using the measure that most accuratel y reflects the financial realities faced by lowand moderate-income households. Housing afford ability is much more complex and dynamic than the ratio and location affordability a pproaches suggest, and is dependent on a number of household-level factors that must be acco unted for in order to accurately measure it. By directly accounting for the effects of these factors, a LSRI approach offers the most robust measure of the landscape of afforda bility for lowand moderate-income households. The LSRI measure therefore enables prac titioners and policymakers to

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Page 148 accurately assess affordability condition, establis h the need for affordable housing at multiple scales down to the neighborhood level, and develop interventions targeted at the specific conditions within particular geographies. However, practitioners employing a LSRI approach must also be mindful of the limitations of its measures and should interpret them as estimates that are subject to measurement error (as discusse d at the end of Chapter 5). Market-rate ‘naturally-occurring’ affordable housin g remains under-studied. In addition to comparing results from a LSRI approach to the three more typical measures, the present chapter also explored the landscape of affo rdability for lowand moderate-income households in the Denver metro using a LSRI approac h. To do so, affordability is assessed for a subset of six lowand moderate-income househ old profiles, each varying on the number of adults, number of children, number of tho se children requiring childcare, and income level. The six household profiles were delib erately selected to serve as ‘canaries in the coal mine’ – that is, analysis of these househo lds provide as a strong indication of affordability for similar households with lower inc omes. The analysis is specifically concerned with assessing conditions among household s whose financial circumstances are not so dire that they qualify for subsidy, but for whom securing affordable housing through the unsubsidized market is likely to be a challenge . Analysis of the ‘canary’ household profiles therefore contributes to knowledge about ‘ naturally-occurring’ market-rate housing, which remains surprisingly under-researched given t hat these supplies constitute the vast majority of affordable housing for lowand moderat e-income households. Many lowand moderate-income households have no fu nds available for housing after paying for basic necessities. Analysis of housing budgets for the six canary profiles indicates that many low-income households spend their entire income on the essential goods and services required to maintain a basic standard of living, leaving no remaining funds for housing. Households with childr en face particularly harsh conditions. In nearly all cases, households composed of one adult and any number of children requiring

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Page 149 childcare must earn at least 80-percent AMI ($51,365) in order for any income t o remain for housing. Similar challenges exist for larger househ olds: Two-adult households with children earning less than 80% AMI are unlikely to retain an y funds for housing after covering their basic necessities, particularly if childcare is req uired. Households with these characteristics earning less than 80-percent AMI must therefore rel y on governmental subsidies or other support to secure affordable housing. Low-income households without children also face challenges. Single-adult and tw oadult childless households must earn at least 30-pe rcent AMI ($19,262) and 50-percent AMI ($32,103), respectively, in order to have any amoun t of remaining income for housing. This means that no housing, no matter how inexpensive, w ill be affordable to a single adult working full-time at the federal minimum wage ($15, 080 annually), since such a worker has insufficient income to pay for housing after coveri ng his or her basic necessities. Only a fraction of rental units in the Denver metro are affordable to low-income households. For most of the household profiles, particularly th ose earning 50-percent AMI and less, only a fraction (two to six-percent) of t he metro’s rental units are affordable. Larger supplies of affordable rental housing (25to 70-pe rcent) are available for moderate-income households earning 80-percent AMI or more. Even mod erate-income households face challenges, particularly when childcare is required : For example, only half of the metro’s rental units are affordable for a household compose d of two adults and two children (one of whom requires childcare) earning 100-percent AMI. Lowand moderate-income households residing in cen tral city locations experience higher levels of affordability than thei r suburban counterparts. Despite scarce regional supplies of affordable housing for lowand moderate-income households, affordability ‘hot spots’ do exist, particularly in central city locations. Housing budget analyses conducted using a LSRI approach indicate t hat lowand moderate-income households residing in central areas of Denver and some smaller cities in the metro have

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Page 150 the largest amount of income available for housing, while those residing in inner suburban areas have the most meager housing budgets. The lar gest supplies of affordable rental housing also exist in areas within the central city , with some pockets of affordability in smaller communities to the north and northwest of D enver. While a large ring-shaped swath just outside of the central city remains entirely u naffordable to lowand moderate-income households, both housing budgets and the supply of affordable housing increase slightly at the outer edges of the metro. This suggests that, d espite the likelihood of higher transportation costs in these outer areas, the fart hest reaches of the Denver metro remain somewhat affordable within the housing budgets of s ome moderate-income households. Global Moran’s I statistics confirm that housing af fordability is quite concentrated in some areas, and entirely lacking in others. An anal ysis of Local Moran’s I reveals statistically-significant ‘hot spot’ clusters of af fordability in the most central parts of Denver, with a handful of significant clusters in other cen tral locations in the metro. These patterns are primarily attributed to variations in transport ation costs, which are likely to be much lower for households living in central areas of the metro than those living in more distant parts. The landscape of affordability may also reflect the existence of larger supplies of rental units in general in central areas. Areas outside of the central cit y are largely lacking in affordable housing, pointing to patterns of exclusionary displ acement. Results lend tentative support to arguments that hi gher housing costs in accessible areas are offset by lower transportation costs. Results of the analysis presented in this chapter generally lend support to the arguments commonly made among advocates that areas of the metro requiring less re liance on private vehicles (and thus, lower transportation costs) offer lowand moderate-incom e households the best opportunities for securing affordable housing even if housing costs a re higher in these locations. However, these results reflect a dynamic set of circumstance s that are likely to change considerably over time in a number of ways. For instance, regional supplies of market-rate rent al housing

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Page 151 are expected to increase to meet growing demand ass ociated with patterns of declining homeownership rates (JCHS, 2015). An abundance of existing research also points to evidence of increased property values in central lo cations with low auto-dependence, resulting in higher rents that may put housing that is currently affordable within lowand moderate-income household housing budgets out of re ach (see Zuk et al., 2015 for a recent review). Accessibility within the metro is also lik ely to change over time in the form of new or altered bus service, bicycle and pedestrian infrast ructure, and/or construction of new fixedrail elements. Any analysis of housing affordability must therefor e be thought of as a snapshot of a highly complex and dynamic system. Regular updates using a LSRI approach to track changing conditions are imperative in orde r to understand the evolving landscape of affordability within the Denver metro. A LSRI approach enables practitioners to accurately assess affordability and develop targeted interventions at multiple scales. In addition to contributing to an existing literature that is thin on spatially-based analyses of housing affordability, the present analysis demonstrates how the novel LSRI approach c an be used in tandem with variety of analytic approaches to develop a nuanced understand ing of the landscape of affordability. Because the LSRI approach provides an accurate asse ssment of affordability at multiple scales, it enables practitioners to explore both re gional patterns of affordability, as well as to develop targeted policy interventions that address the unique circumstances of small subareas within the metro. For example, results outlined here indicate that de spite a dominant narrative pointing to widespread gentrification and displacement in central cities, the regionÂ’s most significant concentrations of affordable renta l housing are still located within DenverÂ’s urban core, suggesting considerable opportunities t o implement preservation programs aimed at maintaining naturally-occurring affordabil ity. The LSRI approach also opens new avenues for investigation when integrated with data related to other dimensions of the built and social environment. Chapters 7 and 8, for instance, combine LSRI measur es of housing

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Page 152 affordability with data on transit accessibility to analyze the extent to which housing affordable to lowand moderate-income households i s located in high-accessibility areas of U.S. metros.

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Page 153 CHAPTER VII EXAMINING LANDSCAPES OF TRANSIT ACCESSIBILITY AND H OUSING AFFORDABILITY IN EIGHT U.S. METROS INTRODUCTION This dissertation began by considering how several theoretical lenses relevant to urban social justice help us in understanding what constitutes a ‘just’ transportation system. I then developed a conceptual framework to guide th e present study by integrating one of these lenses – Sen and Nussbaum’s ‘capabilities app roach’ – with the concept of ‘geographies of opportunity,’ a frame that is commo nly adopted in work around issues of spatial and social justice. In this conceptual framework, geographies of opport unity for lowand moderate-income households are conceptualized as being bounded by t wo circumstances: 1) the ability to access employment opportunities via modes other tha n private auto (‘transit accessibility’) and 2) the ability to afford housing in transit-acc essible areas, and thus benefit from the advantages conferred by transit access (‘housing af fordability’). Two areas of concern around transit accessibility a nd housing affordability are frequently documented in the research literature. T he first relates to direct displacement effects resulting from high property values in area s with access to high-frequency transit that leave long-standing residents no longer able to aff ord housing in transit-accessible neighborhoods (often referred to as ‘transit-induce d gentrification’). The second area of concern relates to increased demand for transit-acc essible locations on a regional scale that leads to exclusionary displacement effects whereby newly-formed and relocating households with lower incomes are unable to afford housing in these neighborhoods and instead locate to more auto-oriented areas of the m etro. However, a strand of literature focused on a ‘locat ion efficiency’ approach to thinking about issues of affordability has emerged in recent years to suggest that local and regional

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Page 154 displacement in transit-rich areas may be less of a threat than commonly thought when the cost of housing and transportation are considered i n combination. A ‘location efficiency narrative’ therefore acknowledges that housing cost s may be higher in transit-accessible areas, but counters that reduced transportation exp enditures are likely to offset these costs resulting in better overall ‘H+T’ affordability. Wh ile research generally lends support to this claim, several shortcomings in the literature leave considerable gaps in our understanding of whether this perspective is supported by on-the-gro und empirics. Perhaps the most serious of these gaps relates to t he widespread use of inherently flawed ratio-based measures of housing affordabilit y. In order to address the shortcomings of typical measures of affordability, I have introd uced an improved measure – the locationsensitive residual income (LSRI) approach – which m ore fully accounts for the financial realities faced by households with limited means. I n the present chapter, I employ LSRI measures to examine the current geographies of tran sit accessibility and housing affordability that lowand moderate-income househo lds are likely to confront as they seek market-rate housing in eight U.S. metros. Specifica lly, I use spatial analytical techniques to address the question: To what extent are supplies of rental housing that are affordable for lowand moderate-income households located in areas with high transit accessibility? (Research Question 1). These investigations are conducted for the universe of U.S. metros with ‘secondgeneration’ regional rail which (as described in Ch apter 3) are likely to experience a specific set of challenges that speak both theoretically and practically to issues of transportation justice. These metros (defined as core-based statis tical areas and identified by their core cities) are: Dallas, Denver, Houston, Los Angeles, Minneapolis, Portland, Salt Lake City, and Seattle. Results yield important contributions to our understanding of the geographies of opportunity that are shaped by transit accessibilit y and housing affordability, as well as

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Page 155 provide insights into the ways in which these geogr aphies are consistent with – and challenge – a location efficiency narrative. DATA AND METHODS Data Two measures – transit accessibility and housing af fordability – are employed at the Census block group level in the present analysis. Measuring housing affordability The data and methods used to construct the LSRI mea sures of housing affordability employed here are discussed in depth in Chapter 5. In short, the LSRI approach considers housing to be affordable when a household is able t o pay for housing while still meeting its basic non-housing needs within the bounds of its in come. LSRI measures are developed for a specified set theoretical lowand moderate-incom e households, which vary based on composition (size, presence of children), financial circumstances (income, childcare requirements) and location within the region (which determines transportation costs). The six household profiles analyzed in the present study we re selected based on their ability to shed light on the challenges faced by households that ar e likely to earn too much to qualify for subsidy, but not enough that the ability to secure stable housing is a foregone conclusion. The following household profiles assessed were anal yzed: · Profile A: Single adult, no children – 30% AMI · Profile B-1: Single adult, one child (not in child care) – 50% AMI · Profile B-2: Single adult, two children (one in ch ildcare) – 80% AMI · Profile C: Two adults, no children – 50% AMI · Profile D-1: Two adults, one child (not in childca re) – 80% AMI · Profile D-2: Two adults, two children (one in chil dcare) – 100% AMI

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Page 156 Two measures are developed for each household profi le. The first identifies a household’s ‘housing budget,’ or the amount of mont hly income that remains available for housing after the household covers the essential no n-housing and transportation costs required to sustain a basic standard of living. Cos ts associated with five non-housing and transportation (non-H+T) items – food, medical expe nses, childcare (if applicable), other goods required for basic personal and household ope rations, and taxes – are calculated separately for each theoretical household profile b ased on its composition and income level, as well as the metropolitan area in which it is loc ated. Data on these expenditures are sourced from the U.S. Bureau of Labor Statistics (B LS) Consumer Expenditure (CE) Survey, a dataset released annually based on findings from interviews and diary surveys that ask American consumers about details related to their h ousehold characteristics, expenditures, and income (U.S. Bureau of Labor Statistics, 2016), as well as from the Living Wage Calculator (LWC) housed at Massachusetts Institute of Technology along with other data sources. A detailed description of these data and c alculations can be found in Chapter 5. Non-H+T costs are then subtracted from household in come to arrive at each household profile’s ‘H+T budget,’ or the amount of income that remains available for combined housing and transportation costs. Next, tr ansportation costs are estimated for each block group (by household profile) using data from HUD’s Location Affordability Index (LAI) and the LWC. In a final step, the total amoun t of income that remains available for housing is calculated for each household profile, a t the block group level. The resulting ‘housing budget’ thus represents the upper limit of what a particular theoretical household living in a particular block group can afford to pa y for housing. Housing budgets vary by household profile, as well as by block group for th e same household profile since transportation costs vary depending on each block g roup’s location within the region. Table 7.1 outlines the minimum, median, and maximum housing budgets calculated for each household profile, by metro. Housing budge ts vary considerably among different

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Page 157 household profiles within the same metro, as well a s across metros. In general, households living in the Portland metro area have the lowest h ousing budgets due to its relatively low AMI. Seattle generally has the largest housing budg ets, which reflects both its higher AMI, as well as lower non-housing and transportation cos ts relative to other metros. Households with a single adult and no children earning 30-perc ent AMI have the smallest housing budgets across all metros due to their exceptionall y low incomes. Households with two adults and one child (not in childcare) earning 80percent AMI generally have the largest amount of income available for housing, even larger than two-adult households earning 100percent AMI but with two children (one of whom requ ires childcare). This result highlights the large burden of childcare costs on a householdÂ’s ab ility to afford housing.

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Page 158 Table 7.1. Summary of housing budgets for all house hold profiles, by metro Metro / Household Profile LSRI Housing budget Percent affordable rental units1 Min. Med. Max. Dallas Area median income = $59,175 Profile A: 1 adult, no children – 30% AMI $0 $107 $472 1.8% Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI $89 $312 $646 8.0% Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI $571 $827 $1,212 66.3% Profile C: 2 adults, no children – 50% AMI $80 $317 $665 8.5% Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI $916 $1,163 $1,522 83.9% Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI $853 $1,142 $1,562 83.2% Denver Area Median Income = $64,206 Profile A: 1 adult, no children – 30% AMI $0 $100 $446 2.2% Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI $100 $355 $670 6.0% Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI $358 $652 $1,015 25.7% Profile C: 2 adults, no children – 50% AMI $62 $328 $660 5.5% Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI $894 $1,178 $1,530 69.4% Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI $594 $926 $1,339 50.5% Houston Area Median Income = $58,689 Profile A: 1 adult, no children – 30% AMI $0 $110 $469 1.7% Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI $47 $307 $634 8.4% Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI $513 $813 $1,190 63.0% Profile C: 2 adults, no children – 50% AMI $43 $312 $651 8.9% Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI $876 $1,149 $1,500 81.2% Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI $804 $1,123 $1,535 80.6% Los Angeles Area Median Income = $60,337 Profile A: 1 adult, no children – 30% AMI $0 $126 $526 1.4% Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI $0 $322 $738 4.0% Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI $317 $683 $1,163 15.1% Profile C: 2 adults, no children – 50% AMI $0 $293 $729 3.6% Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI $741 $1,098 $1,567 44.3% Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI $506 $924 $1,474 31.0% Minneapolis Area Median Income = $68,019 Profile A: 1 adult, no children – 30% AMI $0 $167 $573 6.1% Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI $228 $496 $863 18.7% Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI $642 $949 $1,373 64.5% Profile C: 2 adults, no children – 50% AMI $185 $472 $854 16.9% Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI $1,086 $1,391 $1,795 85.8% Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI $924 $1,280 $1,755 82.6%

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Page 159 Table 7.1, cont’d Metro / Household Profile LSRI Housing budget Percent affordable rental units1 Min. Med. Max. Portland Area Median Income = $58,832 Profile A: 1 adult, no children – 30% AMI $0 $0 $321 0.7% Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI $0 $83 $444 2.1% Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI $39 $365 $874 11.0% Profile C: 2 adults, no children – 50% AMI $0 $35 $408 1.4% Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI $441 $748 $1,245 42.4% Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI $183 $543 $1,147 21.6% Salt Lake City Area Median Income = $61,529 Profile A: 1 adult, no children – 30% AMI $0 $0 $289 0.9% Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI $53 $268 $543 6.1% Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI $493 $741 $1,058 54.4% Profile C: 2 adults, no children – 50% AMI $0 to $216 $500 4.7% Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI $758 $1,029 $1,330 74.7% Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI $687 $973 $1,325 71.5% Seattle Area Median Income = $68,969 Profile A: 1 adult, no children – 30% AMI $13 $266 $709 5.6% Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI $413 $635 $1,037 21.4% Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI $851 $1,107 $1,517 64.6% Profile C: 2 adults, no children – 50% AMI $353 $593 $1,017 18.0% Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI $1,360 $1,624 $2,085 84.4% Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI $1,174 $1,483 $2,024 81.2% 1Represents the sum of all rental units that are aff ordable within the household’s housing budget across all block groups, as a percent of total metr o-wide rental units

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Page 160 A second LSRI ‘supply’ measure is calculated using data from the U.S. Census American Community Survey (ACS) 2010-14 Five-Year E stimates to identify the quantity of rental units that are affordable within the housing budgets of each household profile. This measure details the number of units within each blo ck group that are estimated to be affordable to a particular household, accounting fo r the characteristics of the household and the estimated transportation costs associated with the block group. Supply data can then be summed across all block groups to arrive at the tot al metro-wide supply of rental units that are affordable to each household profile. This data is provided in as a percent of total metrowide rental units. The mean number of rental units that are estimated to be affordable within an average block group in each metro are provided in Table 7.2 , along with standard deviations. The LSRI supply measures are considerab ly over-dispersed for most household profiles, meaning that their distribution contains a large number of zero values and standard deviations are larger than mean values. This result reflects the fact that the variables do not take negative values, and therefore have non-normal distributions.

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Page 161 Table 7.2. Mean and standard deviation values for m easures of transit accessibility and housing afford ability Metro Transit accessibility % of regional jobs accessible by 45-min transit commute Supply of affordable rental units: Number of affordable rental units for six lowand moderate-income households 1 adult 0 children 30% AMI 1 adult 1 child (0 in childcare) 50% AMI 1 adult 2 children (1 in childcare) 80% AMI 2 adults 0 children 50% AMI 2 adults 1 child (0 in childcare) 80% AMI 2 adults 2 children (1 in childcare) 100% AMI µ sd µ sd µ sd µ sd µ sd µ sd µ sd Dallas 2.7% 0.1% 4.5 10.7 20.1 64.3 166.2 235.3 21.4 67.4 210.3 261.9 208.5 263.0 Denver 9.4% 10.0% 4.8 25.9 13.1 43.1 56.0 115.4 12.0 42.0 151.1 205.1 110.0 175.6 Houston 4.8% 7.6% 5.2 24.2 25.7 72.4 193.7 255.6 27.3 76.4 249.6 288.1 247.6 288.0 Los Angeles 4.7% 4.7% 4.0 22.4 11.1 37.8 41.7 87.0 10.1 36.0 122.3 166.2 85.7 137.3 Minneapolis 8.5% 10.5% 10.9 45.1 33.5 83.2 115.7 162.2 30.3 79.5 153.8 186.7 147.9 185.5 Portland 10.6% 12.1% 1.8 12.7 5.2 24.6 27.8 73.9 3.6 18.5 107.4 149.2 54.8 112.0 Salt Lake City 6.6% 9.6% 1.6 10.3 10.8 35.5 96.0 150.6 8.3 30.3 131.8 174.5 126.1 170.3 Seattle 7.3% 10.9% 13.2 42.2 50.8 102.4 153.1 200.5 42.6 92.8 200.2 226.2 192.5 221.8

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Page 162 There exist several limitations, most having to do with qualities of the data sourced to construct them. In particular, the ACS data which s erves as the basis for several of the elements that contribute to the LSRI measure has su bstantial margins of error, particularly at small geographies. While this error is certainly a concern, it is considered to be tolerable when weighed against the utility of the findings th at are generated for small geographies. Location Affordability Index data also poses limita tions having to do with its use of aggregate (versus household-level) data, which a recent study attributes to the LAI reporting higher housing and transportation costs as compared to est imates modeled with more granular data (Salon et al., 2016). Despite this shortcoming , the LAI remains the only comprehensive dataset of estimated transportation costs that is r eadily-available to practitioners. Finally, data on the rent of occupied housing units sourced from the ACS reflects the rent of housing units paid by current residents, and thus may not b e fully representative of the amount of rent that would be asked from new renters. This lik ely has the effect of overestimating supplies of affordable rental housing. As a result of these and other limitations, the LSRI housing budget and supply measures should be consid ered to be estimates subject to measurement error. Measuring transit accessibility The second variable of interest, transit accessibil ity, is defined here as the ease of reaching desired destinations by bus, rail, or othe r transit mode operated by a public transit agency. Measuring transit accessibility requires sp ecifying three elements: The origin of a trip, the desired destination, and bounds on the ti me it takes to travel from the origin to the destination. The present study measures accessibili ty to a single type of destination – jobs – and considers the block group containing the househ old’s home location to be the origin and the location of employment opportunities to be the destination. While there are certainly arguments to be made for the value of assessing tra nsit accessibility to non-work

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Page 163 destinations, doing so requires complicated assumpt ions about the nature of and meanings attached to these trips, all of which are outside t he scope of the present study (Levine et al., 2012). There are two publicly-available sources for nation al data on transit accessibility to jobs. The University of Minnesota (UMN) Accessibili ty Observatory ‘Access Across America: Transit 2014’ database31 provides data on the number of jobs accessible fro m block groups within a 30-minute commute for U.S. metros. The Env ironmental Protection Agency (EPA) ‘Access to Jobs and Workers via Transit’ database p rovides similar data on the number of jobs that can be reached in a 45-minute commute by transit. Both datasets employ a cumulative opportunities approach to measuring tran sit accessibility – that is, they measure accessibility by counting the number of employment opportunities that can be reached from a particular location given a particular travel tim e. Both measures are calculated using employment estimates from the Longitudinal Employer -Household Dynamics (LEHD) Longitudinal Origin-Destination Employment Statisti cs (LODES) and data on transit service that transit agencies publicly share through the Ge neral Transit Feed Specification (GTFS). The EPA Access Jobs and Workers via Transit databas e was selected for use here because of its longer travel time threshold (45 min utes), which more closely mirrors the national average commute time of 53 minutes (Santos et al., 2011) as compared to the UMN data. Transit accessibility is measured for the standard peak period (4:45 to 7 PM) based on data collected in the GTFS during the mont hs of December 2012 and January 2013. In addition to in-vehicle travel time, the EP A data accounts for the time required to walk to a transit stop (up to 15 minutes), transfer between services (up to 10 minutes), and walk to the final destination. The data also accoun ts for cases in which walk travel times are shorter than transit travel times between the same origin-destination pair. Mean and standard deviations for transit accessibility in th e eight metros appear in Table 7.2 . As with 31 http://ao.umn.edu/data/

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Page 164 the housing affordability variables, transit access ibility is over-dispersed in most metros, which reflects the large number of block groups in which zero jobs are accessible by transit. The EPA data (along with the UMN data) poses severa l limitations. First, the LODES LEHD data underlying both datasets is not complete data, but rather are estimated based a small set of sample data. As a result, there are su bstantial margin of errors associated with these synthetic data. Secondly, the EPA and UMN dat asets do not differentiate between lowand high-wage jobs. This may skew results, sin ce evidence suggests that transit use patterns are likely to vary significantly across di fferent occupations (Legrain et al., 2016). For instance, hours for many low-wage jobs are not like ly to follow the standard nine-to-five workday upon which the EPA transit accessibility me asure is based. Future research should account for these differences by disaggregating emp loyment opportunities by occupation and/or wage. Methods After constructing LSRI measures for each metro, I address Research Question 1 by calculating the supply of rental units that are bot h affordable to a defined set of lowand moderate-income households and located in areas with high transit accessibility. I compare this analysis to the supply of affordable units loc ated in areas with zero or low transit accessibility. Areas with values above the non-zero average accessibility for all block groups in a metro are considered ‘high’ accessibility whil e those below the non-zero average are identified as ‘low’ accessibility. ‘Zero’ accessibi lity areas are those in which no jobs are reachable by transit within 45-minutes. Thresholds therefore reflect each metro’s individual landscape of accessibility, with low/high accessibi lity thresholds ranging from 5.9-percent of regional jobs in the Los Angeles metro to 17.5-perc ent of jobs in Portland as summarized in Table 7.3 .

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Page 165 Table 7.3. Transit accessibility by metro Metro Total regional jobs % of regional jobs accessible, by percentile1 High-Low accessibility threshold: Average (non-zero) % of regional jobs accessible2 25th 50th 75th 100th Dallas 2,871,213 0.0% 0.0% 4.1% 26.5% 6.1% Denver 1,364,708 0.8% 5.1% 17.3% 43.3% 11.8% Houston 2,530,059 0.0% 0.0% 7.9% 39.3% 10.8% Los Angeles 5,562,340 0.8% 3.5% 6.4% 24.4% 5.9% Minneapolis 1,679,161 0.0% 2.3% 17.5% 51.7% 13.0% Portland 974,858 0.0% 5.6% 21.1% 48.9% 17.5% Salt Lake City 935,191 0.0% 0.0% 13.5% 39.3% 15.0% Seattle 1,598,296 0.0% 1.8% 10.0% 53.8% 11.9% 1 Includes block groups in which zero jobs are access ible within a 45-minute commute by transit 2 Average only includes block groups with non-zero tr ansit accessibility In addition to observing differences in the supplie s of affordable housing located in high versus zero/low accessibility, ‘accessibility ratios’ are also constructed for each of the household profiles. These ratios divide the number of affordable units located in zero/low accessibility areas by the number of affordable uni ts located in high accessibility areas. Each household profile’s accessibility ratio is the n compared to the accessibility ratio of the metro’s overall supply of rental units (regardless of affordability) in order to detect deviations from metro-wide distributions of rental housing acr oss high and zero/low accessibility areas. RESULTS AND DISCUSSION The present analysis seeks to understand how suppli es of affordable rental housing are distributed across areas with high transit acce ssibility and areas with zero or low transit accessibility. Two approaches are taken in this inv estigation, as described below and summarized in Table 7.4 . Supplies of Affordable Rental Units, by Accessibili ty Level The first column in Table 7.4 outlines the total number of rental units within a metro that are affordable to each household profile (rega rdless of accessibility). The supply of affordable rental units varies quite widely across household profiles. Supplies of affordable housing are lowest among households with a single a dult and no children earning 30-

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Page 166 percent AMI (Profile A), with supplies ranging from 0.9to 6.1-percent of metro-wide rental units (in Salt Lake City and Minneapolis, respectiv ely). The largest supplies of affordable housing are generally found for households with two adults and one child not in childcare earning 80-percent AMI (Profile D-1). Supplies of h ousing affordable to this profile range from 42.4-percent of metro-wide affordable rental u nits in Portland to 85.8-percent in Minneapolis. Additional columns in Table 7.4 outline the percent of rental units that are affordable and located within the three accessibili ty categories. In these columns, cells highlighted in red indicate that the majority of af fordable rental units are located in areas with zero and low accessibility. Cells highlighted in gr een indicate that the majority of affordable rental units are located in areas with high accessibility. The extent to which affordable rental housing is lo cated in areas with high transit accessibility varies from metro-to-metro, and in so me cases, by household profile. In two metros (Denver and Los Angeles), a larger supply of affordable rental units is located in neighborhoods with high transit accessibility for a ll household profiles. In two other metros (Dallas and Houston), the largest supplies of renta l housing affordable to all household profiles are located in areas with zero or low acce ss to transit. In the remaining four metros, findings vary depending on the amount of income ava ilable for housing. In Minneapolis and Portland, supplies of rental units that are afforda ble to households with very small housing budgets (Profiles A, B-1, B-2, and C) are located p redominately in areas with high transit accessibility. In those same regions, the majority of rental units affordable to households with more moderate monthly housing budgets (Profile s D-1 and D-2), are located in areas with zero or low transit accessibility. Salt Lake C ity and Seattle demonstrate similar patterns, although supplies of affordable rental u are larger in areas with high transit accessibility only for households with the smallest housing budgets (P rofile A). For all other household profiles, the majority of affordable rental housing is located in areas with zero or low access to transit.

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Page 167 Accessibility Ratios A final column in Table 7.4 reports ‘accessibility ratios’ representing the ra tio of the number of units located in zero/low accessibility a reas to the number of units located in high accessibility areas. This ratio is reported for bot h total metro-wide rental units, regardless of their affordability, as well as for units affordabl e to each of the household profiles. A value greater than 1.0 indicates that a larger quantity o f units is located in areas with zero/low transit accessibility. A value less than 1.0 indica tes that a larger quantity of units is located high accessibility areas. Accessibility ratios for all metros are greater than 1.0, indicating that in all cases, rental units (regardless of affordabi lity) are located predominately in areas with zero/low transit accessibility. Accessibility ratio s for affordable units vary by region and by household profile. Accessibility ratios highlighted in red in Table 7.4 are those in which the ratio exceeds 1.0 and is larger than the metro-wide ratio . For example, households in the Houston metro with two adults and two children (one of whom requires childcare) earning 100-percent AMI (Profile D-2) have a ratio of 3.00, which exceeds the metro-wide ratio of 2.95. This indicates that the distribution of renta l units affordable to these households skews toward zero/low accessibility areas to a larger deg ree than the distribution of metro-wide rental units. This circumstance is present for only a handful of household profiles, including two in Houston, two in Portland, and two in Seattle . Cells highlighted in green are those in which the r atio is less than 1.0, indicating that a larger proportion of affordable units are located in areas with high transit accessibility. Given that metro-wide accessibility ratios for all metros indicate that a majority of units are located in zero/low transit accessibility for all m etros, cells highlighted in red thus exhibit patterns that are opposite to metro-wide patterns. For example, the metro-wid e accessibility ratio for the Denver metro is 1.13, pointing to lar ger supplies of rental units in zero/low access areas. However, the accessibility ratio for households with two adults and two

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Page 168 children (one of whom requires childcare) earning 1 00-percent AMI is 0.65, indicating that a larger number of affordable rental units are locate d in high access areas. All households in the Denver metro exhibit this circumstance, as do a ll households in the Los Angeles metro. This circumstance is also present in three househol d profiles in Minneapolis, three in Portland, and one in Seattle. Accessibility ratios not highlighted (i.e. neither red nor green) are those in which the distribution of affordable rental units also skews toward zero/low accessibility areas, but to a lesser degree than the distribution of metro-wide r ental units. For example, Profile D-2 households in Dallas show a slightly different patt ern than those in Houston. Although a larger majority of units affordable to the househol d profile in Dallas are located in areas with zero/low accessibility, its accessibility ratio (2. 97) is less than the metro-wide accessibility ratio of 3.07, indicating that the proportion of af fordable units with zero/low access is roughly similar to the proportion of metro-wide units with zero/low access. This circumstance is present for the majority of household across all me tros.

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Page 169 Table 7.4. Supplies of metro-wide affordable rental housing, by accessibility level Metro / Household Profile Total number (%) of metro’s rental units that are affordable % of regional rental units that are affordable, by accessibility level1 Ratio of zero/low access affordable units to high access affordable units2 Zero access Low access High access Dallas Total metro-wide rental units (1,025,612 units) n/a 46.2% 29.3% 24.6% 3.07 Affordable rental units, by household profile Profile A: 1 adult, no children – 30% AMI 18,596 (1.8%) 0.5% 0.7% 0.7% 1.65 Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI 82,234 (8.0%) 2.0% 2.6% 3.4% 1.37 Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI 680,03 7 (66.3%) 26.7% 21.9% 17.7% 2.74 Profile C: 2 adults, no children – 50% AMI 87,410 (8.5%) 2.1% 2.8% 3.6% 1.38 Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI 860,52 1 (83.9%) 36.6% 26.4% 20.9% 3.01 Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI 853,008 (83.2%) 36.0% 26.2% 21.0% 2.97 Denver Total rental units (428,050) n/a 10.1% 42.9% 47.0% 1.13 Total affordable rental units, by household profile Profile A: 1 adult, no children – 30% AMI 9,510 (2.2%) 0.0% 0.2% 2.0% 0.13 Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI 25,786 (6.0%) 0.2% 1.2% 4.6% 0.30 Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI 110,19 1 (25.7%) 0.8% 6.5% 18.5% 0.39 Profile C: 2 adults, no children – 50% AMI 23,551 (5.5%) 0.1% 1.1% 4.3% 0.28 Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI 297,10 3 (69.4%) 4.3% 27.5% 37.6% 0.84 Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI 216,240 (50.5%) 2.2% 17.8% 30.5% 0.65 Houston Total rental units (925,355) n/a 44.8% 29.9% 25.3% 2.95 Total affordable rental units, by household profile Profile A: 1 adult, no children – 30% AMI 15,713 (1.7%) 0.4% 0.7% 0.7% 1.60 Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI 77,373 (8.4%) 1.7% 3.6% 3.1% 1.70 Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI 583,32 6 (63.0%) 22.1% 24.3% 16.6% 2.80 Profile C: 2 adults, no children – 50% AMI 82,327 (8.9%) 1.8% 3.8% 3.3% 1.71 Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI 751,66 9 (81.2%) 33.4% 27.8% 20.0% 3.06 Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI 745,438 (80.6%) 32.7% 27.7% 20.2% 3.00

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Page 170 Table 7.4, cont’d Metro / Household Profile Total number (%) of metro’s rental units that are affordable % of regional rental units that are affordable, by accessibility level1 Ratio of zero/low access affordable units to high access affordable units2 Zero access Low access High access Los Angeles Total rental units (2,260,284) n/a 13.8% 47.3% 38.9% 1.57 Total affordable rental units, by household profile Profile A: 1 adult, no children – 30% AMI 33,254 (1.4%) 0.1% 0.3% 1.1% 0.34 Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI 92,829 (4.0%) 0.3% 1.2% 2.5% 0.64 Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI 348,22 6 (15.1%) 1.4% 4.5% 9.3% 0.63 Profile C: 2 adults, no children – 50% AMI 83,987 (3.6%) 0.3% 1.1% 2.3% 0.61 Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI 1,020, 974 (44.3%) 5.1% 16.9% 22.3% 0.99 Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI 715,542 (31.0%) 3.2% 10.6% 17.3% 0.88 Minneapolis Total rental units (413,925) n/a 23.8% 32.8% 43.6% 1.30 Total affordable rental units, by household profile Profile A: 1 adult, no children – 30% AMI 25,128 (6.1%) 0.3% 1.1% 4.7% 0.30 Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI 77,455 (18.7%) 2.5% 3.7% 12.5% 0.49 Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI 267,15 8 (64.5%) 12.0% 20.6% 31.9% 1.02 Profile C: 2 adults, no children – 50% AMI 70,073 (16.9%) 2.0% 3.4% 11.5% 0.47 Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI 355,33 5 (85.8%) 18.8% 28.5% 38.5% 1.23 Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI 341,761 (82.6%) 17.5% 27.2% 37.9% 1.18 Portland Total rental units (360,001) n/a 29.3% 35.5% 35.2% 1.84 Total affordable rental units, by household profile Profile A: 1 adult, no children – 30% AMI 2,559 (0.7%) 0.2% 0.0% 0.5% 0.52 Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI 7,452 (2.1%) 0.8% 0.2% 1.1% 0.85 Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI 39,492 (11.0%) 6.3% 1.4% 3.3% 2.30 Profile C: 2 adults, no children – 50% AMI 5,056 (1.4%) 0.7% 0.1% 0.7% 1.06 Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI 152,48 8 (42.4%) 14.8% 11.1% 16.5% 1.57 Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI 77,857 (21.6%) 11.2% 2.9% 7.5% 1.88

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Page 171 Table 7.4, cont’d Metro / Household Profile Total number (%) of metro’s rental units that are affordable % of regional rental units that are affordable, by accessibility level1 Ratio of zero/low access affordable units to high access affordable units2 Zero access Low access High access Salt Lake City Total rental units (225,681) n/a 47.4% 18.0% 34.5% 1.90 Total affordable rental units, by household profile Profile A: 1 adult, no children – 30% AMI 2,100 (0.9%) 0.3% 0.1% 0.6% 0.53 Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI 13,772 (6.1%) 2.8% 0.5% 2.8% 1.20 Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI 122,78 9 (54.4%) 24.0% 6.7% 23.7% 1.30 Profile C: 2 adults, no children – 50% AMI 10,580 (4.7%) 2.2% 0.4% 2.2% 1.18 Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI 168,57 3 (74.7%) 34.4% 11.3% 29.1% 1.57 Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI 161,304 (71.5%) 32.7% 10.5% 28.2% 1.53 Seattle Total rental units (584,394) n/a 28.1% 36.8% 35.1% 1.85 Total affordable rental units, by household profile Profile A: 1 adult, no children – 30% AMI 32,652 (5.6%) 0.8% 1.8% 2.9% 0.90 Profile B-1 : 1 adult, 1 child (not in childcare) – 50% AMI 125,117 (21.4%) 5.2% 7.4% 8.8% 1.44 Profile B-2 : 1 adult, 2 children (1 in childcare) – 80% AMI 377,36 5 (64.6%) 17.0% 25.0% 22.6% 1.86 Profile C: 2 adults, no children – 50% AMI 105,073 (18.0%) 4.2% 6.0% 7.8% 1.31 Profile D-1 : 2 adults, 1 child (not in childcare) – 80% AMI 493,50 1 (84.4%) 23.4% 31.4% 29.7% 1.84 Profile D-2 : 2 adults, 2 children (1 in childcare) – 100% AMI 474,524 (81.2%) 22.4% 30.7% 28.1% 1.89 1 Red cells indicate that supplies of rental units affordable to the household profile are greater in areas with zero and low accessibility Green cells indicate that supplies of rental units affordable to the household profile are greater in areas with high accessibility 2 Red cells indicate that the ratio of affordable units located in zero/low accessibility areas to affordable unit s in high accessibility areas is greater than one and exceeds the ratio for metro-wi de units, indicating that a larger proportion of af fordable units are in zero/low access areas as compared to the metro-wide distribution Green cells indicate that the ratio of affordable units located in zero/low accessibility areas to affordable unit s in high accessibility areas is less than one while the metro-wide ratio is greater than one, indicating that a larger proportion of u nits are in high access areas while a larger proportion of metro-wide units are i n zero/low access areas

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Page 172 SUMMARY OF KEY FINDINGS The analysis presented in this chapter employed the LSRI measure of affordability to examine the distribution of affordable housing unit s across areas with zero, low, and high transit accessibility. Results offer insight into t he geographies of accessibility and affordability that lowand moderate-income renters are expected to confront as they seek market-rate housing in eight U.S. metros. Table 7.5 briefly summarizes the key results of this analysis for two household profiles – one with a ‘low housing budget’ (one adult and one child not in childcare earning 50% AMI) and one wit h a ‘moderate housing budget’ (two adults and two children, one of whom requires child care, earning 100% AMI).

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Page 173 Table 7.5. Summary of results (Research Question 1) Metro / Household Profile Distribution of supplies of affordable rental units, by accessibility level Accessibility ratio, as compared to metro-wide supplies of rental units Dallas Metro-wide (regardless of affordability) majority i n zero/low access Low housing budget household majority in zero/low access less pronounced than me tro Moderate housing budget household majority in zero/low access less pronounced than me tro Denver Metro-wide (regardless of affordability) majority i n zero/low access Low housing budget household majority in high access opposite of metro Moderate housing budget household majority in high access opposite of metro Houston Metro-wide (regardless of affordability) majority i n zero/low access Low housing budget household majority in zero/low access less pronounced than me tro Moderate housing budget household majority in zero/low access more pronounced than metro Los Angeles Metro-wide (regardless of affordability) majority i n zero/low access Low housing budget household majority in high access opposite of metro Moderate housing budget household majority in high access opposite of metro Minneapolis Metro-wide (regardless of affordability) majority i n zero/low access Low housing budget household majority in high access opposite of metro Moderate housing budget household majority in zero/low access less pronounced than me tro Portland Metro-wide (regardless of affordability) majority i n zero/low access Low housing budget household majority in high access opposite of metro Moderate housing budget household majority in zero/low access more pronounced than metro Salt Lake City Metro-wide (regardless of affordability) majority i n zero/low access Low housing budget household majority in high access opposite of metro Moderate housing budget household majority in zero/low access less pronounced than me tro Seattle Metro-wide (regardless of affordability) majority i n zero/low access Low housing budget household majority in high access opposite of metro Moderate housing budget household majority in zero/low access more pronounced than metro Red cells results point to ‘weak’ geographies of op portunity Green cells results point to ‘strong’ geographies o f opportunity Table 7.5 highlights that current geographies of transit acc essibility and housing affordability are likely to vary considerably betwe en metros. In some metros – most notably, Denver and Los Angeles – low and moderate housing b udget households are expected to

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Page 174 encounter greater supplies of affordable rental hou sing in transit-accessible areas. These results (cells highlighted in green) point to stron g geographies of opportunity for households with limited means, with positive implications for transportation justice. However, patterns in two other metros – Dallas and Houston – exhibit the opposite pattern, with larger supplies of affordable rental units located in areas with low transit accessibility. These results (highlighted in red) p oint to weaker geographies of opportunity. Geographies of opportunity appear to be particularl y weak for moderate housing budget households, for whom the proportion of affordable u nits located in zero/low access areas is higher than metro-wide distributions of total renta l units. Results for the remaining four metros are mixed acr oss household profiles. While low budget housing budget households in these metros ar e likely to encounter larger supplies of affordable rental units in transit-accessible areas , households with more moderate housing budgets are expected to find larger supplies in are as with zero or low transit access. Results thus point to strong geographies of opportunity for low housing budget households in Minneapolis, Portland, Salt Lake City, and Seattle. However, geographies of opportunity for households with moderate housing budgets appear to be much weaker, particul arly in Portland and Seattle where the affordable rental un its are located in zero/low access areas in higher proportions than metro-wide distributions . Taken together, these results generated using robus t LSRI measures lend mixed support to the location efficiency narrative. Findi ngs for all households in Denver and Los Angeles, and for some households with very limited housing budgets in four other metros, are largely consistent with the argument that areas with high transit accessibility offer lowand moderate-income households the best opportunity for securing affordable housing. In these metros, results suggest that threats of exclu sionary displacement in transit-accessible areas may be cause for less concern than often thou ght. This is not to say that issues of transit-induced gentrification and displacement sho uld be ignored, but rather that conditions

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Page 175 may require a particular set of policy recommendati ons aimed at preserving affordability for lowand moderate-income households. Results for ot her metros are less supportive of a location efficiency narrative. Households in Dallas and Houston, as well as moderate housing budget households in four other metros, are more likely to encounter larger supplies of affordable rental units in areas with little or no transit accessibility (and consequently, high levels of auto-dependency) despite the likelihood o f lower transportation costs in these same areas. These metros exhibit considerable exclu sionary displacement in transitaccessible areas, thus challenging a location effic iency perspective and pointing to the need for an entirely different set of policy recommendat ions. These findings shed light on varying conditions tha t are faced across U.S. metros with regional rail transit, and provide insights fo r metros with similar characteristics that are currently undertaking large transit expansion proje cts. Results should be tempered by two notable considerations. First, analyses are likely to be sensitive to the way in which ‘low’ and ‘high’ transit accessibility areas are defined. Thi s analysis uses a reasonable threshold based on the non-zero average of transit accessibil ity across all metros. However other analyses may yield different results. Second, given the dynamic nature of housing markets, findings from the present analysis using 2014 data may quickly, or already have, become outdated. The measures and methods employed are int ended to be intuitive and easilyreplicable so that practitioners are able to regula rly update analyses for specific metros and households profiles.

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Page 176 CHAPTER VIII EXAMINING THE COMPLEX RELATIONSHIP BETWEEN TRANSIT ACCESSIBILITY and HOUSING AFFORDABILITY IN EIGHT U.S. METROS INTRODUCTION Findings presented in Chapter 7 used LSRI measures of housing affordability to generate insights into the geographies of transit a ccessibility and affordability that lowand moderate-income renters are likely to confront as t hey seek market-rate housing in eight U.S. metros. The research question addressed in the present chapter extends these earlier findings by isolating the relationship between tran sit accessibility and housing affordability through a series of global and local regression ana lyses. The existing literature reviewed in Chapter 3 demonstrates that a multitude of characte ristics of the built and social environment beyond transit accessibility influence affordability. I therefore employ LSRI measures of housing affordability to address the fo llowing question: What is the relationship between transit accessibility and supp lies of affordable rental housing, controlling for key characteristics of the built an d social environments that are likely to influence that relationship as well as for spati al dependence effects? (Research Question 2). I first use multivariate spatial regression to mode l the global (metro-wide) relationship between transit accessibility (conceptualized as th e primary explanatory variable) and supplies of affordable rental (conceptualized as th e outcome variables). These models control for the effects of various aspects of densi ty, land use mix, housing tenure, and socioeconomic conditions that are known to influence hou sing affordability, as well as interaction terms that control for the influence of these chara cteristics on transit accessibility. The presence of spatial dependence is also modelled thr ough inclusion of a spatially-weighted error term. One set of models examines supplies of rental units that are affordable to a theoretical household with relatively little income available for housing and a second set

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Page 177 examines affordability for households with more mod erate housing budgets. I then use the same model specifications in geographically-weighte d regression (GWR) to explore how local relationships between accessibility and affordabili ty vary across space within a single metro. These investigations are conducted for the e ight metros detailed in Chapter 3 and analyzed in Chapter 7. The primary aim of the present chapter is to examin e associations between levels of transit accessibility within neighborhoods (block g roups) and the supplies of affordable rental units that are located therein. The analyses presen ted here are not intended for use in drawing causal conclusions about the relative effec ts of specific factors on supplies of affordable housing. Rather, the models are specifie d in order to allow for the isolation and close examination of the complex relationship betwe en accessibility and affordability. Results deepen our understanding of the geographies of opportunity experienced by lowand moderate-income households across the U.S., and shed further light on the robustness of a location efficiency narrative when affordabili ty is assessed using more nuanced measures and analytical approaches. DATA AND METHODS Data The present analysis employs the same measures of h ousing affordability and transit accessibility described in Chapter 7. In addition t o these variables, a number of explanatory variables are included to control for the influence of key characteristics of the built and social environment on the supply of affordable rental unit s (the outcome variable). The measures and data sources used to operationalize the control variables are summarized in Table 8.1 . The control variables – which include measures of p edestrian-orientation, land use mix, housing tenure, and socio-economic characteristics – were selected based on their demonstrated importance in the existing literature to understanding both housing affordability and transit accessibility. Data is ob tained from a variety of publicly-available

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Page 178 sources including the U.S. Census ACS 2010-14 FiveYear Estimates, EPA Access to Jobs and Workers via Transit database, the EPA Smart Loc ation Database (SLD), and the U.S. Department of Housing and Urban Development (HUD) L ocation Affordability Index (LAI). Methods Two spatial methods are used to support the analysi s presented in this chapter. First, a series of multivariate spatial error regression m odels are developed in order to investigate global (metro-wide) relationships between transit a ccessibility and housing affordability. The same model specifications are then used in GWR mode ls in order to explore how these relationships vary across block groups within a sin gle metro. Two spatial error models and two GWR models are dev eloped for each metro: One set of models examining supplies of affordable rent al units for ‘low housing budget’ households, defined as those composed of a single a dult and one child (not in childcare) earning 50-percent AMI (Household Profile B-1) and another set examining affordability for ‘moderate housing budget’ households composed of tw o adults and two children (one of whom requires childcare) earning 100-percent AMI (P rofile D-2).

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Page 179 Table 8.1. Variables, measures and data sources Variable Measure Data Source Outcome variable LSRI measure of housing affordability Supply of rental units in block group that are affordable to two household profiles (low and moderate housing budget) as a percent of a metroÂ’s total rental units Developed by author as detailed in Chapter 5 (calculated using MIT LWC data, among other sources, and ACS 2010-14 5-Year Estimates) Primary explanatory variable Transit accessibility Percent of regional jobs that can be reached from the block group within 45-minutes by transit As reported by EPA Access to Jobs and Workers via Transit database (calculated from LEHD LODES data) Control variables Gross household density Number of households per ac re of developable land ACS 2010-14 5-Year Estimates and 2010 TIGER data Pedestrian-oriented intersection density Number of intersections that can be traversed by pedestrians per acre 1 As reported in EPA SLD (calculated from NAVTEQ data) Employment-housing entropy Mix of five employment categories (retail, office, industrial, service, entertainment) and occupied housing As reported by EPA SLD (calculated from ACS 2006-2010 5-Year Estimates and 2010 TIGER data) Access to retail amenities Number of retail jobs wi thin half-mile of block group centroid divided by land area As reported by HUD LAI (calculated from LEHD LODES data) Proportion renters Number of renter-occupied units as a percent of the total number of occupied units ACS 2010-14 5-Year Estimates Total housing units Total number of occupied and vacant housing units ACS 2010-14 5-Year Estimates Median household income Median household income of block group ACS 2010-14 5-Year Estimates Proportion non-Hispanic white population Percent of population that identifies as non-Hispanic and white ACS 2010-14 5-Year Estimates Source Notes: ACS = U.S. Census American Community Survey; EPA SLD = U.S. Environmental Protection Agency Smart Location Database; LEHD LOD ES = Longitudinal employer-household dynamics Longitudinal Origin-Destination Employment Statistics; HUD LAI = U.S. Housing and Urban Development Location Affordability Index 1 More details about the calculation of this variable can be found in the EPA SLD User Guide: https://www.epa.gov/sites/production/files/2014-03/ documents/sld_userguide.pdf Spatial error regression model-building Three primary intentions guide the model building p rocess: 1) To capture key factors that are likely to influence accessibility and affo rdability directly (as well as factors that may

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Page 180 mediate the relationship between the two variables) using publicly-available data; 2) To develop relatively intuitive models that maximize p arsimony and avoid multi-collinearity; and 3) To enable comparisons between household profiles within the same metro, as well as across multiple metros. R open-source software (v3.3.1) was used to first s pecify ordinary least squares (OLS) models, then spatial error models following a n iterative approach. Appendix D provides the complete R-code used in the below-desc ribed analysis for a sample metro (Denver)32. As a first step, all explanatory and outcome variab les were converted to standardized z-scores so that values of all measure s are roughly the same magnitude (this is required for analysis in R) and in order to make interpretation of interaction terms more manageable. Next, initial OLS models incorporating theoreticall y-relevant main effect variables were tested and assessed for model fit us ing Adjusted R-square and Akaike information criterion (AIC). Final main effects OLS models for all metros and ho usehold profiles were then specified such that all models c ontain the same set of main effects variables. In order to avoid multicollinearity, variable pairs with correlation coefficients larger than 0.7 and/or Variation Inflation Factor (VIF) va lues greater than 2.5 were inspected, and only one variable was selected for inclusion in the model based on model fit. This led to the exclusion of two variables from the analysis: Block density (which was highly correlated with the intersection density in most models) and percen t single-family homes (which was highlycorrelated with percent renters).Transformations an d quadratic terms of several variables were tested in order to address non-normality and h eteroskedasticity, but none substantially improved normality and were therefore not included in the final models. In order to account for variables that mediate the relationship between transit accessibility and supplies of affordable rental uni ts, all possible interaction terms involving 32 R-code for additional metros and data files used i n the analyses available upon request ( kara.luckey@ucdenver.edu )

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Page 181 the variable ‘transit accessibility’ were tested an d evaluated for inclusion based on statistical significance in the model ( =0.05) and improvement to model fit (Adjusted R-squ ared). Because explanatory factors are likely to interact in different ways across metros, interaction terms were included on a model-by-model basis, such that each final OLS interaction model contains the same set of main effects variables, bu t a unique set of interaction terms. Diagnostics of the final OLS interaction model regr ession residuals were then examined. The presence of spatial autocorrelation in both the outcome variables and the regression residuals were evaluated using Global Mo ran’s I statistics, which gauges the degree to which the values of a variable within a p articular unit are spatially-associated with values of the variable in neighboring units. Neighbors are defined as units that share a border through a row-standardized first-order queen contiguity spatial weights matrix. Moran’s I takes on a value of -1.0 to +1.0, with a statistically-significant posi tive value indicating a direct relationship between a unit’s observation and those of its neigh bors, and a statistically-significant negative value indicating an indirect relationship. A Moran’s I value of zero indicates there is no spatial autocorrelation. A relatively large and statistically-significant value of Moran’s I suggests the existence of some form of spatial depe ndence, which violates the basic assumption underlying linear regression that observ ations are independent. Ignoring spatial dependence in OLS may consequently lead to biased a nd inconsistent estimates of regression coefficients and standard errors. Given the nature of the present investigation, spat ial autocorrelation may be due to any number of issues. Spatial error related to the use of units of analys is (block groups) that do not accurately reflect the actual geography of t he unit of interest (neighborhoods) is likely to exist in this analysis. It is also likely that the explanatory variables ar e distributed across space in ways that do not neatly coincide with the units of analysis, further perpetuating spatial error. Spatial dependence within and among both dependent and independent

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Page 182 variables is also expected to be present. Finally, given the complex nature and causality of the phenomenon under investigation, it is possible that omitted variables and model misspecification may contribute to spatial error. Spatial autocorrelation is typically handled throug h three types of spatial regression: Spatial error models, in which spatial error is con trolled for by incorporating a spatiallyweighted error term into the regression equation; S patial lag models, which treat spatial dependence as a substantive effect of interest by i ncluding a spatially-lagged dependent variable as additional predictor; and Spatial durbi n models, which include both a spatiallylagged dependent variable (as with spatial lag mode ls), as well as spatially-lagged independent variables. Because the present study is interested in controlling for spatial dependence (rather than treating it as a phenomenon of interest), spatial error regression estimated using the maximum likelihood method is em ployed. Results of Lagrange Multiplier (LM) tests conducted for all models were also inspe cted in order confirm that spatial error models were the most appropriate method. Each spatial error regression model is structured identically to its corresponding OLS interaction mo del, with a spatially-weighted error term ( ) included in addition to the usual random error te rm ( ): nnrrnrn n n n n n n n n n n Spatial error regression was chosen among several o ther analytical approaches that are commonly used to answer questions about global relationships associated with housing and transportation. For instance, structural equati on modelling (SEM) can be useful in examining phenomena with complex causality because it accounts for endogeneity by directly modelling not only relationships between t he explanatory and outcomes (as in standard linear models), but also the relationships between the explanatory variables themselves. However, SEM is not able to account for spatial dependence without exceedingly sophisticated techniques. Because the r elationships investigated here exhibit

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Page 183 high levels of spatial autocorrelation (as discusse d in the sections that follow), and given that biased conclusions can result from inattention to issues of spatial error, a-spatial SEM was deemed inappropriate for these investigations. While several of the control variables included in the final spatial error models may inde ed influence the primary explanatory variable of interest (transit accessibility) as wel l as the outcome variable (housing affordability), the models do not have an endogenei ty problem, per se. This is because endogeneity suggests the pursuit of causal explanations, whereas the present research is interested in understanding associations without regard to causality. I instead include interaction terms that account for the influence of the control variables on the relationship between transit accessibility and housing affordabi lity rather than directly modelling this influence (as is done in SEM). Issues with multi-co llinearity were also closely monitored through VIF analysis of the final models. Poisson, Quasi-Poisson, and Negative Binomial distr ibution models were also considered. These models are commonly used with out come variables that do not take on negative values (as is the case here) in order impr ove model fit. However, pilot analyses indicated that the models did not substantially imp rove model fit (as assessed by AIC) and carried the added burden of being difficult to inte rpret. These models were therefore deemed inappropriate given that one of the goals of the modelling effort is to produce models that are relatively intuitive and replicable by a wide audience. Zero-inflated and hurdle models, which first employ logistic regressi on to model the likelihood that the outcome variables takes on a value larger than zero , then use Poisson or other distributions to model the non-zero outcome variables, were elimi nated for consideration for the same reason. The decision to employ spatial error regres sion for the present study is supported by widespread use of linear models (including spatial regression) for over-dispersed variables similar to the ones analyzed here. Model fit diagno stics also support the use of spatial regression.

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Page 184 Geographically-weighted regression Geographically-weighted regression is a local statistical technique that allows for variation in relationships across space. It thus st ands in contrast to standard regression which examine global relationships. GWR is most often used in explorato ry questions that investigate how particular phenomena of interest va ry across space. It is therefore a truly spatial technique in the sense that GWR directly accounts f or non-stationarity (which describes a condition in which relationships betwee n the outcome and explanatory variables are different across space), rather than attempting to ‘model out’ spatial processes (as spatial regression does). In GWR, coefficients are estimated based on the values of neighboring observations using a spatial weights ma trix, which is specified so that more proximate observations are given greater weight tha n observations located farther away (Fotheringham et al., 2003). A ‘fixed weight matrix ’ optimized through corrected Akaike Information Criterion (AICc) minimization is employ ed here. All GWR analysis is conducted using Esri ArcGIS 10.4 software. GWR models are specified using the same sets of var iables included in the spatial error models. This allows for direct comparisons be tween coefficient estimates of the GWR and spatial error models. Comparative model fit of GWR and spatial error models is also assessed using AICc and AIC values. One potential i ssue with GWR is the presence of local multicollinearity. In the present chapter, findings for GWR models that exhibit evidence of local multicollinearity are not reported, since res ults are likely to be unreliable. RESULTS AND DISCUSSION The results presented in Chapter 7 provide importan t insights into the geographies of affordability and accessibility experienced by lowand moderate-income households as they seek affordable market-rate rental units. Results p resented here delve deeper into the mechanisms behind these geographies by analyzing th e relationship between transit accessibility and supplies of affordable rental hou sing controlling for key factors that are

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Page 185 likely to influence affordability and accessibility , as well as for error associated with spatial dependence. Findings are presented in two parts. I first examin e results from global regression models to develop a deeper understanding of the rel ationship between transit accessibility and housing affordability at the metro level. OLS m odels that were specified in the initial steps of the analysis are first described, and expl anatory power and model fit are assessed. I then use results from a series of spatial error r egression models to draw conclusions about the relationship between transit accessibility, hou sing affordability, and other key factors of the built and social environment. Next, I discuss r esults of local (geographically-weighted) regression models to highlight how relationships va ry across space within metros. Examining Global Relationships between Transit Acce ssibility and Housing Affordability: Spatial Error Models Table 8.3 summarizes key results of the OLS and spatial erro r models, including coefficient and standard error estimates for the va riable ‘transit accessibility,’ model fit statistics (Adjusted R-square and AIC), and Moran’s I tests for spatial autocorrelation in the dependent variable as well as in the OLS and spatia l error regression residuals. Full model results for each metro can be found in Appendix E . Interaction terms The same set of interaction terms are included in b oth the OLS and spatial error models in order to control for variables that media te the relationship between affordability and accessibility. Table 8.2 identifies the interaction terms included in the f inal regression models. A statistically-significant interaction term theref ore indicates that the interacting variable has an effect not only on the supply of af fordable housing, but also on transit accessibility. For example, an interaction between gross household density and transit accessibility (which is statistically-significant i n 13 of the 16 models) indicates that the strength and direction of the relationship between the explanatory variable (transit

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Page 186 accessibility) and the outcome variable (supplies o f affordable rental housing) depends on levels of household density. This finding is not surprising given that density p lays a primary role in both the provision of transit service and a vailability of rental units. Interaction terms between the total number of housing units and the p ercent of renters are also common across models. Interactions between transit accessibility and inte rsection density, as well as between transit accessibility and the non-Hispanic white population are statistically significant in less than half of models.

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Page 187 Table 8.2. Statistically-significant interaction te rms included in low and moderate (‘mod’) housing bu dget models Interaction term1 Statistically-significant interaction terms include d in final regression models2 Dallas Denver Houston Los Angeles Minneapolis Portland Salt Lake City Seattle Low Mod Low Mod Low Mod Low Mod Low Mod Low Mod Low Mod Low Mod TA* Gross density TA* Intersection density TA* Employee-housing entropy TA* Local retail access TA* Percent renters TA* Total housing units TA* Median household income TA* Percent non-Hispanic white population 1 “TA” = transit accessibility 2 = 0.05

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Page 188 Table 8.3. Key OLS and spatial error regression res ults Metro Transit accessibility regression coefficient1,2 Model fit Moran’s I tests (se) (OLS) (se) (Spatial) Adj. R-sq (OLS) AIC (OLS) AIC (Spatial) DV3 Residuals (OLS) Residuals (Spatial) Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Dallas 0.07** (0.02) 0.06** (0.02) 0.301 10162 9931 0.269** 0.148** -0.005 n.s. Denver 0.06* (0.03) 0.06* (0.03) 0.392 4618 4596 0.286** 0.065** -0.004 n.s. Houston 0.03 (0.02) 0.02 (0.02) 0.392 7063 6818 0.318** 0.183** -0.013 n.s. Los Angeles 0.08** (0.01) 0.09** (0.02) 0.156 21863 21620 0.226** 0.101** -0.007 n.s. Minneapolis 0.18** (0.02) 0.20** (0.03) 0.608 4413 4379 0.392** 0.074** -0.005 n.s. Portland -0.11** (0.03) -0.12** (0.03) 0.305 3529 3525 0.174** -0.037 n.s. 0.002 n.s. Salt Lake City -0.09** (0.03) -0.03 (0.04) 0.415 2959 2890 0.362** 0.137** -0.006 n.s. Seattle -0.11** (0.02) -0.07** (0.03) 0.551 5042 4854 0.397** 0.166** -0.003 n.s. Moderate housing budget household : 2 adults, 2 children (one in childcare), 100% AMI Dallas 0.07** (0.01) 0.06** (0.01) 0.828 4424 4330 0.299** 0.092** -0.004 n.s. Denver 0.08* (0.02) 0.06** (0.02) 0.762 2777 2729 0.341** 0.096** -0.005 n.s. Houston 0.03* (0.01) 0.03 (0.02) 0.787 3908 3830 0.302** 0.106** -0.006 n.s. Los Angeles 0.12** (0.01) 0.17** (0.02) 0.390 19212 18736 0.472** 0.142** -0.015 n.s. Minneapolis 0.09** (0.01) 0.09** (0.01) 0.863 1984 1984 0.310** 0.019* <-0.001 n.s. Portland -0.29** (0.03) -0.15** (0.05) 0.434 3237 2831 0.456** 0.353** -0.039 n.s. Salt Lake City -0.01 (0.02) -0.01 (0.02) 0.818 1464 1436 0.390** 0.094** -0.004 n.s. Seattle -0.11** (0.01) -0.10** (0.01) 0.878 1830 1783 0.377** 0.08** -0.001 n.s. *p 0.05; **p 0.01; 1 Coefficients related to standardized z-score of ‘tr ansit accessibility’ (% of jobs accessible from blo ck group within a 45-minute transit commute) 2 Green bold text indicates a statistically-significant and posi tive relationship; Bold red text indicates a statistically-significant and nega tive relationship; Plain green text indicates a positive, but not statistically-si gnificant relationship; Plain red text indicates a negative, but not statistically-significant relationship. 3 DV = Dependent variable (block group’s supply of re ntal units affordable to household with two adults, two children (one in childcare) earning 100% AMI

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Page 189 Ordinary Least Squares regression models As summarized in Table 8.3 , the OLS models for low housing budget households exhibit varying degrees of explanatory power with A djusted R-squared ranging from rather low (approximately 0.3 for several models and as lo w as 0.16 for one model) to moderately high (above 0.8 for four models). Explanatory power is highest among the Dallas, Minneapolis, Salt Lake City, and Seattle models and lowest in the Los Angeles and Portland models. Despite the apparent connections between explanator y factors, VIF values for the OLS models included in the full model results ( Appendix E ) demonstrate that multicollinearity is not an issue. The VIF statistic estimates how much the variation of a coefficient is inflated because of linear dependenc e with other predictors. A VIF value of 1.5 would therefore indicate that variation in the coef ficient is 50-percent larger than it would be if the variable was entirely uncorrelated with othe r explanatory factors (Agresti & Finlay, 2009). In the present analysis, VIF values for tran sit accessibility coefficients are less than 5.0 (a threshold commonly used to assess multicolli nearity) in all models. While VIF exceeds 5.0 for some interaction terms and their related ma in effects variables, it is acceptable to ignore high values among interaction terms since th ey by their nature introduce multicollinearity (Allison, 1999). Additional model diagnostics included in Table 8.3 indicate the presence of heteroskedasticity and spatial autocorrelation in a ll models. MoranÂ’s I tests for spatial autocorrelation in the dependent variable are relat ively large and statistically-significant in all models, ranging from 0.17 (Portland low housing bud get model) to 0.47 (Los Angeles moderate housing budget model). MoranÂ’s I tests for spatial dependence in the OLS residuals are also statistically-significant in all but one model (Portland low housing budget). These diagnostics indicate the presence of spatial autocorrelation in the OLS models and suggest that spatial regression methods should be e mployed. For the reasons described under the Data and Methods section, spatial error r egression is used. Results from LM tests

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Page 190 for most models confirm that spatial error models a re most appropriate (results of LM tests appear in full regression results in Appendix E ). Spatial error regression As shown in Table 8.3 , spatial error regression improves model fit (as a ssessed by AIC and log likelihood values) when compared to OLS models, albeit in minor ways for some models. Full model results ( Appendix E ) demonstrate that the spatially-weighted components of the error terms ( , ‘lambda’) are relatively large and significant in all but one model (Minneapolis moderate housing budget), indica ting the presence of spatiallycorrelated errors and further underscoring that spa tial error regression is an appropriate approach. Furthermore, Moran’s I tests of spatial error regre ssion residuals are small and not statistically-significant across all models, in dicating that spatial autocorrelation has been ‘modelled out’ in the spatial error regressions. Co efficient estimates are generally stable between the OLS and spatial error models, although some differences do exist. In particular, coefficients for the Los Angeles and Portland moder ate housing budget models also demonstrate substantial changes in size between OLS and spatial models. Although problems with heteroskedasticity persist, these res ults indicate that spatial error models constitute an improvement to OLS models, underscori ng the importance of accounting for spatial autocorrelation in investigations of issues of housing affordability and transit accessibility. Spatial error regression results presented in Table 8.3 and Appendix E reveal that the relationship between accessibility and affordab ility varies not only across metros, but also for different household profiles within the sa me metro. In half of the metros – Dallas, Denver, Los Angeles, and Minneapolis – models for b oth household profiles predict statistically-significant and positive relationship s between accessibility and affordability holding all else constant. This suggests that in these metros, higher levels o f transit accessibility are associated with larger supplies of affordable rental units. Effect sizes vary

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Page 191 considerably across these models, with coefficient estimates ranging from +0.06 in Dallas and Denver (for both models) to +0.20 for the Minne apolis low housing budget model. In contrast, statistically-significant negative relationships are identified in Portland and Seattle, suggesting that higher levels of trans it accessibility are associated with fewer affordable rental units for both household profiles . The size of this effect ranges from -0.15 (Portland moderate housing budget model) to -0.07 ( Seattle low housing budget model). Models for the remaining two metros (Houston and Sa lt Lake City) exhibit no statisticallysignificant relationship between transit accessibil ity and supplies of affordable rental housing for either household profile. Relationships between the two variables are general ly strongest among moderate housing budget households. Moderate income housing budget models also demonstr ate more robust explanatory power (as evidenced by Adju sted R-square statistics). This is perhaps due to the fact that households with modera te housing budgets are able to afford more for housing, and therefore have access to larg er numbers of rental units (regardless of their level of transit accessibility) while househo lds with limited housing budgets face a general lack of housing affordable . Of all the models, the largest statistically-signif icant positive effects were observed among low housing budget households in Minneapolis ( =0.20, se=0.03) and moderate housing budget households in Los Angeles ( =0.17, se=0.02). Using Minneapolis low budget households as an example, this coefficient m eans that a one standard deviation increase in the percent of jobs accessible within a 45-minute transit commute (10.5-percent in this case) is associated with an increase of 17 affordable rental units, holding all else constant33. The largest statistically-significant negative rela tionships were observed in Portland among low housing budget households ( =-0.12, se=0.03) and moderate income 33 Because the dependent variable (DV) is standardize d as a z-score, the regression coefficient (0.20) is multiplied by the standard deviation of the depe ndent variable (83.2 units) to arrive at the magnitude of change in the DV.

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Page 192 housing budget households ( =-0.15, se=0.05). Using Portland moderate income housing budget households as an example, regression results suggest that controlling for other factors, a one standard deviation (12.1%) increase in transit accessibility is associated with 15 fewer affordable rental units. Influence of control variables on housing affordabi lity in spatial error regression models Results discussed above for the final spatial error models suggest that a large number of control variables and interaction terms a re closely associated with housing affordability. In order to understand the influence of these contr ol variables on housing affordability relative to the influence of transit accessibility, a set of ‘reduced’ spatial error regression models were developed and compared to re sults from the ‘full’ spatial error regression models discussed above. These reduced spatial error models include only a single explanatory – transit accessibility – and om it all other control variables. The full models are identical to those described above and s ummarized in Table 8.3. These full models contain the full set of control variables an d interaction terms as specified in full model results presented in Appendix E . Table 8.4 compares the transit accessibility regression coef ficients for both models, as well as the AIC values for both models. Lower AIC values among the full models indicate that the addition of the control variables improves model fit as compared to the reduced models. In some models, model fit improves substantially. For example, the Dallas, Houston, and Seattle moderate housing budget models demonstrate reductions in AIC values exceeding 60-percent. This result suggests that many factors are likely t o contribute to explaining housing affordability, and that many of these factors may in fact influence housing affordability to a larger degree than trans it accessibility. Comparisons of the regression coefficients for tran sit accessibility in the reduced and full models further underscore this finding. Without controls, the relationship between transit accessibility and housing affordability is positive and quite large for all models, with

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Page 193 coefficients as large as 0.43 in the reduced models . Once key control variables are accounted for, however, the strength of this relati onship drops considerably in all models. Coefficients in the full models remain statisticall y-significant in all but four of the 16 models. Interestingly, models for two metros – Portland and Seattle – exhibit relationships between transit accessibility and housing affordabi lity that are statistically-significant and positive when left uncontrolled, but are statistica lly-significant and negative when controlling for key characteristics of the built and social env ironment. For example, the coefficient for the Seattle moderate housing budget household witho ut controls is 0.37 and -0.10 with controls. This result again underscores that other factors ar e likely to influence the supply of affordable in ways that may mask the nature of the relationship between accessibility and affordability.

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Page 194 Table 8.4. Comparison of reduced spatial error mode ls (with no controls) and full spatial error models (with controls) Metro Transit accessibility regression coefficients1,2 (se) Model diagnostics AIC Reduced model (no controls) Full model (with controls) Reduced model (no controls) Full model (with controls) Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Dallas 0.20** (0.02) 0.06** (0.02) 10892 9931 Denver 0.34** (0.03) 0.06* (0.03) 5175 4596 Houston 0.22** (0.03) 0.02 (0.02) 7862 6818 Los Angeles 0.28** (0.02) 0.09** (0.02) 22025 21620 Minneapolis 0.41** (0.03) 0.20** (0.03) 5771 4379 Portland 0.15** (0.04) -0.12** (0.03) 3926 3525 Salt Lake City 0.22** (0.05) -0.03 (0.04) 3269 2890 Seattle 0.36** (0.04) -0.07** (0.03) 6102 4854 Moderate housing budget household : 2 adults, 2 children (one in childcare), 100% AMI Dallas 0.19** (0.02) 0.06** (0.01) 10796 4330 Denver 0.41** (0.03) 0.06** (0.02) 4994 2729 Houston 0.18** (0.03) 0.03 (0.02) 7960 3830 Los Angeles 0.43** (0.02) 0.17** (0.02) 19433 18736 Minneapolis 0.36** (0.03) 0.09** (0.01) 6008 1984 Portland 0.14** (0.05) -0.15** (0.05) 3451 2831 Salt Lake City 0.27** (0.04) -0.01 (0.02) 3234 1436 Seattle 0.37** (0.03) -0.10** (0.01) 6177 1783 *p 0.05; **p 0.01; 1 Coefficients related to standardized z-score of ‘tr ansit accessibility’ (% of jobs accessible from blo ck group within a 45-minute transit commute); 2 Green bold text indicates a statistically-significant and posi tive relationship; Bold red text indicates a statistically-significant and negative relationsh ip; Plain green text indicates a positive, but not statistically-significant relationship; Plain red text indicates a negative, but not statistically-si gnificant relationship.

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Page 195 Differences in the supply of affordable rental unit s associated with higher levels of transit accessibility In order to further understand what model results m ean in terms of on-the-ground outcomes, the full spatial error models are used to identify the difference in supplies of affordable rental units that are expected to be ass ociated with higher levels of transit accessibility, holding key control variables consta nt. Differences in the supply of affordable housing that are associated with a 10-percent highe r number of regional jobs that can be reached within a 45-minute transit commute are calc ulated for an average block group, while holding all variables at their mean values. R esults of this analysis are presented in Table 8.5 . Holding all else constant, higher levels of transit accessibility are associated with larger supplies of affordable rental units in five metros: Dallas, Denver, Houston, Los Angeles, and Minneapolis. In some cases, modest imp rovements to transit accessibility are associated with quite substantial differences in th e availability of affordable units. For example, an average block group in Dallas with 10-p ercent ‘better’ transit accessibility is associated with the availability of 36 additional r ental units that are affordable to households with moderate housing budgets, holding all other fa ctors at mean values. Predicted differences among moderate housing budget household s in Los Angeles are even larger: 10-percent higher transit accessibility are associa ted with 50 additional units. Differences are generally smaller for low housing budget househ olds, ranging from two to 16 units. In the remaining three metros (Portland, Salt Lake City, and Seattle), higher levels of transit accessibility are associated with the avail ability of fewer affordable units. The largest of these effects occurs among moderate housing budg et households in Portland and Seattle, in which block groups with 10-percent high er transit accessibility are expected to contain14 and 21 fewer affordable rental units (respectively), holding al l other variables at

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Page 196 mean values. Differences are expected to be much sm aller in the remaining models (ranging from one to six fewer units). It bears repeating that these analyses do not descr ibe causal relationships, but rather shed light on the relationship between trans it accessibility and supplies of affordable rental housing that are reflected in current geogra phies. Table 8.5. Differences in the supply of affordable rental units associated with higher levels of transit accessibility Metro Difference in the percent (number) of metro-wide affordable rental units associated with 10% higher level of transit accessi bility1 Low housing budget 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget 2 adults, 2 children (1 in childcare), 100% AMI Dallas 0.0008% (+ 9 units ) 0.0035% (+ 36 units ) Denver 0.0006% (+ 3 units) 0.0023% (+ 10 units) Houston 0.0002% (+ 2 units) 0.0012% (+ 11 units) Los Angeles 0.0003% (+ 8 units) 0.0022% (+ 50 units) Minneapolis 0.0038% (+ 16 units) 0.0039% (+ 16 units) Portland -0.0007% (2 units) -0.0039% (14 units) Salt Lake City -0.0006% (1 unit) -0.0006% (1 unit) Seattle -0.0011% (6 units) -0.0024% (21 units) Green text indicates an expected increase in the percent/number of affordable units associate d with 10% higher transit accessibility; Red text indicates an expected decrease in the percent/number of affordable units associated with 10% higher transit accessibility. Examining Local Relationships between Transit Acces sibility and Housing Affordability: Geographically-Weighted Regression M odels While spatial error models generate important insig hts into dynamics between transit accessibility and housing affordability occurring a t the global (metro) level, they do not allow for an understanding of local dynamics occurring at lower levels of geography. I therefore turn to results of a series of GWR models which are identical to the spatial error models in terms of the variables that are included, but allow for regression coefficients to vary across block groups. Because models are estimated at the b lock group level, there is no need to account for spatial dependence through the inclusio n of an error term, as is done in the spatial error models.

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Page 197 Table 8.6 outlines results of both global (spatial error) an d local (geographicallyweighted) regression models. Global coefficients fo r transit accessibility are the same as those presented in Table 8.6 . Ranges of local coefficients are reported separat ely for block groups located in areas with ‘high’ and ‘low’ trans it accessibility (defined according to the methods described in Chapter 7) in order to detect differences in the dynamics operating within both areas. Local model results are not pres ented for both the Los Angeles models and the Minneapolis low housing budget models due t o the presence of local multicollinearity. While global multicollinearity i s not a concern for these models, high correlations between explanatory variables at the b lock group level render GWR unreliable for these models. Statistical significance is not r elevant to local models, and is thus not reported. Comparisons of AIC and AICc values for gl obal and local models suggest that model fit is roughly similar across GWR and spatial error models. Inspection of the spatial error and GWR model coeff icients for transit accessibility point to considerable discrepancies between local a nd global relationships between accessibility and affordability. Results in three m etros suggest that positive global coefficients are masking the presence of negative local relationships. In both low and moderate housing budget models for Dallas, global c oefficients indicate that metro-wide, higher levels of transit accessibility are associat ed with larger supplies of affordable rental units. However, in some block groups located in bot h low and high accessibility areas, local coefficients are negative, indicating that higher l evels of accessibility are associated with fewer affordable units. The same results hold true for t he Houston moderate housing budget model. The Denver models exhibit similar patterns, although only for block groups located in low accessibility areas. Results for the Salt Lake City and Seattle low hous ing budget models exhibit the opposite pattern. While global coefficients in thes e models are negative, indicating that

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Page 198 transit accessibility is associated with fewer affo rdable units, local coefficients suggest the presence of positive relationships in both low and high accessibility a reas. These results highlight the complex nature of the r elationship between transit accessibility and housing affordability, and the im portance of understanding neighborhoodlevel dynamics when developing policy and planning interventions aimed at maximizing affordability in transit-accessible areas. For exam ple, global statistics indicating a positive relationship may mask the need to address more chal lenging circumstances for lowand moderate-income households at the neighborhood leve l. In other cases, global relationships that point to metro-wide challenges may obscure the need for interventions that preserve pockets of transit-accessible affordable housing.

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Page 199 Table 8.6. Local geographically-weighted regression results, as compared to global spatial error regre ssion results Metro Transit accessibility regression coefficients (full models – with controls) 1 Model diagnostics Global coefficients (spatial error) Range of local coefficients2 (GWR) Global (spatial error) Local (GWR) High accessibility areas Low accessibility areas (se) (min) (max) (min) (max) AIC AICc Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Dallas 0.06** (0.02) -0.09 0.18 -0.24 0.18 9931 9789 Denver 0.06* (0.03) 0.05 0.11 -0.12 0.11 4596 4602 Houston 0.02 (0.02) 0.01 0.13 0.01 0.19 6818 7055 Los Angeles 0.09** (0.02) n/a3 n/a3 n/a3 n/a3 21620 n/a Minneapolis 0.20** (0.03) n/a3 n/a3 n/a3 n/a3 4379 n/a Portland -0.12** (0.03) -0.17 -0.08 -0.16 -0.05 3525 3512 Salt Lake City -0.03 (0.04) -0.07 0.04 -0.08 0.04 2890 2913 Seattle -0.07** (0.03) -0.07 0.12 -0.23 0.13 4854 4742 Moderate housing budget household : 2 adults, 2 children (one in childcare), 100% AMI Dallas 0.06** (0.01) -0.05 0.13 -0.04 0.16 4330 3950 Denver 0.06** (0.02) 0.02 0.08 -0.01 0.09 2729 2244 Houston 0.03 (0.02) -0.08 0.03 -0.07 0.08 3830 3621 Los Angeles 0.17** (0.02) n/a3 n/a3 n/a3 n/a3 18736 n/a Minneapolis 0.09** (0.01) 0.03 0.12 0.03 0.16 1984 1887 Portland -0.15** (0.05) -0.40 -0.14 -0.40 -0.05 2831 2849 Salt Lake City -0.01 (0.02) -0.02 0.01 -0.02 0.01 1436 1378 Seattle -0.10** (0.01) -0.11 -0.06 -0.20 0.02 1783 1612 *p 0.05; **p 0.01 1 Coefficients related to standardized z-score of ‘t ransit accessibility’ (% of jobs accessible from bl ock group within a 45-min. transit commute); Green bold text indicates a statistically-significant and posi tive coefficient estimate; Bold red text indicates a statistically-significant and negative coefficient estimate; Plain green text indicates the estimate is positive, but not st atistically-significant; Plain red text indicates the estimate is negative, but not statistically-signifi cant; 2 Range of local coefficients are reported for block groups with low and high transit accessibility ONL Y (local coefficients for block groups with zero accessibility are excluded). ‘Low’ and ‘high’ transit accessibility are defined according to the methods described in Chapter 7. 3 GWR models suffer from local multicollinearity and therefore do not produce reliable results

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Page 200 SUMMARY OF KEY FINDINGS This chapter has presented several analyses that se ek to understand the relationship between transit accessibility and housing affordabi lity, holding other key characteristics of the built and social environment constant. The thre e most insightful of these are summarized in Table 8.7 . The first column summarizes the results of spatia l error regression models, which shed light on the global relationship s between transit accessibility and housing affordability. Global relationships are ide ntified as either positive or negative, and statistical significance is noted. The same spatial error models were also used to calculate differences in the supplies of affordable housing t hat would be expected to be associated with 10-percent higher levels of transit accessibil ity (summarized in the second column). Decreases or increases are noted as either small, m oderate, or large. The final (third) column summarizes the local relationships between a ccessibility and affordability that result from a series of GWR models. Local relationships ar e identified as being the same as global relationships (either positive or negative), or exh ibiting both positive and negative local relationships (‘positive/negative’). Cells highlighted in green indicate results that ar e suggestive of strong geographies of opportunities for lowand moderate-income house holds. Geographies of opportunity are particularly strong in Dallas, Denver, Los Angeles, and Minneapolis. These four metros all exhibit positive global relationships between trans it accessibility and the supply of affordable rental housing, holding all else constant. Positive , although not statistically-significant, relationships between accessibility and affordable also exist in Houston. These positive relationships are also reflected in local coefficie nts for the Denver models, Houston low housing budget model, and Minneapolis moderate hous ing budget household model. In all these metros, higher levels of transit accessibilit y are associated with larger supplies of affordable rental units, which are quite substantia l in some cases.

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Page 201 Cells highlighted in red indicate results that are suggestive of weak geographies of opportunity. Geographies of opportunity appear to b e particularly weak in Portland and Seattle, where improved transit accessibility is li nked to fewer affordable units. In these metros, results indicate a statistically-significan t and negative global relationship between transit accessibility and supplies of affordable re ntal units, controlling for other factors. These negative relationships are also reflected in local coefficients for all but the Seattle low housing budget household model. Models for Salt Lak e City also demonstrate negative, although not statistically-significant, global rela tionships. In these metros, higher levels of transit accessibility are associated with fewer aff ordable units.

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Page 202 Table 8.7. Summary of results (Research Question 2) Metro / Household Profile global relationship differences in supplies of affordable housing associated with higher transit accessibility local relationships in high transit accessibility areas Dallas Low housing budget household positive** small increases positive/negative Moderate housing budget household positive** large increases positive/negative Denver Low housing budget household positive** small increases same as global (positive) Moderate housing budget household positive** moderate increases same as global (positive) Houston Low housing budget household positive (n.s.) small increases same as global (positive) Moderate housing budget household positive (n.s.) moderate increases positive/negative Los Angeles Low housing budget household positive** small increases n/a1 Moderate housing budget household positive** moderate increases n/a1 Minneapolis Low housing budget household positive** large increases n/a1 Moderate housing budget household positive** large increases same as global (positive) Portland Low housing budget household negative** large decreases same as global (negative) Moderate housing budget household negative** small decreases same as global (negative) Salt Lake City Low housing budget household negative (n.s.) small decreases positive/negative Moderate housing budget household negative (n.s.) s mall decreases positive/negative Seattle Low housing budget household negative** large decreases positive/negative Moderate housing budget household negative** moderate decreases same as global (negative) Red cells results point to ‘weak’ geographies of op portunity Green cells results point to ‘strong’ geographies o f opportunity 1 GWR results not reported due to the existence of lo cal multicollinearity; **statistically-significant at =0.01; n.s. = not significant at =0.05

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Page 203 Taken together, results generated using robust LSRI measures lend mixed support for a location efficiency narrative. As with Reving ton & Townsend (2016), results of the present study indicate that more nuanced measures o f housing affordability yield findings that are less consistent with a location efficiency narrative than findings from previous studies that use ratio-based measures. Findings for some metros – Denver and Los Angeles most notably – are generally consistent with a loca tion efficiency narrative, with higher levels of transit accessibility associated with larger sup plies of rental housing affordable for most lowand moderate-income households. Findings in ot her metros, Portland and Seattle in particular, are less supportive, with higher levels of transit accessibility associated with fewer affordable rental units. Results also point to several methodological conclu sions. First, the presence of statistically-significant spatial autocorrelation ( as evidenced by Moran’s I tests of the dependent variables and OLS regression residuals), along with the improvement in model fit achieved by the spatial error models, underscores t he importance of using spatial regression techniques in future investigations arou nd transit accessibility, housing affordability, and related phenomena. Comparisons b etween the OLS and spatial error models demonstrate that failing to account for spat ial dependence leaves analyses vulnerable to biased estimates and possible mischar acterization of the effects of key variables, issues that should be taken seriously gi ven the policy relevance of work in this arena. Second, findings suggest that many factors a re likely to explain housing affordability, and that many of these may in fact influence housin g affordability to a larger extent than transit accessibility. While the present analysis f ocuses primarily on the relationship between transit accessibility and housing affordability in isolation, it is important to acknowledge the complex relationships that exist among other charac teristics of the built and social environments. Finally, results also highlight that relying exclusively on global models to

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Page 204 understand affordability and accessibility may mask considerable local variation, and thus may obscure the need for nuanced policy prescriptio ns.

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Page 205 CHAPTER IX GEOGRAPHIES OF OPPORTUNITY FOR LOWAND MODERATE-IN COME HOUSEHOLDS IN EIGHT U.S. METROS: A SYNTHESIS OF FIN DINGS INTRODUCTION Conceptual Basis This dissertation began by considering how several contemporary theoretical perspectives help in exploring issues of social jus tice in the context of U.S. metropolitan planning and policy, and of transportation justice in particular. The conceptual framework developed to guide the present study adopts princip les of one of these perspectives – Sen and Nussbaum’s ‘capabilities approach’ – to define a ‘just’ transportation system as one in which all individuals are able to access the opport unities that are necessary to reach their full potential. The conceptual framework also integ rates a ‘geographies of opportunity,’ frame which is commonly used among practitioners an d advocates in work around issues of spatial and social justice. In this conceptual framework, an individual’s ‘geog raphy of opportunity’ (or in the language of the capabilities approach, her/his set of ‘ capabilities ‘) represents the opportunities that are available to a person in the ir pursuit of well-being. Three components (‘ primary goods ‘) related to physical planning and policy shape ge ographies of opportunity: 1) the quantity and qualities of the opportunities themselves; 2) the home location from which an individual seeks to access opportunities; and 3) the transportation options that enable their ability to access opportunities outsid e their home locations. A multitude of other ‘ personal and social conversion factors’ also influence geographies of opportunity. For the purposes of the present study, the most important o f these factors is a household’s ‘housing budget,’ defined as the amount it can afford to spe nd on housing while still meeting the essential non-housing needs required to support a b asic standard of living.

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Page 206 Given the costs associated with car ownership, and given that low-income households are much less likely to have access to a private vehicles than more affluent households, public transit often plays a vital role in providing access to opportunities for those with limited means. The present study therefo re conceptualizes geographies of opportunity for lowand moderate-income households as being bounded by two circumstances: 1) the ability to access employment opportunities via modes other than private auto (‘transit accessibility’); and 2) the ability to afford housing in transit-accessible areas, and thus benefit from the advantages conferr ed by access to transit (‘housing affordability’).

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Page 207 Figure 9.1. Conceptual framework Existing Literature Two areas of concern around transit accessibility a nd housing affordability are frequently documented in the research literature. T he first relates to direct displacement effects resulting from high property values in area s with high-frequency transit that leave long-standing residents no longer able to afford ho using in transit-accessible neighborhoods (‘transit-induced displacement’). The second area o f concern relates to increased demand

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Page 208 for transit-accessible locations on a regional scal e leading to exclusionary displacement effects whereby newly-formed and relocating househo lds with lower incomes are unable to afford housing in these neighborhoods and must inst ead locate to more auto-oriented areas of the metro. However, a strand of literature focus ed on a ‘location efficiency’ approach to thinking about issues of affordability has emerged in recent years to suggest that local and regional displacement in transit-rich areas may be less of a threat than commonly thought when the cost of housing and transportation are con sidered in combination. A ‘location efficiency narrative’ acknowledges that housing cos ts may be higher in transit-accessible areas, but counters that reduced transportation exp enditures are likely to offset these costs resulting in better overall affordability. While th is location efficiency narrative has gained prominence in recent years, it remains unclear whet her it is supported by on-the-ground empirics, especially given growing demand for housi ng in transit-accessible areas and concerns about the robustness of the measures typic ally used to assess affordability. A critical review of existing research that focuses on the relationship between transit accessibility and housing affordability in U.S. met ros has led to further questions about the robustness of the location efficiency perspective. In particular, four significant gaps in the literature are identified in Chapter 2. First, the literature focuses predominately on effects associated with fixed-rail transit, thus neglecting the large role buses play in providing access across U.S. metros. Second, existing researc h has little to say about landscapes of affordable housing in transit-accessible neighborho ods for market-rate renters, who are arguably the group most vulnerable to displacement. Third, only a handful of studies account for spatial error, despite the clear presen ce of spatial dependence associated with these phenomenon and well-documented evidence that ignoring these effects may lead to unreliable findings. Finally, and most seriously, a ll but one study relies upon flawed ratiobased measures of housing affordability, which – as described in Chapter 4 and demonstrated empirically in Chapter 6 – are likely to mischaracterize (and in most cases,

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Page 209 underestimate) the challenges faced by households w ith limited means in securing affordable housing. Research Questions and Approach The present dissertation therefore takes as its sta rting point a puzzle about whether transit-rich neighborhoods are indeed more affordab le, as a location efficiency approach would suggest, when affordability is examined using measures and methods that address the four gaps in the existing literature. To addres s this puzzle, I first developed the locationsensitive residual income (LSRI) measure of housing affordability which provides a more accurate account of the financial realities facing lowand moderate-income household as compared to traditionally-used measures. I then use LSRI measures to examine two research questions that explore the current landsca pes of transit accessibility and housing affordability that lowand moderate-income househo lds experience as they seek marketrate rental housing, as well as the complex relatio nships that exist between these variables when other key factors are accounted for. Specifica lly, I ask: (1) To what extent are supplies of rental housing t hat are affordable for lowand moderate-income households located in areas with hi gh transit accessibility? (Chapter 7) (2) What is the relationship between transit access ibility and supplies of affordable rental housing, when controlling for key characteri stics of the built and social environments that are likely to influence that rela tionship, as well as for spatial dependence effects? (Chapter 8) These investigations are conducted for the universe of U.S. metros with ‘secondgeneration’ regional rail which, as described in Ch apter 3, are likely to experience a specific set of challenges that shed light both theoreticall y and practically on issues of transportation justice. These metros (defined as core-based statis tical areas and identified by their core cities) are: Dallas, Denver, Houston, Los Angeles, Minneapolis, Portland, Salt Lake City,

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Page 210 and Seattle. Analyses focus exclusively on the affo rdability of market-rate rental housing for households who are likely to earn too much to quali fy for subsidy, but too little that securing stable affordable housing is a foregone conclusion. These households are highly vulnerable to displacement effects since they are subject to t he whims of rental markets but have little available income with which to afford higher premiu ms. Market-rate rental housing is also important to study because it provides the vast maj ority of the nation’s affordable housing: Only one-quarter of eligible households are able to secure public rental assistance, a proportion that is expected to continue to decline as affordability requirements sunset and federal support retreats (Ault et al., 2015). Given the cases analyzed, findings provide insights for metros that are currently undertaking or considering large transit expansions, and particularly those experiencing high levels of population and employment growth. Results are less relevant – although are likely to provide lessons for – metros with transit systems centered around older ‘legacy’ rail systems . To address Research Question 1, LSRI measures were used to calculate the supply of rental units that are both affordable to a defin ed set of lowand moderate-income households and located in areas with high transit a ccessibility. Results of this analysis were then compared to the calculated supply of affordabl e units located in areas with zero or low transit accessibility. Transit accessibility is def ined here as the percent of regional jobs that can be reached within a 45-minute transit commute. Areas with accessibility levels above the non-zero average accessibility are considered ‘ high’ accessibility while those below the non-zero average are defined as ‘low’ accessibility . ‘Zero’ accessibility areas are those in which no jobs are reachable by transit within 45-mi nutes. ‘Accessibility ratios’ – the ratio of the number of affordable units located in zero/low accessibility areas to the number of affordable units located in high accessibility area s – were constructed for each of the household profiles. These accessibility ratios were then compared to the ratios for metro-

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Page 211 wide supplies of rental units (regardless of their affordability) to detect deviations from metro-wide distributions. Research Question 2 delves deeper into the complex relationship between transit accessibility and housing affordability (as measure d using a LSRI approach) by accounting for key factors that are likely to influence both p henomena. For this analysis, I first used multivariate spatial error regression to model the global relationship between transit accessibility (conceptualized as the primary explan atory variable) and supplies of affordable rental units (conceptualized as the outcome variabl es). These models control for the effects of various aspects of density, land use mix, housin g tenure, and socio-economic conditions that have been shown to influence affordability. Th e presence of spatial dependence was also modelled through inclusion of a spatially-weig hted error term (‘lambda’). This effort resulted in two models for each metro: One for a ‘l ow housing budget’ household (one adult earning 50% AMI with one child who does not require childcare) and another for a ‘moderate housing budget household’ (two adults earning 100% AMI and two children, one of whom requires childcare). I then used the same model spe cifications in geographically-weighted regression (GWR) to explore how local relationships between accessibility and affordabili ty vary across space. Analyses supporting Research Que stion 2 are not intended for use in drawing causal conclusions about the relative effec ts of specific factors on supplies of affordable housing. Rather, the models are specifie d in order to allow for the isolation and close examination of the complex relationship betwe en accessibility and affordability both within and across metros. In the sections that follow, I synthesize findings from the investigations undertaken in previous chapters to draw conclusions about the geo graphies of opportunity that households with limited means are likely to experience in eigh t U.S. metros, and to identify the ways in which these geographies support – and challenge – a location efficiency narrative. I first describe the improved LSRI approach used to measure affordability – which constitutes one

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Page 212 of the main contributions of the study – and summar ize how its products compare to those of standard measures. I then present a typology tha t synthesizes the combined results of the two research questions to describe four general types of geographies of opportunity experienced by lowand moderate-income households and discuss policy implications associated with each. I conclude with a summary of the key contributions of these investigations, as well as limitations and opportun ities for future research. THE LSRI MEASURE OF HOUSING AFFORDABILITY As described in Chapter 4, housing affordability is typically measured using threshold-based approaches in which housing is cons idered ‘affordable’ when it consumes less than 30-percent of household income (the ‘rati o’ approach), or when combined housing and transportation costs consume less than 45-perce nt of income (the ‘location affordability’ approach). Despite their widespread use, these appr oaches are subject to much criticism around their insensitivity to the effects of househ old income and household characteristics (in particular, size and the presence of children) on the ability of lowand moderate-income households to afford housing. Ratio approaches also neglect the effects of residential location on transportation costs, which are likely to vary quite widely across metros. The alternative LSRI approach developed in the pres ent study addresses these shortcomings by accounting for the nuanced financia l realities of lowand moderate-income households with different characteristics and resid ential locations. Under the LSRI approach, affordability is assessed by calculating the amount a theoretical household is able to pay for housing after covering all of the other essential goods and services required to support a basic standard of living. The amount rema ining for housing after all other essential expenses are paid is referred to as a household’s ‘ housing budget’. Housing budgets vary widely depending on household composition (size, pr esence of children), financial circumstances (income, childcare requirements), and residential location (which determines transportation costs). In addition to housing budge ts, the LSRI approach generates a

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Page 213 second ‘supply’ measure which uses U.S. Census Amer ican Community Survey (ACS) data to identify the number of rental units that are aff ordable within a particular household’s housing budget. The two LSRI measures are calculate d in the present study for six household profiles theoretically residing in each o f the eight metros. Data is calculated at the Census block group level, which serves as a proxy f or the neighborhood. Analysis presenting in Chapter 6 that compares resu lts of an analysis undertaken for the Denver metro using LSRI measures to results for the same metro generated using more typical measures demonstrate how standard approache s mischaracterize how much households with limited means can afford to spend o n housing. As a consequence, analyses relying on typical measures, including tho se related to the location efficiency perspective, are likely to underestimate the challe nges facing lowand moderate-income households and over estimate the supply of rental units affordable to t hem. For example, the LSRI approach indicates that 6.0-percent of rental units in the Denver metro are affordable to low housing budget households, as shown in Figure 9.2 . However, the location affordability measure estimates that over two times more rental units (13.8%) are affordable to the same household. A similar pattern emerges in assessing supplies of affordable rental units for moderate housing budget households. A loc ation affordability measure estimates that nearly 80-percent of the metro’s rental housin g is affordable to this household, while a LSRI measure estimates supplies of affordable units to be much lower (approximately 50% of units). Full results of this analysis demonstrat e particularly stark discrepancies among households with children requiring childcare, point ing to the importance of accurately addressing the substantial effects of childcare cos ts on a household’s ability to secure affordable housing. More generally, results of this comparison also underscore the importance of accounting for the impact of househol d composition and financial circumstances in measuring housing affordability.

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Page 214 Figure 9.2. Total supplies of rental units affordab le to low and moderate housing budget households: Comparison of the LSRI and locat ion affordability measures (Denver) The analysis presented in Chapter 6 also demonstrat es how LSRI measures can be deployed in empirical analyses aimed at understandi ng landscapes of housing affordability. By directly incorporating the effects of household composition and financial circumstances, as well as variations in transportation costs assoc iated with residential location, the LSRI approach offers a robust measure of the realities f aced by lowand moderate-income households in securing affordable housing. The LSRI measure therefore enables practitioners and policymakers to accurately assess affordability condition, establish the need for affordable housing at multiple scales down to the neighborhood level, and develop interventions targeted at specific conditions withi n particular geographies. However, practitioners employing a LSRI approach must also b e aware of the limitations of the measures outlined in Chapter 5, and should interpre t LSRI measures as estimates subject to measurement error.

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Page 215 SYNTHESIS OF FINDINGS: CURRENT GEOGRAPHIES OF OPPOR TUNITY FOR LOWAND MODERATE-INCOME HOUSEHOLDS Findings yielded from the investigations presented in the preceding chapters highlight the relationships between transit accessi bility and housing affordability that underlie geographies of opportunity for lowand moderate-in come households. Results vary considerably among metros, among households with di fferent characteristics and circumstances in the same metro, and across space. These investigations therefore suggest that if there is a single generalizable finding tha t extends to the broad universe of metros with robust transit systems, it is that the relatio nships between transit accessibility and housing affordability are complex and are likely to manifest in widely varying geographies of opportunity for households with limited means. However, some clear threads can be wrested from the se complexities. In particular, a typology that synthesizes the combined results of Research Questions 1 and 2 emerged to describe the four general types of geographies o f opportunity likely to be experienced by lowand moderate-income households. In the present section, elements of this typology a nd the resulting categories are first described, and t hen are used as a framework to briefly discuss appropriate policy prescriptions. The typology is also used to understand the ways in which the emergent typologies are consistent wit h – and challenge – a location efficiency narrative. The chapter concludes with a summary of the key contributions and limitations of this work. Geographies of Opportunity: A Typology As discussed in Chapter 2, geographies of opportuni ty are conceptualized in these investigations as being bounded by two circumstance s: 1) the ability to access employment opportunities via modes other than private auto (‘t ransit accessibility’) and 2) the ability to afford housing in transit-accessible areas and thus benefit from the advantages it confers

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Page 216 (‘housing affordability’). The typology presented h ere synthesizes results along two dimensions, as shown in Figure 9.3 . The horizontal axis of the typology draws from th e results of Research Question 1 to identify whether a majority of the metro’s affordable rental units are located in zero/low accessibility areas ( indicating weaker geographies, left quadrants) or in high accessibility areas (indicati ng stronger geographies, right quadrants). The vertical axis draws from the results of Researc h Question 2 to describe whether, when accounting for key control factors and spatial erro r, higher levels of accessibility are associated with additional affordable rental units (stronger geographies, upp er quadrants) or fewer affordable units (weaker geographies, lower quadra nts). These axes form four general typologies, each of which suggests the need for a u nique set of policy prescriptions. Figure 9.3. Typology framework Metro-wide Geographies of Opportunity A matrix summarizing the key results generated from Research Questions 1 and 2 are provided in Table 9.1 below. Results are summarized for both low housing budget and

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Page 217 moderate housing budget households. The first colum ns summarize findings from Research Question 1. Cells highlighted in dark green are tho se in which a larger majority of affordable rental units are located in high accessibility area s, suggesting stronger geographies of opportunity. Cells highlighted in red and pink demo nstrate the opposite patterns, with affordable rental units located predominately in ar eas with zero/low accessibility, suggesting weaker geographies. Geographies of opportunity appe ar to be particularly weak for metros and households highlighted in red, in which the pro portion of affordable units located in zero/low access areas is higher than metro-wide dis tributions of total rental units. Geographies of opportunity for metros and household s highlighted in pink are also weak, but to a lesser a degree. In these cases, the proportio n of affordable units located in zero/low access areas is lower than metro-wide distributions . The remaining three columns summarize results from Research Question 2. Global relationships between transit accessibility and hou sing affordability that have been isolated by controlling for key characteristics of the built and social environments using spatial error regression, are identified as either positive and s tatistically-significant (strong geographies of opportunity, in dark green), positive but not stati stically-significant (somewhat strong geographies, in light green), negative and statisti cally-significant (weak geographies, in red), and negative but not statistically-significant (som ewhat weak, in pink). The same spatial error models were used to calculate differences in supplies of affordable housing that are expected to be associated with 10-percent higher tr ansit accessibility. Differences are noted as either small, moderate, or large. Increases are shaded in dark/light green (indicating stronger geographies of opportunity) and decreases are shaded in red/pink (indicating weaker geographies). A final column summarizes the local relationships between accessibility and affordability that result from GW R modelling. Local relationships are identified as being the same as global relationship s (either positive or negative), or exhibiting both positive and negative local relatio nships (‘positive/negative’).

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Page 218 Table 9.1. Summary of results (all analyses) Metro / Household Profile Research Question 1 Research Question 2 distribution of supplies of affordable rental units, by accessibility level global relationship difference in supplies associated with 10% higher accessibility local relationships in high transit accessibility areas Dallas Low housing budget household majority in zero/low access positive** small increases positive/negative Moderate housing budget household majority in zero/low access positive** large increases positive/negative Denver Low housing budget household majority in high access positive** small increases positive Moderate housing budget household majority in high access positive** moderate increases positive Houston Low housing budget household majority in zero/low access positive (n.s.) small increases positive Moderate housing budget household majority in zero/low access positive (n.s.) moderate increases positive/negative Los Angeles Low housing budget household majority in high access positive** small increases n/a1 Moderate housing budget household majority in high access positive** moderate increases n/a1 Minneapolis Low housing budget household majority in high access positive** large increases n/a1 Moderate housing budget household majority in zero/low access positive** large increases positive Portland Low housing budget household majority in high access negative** large decreases negative Moderate housing budget household majority in zero/low access negative** small decreases negative Salt Lake City Low housing budget household majority in high access negative (n.s.) small decreases positive/negative Moderate housing budget household majority in zero/low access negative (n.s.) small decreases positive/negative Seattle Low housing budget household majority in high access negative** large decreases positive/negative Moderate housing budget household majority in zero/low access negative** moderate decreases negative Red/pink cells results point to relatively ‘weak’ g eographies of opportunity Dark/light green cells results point to relatively ‘strong’ geographies of opportunity 1 GWR results not reported due to the existence of lo cal multicollinearity; **statistically-significant at =0.01; n.s. = not significant at =0.05

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Page 219 Figure 9.4 applies the metro-wide results summarized in the ab ove matrix to the typology described earlier to arrive at four genera l geographies of opportunity. Households in Denver and Los Angeles with both low and moderat e housing budgets are likely to encounter ‘ very strong’ geographies of opportunity , as are low housing budget households in Minneapolis. In these metros, the maj ority of affordable rental units are located in high accessibility areas, and global mod els indicate that higher transit accessibility is associated with additional affordable units. Met ros in this quadrant have the highest potential for promoting transportation justice. Pol icy prescriptions should thus focus on the preservation of affordable, transit-accessible hous ing through various programs designed to maintain and protect market-rate afford ability. Transportation policies should also focus on increasing the number of transit-acce ssible locations through expansion of transit service to areas with high affordability alongside programs to preserve and maintain affordability in those areas. Because thes e investigations are cross-sectional, no conclusions can be drawn about what the future hold s for geographies of opportunity in these metros. However, given evidence of the growin g demand for transit-accessible housing, it would be prudent to assume that afforda bility will not remain stable without interventions to ensure its maintenance. These metr os thus have the unique opportunity to get in front of direct and exclusionary displacemen t by preserving transit-accessible affordable housing before it is lost to increasing housing costs. Low housing budget households in Salt Lake City and Portland demonstrate ‘ somewhat strong’ geographies of opportunity . In these cases, supplies of affordable rental units are larger in high accessibility areas . However, global models indicate that higher transit accessibility is associated with fewer affordable units, holding all else constant. Metros and households in this quadrant may therefor e be experiencing changing conditions whereby geographies of opportunity are currently re latively strong, but may be getting

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Page 220 weaker due to the loss of affordable units in trans it-accessible areas. Policies in these cases should therefore be focused on stemming any loss of affordable market-rate units in high accessibility areas through both preservation of existing market-rate units and crea tion of subsidized affordable units . The fact that only low housing budget households are included in this quadrant could indicate that housi ng stocks in central, transit-accessible areas of Salt Lake City and Portland still manage t o provide decent supplies of affordable units for those with very limited incomes and housi ng budgets, but not for those with more moderate incomes. Interventions should therefore be targeted at these discrepancies. Low and moderate housing budget households in Seatt le, as well as moderate housing budget households in Salt Lake City and Por tland, appear to be less fortunate. Results indicate households in these metros face ‘ very weak’ geographies of opportunity , with larger supplies of affordable units in zero/lo w accessibility areas as well as evidence that higher transit accessibility is associated wit h fewer affordable units, holding all else constant. The cases in the left side of this quadra nt (Seattle and Portland moderate housing budget households) are those in which the proportio n of affordable units located in zero/low access areas is larger than for the metro-wide dist ribution of rental units suggests particularly weak geographies of opportunity. While preservation of affordability is a laudable goal in all metros, supplies of market-rate units i n transit-accessible locations are so minimal in these ‘very weak’ metros that interventions shou ld primarily focus on the creation of subsidized transit-accessible affordable units . This can be done through a number of mechanisms, the most fruitful of which is likely to be inclusionary housing policies that incentivize or mandate that affordable units be cre ated through new development. Low and moderate housing budget households in Dalla s and Houston, as well as moderate housing budget households in Minneapolis, demonstrate ‘ somewhat weak’ geographies of opportunity . In these metros, higher accessibility is associat ed with larger supplies of affordable housing, holding other facto rs constant. Yet analysis indicates that the

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Page 221 majority of affordable rental units are located in areas with zero/low accessibility areas. As with cases in the ‘somewhat strong’ quadrant, ‘some what weak’ cases may be undergoing changing conditions whereby housing markets which t raditionally focus on suburban development may be beginning to respond to increase d demand for more central, transitaccessible locations. These metros have an opportun ity to harness the relatively strong relationship between accessibility and affordabilit y through programs that preserve affordability in transit-accessible locations and through policies that incentivize the creation of both market-rate and subsidized units i n transit-accessible areas that are becoming more attractive for development. Figure 9.4. A typology of metro-wide geographies of opportunity

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Page 222 SUMMARY OF CONTRIBUTIONS AND LIMITATIONS The investigations undertaken in this study and syn thesized above make a number of contributions to understanding the complex relat ionships between transit accessibility and housing affordability that exist across U.S. metros , and the ways in which these relationships are manifested in the geographies of opportunity experienced by lowand moderate-income households in these metros. Investi gations have specifically offered a cross-sectional view of the conditions facing house holds with limited means as they seek affordable rental housing, accounting for the compl ex financial realities resulting from different household compositions and circumstances. Findings shed light on the varying conditions that exist across U.S. metros with ‘seco nd-generation’ regional rail transit, and thus provide insights for metros with similar chara cteristics that are currently undertaking or considering large transit expansions. Given the geo graphic distribution of selected cases, results are particularly relevant to high-growth me tros in the western U.S. Results are less relevant – although still may provide lessons for – metros with older ‘legacy’ transit systems. Investigations also make considerable contributions to the literature by filling four key gaps in existing research around transit-induced di splacement and location efficiency. First, the analysis has focused on transit accessibility r egardless of mode, thus complementing a body of literature that until now has largely focus ed on housing costs and affordability associated specifically with fixed-rail transit. Se cond, results speak directly to the landscapes of affordability that face lowand mode rate-income renters (as opposed to home owners, as is the subject of most existing research ), thus shedding light on conditions for the households most vulnerable to exclusionary displace ment in transit-accessible areas. Finally, findings address many of the methodologica l shortcomings associated with the existing literature by introducing a measure of aff ordability that vastly improves more typical approaches and by employing regression techniques t hat account for spatial dependence.

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Page 223 In the sections that follow, I outline the key cont ributions of these investigations and discuss their implications in terms of the strength of geographies of opportunity that households with limited means are likely to experie nce in eight U.S. metros and the ways in which these geographies support – and challenge – a location efficiency narrative. I also identify the key methodological contributions of th e study and discuss limitations of the study and opportunities for future research. Key Contributions Geographies of opportunity are stronger than antici pated in some metros. Results for some metros – most notably, Denver and Los Angeles – indicate that lowand moderate-income households are likely to experience relatively strong geographies of opportunity, with positive implications for transpo rtation justice. In these metros, the majority of affordable rental units are located in high acce ssibility areas, and higher accessibility is associated with larger supplies of affordable units (holding all else constant). Findings for these metros are thus consistent with a location ef ficiency narrative that predicts overall affordability to be better in areas with high trans it accessibility. The existence of strong geographies of opportunity in these metros is somew hat surprising, given that the investigations began with the expectation that land scapes of affordability and accessibility would reflect the growing demand for (and thus hous ing costs associated with) transitaccessible locations. It is interesting that both D enver and Los Angeles are in the midst of the largest transit expansions in the nation. These expansions are essentially increasing the number of transit-accessible units, many of which m ay still remain at affordable market rates. However, given evidence of growing demand fo r transit-accessible housing, it is reasonable to expect that housing may not remain af fordable. These metros thus have the unique opportunity to set policies that preserve af fordability in transit-accessible locations before it is lost to direct and exclusionary displa cement.

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Page 224 Weak geographies of opportunity exist in a larger n umber of metros. The majority of metros demonstrate evidence of consider able exclusionary displacement in transit-accessible areas. Geographies of opportunit y are particularly weak for low and moderate housing budget households in Seattle, as w ell as for moderate housing budget households in Salt Lake and Portland. In these case s, the majority of affordable rental units are located in zero/low access areas and higher acc essibility is associated with fewer affordable units, holding all else constant. Geogra phies are also somewhat weak in Dallas and Houston, where the majority of affordable units are also located in zero/low access areas despite evidence that higher accessibility is associated with larger supplies of affordable units. Households with limited means in metros with weak geographies of opportunity are therefore likely to encounter bette r overall affordability in zero/low access areas thereby requiring greater reliance on private autos and challenging a location efficiency narrative. Given the considerable social and financial impacts of autodependency, this finding has negative implications for transportation justice. Dynamics in metros with weak geographies of opportunity are lik ely to worsen if demand for transitaccessible locations continues to grow. Metros with very weak geographies must therefore look to bolster supplies of transit-accessible affo rdable housing through the creation of subsidized units in existing transit-accessible are as and the expansion of transit areas with high affordability that are not currently served by transit. Geographies of opportunity vary for households with different financial circumstances within the same metro. In three metros – Minneapolis, Salt Lake City, and Portland – geographies of opportunity for household s with low housing budgets are stronger than for those with more moderate housing budgets. This result suggests a ‘barbell’ effect whereby the rental market may do a reasonably good job of providing transit-accessible affordable housing for households with very limited incomes, but not for those with more moderate incomes. These metros may therefore consid er adopting policies that specifically

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Page 225 target the creation and preservation of housing tha t is affordable to middle-income families in order to avoid perpetuating a circumstance where only the very poor and very affluent are able to secure affordable transit-accessible housin g. Metro-wide geographies of opportunity may obscure v ariations that exist at the neighborhood level. Results of analyses examining local relationships between transit accessibility and housing affordability highlight t he complex nature of these relationships, and the importance of understanding neighborhood-le vel dynamics when developing policy and planning interventions aimed at maximizing affo rdability in transit-accessible areas. For example, global statistics that suggest strong metr o-wide geographies of opportunity may mask the need to address weaker geographies of oppo rtunity that occur at the block group level, as appears to be the case in Denver and Dall as. Similarly, evidence of weak metrowide geographies of opportunity may obscure the nee d for interventions that preserve pockets of stronger local geographies of opportunity, as with low housing bud get households in Seattle. Taken together, results generated using robust LSRI measures lend limited support to a location efficiency narrative. As with Revington & Townsend (2016), results of these investigations indicate that more nuanced measures of housing affordability yield findings that are less consistent with a location e fficiency narrative than is the case for findings from previous studies that use ratio-based measures. Conditions in Denver and Los Angeles, as well as for some households with very l imited housing budgets in four other metros, are largely consistent with the argument th at areas with high transit accessibility offer lowand moderate-income households the best opportunity to secure affordable housing. However in a greater number of metros, the re is evidence of considerable exclusionary displacement in transit-accessible are as, thus challenging a location efficiency narrative. In these metros – Dallas, Houston and Se attle in particular – lowand moderateincome households are likely to encounter larger su pplies of affordable rental units in areas

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Page 226 with little or no transit accessibility lower trans portation costs, thus calling into question the robustness of a location efficiency narrative that suggests the opposite would be true. This finding underscores that although the location effi ciency approach offers a useful perspective, policymakers, planners, and advocates cannot assume that high housing costs will be inherently offset by lower transportation c osts. Results make a number of methodological contributio ns that underscore the importance of accounting for spatial dependence, co nfounding variables, and local variation. Findings from analyses using spatial error regressi on demonstrate that failing to account for spatial dependence is likely to lead to biased results that may mischaracterize the effects of key variables. Results thus highligh t the importance of addressing issues of spatial dependence and error, particularly given th e policy relevance of investigations around accessibility, affordability, and related ph enomena. Model results also point to the large influence that key characteristics of the bui lt and social environments may have on the relationships between accessibility and affordabili ty and highlight the need to fully account for these confounding factors. While the present an alysis focuses on the relationship between transit accessibility and housing affordabi lity in isolation, it is important to acknowledge the complex relationships that exist am ong other characteristics of the built and social environments. Furthermore, results of an alyses using GWR further demonstrate that exclusively relying on global analyses to unde rstand affordability and accessibility may mask considerable variations in neighborhood-level dynamics, and thus may obscure the need for policy prescriptions that target these nua nced conditions. Finally, the largest methodological contribution of this work is the LSR I measure itself, which equips policymakers and practitioners with tools to suppor t analysis and decision-making around the preservation and creation of affordable housing , particularly as it relates to maximizing geographies of opportunity associated with transit accessibility.

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Page 227 Findings lend further empirical substance to a ‘cap abilities approach’ framework. This dissertation adopted a conceptual framework ro oted in Sen and Nussbaum’s ‘capabilities approach,’ which defines a ‘just’ transportation system as one in which all individuals are able to access the opport unities that are necessary to reach their full potential. The conceptual framework also incorporates a ‘geogr aphies of opportunity’ perspective, which is commonly used among practitio ners and advocates. Through this framework, two elements are conceptualized as shapi ng the strength of an individual’s ‘geography of opportunity’: transit accessibility ( the extent to which employment opportunities are accessible via public transit) an d housing affordability (the extent to which housing in areas with high transit accessibility is affordable to lowand moderate-income households). Using the vernacular of a capabilities approach, a person’s ‘capabilities set’ (or their geography of opportunity) are a direct extension of the interaction between three ‘primary goods’ (a metro’s transit network, housing stock, a nd availability of resources that support individual well-being). It is important to note that the conceptual framewo rk employed in this study recognizes that a person may or may not choos e to capitalize upon their capability set. For instance, it is entirely conceivable that an individual living in areas with strong geographies of opportunity – meaning areas with bot h high transit accessibility and large supplies of affordable housing – may not choose to take advantage of transit access (for example, by using a private vehicle instead). These individuals may therefore end up having lower achieved functionings than might be expected based on the strength of their geography of opportunity. However a capabilities approach suggests that ‘just ice’ should ultimately be judged on individual’s capabilities s ets, rather than what people actually choose to achieve with them. It thus recognizes the role that individual choice plays in achieving well-being.

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Page 228 It is also important to note that the ultimate outc ome of interest to a capabilities approach is ‘well-being,’ as defined by whatever co nception an individual has about what it means to live a ‘good life.’ Admittedly, a person’s notion of ‘well-being’ may h ave little to do with either transit accessibility or housing afford ability. However, existing research suggests that for many lowand moderate-income households, the availability of reliable and efficient transit has a large bearing on their ability to acc ess opportunities (and jobs in particular1) and thus is likely to play a considerable role in achieving well-being. The conceptual framework used here has thus offered a useful way o f assessing one facet of transportation justice, and is likely to be similarly valuable in evaluating the ‘justness’ of any number of other aspects of metropolitan planning and policyma king. Limitations The key contributions summarized above should be te mpered by the acknowledgement of several data and methodological limitations. First, LSRI measures are limited in a number of ways, most having to do to w ith qualities of the data used to construct them. In particular, U.S. Census ACS data which ser ves as the basis for many of the elements of the LSRI measures has substantial margi ns of error, particularly at small geographies. While this error is certainly a concer n, it is considered to be tolerable when weighed against the utility of the findings that ar e generated for small geographies. The Location Affordability Index (LAI) used in developi ng transportation costs data also poses limitations having to do with its use of aggregate (versus household-level) data, which a recent study attributes to the LAI reporting higher housing and transportation costs as compared to estimates modeled with more granular da ta (Salon, et al., 2016). Despite this shortcoming, the LAI remains the only comprehensive dataset of estimated transportation costs that is readily-available to practitioners. A LSRI approach can easily incorporate improved data on transportation costs as it becomes available. Finally, data sourced from 1 See extensive literature cited in Chapter 3.

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Page 229 the ACS on rents of occupied housing units reflects the rent paid by current residents, many of whom may be long-term renters, and thus may not be fully representative of the amount of rent that would be asked from new renters. This likely has the effect of overestimating supplies of affordable rental housing, and may ther efore under estimate the challenges lowand moderate-income household face in securing affo rdable rental housing. Because of these shortcomings, both the LSRI housing budget an d supply measures should be interpreted as estimates that are subject to measur ement error originating with several data sources. Beyond issues with data sources, LSRI measures requ ire numerous calculations which while certainly more onerous that those requi red for simple ratio-based approaches, do not require any sophisticated expertise or softw are. The LSRI approach also requires a series of analytical choices and normative judgment s about which households will be assessed, which goods and services should be accoun ted for in calculating non-housing costs, and what constitutes a ‘basic’ standard of l iving. While clear justifications can be made for all of these decisions (as is done in the Chapter 5), their subjective nature make it challenging to compare measures across different ge ographies, time periods, and analysts. Finally, the depth of information generated by a LS RI approach render it less universal than blunt ratio-based measures. Although I argue that t his depth is a benefit, it is likely that practitioners using a LSRI approach will need to ma ke decisions about how to reduce data so that it is digestible to policymakers and the ge neral public. While there will undoubtedly be circumstances in which the use of ratio-based ap proaches are warranted, findings from the present investigations demonstrate that more nu anced measures should be used when at all possible in order to maximize the robustness and validity of analyses. Limitations associated with measures of transit acc essibility also exist. First, the EPA Access to Jobs and Workers via Transit dataset used to measure transit accessibility provides synthetic data based on estimates generate d from a small set of sample data,

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Page 230 resulting in considerable margins of error. Secondl y, the EPA datasets does not differentiate between lowand high-wage jobs, which could skew r esults given that evidence that transit use patterns are likely to vary significantly acros s different occupations (Legrain et al., 2016). For instance, hours for many low-wage jobs a re not likely to follow the standard nineto-five workday upon which the EPA transit accessib ility measure is based. Future research should account for these differences by disaggregat ing employment opportunities by occupation and/or wage. Results are also likely to be sensitive to definitions of ‘low’ and ‘high’ transit accessibility areas. This analysis h as used a reasonable threshold based on the non-zero average transit accessibility for each metro. However, other definitions may yield different results. Finally, and perhaps most important to note are lim itations associated with the crosssectional nature of these investigations. This stud y has used data current to the year 2014 to analyze conditions faced by lowand moderate-in come households as they sought affordable rental housing. Given the dynamic nature of housing markets, findings from the present analysis may quickly (and possibly already have) become outdated. Transit accessibility is also likely to change over time as service is expanded or reduced. Regular updates using current data in a LSRI approach are t herefore imperative in order to track changing conditions and understand the evolving nat ure of geographies of opportunity as shaped by current landscapes of affordability and a ccessibility. Future Research These investigations open up innumerable avenues fo r future research both in terms of methodological advancements and new questions. T he use of more sophisticated models offer a logical next step in understanding the comp lexities embedded in the relationship between transit accessibility, housing affordabilit y, and the multitude of factors that are likely to influence both these variables. In particular, s tructural equation modelling (SEM) that accounts for spatial dependence should be pursued i n order to directly model the mediating

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Page 231 effects of key characteristics of the built and soc ial environments on the relationship between transit accessibility and housing affordabi lity. Spatial SEM models would enable a deeper understanding about relative effects of vari ous factors on affordability, something that is not feasible through the spatial error mode ls employed in the current investigations. Future modelling efforts should also attempt to mea sure transit accessibility in a way that accounts more fully for non-work destinations, and that disaggregates employment destinations by occupation and/or wage category. Th e LSRI approach would also benefit from use in community-based research in which the m easures are subjected to in situ work by practitioners and refined based on their experie nces. In revisiting the conceptual framework that has gui ded this work ( Figure 9.1 ), a number of questions emerge around the social and en vironmental ‘ conversion factors ’ (in the language of the capabilities approach) that may influence individual’s ‘ capability sets ’ (i.e. geographies of opportunity) and the ability o f individuals to convert those capabilities into ‘ achieved functions .’ In particular, future studies should specificall y seek to investigate the ways in which social, institutional, and contex tual factors may explain variations in geographies of opportunity, as shaped by landscapes of affordability and accessibility. Existing literature suggests that the interplay bet ween social mobilization and collaboration on the one hand and institutional and other types o f ‘vertical’ support on the other may be a particularly fruitful arena for research (Pendall e t al., 2012; Weir et al., 2008). Work in this area could go far in understanding the factors that are most effective in promoting affordability in transit-accessible locations, and thus maximizing geographies of opportunity for lowand moderate-income households.

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Page 243 APPENDIX A SUMMARY OF NON-HOUSING AND NON-TRANSPORATION (‘NONH+T’) COSTS BY METRO Table A.1. Estimated annual childcare costs by numb er of children requiring childcare (all metros) Household type Dallas Denver Houston Los Angeles Minneapolis Portland Salt Lake City Seattle MN WI Single adult, no children $0 $0 $0 $0 $0 $0 $0 $0 $0 Single adult, 1 child $6,004 $8,638 $6,004 $7,473 $8,664 $7,593 $6,752 $5,707 $8,602 Single adult, 2 children $12,008 $17,276 $12,008 $1 4,947 $17,329 $15,186 $13,504 $11,414 $17,205 Two adults, no children $0 $0 $0 $0 $0 $0 $0 $0 $0 Two adults, 1 child $6,004 $8,638 $6,004 $7,473 $8 ,664 $7,593 $6,752 $5,707 $8,602 Two adults, 2 children $12,008 $17,276 $12,008 $14, 947 $17,329 $15,186 $13,504 $11,414 $17,205 Source: Childcare Aware of America, 2014 Table A.2. Estimated annual food costs by household composition type (all metros) Household type Dallas Denver Houston Los Angeles Minneapolis Portland Salt Lake City Seattle Single adult, no children $3,022 $3,607 $3,022 $3,607 $3,087 $3,607 $3,607 $3 ,607 Single adult, 1 child $4,457 $5,319 $4,457 $5,319 $4,553 $5,319 $5,319 $5,319 Single adult, 2 children $6,704 $8,002 $6,704 $8,00 2 $6,849 $8,002 $8,002 $8,002 Two adults, no children $5,540 $6,612 $5,540 $6,612 $5,659 $6,612 $6,612 $6,612 Two adults, 1 child $6,898 $8,234 $6,898 $8,234 $7 ,047 $8,234 $8,234 $8,234 Two adults, 2 children $8,903 $10,627 $8,903 $10,62 7 $9,095 $10,627 $10,627 $10,627 Source: MIT Living Wage Calculator (Glasmeier, 2014 )

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Page 244 Table A.3. Estimated annual medical costs by househ old composition type (all metros) Household type Dallas Denver Houston Los Angeles Minneapolis Portland Salt Lake City Seattle MN WI OR WA Single adult, no children $2,144 $2,172 $2,144 $2,0 99 $2,231 $2,243 $1,806 $1,679 $2,097 $1,679 Single adult, 1 child $6,745 $6,167 $6,745 $6,363 $5,727 $6,048 $6,167 $5,761 $5,433 $5,761 Single adult, 2 children $6,534 $5,956 $6,534 $6,15 1 $5,516 $5,836 $5,956 $5,550 $5,221 $5,550 Two adults, no children $4,962 $4,561 $4,962 $4,817 $4,542 $4,596 $4,839 $4,326 $4,123 $4,326 Two adults, 1 child $6,534 $5,956 $6,534 $6,151 $5 ,516 $5,836 $5,956 $5,550 $5,221 $5,550 Two adults, 2 children $6,597 $6,020 $6,597 $6,215 $5,580 $5,900 $6,020 $5,614 $5,285 $5,614 Source: MIT Living Wage Calculator (Glasmeier, 2014 ) Table A.4. Estimated annual costs of other basic ne cessities by household composition type (all metros ) Household type Dallas Denver Houston Los Angeles Minneapolis Portland Salt Lake City Seattle Single adult, no children $2,253 $2,284 $2,253 $2,284 $2,127 $2,284 $2,284 $2 ,284 Single adult, 1 child $3,916 $3,971 $3,916 $3,971 $3,699 $3,971 $3,971 $3,971 Single adult, 2 children $4,284 $4,344 $4,284 $4,34 4 $4,046 $4,344 $4,344 $4,344 Two adults, no children $3,916 $3,971 $3,916 $3,971 $3,699 $3,971 $3,971 $3,971 Two adults, 1 child $4,284 $4,344 $4,284 $4,344 $4 ,046 $4,344 $4,344 $4,344 Two adults, 2 children $5,178 $5,250 $5,178 $5,250 $4,891 $5,250 $5,250 $5,250 Source: MIT Living Wage Calculator (Glasmeier, 2014 ) Table A.4. Estimated annual cost of taxes by househ old income (all metros) Household type Dallas Denver Houston Los Angeles Minneapolis Portland Salt Lake City Seattle MN WI OR WA 30% AMI $2,045 $3,111 $2,028 $2,447 $3,542 $3,789 $3,622 $2,033 $3,049 $2,384 50% AMI $3,408 $5,185 $3,380 $4,079 $5,904 $6,316 $6,036 $3,389 $5,082 $3,973 80% AMI $5,454 $8,295 $5,409 $6,526 $9,446 $10,105 $9,658 $5,422 $8,132 $6,356 100% AMI $6,817 $10,369 $6,761 $8,158 $11,808 $12, 631 $12,072 $6,777 $10,165 $7,945 120% AMI $8,180 $12,443 $8,113 $9,789 $14,170 $15, 157 $14,487 $8,133 $12,198 $9,534 Source: Tax Policy Center of the Brookings Institut ion and Urban Institute

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Page 245 APPENDIX B SUMMARY OF TRANSPORTATION COSTS BY METRO Table B.1. Estimated monthly transportation costs ( minimum, median, maximum) by household composition (all metros) Household type Dallas Denver Houston Los Angeles Minneapolis Portland Salt Lake City Seattle Single adult, no children Minimum $219 $228 $211 $113 $190 $207 $329 $186 Median $584 $574 $570 $513 $600 $587 $623 $629 Maximum $836 $864 $864 $871 $900 $882 $868 $881 Single adult, 1 child Minimum $276 $286 $270 $132 $254 $270 $370 $251 Median $611 $600 $597 $547 $624 $617 $645 $653 Maximum $832 $855 $857 $866 $888 $877 $861 $875 Single adult, 2 children Minimum $318 $329 $311 $152 $292 $311 $427 $290 Median $704 $692 $688 $631 $719 $711 $744 $753 Maximum $959 $986 $988 $998 $1,024 $1,011 $992 $1,009 Two adults, no children Minimum $315 $321 $311 $162 $291 $304 $414 $283 Median $664 $653 $650 $598 $676 $669 $699 $707 Maximum $900 $919 $919 $933 $960 $942 $929 $947 Two adults, 1 child Minimum $493 $515 $485 $351 $487 $482 $611 $472 Median $852 $867 $837 $820 $895 $866 $912 $934 Maximum $1,098 $1,151 $1,110 $1,176 $1,196 $1,150 $1,156 $1 ,198 Two adults, 2 children Minimum $577 $603 $569 $411 $571 $565 $716 $553 Median $999 $1,016 $981 $961 $1,049 $1,015 $1,069 $1,094 Maximum $1,287 $1,348 $1,300 $1,379 $1,401 $1,348 $1,354 $1 ,404

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Page 246 Table B.2. Multipliers used to calculate estimated transportation costs, by household type (all metros ) LSRI household profile Corresponding HUD LAI* household profile Multiplier** Dallas Denver Houston Los Angeles Minneapolis Portland Salt Lake City Seattle Single adult, no children “Working individual” Single adult, no children (50% AMI) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Single adult, 1 child “Single-parent family” Single adult, 2 children (50% AMI) 0.8676 0.8676 0.8676 0.8676 0.8677 0.8676 0.8676 0. 8676 Single adult, 2 children “Single-parent family” Single adult, 2 children (50% AMI) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Two adults, no children “Moderate income family” Two adults, 1 child (80% AMI) 0.8676 0.8676 0.8676 0.8676 0.8677 0.8676 0.8676 0. 8676 Two adults, 1 child “Median income family” Two adults, 2 children (100% AMI) 0.8534 0.8535 0.8534 0.8535 0.8534 0.8535 0.8535 0. 8535 Two adults, 2 children “Median income family” Two adults, 2 children (100% AMI) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 *U.S. Department of Housing and Urban Development L ocation Affordability Index **Multiplier calculated as described in Chapter 4

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Page 247 APPENDIX C LSRI MEASURES OF HOUSING AFFORDABILITY (DENVER REGI ON) Table C.1. Housing budgets and supplies of affordab le rental units, by household profile (Denver) Household Type/ Household Income* Monthly housing budget, by block group (2014$) % of regional rental housing units affordable within housing budget1 Minimum Median Maximum Single adult, no children $19,262 (30% AMI)* -$190 $100 $446 2.2% $32,103 (50% AMI) $707 $997 $1,343 54.7% $51,365 (80% AMI) $2,053 $2,343 $2,689 n/a2 $64,206 (100% AMI) $2,950 $3,240 $3,586 n/a2 $77,047 (120% AMI) $3,848 $4,137 $4,484 n/a2 Single adult, 1 child (in childcare) $19,262 (30% AMI) -$1,517 -$1,262 -$948 n/a3 $32,103 (50% AMI) -$620 -$365 -$50 n/a3 $51,365 (80% AMI) $726 $981 $1,296 52.8% $64,206 (100% AMI) $1,623 $1,878 $2,193 95.3% $77,047 (120% AMI) $2,520 $2,775 $3,090 n/a2 Single adult, 1 child (not in childcare) $19,262 (30% AMI) -$798 -$543 -$228 n/a3 $32,103 (50% AMI)* $100 $355 $670 6.0% $51,365 (80% AMI) $1,446 $1,701 $2,015 87.4% $64,206 (100% AMI) $2,343 $2,598 $2,913 n/a2 $77,047 (120% AMI) $3,240 $3,495 $3,810 n/a2 Single adult, 2 children (both in childcare) $19,262 (30% AMI) -$2,605 -$2,311 -$1,948 n/a3 $32,103 (50% AMI) -$1,708 -$1,414 -$1,051 n/a3 $51,365 (80% AMI) -$362 -$68 $295 0.5% $64,206 (100% AMI) $536 $830 $1,192 43.0% $77,047 (120% AMI) $1,433 $1,727 $2,090 88.7% Single adult, 2 children (1 in childcare) $19,262 (30% AMI) -$1,885 -$1,591 -$1,228 n/a3 $32,103 (50% AMI) -$988 -$694 -$331 n/a3 $51,365 (80% AMI)* $358 $652 $1,015 25.7% $64,206 (100% AMI) $1,255 $1,549 $1,912 83.3% $77,047 (120% AMI) $2,153 $2,447 $2,810 n/a2 Single adult, 2 children (not in childcare) $19,262 (30% AMI) -$1,165 -$871 -$508 n/a3 $32,103 (50% AMI) -$268 $26 $389 1.2% $51,365 (80% AMI) $1,078 $1,372 $1,735 78.9% $64,206 (100% AMI) $1,975 $2,269 $2,632 n/a2 $77,047 (120% AMI) $2,872 $3,167 $3,529 n/a2

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Page 248 Table C.1, cont’d Household Type/ Household Income* Monthly housing budget, by block group (2014$) % of regional rental housing units affordable within housing budget1 Minimum Median Maximum Two adults, no children $19,262 (30% AMI) -$835 -$569 -$237 n/a3 $32,103 (50% AMI)* $62 $328 $660 5.5% $51,365 (80% AMI) $1,408 $1,674 $2,006 86.3% $64,206 (100% AMI) $2,305 $2,571 $2,903 n/a2 $77,047 (120% AMI) $3,202 $3,469 $3,801 n/a2 Two adults, 1 child (in childcare) $19,262 (30% AMI) -$2,069 -$1,785 -$1,433 n/a3 $32,103 (50% AMI) -$1,172 -$888 -$536 n/a3 $51,365 (80% AMI) $174 $458 $810 10.5% $64,206 (100% AMI) $1,071 $1,355 $1,708 78.0% $77,047 (120% AMI) $1,969 $2,252 $2,605 n/a2 Two adults, 1 child (not in childcare) $19,262 (30% AMI) -$1,349 -$1,066 -$713 n/a3 $32,103 (50% AMI) -$452 -$168 $184 0.1% $51,365 (80% AMI)* $894 $1,178 $1,530 69.4% $64,206 (100% AMI) $1,791 $2,075 $2,427 98.5% $77,047 (120% AMI) $2,688 $2,972 $3,325 n/a2 Two adults, 2 children (2 in childcare) $19,262 (30% AMI) -$3,215 -$2,883 -$2,470 n/a3 $32,103 (50% AMI) -$2,517 -$2,184 -$1,771 n/a3 $51,365 (80% AMI) -$1,351 -$787 -$374 n/a3 $64,206 (100% AMI) -$420 -$87 $325 0.6% $77,047 (120% AMI) $628 $961 $1,373 53.6% Two adults, 2 children (1 in childcare) $19,262 (30% AMI) -$2,547 -$2,214 -$1,802 n/a3 $32,103 (50% AMI) -$1,650 -$1,317 -$904 n/a3 $51,365 (80% AMI) -$304 $29 $442 1.6% $64,206 (100% AMI)* $594 $926 $1,339 50.5% $77,047 (120% AMI) $1,491 $1,823 $2,236 92.7% Two adults, 2 children (not in childcare) $19,262 (30% AMI) -$1,827 -$1,495 -$1,082 n/a3 $32,103 (50% AMI) -$930 -$597 -$185 n/a3 $51,365 (80% AMI) $416 $749 $1,161 36.2% $64,206 (100% AMI) $1,313 $1,646 $2,059 86.0% $77,047 (120% AMI) $2,211 $2,543 $2,956 n/a2 * ( BOLD text) Household type and income level selected as ‘canary’ household profile 1Total number of housing units in Denver region = 42 8,050 2Median monthly housing budget exceeds amount for wh ich U.S. Census data is available ($2,000/month) 3Maximum monthly housing budget is less than $0/mont h

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Page 249 APPENDIX D SAMPLE R-CODE (DENVER) #ESTABLISH R ENVIRONMENT install.packages("ctv") install.packages("rgdal") install.packages("spdep") install.views ("Spatial") library ("ctv") library(maptools) library(rgdal) library(spdep) library(lmtest) #LOAD DATA getinfo.shape("C:/Users/kara/My Files/Dissertation_spatial/KSL_AffordAccess/DEN_Aff ordAccessControls _20160923.shp") DEN<-readShapePoly("C:/Users/kara/My Files/Dissertation_spatial/KSL_AffordAccess/DEN_Aff ordAccessControls _20160923.shp") summary(DEN) ##INSPECT, PREPARE VARIABLES #normality in DVs, testing transformations, standar dizing (z) hist(DEN$B10_50P) qqnorm(DEN$B10_50P) qqline(DEN$B10_50P) DEN$sqrtB10_50<-sqrt(DEN$B10_50P) hist(DEN$sqrtB10_50) qqnorm(DEN$sqrtB10_50) qqline(DEN$sqrtB10_50) DEN$B10_50_z<-(DEN$B10_50P-mean(DEN$B10_50P))/sd(DE N$B10_50P) hist(DEN$B10_50_z) qqnorm(DEN$B10_50_z) qqline(DEN$B10_50_z) DEN$sqrtB10_50<-sqrt(DEN$B10_50P) hist(DEN$sqrtB10_50) qqnorm(DEN$sqrtB10_50) qqline(DEN$sqrtB10_50) DEN$sqrtB10_50_z<-(DEN$sqrtB10_50P-mean(DEN$sqrtB10_50P))/sd(DEN$sqrtB10_50P) hist(DEN$sqrtB10_50_z) hist(DEN$D21_100P) qqnorm(DEN$D21_100P) qqline(DEN$D21_100P) DEN$sqrtD21_100<-sqrt(DEN$D21_100P) hist(DEN$sqrtD21_100) qqnorm(DEN$sqrtD21_100)

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Page 250 qqline(DEN$sqrtD21_100) DEN$D21_100_z<-(DEN$D21_100P-mean(DEN$D21_100P))/sd (DEN$D21_100P) hist(DEN$D21_100_z) qqnorm(DEN$D21_100_z) qqline(DEN$D21_100_z) #STANDARDIZE IVs (z) DEN$TA_z<-(DEN$TA-mean(DEN$TA))/sd(DEN$TA) DEN$GD_z<-(DEN$GD-mean(DEN$GD))/sd(DEN$GD) DEN$BD_z<-(DEN$BD-mean(DEN$BD))/sd(DEN$BD) DEN$ID_z<-(DEN$ID-mean(DEN$ID))/sd(DEN$ID) DEN$EH_z<-(DEN$EH-mean(DEN$EH))/sd(DEN$EH) DEN$LR_z<-(DEN$LR-mean(DEN$LR))/sd(DEN$LR) DEN$RE_z<-(DEN$RE-mean(DEN$RE))/sd(DEN$RE) DEN$SF_z<-(DEN$SF-mean(DEN$SF))/sd(DEN$SF) DEN$HU_z<-(DEN$HU_ALL-mean(DEN$HU_ALL))/sd(DEN$HU_A LL) DEN$MI_z<-(DEN$MI-mean(DEN$MI))/sd(DEN$MI) DEN$WH_z<-(DEN$WH-mean(DEN$WH))/sd(DEN$WH) #INSPECT NORMALITY IN IVs, TEST IV TRANSFORMATIONS hist(DEN$TA) qqnorm(DEN$TA) DEN$logTA<-log(DEN$TA) hist(DEN$logTA) DEN$sqrtTA<-sqrt(DEN$TA) hist(DEN$sqrtTA) qqnorm(DEN$sqrtTA) qqline(DEN$sqrtTA) DEN$sqrtTA_z<-(DEN$sqrtTA-mean(DEN$TA))/sd(DEN$TA) hist(DEN$GD) DEN$logGD<-log(DEN$GD) hist(DEN$logGD) qqnorm(DEN$logGD) qqline(DEN$logGD) DEN$sqrtGD<-sqrt(DEN$GD) hist(DEN$sqrtGD) qqnorm(DEN$sqrtGD) qqline(DEN$sqrtGD) DEN$sqrtGD_z<-(DEN$sqrtGD-mean(DEN$sqrtGD))/sd(DEN$ sqrtGD) hist(DEN$BD) DEN$logBD<-log(DEN$BD) hist(DEN$logBD) DEN$sqrtBD<-sqrt(DEN$BD) hist(DEN$sqrtBD) qqnorm(DEN$sqrtBD) qqline(DEN$sqrtBD) DEN$sqrtBD_z<-(DEN$sqrtBD-mean(DEN$sqrtBD))/sd(DEN$ sqrtBD) hist(DEN$ID) DEN$logID<-log(HATA$ID)

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Page 251 hist(DEN$logID) DEN$sqrtID<-sqrt(DEN$ID) hist(DEN$sqrtID) qqnorm(DEN$sqrtID) qqline(DEN$sqrtID) DEN$sqrtID_z<-(DEN$sqrtID-mean(DEN$sqrtID))/sd(DEN$ sqrtID) hist(DEN$EH) qqnorm(DEN$EH) qqline(DEN$EH) DEN$logEH<-log(DEN$EH) hist(DEN$logEH) DEN$sqrtEH<-sqrt(DEN$EH) hist(DEN$sqrtEH) qqnorm(DEN$sqrtEH) qqline(DEN$sqrtEH) hist(DEN$RE) qqnorm(DEN$RE) qqline(DEN$RE) DEN$logRE<-log(DEN$RE) hist(DEN$logRE) qqnorm(DEN$RE) qqline(DEN$RE) DEN$sqrtRE<-sqrt(DEN$RE) hist(DEN$sqrtRE) qqnorm(DEN$sqrtRE) qqline(HATA$sqrtRE) DEN$sqrtRE_z<-(DEN$sqrtRE-mean(DEN$sqrtRE))/sd(DEN$ sqrtRE) DEN$sqRE<-(DEN$RE)*(DEN$RE) DEN$sqRE_z<-(DEN$sqRE-mean(DEN$sqRE))/sd(DEN$sqRE) hist(DEN$SF) qqnorm(DEN$SF) qqline(DEN$SF) DEN$logSF<-log(DEN$SF) hist(DEN$logSF) DEN$sqrtSF<-sqrt(DEN$SF) hist(DEN$SF) qqnorm(DEN$SF) DEN$sqrtSF_z<-(DEN$sqrtSF-mean(DEN$sqrtSF))/sd(DEN$ sqrtSF) hist(DEN$MI) qqnorm(DEN$MI) qqline(DEN$MI) DEN$logMI<-log(DEN$MI) hist(DEN$logMI) DEN$sqrtMI<-sqrt(DEN$MI) hist(DEN$sqrtMI) qqnorm(DEN$sqrtMI) qqline(DEN$sqrtMI) DEN$sqrtMI_z<-(DEN$sqrtMI-mean(DEN$sqrtMI))/sd(DEN$ sqrtMI)

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Page 252 DEN$sqMI<-(DEN$MI)*(DEN$MI) DEN$sqMI_z<-(DEN$sqMI-mean(DEN$sqMI))/sd(DEN$sqMI) hist(DEN$WH) qqnorm(DEN$WH) DEN$logWH<-log(DEN$WH) hist(DEN$logWH) qqnorm(DEN$logWH) DEN$sqrtWH<-sqrt(DEN$WH) hist(DEN$sqrtWH) qqnorm(DEN$sqsrtWH) DEN$sqWH<-(DEN$WH)^2 hist(DEN$sqWH) qqnorm(DEN$sqWH) #INSPECT RELATIONSHIPS FOR LINEARITY plot(DEN$B10_50P, DEN$TA) plot(DEN$B10_50_z, DEN$TA_z) plot(DEN$sqrtB10_50_z, DEN$sqrtTA_z) plot(DEN$B10_50P, DEN$GD) plot(DEN$B10_50_z, DEN$GD_z) plot(DEN$sqrtB10_50_z, DEN$sqrtGD_z) plot(DEN$B10_50P, DEN$BD) plot(DEN$B10_50_z, DEN$BD_z) plot(DEN$sqrtB10_50_z, DEN$sqrtBD_z) plot(DEN$B10_50P, DEN$ID) plot(DEN$B10_50_z, DEN$ID_z) plot(DEN$B10_50_z, DEN$sqrtID_z) plot(DEN$sqrtB10_50_z, DEN$sqrtID_z) plot(DEN$B10_50P, DEN$EH) plot(DEN$B10_50_z, DEN$EH_z) plot(DEN$sqrtB10_50_z, DEN$EH_z) plot(DEN$B10_50P, DEN$RE) plot(DEN$B10_50_z, DEN$RE_z) plot(DEN$B10_50_z, DEN$sqrtRE_z) plot(DEN$sqrtB10_50_z, DEN$sqrtRE_z) plot(DEN$B10_50P, DEN$SF) plot(DEN$B10_50_z, DEN$SF_z) plot(DEN$sqrtB10_50_z, DEN$SF_z) plot(DEN$B10_50P, DEN$MI) plot(DEN$B10_50_z, DEN$MI_z) plot(DEN$sqrtB10_50_z, DEN$MI_z) plot(DEN$B10_50P, DEN$WH) plot(DEN$B10_50_z, DEN$WH_z)

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Page 253 plot(DEN$sqrtB10_50_z, DEN$SF_z) plot(DEN$D21_100P, DEN$TA) plot(DEN$D21_100_z, DEN$sqrtTA_z) plot(DEN$D21_100P, DEN$GD) plot(DEN$D21_100_z, DEN$sqrtGD_z) plot(DEN$D21_100P, DEN$BD) plot(DEN$D21_100_z, DEN$sqrtBD_z) plot(DEN$D21_100P, DEN$ID) plot(DEN$D21_100_z, DEN$sqrtID_z) plot(DEN$D21_100P, DEN$EH) plot(DEN$D21_100_z, DEN$EH_z) plot(DEN$D21_100P, DEN$RE) plot(DEN$D21_100_z, DEN$sqrtRE_z) plot(DEN$D21_100P, DEN$SF) plot(DEN$D21_100_z, DEN$SF_z) plot(DEN$D21_100P, DEN$MI) plot(DEN$D21_100_z, DEN$sqrtMI_z) plot(DEN$D21_100P, DEN$WH) plot(DEN$D21_100_z, DEN$WH_z) ##RUN MAIN EFFECTS OLS MODELS #DV:B10_50 DEN_OLS_B10_50_main<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z, data=DEN) summary(DEN_OLS_B10_50_main) vif(DEN_OLS_B10_50_main) #DV: D21_100P DEN_OLS_D21_100_main<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z, data=DEN) summary(DEN_OLS_D21_100_main) vif(DEN_OLS_D21_100_main) ##SPECIFY INTERACTIONS EFFECTS OLS MODEL #DV: B10_50P AIC(DEN_OLS_B10_50_main) DEN_OLS_B10_50_int1<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*GD_z, data=DEN) summary(DEN_OLS_B10_50_int1) AIC(DEN_OLS_B10_50_int1)

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Page 254 DEN_OLS_B10_50_int2<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*ID_z, data=DEN) summary(DEN_OLS_B10_50_int2) AIC(DEN_OLS_B10_50_int2) DEN_OLS_B10_50_int3<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*EH_z, data=DEN) summary(DEN_OLS_B10_50_int3) AIC(DEN_OLS_B10_50_int3) DEN_OLS_B10_50_int4<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*LR_z, data=DEN) summary(DEN_OLS_B10_50_int4) AIC(DEN_OLS_B10_50_int4) DEN_OLS_B10_50_int5<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*RE_z, data=DEN) summary(DEN_OLS_B10_50_int5) AIC(DEN_OLS_B10_50_int5) DEN_OLS_B10_50_int6<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*HU_z, data=DEN) summary(DEN_OLS_B10_50_int6) AIC(DEN_OLS_B10_50_int6) DEN_OLS_B10_50_int7<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*MI_z, data=DEN) summary(DEN_OLS_B10_50_int7) AIC(DEN_OLS_B10_50_int7) DEN_OLS_B10_50_int8<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*WH_z, data=DEN) summary(DEN_OLS_B10_50_int8) AIC(DEN_OLS_B10_50_int8) DEN_OLS_B10_50_int9<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*GD_z + TA_z*ID_z + TA_z*EH_z + TA_z*LR_z + TA_z*RE_z + TA_z*HU_z + TA_z*MI_z + TA_ z*WH_z, data=DEN) summary(DEN_OLS_B10_50_int9) AIC(DEN_OLS_B10_50_int9) DEN_OLS_B10_50_int<-lm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*GD_z + TA_z*ID_z + TA_z*LR_z + TA_z*RE_z + TA_z*HU_z + TA_z*MI_z, data=DEN) summary(DEN_OLS_B10_50_int) AIC(DEN_OLS_B10_50_int) vif(DEN_OLS_B10_50_int) #DV: D21_100P AIC(DEN_OLS_D21_100_main)

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Page 255 DEN_OLS_D21_100_int1<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*GD_z, data=DEN) summary(DEN_OLS_D21_100_int1) AIC(DEN_OLS_D21_100_int1) DEN_OLS_D21_100_int2<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*ID_z, data=DEN) summary(DEN_OLS_D21_100_int2) AIC(DEN_OLS_D21_100_int2) DEN_OLS_D21_100_int3<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*EH_z, data=DEN) summary(DEN_OLS_D21_100_int3) AIC(DEN_OLS_D21_100_int3) DEN_OLS_D21_100_int4<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*LR_z, data=DEN) summary(DEN_OLS_D21_100_int4) AIC(DEN_OLS_D21_100_int4) DEN_OLS_D21_100_int5<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*RE_z, data=DEN) summary(DEN_OLS_D21_100_int5) AIC(DEN_OLS_D21_100_int5) DEN_OLS_D21_100_int6<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*HU_z, data=DEN) summary(DEN_OLS_D21_100_int6) AIC(DEN_OLS_D21_100_int6) DEN_OLS_D21_100_int7<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*MI_z, data=DEN) summary(DEN_OLS_D21_100_int7) AIC(DEN_OLS_D21_100_int7) DEN_OLS_D21_100_int8<-lm(D21_100_z~TA_z + GD_z + ID _z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*WH_z, data=DEN) summary(DEN_OLS_D21_100_int8) AIC(DEN_OLS_D21_100_int8) DEN_OLS_D21_100_int<-lm(D21_100_z~TA_z + GD_z + ID_ z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*GD_z + TA_z*EH_z + TA_z*RE_z + TA_z*HU_z + TA_z*MI_z, data=DEN) summary(DEN_OLS_D21_100_int) AIC(DEN_OLS_D21_100_int) vif(DEN_OLS_D21_100_int) ##INSPECT REGRESSION DIAGNOSTICS OLS MODELS #TEST VIF (OLS) install.packages("car") library(car) vif(DEN_OLS_B10_50_int)

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Page 256 vif(DEN_OLS_D21_100_int) #OLS REGRESSION DIAGNOSTICS – NORMALITY OF ERROR TE RSM mean(DEN_OLS_B10_50_int$residuals) hist(DEN_OLS_B10_50_int$residuals) qqnorm(DEN_OLS_B10_50_int$residuals) qqline(DEN_OLS_B10_50_int$residuals) mean(DEN_OLS_D21_100_int$residuals) hist(DEN_OLS_D21_100_int$residuals) qqnorm(DEN_OLS_D21_100_int$residuals) qqline(DEN_OLS_D21_100_int$residuals) #OLS REGRESSION DIAGNOSTICS – LINEARITY plot(DEN$TA_z, DEN_OLS_B10_50_int$residuals) abline(h=0) plot(DEN$GD_z, DEN_OLS_B10_50_int$residuals) abline(h=0) plot(DEN$BD_z, DEN_OLS_B10_50_int$residuals) abline(h=0) plot(DEN$ID_z, DEN_OLS_B10_50_int$residuals) abline(h=0) plot(DEN$EH_z, DEN_OLS_B10_50_int$residuals) abline(h=0) plot(DEN$RE_z, DEN_OLS_B10_50_int$residuals) abline(h=0) plot(DEN$MI_z, DEN_OLS_B10_50_int$residuals) abline(h=0) plot(DEN$WH_z, DEN_OLS_B10_50_int$residuals) abline(h=0) plot(DEN$TA_z, DEN_OLS_D21_100_int$residuals) abline(h=0) plot(DEN$GD_z, DEN_OLS_D21_100_int$residuals) abline(h=0) plot(DEN$BD_z, DEN_OLS_D21_100_int$residuals) abline(h=0) plot(DEN$ID_z, DEN_OLS_D21_100_int$residuals) abline(h=0) plot(DEN$EH_z, DEN_OLS_D21_100_int$residuals) abline(h=0) plot(DEN$RE_z, DEN_OLS_D21_100_int$residuals) abline(h=0) plot(DEN$IN_z, DEN_OLS_D21_100_int$residuals) abline(h=0) plot(DEN$WH_z, DEN_OLS_D21_100_int$residuals) abline(h=0) #OLS REGRESSION DIAGNOSTICS – CONSTANT VARIANCE OF ERROR, ERROR TERM INDEPENDENCE plot(DEN_OLS_B10_50_int$fitted.values, DEN_OLS_B10_ 50_int$residuals) abline(h=0)

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Page 257 plot(DEN_OLS_D21_100_int$fitted.values, DEN_OLS_D21_100_int$residuals) abline(h=0) ##PREPARE FOR SPATIAL REGRESSION MODELS #DEFINE SPATIAL WEIGHTS MATRIX DEN_nbq<-poly2nb(DEN) DEN_nbq_w<-nb2listw(DEN_nbq) #TEST FOR SPATIAL AUTOCORRELATIO IN DV moran.test(DEN$B10_50_z, listw=DEN_nbq_w) moran.test(DEN$D21_100_z, listw=DEN_nbq_w) #TEST FOR SPATIAL AUTOCORRELATIO IN OLS RESIDUALS moran.test(DEN_OLS_B10_50_int$residuals, listw=DEN_ nbq_w) moran.test(DEN_OLS_D21_100_int$residuals, listw=DEN _nbq_w) #RUN LAGRANGE MULTIPLIER TESTS, TEST FOR HETEROSKED ASTICITY lm.LMtests(DEN_OLS_B10_50_int, DEN_nbq_w, test="all ") bptest(DEN_OLS_B10_50_int) lm.LMtests(DEN_OLS_D21_100_int, DEN_nbq_w, test="al l") bptest(DEN_OLS_D21_100_int) ##SPECIFY SPATIAL ERROR MODELS #DV: B10_50P DEN_ERR_B10_50_int<-errorsarlm(B10_50_z~TA_z + GD_z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*GD_z + TA_z *ID_z + TA_z*LR_z + TA_z*RE_z + TA_z*HU_z + TA_z*MI_z, data=DEN, list w = DEN_nbq_w) summary(DEN_ERR_B10_50_int) #DV: D21_100P DEN_ERR_D21_100_int<-errorsarlm(D21_100_z~TA_z + GD _z + ID_z + EH_z + LR_z + RE_z + HU_z + MI_z + WH_z + TA_z*GD_z + TA _z*EH_z + TA_z*RE_z + TA_z*HU_z + TA_z*MI_z, data=DEN, listw= DEN_nbq_w) summary(DEN_ERR_D21_100_int) ##INSPECT SPATIAL ERROR MODEL DIAGNOSTICS #TEST FOR SPATIAL AUTOCORRELATION IN OLS RESIDUALS moran.test(DEN_ERR_B10_50_int$residuals, listw=DEN_ nbq_w) bptest.sarlm(DEN_ERR_B10_50_int) moran.test(DEN_ERR_D21_100_int$residuals, listw=DEN _nbq_w) bptest.sarlm(DEN_ERR_D21_100_int) ##SPATIAL ERROR MODELS REGRESSION DIAGNOSTICS #REGRESSION DIAGNOSTICS (SPATIAL ERROR) – NORMALITY OF ERROR TERMS mean(DEN_ERR_B10_50_int$residuals) hist(DEN_ERR_B10_50_int$residuals) qqnorm(DEN_ERR_B10_50_int$residuals) qqline(DEN_ERR_B10_50_int$residuals)

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Page 258 mean(DEN_ERR_D21_100_int$residuals) hist(DEN_ERR_D21_100_int$residuals) qqnorm(DEN_ERR_D21_100_int$residuals) qqline(DEN_ERR_D21_100_int$residuals) #REGRESSION DIAGNOSTICS (SPATIAL ERROR) – LINEARITY plot(DEN$TA_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$GD_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$BD_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$ID_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$EH_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$RE_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$SF_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$MI_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$WH_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN$TA_z, DEN_ERR_D21_100_int$residuals) abline(h=0) plot(DEN$GD_z, DEN_ERR_D21_100_int$residuals) abline(h=0) plot(DEN$BD_z, DEN_ERR_D21_100_int$residuals) abline(h=0) plot(DEN$ID_z, DEN_ERR_D21_100_int$residuals) abline(h=0) plot(DEN$EH_z, DEN_ERR_D21_100_int$residuals) abline(h=0) plot(DEN$RE_z, DEN_ERR_D21_100_int$residuals) abline(h=0) plot(DEN$SF_z, DEN_ERR_D21_100_int$residuals) abline(h=0) plot(DEN$MI_z, DEN_ERR_D21_100_int$residuals) abline(h=0) plot(DEN$WH_z, DEN_ERR_D21_100_int$residuals) abline(h=0) ##REGRESSION DIAGNOSTICS (SPATIAL ERROR) – CONSTANT VARIANCE OF ERROR, ERROR TERM INDEPENDENCE plot(DEN_ERR_B10_50_int$fitted.values, DEN_ERR_B10_ 50_int$residuals) abline(h=0) plot(DEN_ERR_D21_100_int$fitted.values, DEN_ERR_D21_100_int$residuals) abline(h=0)

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Page 259 ##TEST VARIABLE TRANSFORMATIONS (SPATIAL ERROR MODE LS) #B10_50 DEN_ERR_B10_50_trans_test<-errorsarlm(B10_50_z~TA_z + GD_z + BD_z + ID_z + EH_z + RE_z + SF_z + MI_z + WH_z + TA_z*GD_z + TA_z*ID_z + TA_z*EH_z + TA_z*RE_z + TA_z*MI_z, data=DEN, listw = DEN_nbq_w) summary(DEN_ERR_B10_50_int) summary(DEN_ERR_B10_50_trans_test) mean(DEN_ERR_B10_50_trans_test$residuals) hist(DEN_ERR_B10_50_trans_test$residuals) qqnorm(DEN_ERR_B10_50_trans_test$residuals) qqline(DEN_ERR_B10_50_trans_test$residuals) plot(DEN_ERR_B10_50_trans_test$fitted.values, DEN_ERR_B10_50_trans_test$residuals) abline(h=0) plot(DEN_ERR_B10_50_int$fitted.values, DEN_ERR_B10_ 50_int$residuals) abline(h=0) #TA DEN_ERR_B10_50_trans_test<-errorsarlm(B10_50_z~sqrt TA_z + GD_z + BD_z + ID_z + EH_z + RE_z + SF_z + MI_z + WH_z + sq rtTA_z*GD_z + sqrtTA_z*ID_z + sqrtTA_z*EH_z + sqrtTA_z*RE_z + sqr tTA_z*MI_z, data=DEN, listw = DEN_nbq_w) summary(DEN_ERR_B10_50_int) summary(DEN_ERR_B10_50_trans_test) mean(DEN_ERR_B10_50_trans_test$residuals) hist(DEN_ERR_B10_50_trans_test$residuals) qqnorm(DEN_ERR_B10_50_trans_test$residuals) qqline(DEN_ERR_B10_50_trans_test$residuals) plot(DEN$sqrtTA_z, DEN_ERR_B10_50_trans_test$residu als) abline(h=0) plot(DEN$TA_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN_ERR_B10_50_trans_test$fitted.values, DEN_ERR_B10_50_trans_test$residuals) abline(h=0) plot(DEN_ERR_B10_50_int$fitted.values, DEN_ERR_B10_ 50_int$residuals) abline(h=0) #GD DEN_ERR_B10_50_trans_test<-errorsarlm(B10_50_z~TA_z + sqrtGD_z + BD_z + ID_z + EH_z + RE_z + SF_z + MI_z + WH_z + TA _z*sqrtGD_z + TA_z*ID_z + TA_z*EH_z + TA_z*RE_z + TA_z*MI_z, data =HATA, listw = DEN_nbq_w) summary(DEN_ERR_B10_50_int) summary(DEN_ERR_B10_50_trans_test)

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Page 260 mean(DEN_ERR_B10_50_trans_test$residuals) hist(DEN_ERR_B10_50_trans_test$residuals) qqnorm(DEN_ERR_B10_50_trans_test$residuals) qqline(DEN_ERR_B10_50_trans_test$residuals) plot(DEN$sqrtGD_z, DEN_ERR_B10_50_trans_test$residu als) abline(h=0) plot(DEN$GD_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN_ERR_B10_50_trans_test$fitted.values, DEN_ERR_B10_50_trans_test$residuals) abline(h=0) plot(DEN_ERR_B10_50_int$fitted.values, DEN_ERR_B10_ 50_int$residuals) abline(h=0) #ID DEN_ERR_B10_50_trans_test<-errorsarlm(B10_50_z~TA_z + GD_z + BD_z + sqrtID_z + EH_z + RE_z + SF_z + MI_z + WH_z + TA_z* GD_z + TA_z*sqrtID_z + TA_z*EH_z + TA_z*RE_z + TA_z*MI_z, data=DEN, listw = DEN_nbq_w) summary(DEN_ERR_B10_50_int) summary(DEN_ERR_B10_50_trans_test) mean(DEN_ERR_B10_50_trans_test$residuals) hist(DEN_ERR_B10_50_trans_test$residuals) qqnorm(DEN_ERR_B10_50_trans_test$residuals) qqline(DEN_ERR_B10_50_trans_test$residuals) plot(DEN$sqrtID_z, DEN_ERR_B10_50_trans_test$residu als) abline(h=0) plot(DEN$ID_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN_ERR_B10_50_trans_test$fitted.values, DEN_ERR_B10_50_trans_test$residuals) abline(h=0) plot(DEN_ERR_B10_50_int$fitted.values, DEN_ERR_B10_ 50_int$residuals) abline(h=0) #RE DEN_ERR_B10_50_trans_test<-errorsarlm(B10_50_z~TA_z + GD_z + BD_z + ID_z + EH_z + sqrtRE_z + SF_z + MI_z + WH_z + TA_z* GD_z + TA_z*ID_z + TA_z*EH_z + TA_z*sqrtRE_z + TA_z*MI_z, data=DEN, listw = DEN_nbq_w) summary(DEN_ERR_B10_50_int) summary(DEN_ERR_B10_50_trans_test) mean(DEN_ERR_B10_50_trans_test$residuals) hist(DEN_ERR_B10_50_trans_test$residuals) qqnorm(DEN_ERR_B10_50_trans_test$residuals) qqline(DEN_ERR_B10_50_trans_test$residuals)

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Page 261 plot(DEN$sqrtRE_z, DEN_ERR_B10_50_trans_test$residu als) abline(h=0) plot(DEN$RE_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN_ERR_B10_50_trans_test$fitted.values, DEN_ERR_B10_50_trans_test$residuals) abline(h=0) plot(DEN_ERR_B10_50_int$fitted.values, DEN_ERR_B10_ 50_int$residuals) abline(h=0) #MI DEN_ERR_B10_50_trans_test<-errorsarlm(B10_50_z~TA_z + GD_z + BD_z + ID_z + EH_z + RE_z + SF_z + sqrtMI_z + WH_z + TA_z* GD_z + TA_z*ID_z + TA_z*EH_z + TA_z*RE_z + TA_z*sqrtMI_z, data=DEN, listw = DEN_nbq_w) summary(DEN_ERR_B10_50_int) summary(DEN_ERR_B10_50_trans_test) mean(DEN_ERR_B10_50_trans_test$residuals) hist(DEN_ERR_B10_50_trans_test$residuals) qqnorm(DEN_ERR_B10_50_trans_test$residuals) qqline(DEN_ERR_B10_50_trans_test$residuals) plot(DEN$sqrtIN_z, DEN_ERR_B10_50_trans_test$residu als) abline(h=0) plot(DEN$RE_z, DEN_ERR_B10_50_int$residuals) abline(h=0) plot(DEN_ERR_B10_50_trans_test$fitted.values, DEN_ERR_B10_50_trans_test$residuals) abline(h=0) plot(DEN_ERR_B10_50_int$fitted.values, DEN_ERR_B10_ 50_int$residuals) abline(h=0) ##TEST *UNCONTROLLED* SPATIAL ERROR MODEL #DV: B10_50P DEN_ERR_B10_50_unc<-errorsarlm(B10_50_z~TA_z, data= DEN, listw = DEN_nbq_w) summary(DEN_ERR_B10_50_unc) #DV: D21_100P DEN_ERR_D21_100_unc<-errorsarlm(D21_100_z~TA_z, dat a=DEN, listw=DEN_nbq_w) summary(DEN_ERR_D21_100_unc) ##TEST OTHER MODELS #QUASI-POISSON DEN_QUASPOISSON_B10_50<-glm(B10_50~TA_c + GD_c + BD _c + ID_c + EH_c + RE_c + SF_c + MI_c + WH_c + TA_c*GD_c + TA_c*ID_c + TA_c*EH_c + TA_c*RE_c + TA_c*MI_c, family="quasipoisson", data= DEN)

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Page 262 summary(HATA_QUASPOISSON_B10_50) #NEGATIVE BINOMIAL library("MASS") DEN_NB_B10_50<-glm.nb(B10_50~TA_c + GD_c + BD_c + I D_c + EH_c + RE_c + SF_c + MI_c + WH_c + TA_c*GD_c + TA_c*ID_c + TA_c *EH_c + TA_c*RE_c + TA_c*MI_c, data=DEN) summary(DEN_NB_B10_50) #MISC HOUSEKEEPING #EXPORT DATA AS .SHP install.packages("rgdal") library(rgdal) writeOGR(HATA, 'C:/Users/kara/My Files/Dissertation_spatial/KSL_AffordAccess/DEN_Aff ordAccessControlV ariables_20160818_standardized.shp', 'DEN_AffordAccessControlVariables_20160818_standard ized', driver = 'ESRI Shapefile') ##WRITE REGRESSION OUTPUT TO .CSV FILE #OLS MODELS install.packages("broom") install.packages("psych") library(broom) DEN_OLS_B10_50_int_tidy<-tidy(DEN_OLS_B10_50_int) write.csv(DEN_OLS_B10_50_int_tidy, "DEN_OLS_B10_50_ int_tidy.csv") DEN_OLS_D21_100_int_tidy<-tidy(DEN_OLS_D21_100_int) write.csv(DEN_OLS_D21_100_int_tidy, "DEN_OLS_D21_10 0_int_tidy.csv") #ERROR MODELS install.packages("stargazer") library(stargazer) stargazer(DEN_ERR_B10_50_int, type = "text", digits =4, out="DEN_ERR_B10.txt") stargazer(DEN_ERR_D21_100_int, type = "text", digit s=4, out="DEN_ERR_D21.txt") #VIF VALUES DEN_OLS_B10_50_VIF<-vif(DEN_OLS_B10_50_int) stargazer(DEN_OLS_B10_50_VIF, type="text", digits=4 , out="DEN_B10_VIF.txt") DEN_OLS_D21_100_VIF<-vif(DEN_OLS_D21_100_int) stargazer(DEN_OLS_D21_100_VIF, type="text", digits= 4, out="DEN_D21_VIF.txt") ##SUMMARY STATISTICS #DV:B10_50 summary(DEN_OLS_B10_50_int) logLik(DEN_OLS_B10_50_int)

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Page 263 AIC(DEN_OLS_B10_50_int) moran.test(DEN_OLS_B10_50_int$residuals, listw=DEN_ nbq_w) summary(DEN_ERR_B10_50_int) moran.test(DEN_ERR_B10_50_int$residuals, listw=DEN_ nbq_w) lm.LMtests(DEN_OLS_B10_50_int, DEN_nbq_w, test="all ") #DV:D21_100 summary(DEN_OLS_D21_100_int) logLik(DEN_OLS_D21_100_int) AIC(DEN_OLS_D21_100_int) moran.test(DEN_OLS_D21_100_int$residuals, listw=DEN _nbq_w) summary(DEN_ERR_D21_100_int) moran.test(DEN_ERR_D21_100_int$residuals, listw=DEN _nbq_w) lm.LMtests(DEN_OLS_D21_100_int, DEN_nbq_w, test="al l") #DESCRIPTIVES mean(DEN$A_30P) mean(DEN$B10_50P) mean(DEN$B21_80P) mean(DEN$C_50P) mean(DEN$D10_80P) mean(DEN$D21_100P) sd(DEN$A_30P) sd(DEN$B10_50P) sd(DEN$B21_80P) sd(DEN$C_50P) sd(DEN$D10_80P) sd(DEN$D21_100P)

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Page 264 APPENDIX E FULL OLS and SPATIAL ERROR REGRESSION RESULTS Table E.1. OLS and spatial error regression model r esults and diagnostics (Dallas) Explanatory variables Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget household : 2 adults, 2 children (1 in childcare), 100% AMI OLS regression Spatial error model OLS regression Spatial error model se VIF se se VIF se Transit accessibility (TA) 0.074 ** (0.018) 1.92 0.061 ** (0.023) 0.068 ** (0.010) 2.15 0.063 ** (0.011) Gross household density (GD) 0.132 ** (0.017) 1.74 0.136 ** (0.017) 0.067 ** (0.009) 1.78 0.061 ** (0.009) Intersection density (ID) -0.054 ** (0.015) 1.23 -0.042 ** (0.016) -0.025 ** (0.008) 1.49 -0.020 ** (0.009) Employee-housing entropy (EH) -0.061 ** (0.014) 1.21 -0.045 ** (0.014) -0.025 ** (0.007) 1.19 -0.024 ** (0.007) Local retail access (LR) 0.035 * (0.018) 1.97 0.030 n.s. (0.021) 0.035 ** (0.008) 1.38 0.028 ** (0.008) Percent renters (RE) 0.280 ** (0.019) 2.10 0.265 ** (0.020) 0.687 n.s. (0.009) 2.11 0.674 ** (0.010) Total housing units (HU) 0.137 ** (0.014) 1.19 0.142 ** (0.014) 0.432 n.s. (0.007) 1.20 0.442 ** (0.007) Median household income (MI) -0.041 * (0.018) 1.93 -0.024 n.s. (0.020) -0.017 n.s. (0.009) 1.94 -0.021 ** (0.010) Percent non-Hispanic white (WH) -0.071 ** (0.017) 1.68 -0.072 ** (0.020) -0.019 * (0.008) 1.65 -0.020 ** (0.009) Interaction term: TA*GD 0.051 ** (0.017) 2.33 0.038 ** (0.018) -0.046 ** (0.009) 2.66 -0.046 ** (0.009) Interaction term: TA*ID ----0.013 * (0.006) 1.48 -0.006 n.s. (0.006) Interaction term: TA*EH -0.053 ** (0.015) 1.40 -0.041 ** (0.015) -0.045 ** (0.007) 1.38 -0.039 ** (0.007) Interaction term: TA*LR -0.027 ** (0.009) 2.12 -0.021 ** (0.009) --Interaction term: TA*RE ----0.094 ** (0.008) 2.44 -0.089 ** (0.008) Interaction term: TA*HU 0.091 ** (0.013) 1.27 0.089 ** (0.013) 0.137 ** (0.007) 1.33 0.133 ** (0.007) Interaction term: TA*MI -0.050 ** (0.017) 1.86 -0.053 ** (0.017) ---Interaction term: TA*WH -0.096 ** (0.017) 1.92 -0.087 ** (0.019) -0.048 ** (0.007) 1.43 -0.050 ** (0.008) Constant -0.021 n.s. (0.014) 1.92 -0.018 n.s. (0.021) 0.051 ** (0.007) 2.15 0.046 ** (0.009) Lambda -0.366 ** -0.248 ** No. Observations 4091 4091 Measure of fit Adj-R 2 0.301 -0.828 -Log likelihood -5064 -4947 -2195 -2147 AIC 10162 9931 4424 4330 Tests for spatial dependence MoranÂ’s I for residuals 0.148** -0.005 n.s. 0.092** -0.004 n.s. Lagrange Multiplier (LM)-Error 274.83** -105.46** -Robust LM-Error 311.25** -69.60** -LM-Lag 3.68 n.s. -51.08** -Robust LM-Lag 40.10** -15.22** -Notes: *p 0.05; **p 0.01; Coefficients relate to standardized z-scores for all variables

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Page 265 Table E.2. OLS and spatial error regression model r esults and diagnostics (Denver) Explanatory variables Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget household : 2 adults, 2 children (1 in childcare), 100% AMI OLS regression Spatial error model OLS regression Spatial error model se VIF se se VIF se Transit accessibility (TA) 0.056 * (0.027) 2.36 0.059 * (0.03) 0.079 * (0.017) 2.38 0.056 ** (0.020) Gross household density (GD) 0.050 n.s. (0.033) 3.61 0.061 * (0.034) 0.287 ** (0.020) 3.35 0.295 ** (0.021) Intersection density (ID) 0.011 n.s. (0.033) 3.53 -0.011 n.s. (0.034) -0.076 ** (0.015) 1.80 -0.063 ** (0.015) Employee-housing entropy (EH) 0.015 n.s. (0.021) 1.45 0.015 n.s. (0.021) 0.026 ** (0.013) 1.44 0.027 ** (0.013) Local retail access (LR) -0.001 n.s. (0.024) 1.82 0.000 n.s. (0.025) 0.007 * (0.013) 1.36 0.004 n.s. (0.014) Percent renters (RE) 0.102 ** (0.028) 2.60 0.101 ** (0.029) 0.476 n.s. (0.018) 2.57 0.479 ** (0.018) Total housing units (HU) 0.117 ** (0.019) 1.23 0.116 ** (0.02) 0.231 ** (0.012) 1.21 0.238 ** (0.012) Median household income (MI) -0.192 ** (0.026) 2.20 -0.188 ** (0.027) -0.065 ** (0.016) 2.15 -0.059 ** (0.017) Percent non-Hispanic white (WH) -0.017 n.s. (0.023) 1.67 -0.018 n.s. (0.025) -0.049 ** (0.014) 1.66 -0.065 ** (0.016) Interaction term: TA*GD 0.086 ** (0.02) 3.12 0.093 ** (0.021) -0.056 ** (0.012) 2.89 -0.056 ** (0.013) Interaction term: TA*ID 0.092 *** (0.021) 2.79 0.091 ** (0.022) ---Interaction term: TA*EH ----0.044 ** (0.012) 1.22 -0.038 ** (0.013) Interaction term: TA*LR 0.043 ** (0.027) 1.71 0.034 * (0.028) ---Interaction term: TA*RE 0.082 ** (0.018) 2.45 0.078 ** (0.018) 0.091 ** (0.018) 2.57 0.095 ** (0.018) Interaction term: TA*HU 0.132 ** (0.025) 1.32 0.121 ** (0.025) 0.139 ** (0.011) 1.31 0.141 ** (0.011) Interaction term: TA*MI -0.192 ** (0.025) 1.86 -0.192 ** (0.026) -0.060 * (0.015) 1.85 -0.064 ** (0.016) Interaction term: TA*WH ------Constant -0.206 ** (0.023) -0.206 ** (0.026) 0.051 ** (0.007) 2.38 -0.031 * (0.016) Lambda 0.183 ** 0.260 ** No. Observations 1966 1966 Measure of fit Adj-R 2 0.392 -0.762 -Log likelihood -2292 -2280 -1373 -1347 AIC 4618 4596 2777 2729 Tests for spatial dependence MoranÂ’s I for residuals 0.065** -0.004 n.s. 0.096** -0.005 n.s. Lagrange Multiplier (LM)-Error 25.58** -54.93** Robust LM-Error 31.88** -5.41* -LM-Lag 0.15 n.s. -56.85** -Robust LM-Lag 6.45* -7.33** -Notes: *p 0.05; **p 0.01; Coefficients relate to standardized z-scores for all variables

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Page 266 Table E.3. OLS and spatial error regression model r esults and diagnostics (Houston) Explanatory variables Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget household : 2 adults, 2 children (1 in childcare), 100% AMI OLS regression Spatial error model OLS regression Spatial error model se VIF se se VIF se Transit accessibility (TA) 0.031 n.s. (0.021) 2.18 0.023 n.s. (0.028) 0.028 * (0.014) 2.73 0.030 * (0.016) Gross household density (GD) 0.477 ** (0.024) 2.83 0.514 ** (0.024) 0.172 ** (0.014) 2.86 0.181 ** (0.015) Intersection density (ID) -0.094 ** (0.017) 1.51 -0.091 ** (0.020) -0.108 ** (0.01) 1.51 -0.095 ** (0.011) Employee-housing entropy (EH) 0.029 n.s. (0.017) 1.42 0.039 ** (0.017) 0.012 n.s. (0.01) 1.43 0.011 n.s. (0.010) Local retail access (LR) -0.117 ** (0.029) 4.24 -0.094 ** (0.033) 0.081 ** (0.017) 4.29 0.077 ** (0.019) Percent renters (RE) 0.217 ** (0.022) 2.42 0.192 ** (0.022) 0.657 ** (0.013) 2.46 0.647 ** (0.013) Total housing units (HU) 0.035 * (0.015) 1.13 0.049 ** (0.015) 0.434 ** (0.012) 1.87 0.443 ** (0.012) Median household income (MI) -0.039 n.s. (0.021) 2.17 -0.034 n.s. (0.022) -0.051 ** (0.012) 2.17 -0.047 ** (0.013) Percent non-Hispanic white (WH) -0.085 ** (0.019) 1.75 -0.058 ** (0.023) -0.007 n.s. (0.011) 1.78 -0.007 n.s. (0.013) Interaction term: TA*GD -0.051 ** (0.014) 2.14 -0.069 ** (0.015) -0.027 ** (0.009) 2.71 -0.034 ** (0.010) Interaction term: TA*ID 0.037 ** (0.011) 1.52 0.039 ** (0.013) 0.034 ** (0.007) 1.54 0.033 ** (0.007) Interaction term: TA*EH -0.037 * (0.016) 1.29 -0.031 ** (0.016) -0.029 ** (0.01) 1.45 -0.028 ** (0.010) Interaction term: TA*LR 0.038 ** (0.012) 3.92 0.023 * (0.014) -0.031 ** (0.008) 4.13 -0.028 ** (0.008) Interaction term: TA*RE ----0.119 ** (0.011) 2.25 -0.119 ** (0.012) Interaction term: TA*HU ---0.236 ** (0.015) 1.99 0.234 ** (0.015) Interaction term: TA*MI ------Interaction term: TA*WH -0.156 ** (0.015) 1.19 -0.127 ** (0.018) -0.050 ** (0.01) 1.61 -0.052 ** (0.011) Constant -0.014 n.s. (0.016) -0.015 n.s. (0.025) 0.083 ** (0.01) 0.082 ** (0.013) Lambda 0.419 ** 0.244 ** No. Observations 3011 3011 Measure of fit Adj-R 2 0.392 -0.787 -Log likelihood -3515 -3392 -1936 -1896 AIC 7063 6818 3908 3830 Tests for spatial dependence MoranÂ’s I for residuals 0.183** -0.014 n.s. 0.106** -0.006 n.s. Lagrange Multiplier (LM)-Error 305.55** -102.56** -Robust LM-Error 263.99** -47.64** -LM-Lag 47.53* -58.00 n.s. -Robust LM-Lag 5.97* -3.08 n.s. -Notes: *p 0.05; **p 0.01; Coefficients relate to standardized z-scores for all variables

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Page 267 Table E.4. OLS and spatial error regression model r esults and diagnostics (Los Angeles) Explanatory variables Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget household : 2 adults, 2 children (1 in childcare), 100% AMI OLS regression Spatial error model OLS regression Spatial error model se VIF se se VIF se Transit accessibility (TA) 0.080 ** (0.015) 2.12 0.094 ** (0.018) 0.117 ** (0.013) 2.24 0.172 ** (0.017) Gross household density (GD) 0.060 ** (0.019) 3.39 0.067 ** (0.020) 0.227 ** (0.016) 3.33 0.175 ** (0.017) Intersection density (ID) 0.017 n.s. (0.011) 1.19 0.023 * (0.012) 0.048 ** (0.009) 1.20 0.042 ** (0.010) Employee-housing entropy (EH) 0.043 ** (0.012) 1.30 0.045 ** (0.012) 0.038 ** (0.010) 1.29 0.033 ** (0.010) Local retail access (LR) 0.018 n.s. (0.012) 1.34 0.012 n.s. (0.014) -0.028 ** (0.010) 1.36 -0.007 n.s. (0.012) Percent renters (RE) 0.046 ** (0.017) 2.73 0.042 ** (0.018) 0.162 ** (0.014) 2.78 0.117 ** (0.015) Total housing units (HU) -0.011 n.s. (0.011) 1.28 -0.029 ** (0.012) 0.000 n.s. (0.010) 1.29 -0.016 n.s. (0.010) Median household income (MI) -0.099 ** (0.017) 2.70 -0.069 ** (0.017) -0.108 ** (0.014) 2.78 -0.084 ** (0.015) Percent non-Hispanic white (WH) -0.009 n.s. (0.013) 1.75 -0.011 n.s. (0.016) -0.079 ** (0.011) 1.77 -0.064 ** (0.014) Interaction term: TA*GD 0.101 ** (0.008) 2.17 0.104 ** (0.009) 0.034 ** (0.008) 2.81 0.044 ** (0.009) Interaction term: TA*ID -0.060 ** (0.011) 1.08 -0.026 ** (0.011) ---Interaction term: TA*EH 0.077 ** (0.011) 1.10 0.069 ** (0.012) 0.036 ** (0.010) 1.15 0.033 ** (0.010) Interaction term: TA*LR ------Interaction term: TA*RE ---0.088 ** (0.015) 3.15 0.066 ** (0.016) Interaction term: TA*HU ---0.022 ** (0.009) 1.29 0.004 n.s. (0.009) Interaction term: TA*MI -0.118 ** (0.013) 1.63 -0.085 ** (0.015) -0.096 ** (0.014) 2.46 -0.077 ** (0.016) Interaction term: TA*WH ------Constant -0.091 ** (0.012) 2.12 -0.082 ** (0.015) -0.103 ** (0.010) -0.088 ** (0.015) Lambda 0.284 ** 0.386 ** No. Observations 8188 8188 Measure of fit Adj-R 2 0.156 -0.390 -Log likelihood -10917 -10794 -9590 -9351 AIC 21863 21620 19212 18736 Tests for spatial dependence MoranÂ’s I for residuals 0.101** -0.007 n.s. 0.142** -0.015 n.s. Lagrange Multiplier (LM)-Error 260.28** -508.50** -Robust LM-Error 322.51** -924.88** -LM-Lag 28.95** -148.45** -Robust LM-Lag 91.19** -564.84** -Notes: *p 0.05; **p 0.01; Coefficients relate to standardized z-scores for all variables

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Page 268 Table E.5. OLS and spatial error regression model r esults and diagnostics (Minneapolis) Explanatory variables Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget household : 2 adults, 2 children (1 in childcare), 100% AMI OLS regression Spatial error model OLS regression Spatial error model se VIF se se VIF se Transit accessibility (TA) 0.194 ** (0.023) 3.07 0.200 ** (0.025) 0.091 ** (0.013) 2.94 0.089 ** (0.014) Gross household density (GD) -0.101 ** (0.026) 3.90 -0.105 ** (0.026) -0.007 n.s. (0.008) 1.00 -0.006 n.s. (0.008) Intersection density (ID) 0.012 n.s. (0.019) 2.03 0.000 n.s. (0.019) -0.013 n.s. (0.011) 2.03 -0.012 n.s. (0.011) Employee-housing entropy (EH) -0.030 * (0.014) 1.18 -0.030 ** (0.014) -0.024 ** (0.008) 1.17 -0.023 ** (0.008) Local retail access (LR) -0.017 n.s. (0.017) 1.72 -0.010 n.s. (0.018) 0.033 ** (0.010) 1.70 0.032 ** (0.010) Percent renters (RE) 0.293 ** (0.022) 2.96 0.285 ** (0.023) 0.760 ** (0.013) 2.89 0.760 ** (0.013) Total housing units (HU) 0.283 ** (0.015) 1.40 0.283 ** (0.016) 0.450 ** (0.009) 1.38 0.450 ** (0.009) Median household income (MI) -0.115 ** (0.019) 2.12 -0.116 ** (0.020) -0.022 * (0.011) 2.00 -0.021 * (0.011) Percent non-Hispanic white (WH) 0.019 n.s. (0.019) 2.18 0.010 n.s. (0.021) 0.005 n.s. (0.010) 1.75 0.003 n.s. (0.011) Interaction term: TA*GD 1.037 ** (0.225) 3.99 1.075 ** (0.224) ---Interaction term: TA*ID ------Interaction term: TA*EH -0.079 ** (0.015) 1.18 -0.075 ** (0.015) -0.032 ** (0.009) 1.18 -0.032 ** (0.009) Interaction term: TA*LR -0.054 ** (0.01) 1.91 -0.053 ** (0.011) -0.039 ** (0.006) 1.86 -0.038 ** (0.006) Interaction term: TA*RE 0.133 ** (0.021) 3.92 0.110 ** (0.022) -0.058 ** (0.008) 1.72 -0.057 ** (0.008) Interaction term: TA*HU 0.324 ** (0.016) 1.41 0.324 ** (0.016) 0.267 ** (0.009) 1.36 0.266 ** (0.009) Interaction term: TA*MI -0.120 ** (0.021) 2.77 -0.127 ** (0.022) ---Interaction term: TA*WH -0.102 ** (0.016) 1.98 -0.120 ** (0.018) ---Constant -0.081 ** (0.016) 3.07 -0.077 ** (0.019) 0.096 ** (0.009) 0.095 ** (0.01) Lambda 0.213 ** 0.058 n.s. No. Observations 2310 2310 Measure of fit Adj-R 2 0.608 -0.863 -Log likelihood -2189 -2170 -977 -976 AIC 4413 4379 1984 1984 Tests for spatial dependence MoranÂ’s I for residuals 0.074** -0.005 n.s. Lagrange Multiplier (LM)-Error 37.95** -2.57 n.s. -Robust LM-Error 34.98** -0.15 n.s. -LM-Lag 7.19** -3.96* -Robust LM-Lag 4.22* -1.54 n.s. -Notes: *p 0.05; **p 0.01; Coefficients relate to standardized z-scores for all variables

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Page 269 Table E.6. OLS and spatial error regression model r esults and diagnostics (Portland) Explanatory variables Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget household : 2 adults, 2 children (1 in childcare), 100% AMI OLS regression Spatial error model OLS regression Spatial error model se VIF se se VIF se Transit accessibility (TA) -0.112 ** (0.033) 2.25 -0.120 ** (0.030) -0.287 ** (0.030) 2.25 -0.153 ** (0.045) Gross household density (GD) 0.262 ** (0.033) 2.20 0.266 ** (0.032) 0.207 ** (0.029) 2.17 0.199 ** (0.028) Intersection density (ID) 0.099 ** (0.031) 1.94 0.106 ** (0.029) 0.114 ** (0.028) 1.94 -0.008 n.s. (0.028) Employee-housing entropy (EH) 0.041 n.s. (0.026) 1.39 0.043 * (0.025) 0.009 n.s. (0.024) 1.39 0.016 n.s. (0.020) Local retail access (LR) -0.174 ** (0.053) 5.69 -0.181 ** (0.050) 0.057 n.s. (0.048) 5.69 0.044 n.s. (0.052) Percent renters (RE) 0.094 ** (0.038) 2.87 0.109 ** (0.036) 0.405 ** (0.034) 2.85 0.339 ** (0.030) Total housing units (HU) 0.043 n.s. (0.024) 1.17 0.036 n.s. (0.023) 0.087 ** (0.022) 1.16 0.139 ** (0.018) Median household income (MI) -0.123 ** (0.031) 1.92 -0.111 ** (0.029) -0.120 ** (0.027) 1.86 -0.107 ** (0.028) Percent non-Hispanic white (WH) 0.025 n.s. (0.026) 1.34 0.027 n.s. (0.024) 0.065 ** (0.023) 1.34 -0.020 n.s. (0.022) Interaction term: TA*GD ------Interaction term: TA*ID ------Interaction term: TA*EH ------Interaction term: TA*LR 0.223 ** (0.023) 5.15 0.225 ** (0.022) 0.094 ** (0.021) 5.15 0.089 ** (0.023) Interaction term: TA*RE -0.202 ** (0.035) 3.06 -0.198 ** (0.033) -0.202 ** (0.031) 2.95 -0.224 ** (0.029) Interaction term: TA*HU 0.055 * (0.022) 1.22 0.059 ** (0.022) 0.047 * (0.020) 1.22 0.010 n.s. (0.017) Interaction term: TA*MI -0.138 ** (0.034) 2.35 -0.129 ** (0.032) -0.080 ** (0.030) 2.29 -0.129 ** (0.028) Interaction term: TA*WH -0.059 * (0.028) 1.27 -0.061 ** (0.026) ---Constant -0.058 * (0.025) -0.058 ** (0.023) 0.020 n.s. (0.023) 0.033 n.s. (0.049) Lambda -0.128 ** 0.654 ** No. Observations 1420 1420 Measure of fit Adj-R 2 0.305 -0.434 -Log likelihood -1749 -1745 -1604 -1399 AIC 3529 3525 3237 2831 Tests for spatial dependence MoranÂ’s I for residuals -0.037 n.s. 0.002 n.s. 0.35 3** -0.039 n.s. Lagrange Multiplier (LM)-Error 5.86* -536.20 -Robust LM-Error 3.28 n.s. -446.89 -LM-Lag 3.53 n.s. -99.68 -Robust LM-Lag 0.95 n.s. -10.36 -Notes: *p 0.05; **p 0.01; Coefficients relate to standardized z-scores for all variables

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Page 270 Table E.7. OLS and spatial error regression model r esults and diagnostics (Salt Lake City) Explanatory variables Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget household : 2 adults, 2 children (1 in childcare), 100% AMI OLS regression Spatial error model OLS regression Spatial error model se VIF se se VIF se Transit accessibility (TA) -0.085 ** (0.028) 1.67 -0.034 n.s. (0.036) -0.009 n.s. (0.015) 1.66 -0.007 n.s. (0.018) Gross household density (GD) 0.286 ** (0.034) 2.55 0.285 ** (0.036) 0.185 ** (0.019) 2.58 0.211 ** (0.020) Intersection density (ID) 0.008 n.s. (0.025) 1.32 0.002 n.s. (0.025) -0.034 * (0.014) 1.31 -0.039 ** (0.014) Employee-housing entropy (EH) 0.023 n.s. (0.026) 1.46 0.037 n.s. (0.025) 0.051 ** (0.014) 1.45 0.048 ** (0.014) Local retail access (LR) -0.026 n.s. (0.028) 1.69 -0.011 n.s. (0.031) 0.045 ** (0.015) 1.55 0.050 ** (0.016) Percent renters (RE) 0.274 ** (0.033) 2.35 0.217 ** (0.034) 0.599 ** (0.018) 2.36 0.604 ** (0.019) Total housing units (HU) 0.159 ** (0.023) 1.18 0.166 ** (0.024) 0.333 ** (0.013) 1.19 0.339 ** (0.013) Median household income (MI) -0.058 n.s. (0.031) 2.08 -0.065 * (0.032) -0.033 * (0.017) 2.05 -0.026 n.s. (0.018) Percent non-Hispanic white (WH) 0.044 n.s. (0.026) 1.48 0.087 ** (0.029) -0.033 * (0.014) 1.43 -0.022 n.s. (0.016) Interaction term: TA*GD -0.090 ** (0.018) 1.64 -0.091 ** (0.019) -0.049 ** (0.011) 1.86 -0.058 ** (0.011) Interaction term: TA*ID ------Interaction term: TA*EH ------Interaction term: TA*LR 0.174 ** (0.020) 1.61 0.144 ** (0.022) ---Interaction term: TA*RE ---0.071 ** (0.014) 1.73 0.073 ** (0.014) Interaction term: TA*HU 0.264 ** (0.026) 1.24 0.255 ** (0.025) 0.219 ** (0.014) 1.27 0.219 ** (0.014) Interaction term: TA*MI -0.072 ** (0.027) 1.54 -0.087 ** (0.028) ---Interaction term: TA*WH ------Constant -0.047 * (0.023) -0.047 n.s. (0.035) -0.007 n.s. (0.013) -0.005 n.s. (0.016) Lambda 0.383 ** 0.242 ** No. Observations 1279 1279 Measure of fit Adj-R 2 0.415 -0.818 -Log likelihood -1465 -1429 -718 -703 AIC 2959 2890 1464 1436 Tests for spatial dependence MoranÂ’s I for residuals 0.137** -0.006 n.s. 0.094** -0.004** Lagrange Multiplier (LM)-Error 75.04** -34.98** Robust LM-Error 104.95** -<0.01 n.s. -LM-Lag 0.08 n.s. -47.40** -Robust LM-Lag 29.99** -12.42** -Notes: *p 0.05; **p 0.01; Coefficients relate to standardized z-scores for all variables

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Page 271 Table E.8. OLS and spatial error regression model r esults and diagnostics (Seattle) Explanatory variables Low housing budget household : 1 adult, 1 child (not in childcare), 50% AMI Moderate housing budget household : 2 adults, 2 children (1 in childcare), 100% AMI OLS regression Spatial error model OLS regression Spatial error model se VIF se se VIF se Transit accessibility (TA) -0.114 ** (0.023) 2.91 -0.069 ** (0.029) -0.112 ** (0.012) 2.68 -0.105 ** (0.013) Gross household density (GD) 0.466 ** (0.044) 10.58 0.467 ** (0.046) 0.325 ** (0.023) 10.57 0.319 ** (0.024) Intersection density (ID) 0.021 n.s. (0.021) 2.35 -0.016 n.s. (0.024) -0.050 ** (0.011) 2.35 -0.045 ** (0.012) Employee-housing entropy (EH) 0.067 ** (0.016) 1.38 0.048 ** (0.016) 0.027 ** (0.008) 1.38 0.024 ** (0.008) Local retail access (LR) -0.093 * (0.044) 10.50 -0.036 n.s. (0.050) 0.065 ** (0.023) 10.50 0.063 ** (0.025) Percent renters (RE) 0.311 ** (0.023) 3.00 0.276 ** (0.023) 0.585 ** (0.012) 3.00 0.583 ** (0.012) Total housing units (HU) 0.144 ** (0.016) 1.36 0.161 ** (0.015) 0.348 ** (0.008) 1.35 0.357 ** (0.008) Median household income (MI) -0.111 ** (0.019) 1.88 -0.108 ** (0.020) -0.041 ** (0.010) 1.88 -0.037 ** (0.010) Percent non-Hispanic white (WH) -0.059 ** (0.016) 1.39 -0.057 ** (0.019) -0.027 ** (0.008) 1.36 -0.026 ** (0.009) Interaction term: TA*GD -0.064 ** (0.015) 9.33 -0.069 ** (0.015) -0.066 ** (0.008) 9.31 -0.066 ** (0.008) Interaction term: TA*ID 0.034 ** (0.012) 2.46 0.044 ** (0.013) 0.037 ** (0.006) 2.46 0.032 ** (0.007) Interaction term: TA*EH ------Interaction term: TA*LR 0.056 ** (0.013) 9.98 0.025 * (0.015) -0.021 ** (0.007) 9.97 -0.023 ** (0.007) Interaction term: TA*RE -0.093 ** (0.023) 4.31 -0.082 ** (0.023) -0.036 ** (0.010) 3.04 -0.033 ** (0.010) Interaction term: TA*HU 0.057 ** (0.013) 1.99 0.084 ** (0.013) 0.091 ** (0.007) 1.87 0.095 ** (0.007) Interaction term: TA*MI -0.085 ** (0.018) 2.19 -0.086 ** (0.019) ---Interaction term: TA*WH -0.106 ** (0.016) 1.48 -0.087 ** (0.019) -0.047 ** (0.008) 1.39 -0.045 ** (0.009) Constant -0.007 n.s. (0.017) -0.001 n.s. (0.025) 0.019 * (0.009) 0.021 ** (0.011) Lambda 0.432 ** 0.228 ** No. Observations 2465 2465 Measure of fit Adj-R 2 0.551 -0.878 -Log likelihood -2503 -2408 -898 -873 AIC 5042 4854 1830 1783 Tests for spatial dependence MoranÂ’s I for residuals 0.166** 0.085** -0.001 n.s . Lagrange Multiplier (LM)-Error 200.83** -52.55** -Robust LM-Error 173.87** -7.57** -LM-Lag 37.02** -45.33** -Robust LM-Lag 10.06** -0.36 n.s. -Notes: *p 0.05; **p 0.01; Coefficients relate to standardized z-scores for all variables