Citation
Econometric model of sales of existing single family residences in the Denver Metropolitan Area

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Title:
Econometric model of sales of existing single family residences in the Denver Metropolitan Area
Creator:
Griffith, Kinny Jay
Publication Date:
Language:
English
Physical Description:
vii, 173 leaves : illustrations ; 29 cm

Subjects

Subjects / Keywords:
Residential real estate -- Econometric models -- Colorado -- Denver ( lcsh )
Housing, Single family -- Econometric models -- Colorado -- Denver ( lcsh )
Housing -- Prices -- Econometric models -- Colorado -- Denver ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 169-170).
General Note:
Department of Economics
Statement of Responsibility:
by Kinny Jay Griffith.

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Source Institution:
|University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
40283101 ( OCLC )
ocm40283101
Classification:
LD1190.L53 1998m .G74 ( lcc )

Full Text
1
ECONOMETRIC MODEL
OF
SALES OF
EXISTING SINGLE FAMILY RESIDENCES
IN THE
DENVER METROPOLITAN AREA
by
Kinny Jay Griffith
B.A., University of Colorado, 1978
M.A., University of Denver, 1989
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Masters of Arts
Economics
1998
1
k


This thesis for the Masters of Arts
degree by
Kinny Jay Griffith
has been approved
by
Steven R. Beckman
Daniel I. Rees

Date


Griffith, Kinny Jay (M.A. Economics)
Econometric Model of Sales of Existing Single Family Residences in the Denver
Metropolitan Area
Thesis directed by Associate Professor Steven R. Beckman
This study identifies variables that are significant in explaining the price and
quantity of sales of existing single family residences (SFRs) in the Denver metro area.
The study covers 1974 through 1992 including monthly data from the following: price
and quantity of dependent variable, price and cost of substitutes, household income,
income tax policy and other government subsidies, population size, demographics,
appreciation in investment, inventory factors, transaction costs, and budget constraint.
In contrast to most studies of the residential real estate market, which are based
on new construction, this study focuses on existing SFR's, which had approximately
twice the number of sales as new SFR's in the Denver metro area over this time period.
Standardized coefficients reflect that of the significant variables in the quantity
equation several had larger impacts on the dependent variable than most of the others:
a one standard deviation increase in the change in new listings resulted in 207 additional
units sold, or 42% of one standard deviation in the number of units sold; and one
standard deviation increase in the percent of the population under age 18 resulted in 169
additional units sold, or 34% of one standard deviation in the number of units sold. In
the price equation, one standard deviation increase in net migration resulted in higher
prices by $5,254, or 28% of one standard deviation in the price of units sold; and one
standard deviation increase in the percent of the population under age 18 resulted in
lower prices by $13,524, or 72% of one standard deviation of the price of units sold.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
ABSTRACT
Sign<
Steven R. Beckman
in


CONTENTS
CHAPTER
1. INTRODUCTION...................................................... I
Existing SFRs Versus Newly Constructed SFRs ....................1
Unique Demand Incentives and Commodity Characteristics............2
Economic Cycle....................................................2
Credit............................................................4
Possible Delay in Market Clearing.................................4
2. VARIABLES........................................................ 6
Quantity and Price of Dependent Variable..........................6
Characteristics of the SFRs being sold.......................7
Quantity and Price............................................9
Mortgage Rate ............................................... 9
Price Discounts..............................................11
Other Price Considerations ..................................12
Quantity and Price of Substitutes ...............................12
Condominiums.................................................12
New Single Family Residences ................................13
Substitute Remodel Current SFR.............................13
Factor Costs ................................................14
Rent ........................................................14
Income Variables.................................................16
Household Income-Permanent and Temporary.....................16
Income Stability Unemployment..............................18
Budget constraint............................................18
Income Tax Policy and other Government Subsidies.................19
Marginal Income Tax Rates....................................19
Capital Gain Tax Preferences ................................20
Government Subsidies Through Credit Markets..................22
Investment Variables.............................................25
Appreciation.................................................25
Transaction Costs ...............................................27
Transaction Costs Related to Change in Ownership.............29
Financing Costs .............................................30
Inventory Variables..............................................31
iv


Number of Days to Sale.......................................30
Number of New Listings ......................................31
Change in Inventory..........................................31
Population and Demographic Variables.............................32
Size of the Demand Market....................................32
Migrations ..................................................32
Demographics.................................................33
Other Variables..................................................34
User Costs ..................................................34
Physical Depreciation........................................36
Wealth ......................................................36
3. THE MODEL........................................................ 37
Unit Root Tests..................................................37
Serial Correlation ..............................................38
Supply and Demand Model..........................................38
4. RESULTS ......................................................... 40
Signs of Coefficients............................................42
Quantity Equation ......................................... 42
Price Equation ..............................................44
Standardized Coefficients........................................45
Elasticities.....................................................46
GRAPHS OF VARIABLES......................................................vi
APPENDCES............................................................... 87
A. RATS Printed Results.............................................88
B. Summary of Variables ............................................93
C. Correlation Matrix ..............................................97
D. Standardized Coefficients.......................................103
E. Elasticities....................................................105
F. Unit Root Test Results..........................................107
G. Serial Correlation Results......................................110
H. Data Detail ....................................................127
BIBLIOGRAPHY........................................................... 170
v


GRAPHS OF VARIABLES
RNS...................Number of Existing SFR Units Sold........
RNSDIFF....................First Differences of RNS ...........
RP................. Average Price of Existing SFR Units Sold
RPDIFF ....................First Differences of RP ............
MR......................... Mortgage Interest Rates............
MRDIFF..................... First Differences of MR............
CP............Average Price of Existing Condominium Units Sold
CPDIFF ....................First Differences of CP.............
CHE........... Average Hourly Earnings Construction Industry .
CHEDIFF....................First Differences of CHE ...........
MPI................... Construction Material Price Index.......
MPIDIFF ................... First Differences of MPI...........
MWE3A.........................Permanent Income.................
MWE3ADIFF............... First Differences of MWE3A............
TY ........................... Temporary Income................
UNR...........................Unemployment Rate................
CPI........................ Consumer Price Index ..............
CPIDIFF.................... First Differences of CPI...........
MTR..................... Marginal Income Tax Rate..............
CAP .......................Capital Gains Preference ...........
FED ....................Federal Financing -% of Total..........
FEDDIFF ...................First Differences of FED............
APPREC..................Three Year Appreciation Rate ..........
APPRECDIFF ............. First Differences of APPREC...........
FEE.............................Closing Fees ..................
FEEDIFF ................... First Differences of FEE...........
RDM .................. Average Number of Days on Market........
RDMDIFF ...................First Differences of RDM............
NEWL............ Number of New Listings of Existing SFRs for Sale
NEWLDIFF................ First Differences of NEWL.............
SFP...................Permits for New Construction SFRs .....
SFPDIFF.................... First Differences of SFP...........
LAF .......................Labor Force (Population) ...........
LAFDDFF .................. First Differences of LAF............
MIG.............................Net Migrations ................
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
vi


GRAPHS OF VARIABLES (Continued)
AGE........................ Average Population Age..........................84
P18................. Percent of Population Under Age 18 ....................85
P50.................Percent of Population Age 50 and Above..................86
Vll


CHAPTER 1
INTRODUCTION
The purpose of this study is to identify the variables that are significant in
explaining the price and quantity of sales of existing single family residences (SFRs)
in the Denver metro area. The optimal quantity demanded and supplied of SFRs is
assumed to depend upon the following variables: price of dependent variable; price
and cost of substitute variables; household income; income tax policy and other
government subsidies; population size and demographics; appreciation in investment;
inventory factors; transaction costs; and budget constraint.
Existing SFRs Versus Newlv Constructed SFRs
This study focuses on the sale of existing residences rather than new
residences since there is a lack of studies on this aspect of the residential market.
Most of the studies of the residential real estate market are based on the new
construction of residences since construction activity makes up a substantial portion
of the economy and represents new housing stock. In contrast, the number of sales of
existing SFR's has been approximately twice the number of newly constructed SFR's
in the Denver metro area over the past twenty years. And, on the national level,
Rosen and Smith (1986) indicates that the "ratio of housing resales to starts rose
substantially during the [1980's] from 2.0 to 3.4" and that "real expenditures for
alterations and additions to the existing stock have been rising steadily and in 1982
were approximately 25% of the value of expenditures for single-family new
1


construction." This indicates that sales of existing SFR's also have a significant
impact on the economy and therefore merit separate study. Especially interested in
this type of study are Realtors and mortgage lenders, both of whom have an economic
interest in the volume and price of residential sales, new or resale.
Unique Demand Incentives and Commodity Characteristics
The SFR market is different than most other markets in the rare combination
of the two distinct demand incentives: investment and consumption. However, the
portion of the price paid for each purpose is not separately definable. Other
differences of the SFR market are identified by Smith, Rosen and Fallis (1988) when
they state that"... although housing is a commodity that responds to market forces it
has a number of special characteristics which require that the standard neoclassical
model be modified if they are to be adequately analyzed. Other commodities have
some of these characteristics, but few have them all. Foremost among the special
characteristics are the durability, spatial fixity, and heterogeneity of housing and the
extensive involvement of governments in housing and related input markets." They
go on to point out that "It has proven impossible to incorporate all of these into one
model of the housing market." This model includes representative variables of as
many characteristics as possible.
Economic Cycle
The study of economic cycles is critical to understanding variations in sales of
existing SFRs. Smith, Rosen and Fallis (1988) indicated that since 1953, new
2


"housing cycles have occurred on average every three and a half years, with an
average peak to trough decline in housing starts of 45 percent." and that this cycle
"precedes or is coincident with the ordinary business cycle ..." In comparing existing
SFR's to newly constructed SFR's, Smith, Rosen and Fallis (1988) indicated that
"Mirroring the greater stability in activities associated with the existing housing
stock, resales of existing homes have grown steadily with relatively little cyclical
fluctuation compared to sales of new houses. Existing home sales show less than half
the cyclical volatility of new housing starts."
Not only does the economic cycle have a major influence on the housing
market, but, as a component of the economic cycle, the housing market can have a
major influence on the overall economic cycle. For example, Case (1992) studied the
impact of the new construction in Massachusetts on the economic cycle. Case asked
"How could a state go from having the lowest unemployment rate in the United
States to having the second highest in the space of less than 4 years?" Case provided
strong evidence that the "dramatic real estate cycle, which began with a housing price
boom between 1984 and 1987, was an important element that not only contributed to
but also very significantly amplified the economic fortunes and misfortunes of the
Commonwealth and the region." Similar arguments can be made about the
economic cycle in Colorado during the study period, where new residential
construction expanded so quickly that an oversupply occurred. The corresponding
slowdown in the residential housing industry combined with the slowdown of two
other major Colorado industries led to negative migration and therefore a reduction
in demand for housing that lasted for approximately ten years: the number of existing
SFRs sold went from 1,779 in June, 1974, to a peak of 2,931 in June, 1979, then
dropped to 1,349 in June, 1982, and back up to 2,717 in June, 1992, ten years later.
3


Credit
SFR's are a capital good that costs more than most buyers make in a year,
therefore it is rare to see sales of SFR's for cash. Since most sales use financing and
since we do not have perfect capital markets, then the credit market requirements are
an important part of any study on sales of residences. As pointed out by Smith,
Rosen, and Fallis (1988) "Housing starts react significantly to changing capital
market conditions, and also to changes in income. Often when capital markets are
tightening, incomes are rising, but the capital market effect usually outweighs the
effect of changes in income."
Possible Delay in Market Clearing
The housing market also differs from most consumer goods in that there is a
slower adjustment to changes in the independent variables because of high
transaction costs and the rationing of mortgage credit. Landlords may not respond
initially to an increase in demand by raising rents, typically accepting increases in
income resulting from an increase in occupancy. Once the consumer makes the
decision based on changes in the independent variables, the closing will not occur
until one or more months later due to many factors, including the fact that most
buyers need to sell their existing residences, and due to transaction time requirements
such as title searches and credit qualifications.
"... because the housing response of households often occurs slowly,
demand side adjustments are inhibited from instantaneously moving housing
prices and vacancies to their long-run equilibrium levels.... This slow
response is supported econometrically by both aggregate time series and
micro cross-section studies. Muth (1960), using time series analysis, found
that on average of those households faced with a gap between their actual and
4


desired stock, approximately one-third move during a year. Hanushek and
Quigley (1979) supported this slow adjustment as they found that, on average,
19 percent of the gap between initial and desired consumption was closed in
one year in Pittsburgh and 35 percent in Phoenix." Smith, Rosen, and Fallis
(1988)
The investment aspect of purchasing SFRs will typically provide incentives
to speed up the process rather than lead to a time lag, especially during times of high
inflation. The following summarizes the time lags and timing impacts in this market:
"... the decision to buy a house ... [requires] a down payment [and]
therefore, depends upon savings decisions in previous periods ... [and]
commits the household to a pattern of future payments of principal and
interest, and therefore commits the household to a savings pattern in future
periods.... The static model also cannot deal explicitly with the effects of
changes in expected future prices whether general prices or the relative price
of housing services on current demand for housing services. Finally, the
static model cannot deal with the investment aspects of home ownership."
Smith, Rosen and Fallis (1988)
During different market conditions there are counter forces delaying and speeding up
incentives for consumers to make decisions resulting in market clearing. This study
does not address the long term lags that might be involved in market clearing. This is
an opportunity for future modification to the current study.
As identified in this section, characteristics of the existing SFR market are
substantially different than most consumer markets.
5


CHAPTER 2
VARIABLES
Most of the variables in the research studies reviewed are typical for studies
of equilibrium quantities supplied and demanded: price of dependent variable, price
of substitutes, income, population, stock, transaction costs, opportunity costs, supply
costs, credit restrictions, demographics, etc. The following sections convey the key
components and the related variables selected to represent them for this model.
Quantity and Price of Dependent Variable
The price variable for SFRs could be represented in a number of different
forms. Some of the studies use a composite of several price variables, arriving at a
monthly cost. For example, Poterba (1986) and Engelhardt and Poterba (1991) use
an equation to arrive at the per period after-tax "user cost" that includes
"expenses such as mortgage interest and property tax payments,
maintenance and repairs, physical depreciation, the foregone return on the
owners equity, and any expected capital appreciation which would reduce the
cost of owning a home. Following Poterba (1986), the user cost for the
United States is defined as
Cus =[(I+y)*(l-t)+x+xx+m+xx],
where I is the nominal interest rate, y is the property tax rate (0.02), t is the
household's marginal tax rate, x is a risk premium (0.05), xx is the rate of
physical decay (0.025), m is the required cost of maintenance and repairs
(0.014), and xx is the expected rate of house price appreciation." Engelhardt
and Poterba (1991)
Smith, Rosen, and Fallis (1988) lay out a similar equation:
6


"the expected user cost over any time period, Euc, may be defined as in
equation (1) where c is expected operating costs (excluding property taxes), d
is the expected nominal cost of physical depreciation, <}> is the owners
expected marginal tax rate, t is the expected property tax [rate], m is the
expected mortgage interest, Ei is the expected foregone interest rate at rate /
on equity E, and *PH is the expected capital gain on the depreciated unit of
stock (see Douglas Diamond 1980):
Em = c + d + (I For this study, each component of user costs are reflected separately from
price. One advantage of using a combined user cost is the ease of arriving at
substitution elasticity. However, the advantage of separately reflecting the
components is to arrive at separate coefficients for each component.
Characteristics of the SFRs being sold
The price of an existing SFR is the largest dollar amount of the user costs of
the price variables. There is a substantial amount of literature concerning the
heterogeneity of the housing product and the implications thereof on price and
simultaneity. Rosen (1974) was the first to point out the issue.
"A class of differentiated products is completely described by a vector
of objectively measured characteristics. Observed product prices and the
specific amounts of characteristics associated with each good define a set of
implicit or "hedonic" prices. A theory of hedonic prices is formulated as a
problem in the economics of spatial equilibrium in which the entire set of
implicit prices guides both consumer and producer locational decisions in
characteristics space." Rosen (1974)
Rosen was pointing out that housing consists of a bundle of characteristics,
each with separate values. It can be misleading to look only at the total house price.
Therefore, quality, size and other features need to be identified. It is possible to run a
7


regression of all housing characteristics on the total price to arrive at the price for
each characteristic. These hedonic prices could then be used to arrive at standard
characteristic indices. Rather than use this time consuming and imperfect process,
substantially all post-Rosen literature have addressed this concern by using either
multiple time periods or multiple locations, which provides some variation in the
prices other than from the bundle of characteristics. Kinzy (1992) indicates that "It is
reasonable to assume that the market demand for housing will shift due to any
number of causes that affect the economy of a city, suck as employment and changes
in the relative availability of locational attributes."
Some recent studies have pointed out that the previously suggested solutions
only work if there is sufficient price variation due to exogenous factors other than the
demand (or supply) being studied.
"In turn, the effectiveness of the multiple-time-period approach used
in the estimation of the Rosen model is difficult to test. The instrumental
variables may not be completely uncorrelated with the error term or the price
variation over time may not be sufficient, leading to what Murray [6] has
identified as the "spurious correlation" problem. This problem occurs when
the differences in market demand over time are not "large enough" to
eliminate the simultaneity problem as discussed in detail by Oshfeldt and
Smith [7]. Whether "enough" variation in market prices that is independent of
supply has been introduced is unknown. The validity of the instruments is
also questionable, which may also explain the less-than-ideal results obtained
from the supply estimations." Kinzy (1992)
Although there is much consensus on the heterogeneity price problem, there is less
consensus on the solution.
"Post-Rosen literature stresses that housing is not repackageable in
unlimited combinations of quality and quantity. As a result, the marginal
price of quality need not equal the average price (Diamond and Smith [5] and
Oshfeldt and Smith[17])." Smith and Tesarek (1991)
"While theory explicitly recognizes the existence of a market price
8


function instead of a single price, users of the hedonic technique invariably
seek to create a single price index that falls short of describing both market
outcomes and the incentives that a new price structure might have on market
participants." Smith and Tesarek (1991)
This study includes only one location, Denver-metro area, but it does cover
demand and supply variables for an extended time period (180 months/periods).
Therefore, this study should include enough variation of price due to factors other
than for the bundle of characteristics that it should not have a simultaneity problem.
However, caution is advised for any future modifications of this model which address
short periods of time.
Quantity and Price
For this study, the quantity and price variables were derived from the average
selling price of existing SFRs (RP) sold and the total SFR number of sales (RNS) in
the Denver metropolitan area as per the Denver Metropolitan Listing Service (MLS).
The MLS includes sales of real estate handled through a Realtor. It therefore
includes some new sales, but does not include private transactions handled by
attorneys such as those sold as For Sale by Owner.
Mortgage Rate
The mortgage rate is a significant component of the price of the housing
market since most sales are financed and since there was a substantial amount of
variation over the study period. The interest costs are identified by some studies as
user costs. This study includes mortgage rates as a price variable, since very few
9


purchases are made without financing, but that does not preclude it being evaluated
for all of its influences. With a separate coefficient, it can be interpreted with either
strategy. There are two traits for mortgage rates that need to be considered: their
variability and government subsidies relating thereto.
There has been several studies on the adjustable rate mortgage (ARM). The
ARMs were introduced into the market around 1983, when fixed rate mortgages were
extremely high due to high inflation rates and expectations. One of the more recent
studies of the ARMs was done by Phillips and Vanderhoff (1992). They emphasized
that ARMs were important for two reasons "(1) demand constrained buyers may
increase the quantity of housing services demanded to levels that are more consistent
with long-term preferences, and (2) unconstrained buyers may tend to increase the
level of housing demanded due to the impact of lower level of expected user costs."
Phillips and Vanderhoff (1992) point out the high level of variability in their use:
from approximately 60 percent in 1986 to a low of 20 percent in 1987." Stutzer and
Roberds (1988) doubted the long-term impact of ARMs: "While the use of adjustable
rate mortgages (ARMs) and housing activity grew concurrently between 1982 and
1984, we cast doubt on claims in the trade literature that the former caused much of
the latter."
This study includes nominal fixed mortgage rates (MR) for the Denver
metropolitan area for the time period studied. Variable rate information is not
available for the Denver metropolitan area. Future studies may want to test the
impact of ARMs on quantity and price.
There has been a substantial amount of variation in interest rates over the time
period studied. Generally interest rates increased from 1974 to 1981 and then
declined through 1992. Since most purchases of residences are financed with fixed
rate mortgages, when interest rates either increase or decrease it creates a value of
having a lower interest rate or an incentive to not move if you will get higher rate.
10


During a period of interest rate declines homeowners will refinance to the lower
interest rates. The refinance costs are comparable to the transaction costs of a change
in ownership. This reduction in net transaction costs increases the likelihood of a
change in ownership.
If the favorable interest rate loan is assumable then it's value will be reflected
in the selling price. If it is not assumable then it becomes a deterrent to a change in
ownership.
"In 1979, the mortgage premium held by the average household was
worth about $570. In 1980, this premium had increased to approximately
$800. By 1981, the average premium enjoyed by households with existing
mortgages was about $1,800 when compared to a newly written mortgage for
the same term at market rates." Quigley (1987).
Quigley computed the present value of the mortgage premium, x2, defined as the
difference between the outstanding balance of the mortgage (the present value of the
mortgage at the contract interest rate) and the present interest rates.
Price Discounts
The price at which SFRs sale for is usually less than it's listed price. The
MLS has data on the "Percent of List." The difference between the listed price and
the actual selling price represents a price discount. This price discount varies over
time. The expectation is that a larger discount will occur when there are few
transactions in SFR's, and that a smaller discount will occur when there are a high
number of transactions. For this model the "percent of list" is not included, since it
was only available since July, 1984. This is an opportunity for future expansions of
this study.
11


Other Price Considerations
Other price considerations include the quality of the housing units and their
spatial fixity. See previous discussions on quality and varying characteristics of
specific homes sold. In regard to spatial fixity, during the time period of this study
there was substantial new development of residential units in the suburban areas,
farther away from the central business districts than previous studies. This study
does not consider the gradual changes in spatial fixity over time to have a macro
impact on the number of transactions. Most of the studies on spatial fixity reflect
that it has a significant effect on the price of housing units rather than number of
transactions.
Quantity and Price of Substitutes
Substitutes to the existing SFRs include existing and new condominiums, new
SFRs, remodeling existing residences, and rental residences.
Condominiums
Included in this study as a price variable for a substitute is the average selling
price of existing condominiums (CP) sold in the Denver metropolitan area as per the
Denver Metropolitan Listing Service (MLS). Information on the average sale prices
of new condominiums was not available before recent years.
12


New Single Family Residences
The American Chamber of Commerce Research Association (ACCRA)
publishes a quarterly Cost of Living Index which includes average prices of new
homes for metropolitan areas, but the data only goes back to 1982. Their housing
index goes further back in time, but is an index of the cost of housing in the Denver
metropolitan area compared to the national averages, with no data on the price itself.
This study has excluded prices of new SFRs due to the short period that they are
available. The market conditions for SFRs and several independent variables were
substantially different for the period from 1974 to the early 1980's than after that time
period. See following section on Factor Costs, which are the best representation for
the price of new SFRs. Also see the section on Stock Substitutes for information
about the supply of new SFRs.
Substitute Remodel Current SFR
For some sellers, those selling because of obsolescence, the alternative to
selling is renovation. Rosen and Smith (1986) developed aggregative models of sales
and renovation activity that demonstrated that the decision to move is significantly
influenced by the relative transactions costs of moving versus renovating.
Transaction costs are accounted for elsewhere in this study. The costs of renovating
and remodeling are also reflected in the following section for factor costs.
13


Factor Costs
As with the supply of most goods, an increase in factor prices increase the
selling price of the goods. For the construction of new SFRs the factor prices are
generally considered to be land, labor, materials and the cost of capital. Topel and
Rosen (1988) found a strong response of housing starts to changes in both the real
rate of interest and expected inflation, and found that the hypothesis that nominal
rates of interest affect housing investment cannot be rejected. An increase in the
prices of these factors should also lead to an increase in the selling price of existing
SFRs. Supply and demand relationships of substitutes generally prove that increases
in the price of a substitute result in a price increase in the dependent variable. In the
residential market, construction costs are not only a substitute since they are factor
costs for new SFRs, but are also factor costs for remodeling existing SFRs.
Remodeling existing SFRs is a substitute for replacing the current SFR with a SFR
with different characteristics. (Buying up.)
This study includes factor prices for the average construction hourly earnings
(CHE) as published monthly by the Colorado Department of Labor and Employment,
and the construction material price index (MPI) as published monthly in the
Engineering Record (ENR). Mortgage rates are already included in this model.
They represent a cost to the builder of new SFRs. Land prices were not available for
the Denver metro area for the complete time period studied for consistent lot sizes.
Rent
There are many reasons that a household would prefer renting over owning a
residence. Most of the studies deriving the elasticity of substitution of rent and
14


ownership concentrate on the wealth required for the down payment and transaction
costs and on the demographic variables. Wealth would not be an issue if there were
perfect capital (100% financing) and perfect housing (no transaction costs and quick
adjustments). In such a situation households would be indifferent to owning or
renting, other than for investment incentives.
The rent price variable is significant since rent has changed at different times
in the economic cycle. Smith, Rosen and Fallis (1988) pointed out that at the
national level real house prices have risen 30 percent since 1960 as compared to real
rents which have declined 21 percent.
Income tax policy has changed several times related to the treatment of
investments in rental property. See previous discussions for capital gains treatment
and rates on investments. The income or losses from owning rental properties is also
subject to income taxes. One of the deductions available for income tax purposes is a
annual deduction for depreciation of the original cost, whether a depreciation in
value is recognized or not. The tax savings from this non-cash flow deduction
increases the after tax rate of return. Therefore, the larger the depreciation deduction
the greater the increase in after tax rate of return. Prior to 1982 most real estate
depreciation was taken over 30 years. From 1982 to 1984, the depreciation was
reduced to 15 years, thus doubling the depreciation deduction and therefore
increasing the after tax rate of return. Some of the gain was reverse in 1984. After
1986, the number of years was increased to 27.5 years and then to 31 years by 1992.
Added to this effect was the effect of the marginal income tax rate. For post
1986 there was a lower marginal income tax rate for higher income households and
less depreciation deduction. Both of these reduced the incentives for investing in
rental properties.
The Colorado Division of Local Government publishes the annual vacancy
rate for rental properties in the Denver metro area, but the data only goes back to
15


1980. The Apartment Association of Metro Denver publishes quarterly rental rates
for the Denver metro area, but the data only goes back to 1981. This study has
excluded both rental variables due to the short period that they are available. The
market conditions for SFRs and several independent variables were substantially
different for the period from 1974 to the early 1980s than after that time period. The
loss to the study for not including an important substitute like rent was considered to
be less than the loss to the study that would have occurred by shortening the study
period, excluding a time period with significantly different market conditions. This
is an opportunity for future expansion of this study.
Income Variables
The income variables included in this study are average household income
and a income stability variable. While some studies use after-tax income in their
studies, this study leaves the income tax effects as separate variables, allowing for
separate analysis of the effect of changes in income from the changes of income
taxes. See the section on income tax policy and government policy for additional
information on the income tax effect.
Household Income Permanent and Temporary
Household income is included in every study of supply and/or demand for
housing. Income is sometimes separated into permanent income and temporary
income. Permanent income is considered a good indictor for the demand for
ownership since it represents the long-term income and the purchase is a long-term
16


commitment of income resources. In theory, if household income is not stable at a
sufficient level to afford the size of house desired then it will delay the purchase.
Some of the studies also include temporary income as a separate variable. One of the
arguments in favor of this inclusion is that the move typically involves other
purchases such as new furniture, appliances, fixtures, improvements, etc. The
combination of the these and the transaction costs will influence a household to delay
a purchase until it has temporary income to help pay for them.
Some of the recent studies have concluded that permanent income is not
significantly different than current income in arriving at housing demand.
"Empirical housing demand studies have treated housing largely as a
consumption service flow and, consequently, have estimated demand
equations which employ permanent income or full permanent wealth in the
budget constraint equation. In recent years, however, the permanent income
hypothesis has come under substantial criticism in the context of aggregate
consumption modeling (Flavin, 1981), in the recognition of the role of
liquidity in determining the demand for consumer durables (Pissarides, 1978),
and in the evidence of the contribution of transitory income to explaining
housing demand of owner-occupiers (Dynarski and Sheffrin, 1985). In
addition, Jones (1989) concludes that, for Canadian households, accumulated
nonhuman wealth, not permanent income derived from human capital, is the
dominant factor determining the timing of the initial tenure transition from
rental to ownership." Jones (1990)
Also, Cooperstein (1989) points out the obvious: Lenders rarely make loans
based on permanent income. He then points out that households are far more likely
to buy as soon as it is financially possible and congruent with their housing demand
expectations, and move up later into the housing they demand based on permanent
income.
For many of the studies, permanent income is typically computed as a simple
average of the last three years income. This average substantially removes the
temporary changes in income. For this study permanent income {MWE3A) and
temporary income (77) have both been included. Permanent income is computed as
17


the average of the last three years income, and temporary income is the difference
between current income and permanent income.
Income for this study is based on the average manufacturing weekly earnings
for the Denver metro area as published by the Colorado Department of Labor on a
monthly basis. Two other sources of income considered were only published on an
annual basis: Per Capita Income by the Colorado Division of Employment and
Training and Effective Buying Income by Sales & Marketing Management Annual
Survey of Buying Power. Manufacturing weekly earnings has a 99.5 percent
correlation to per capita income. Manufacturing weekly earnings has a 94.6 percent
correlation to effective buying income.
Income Stability Unemployment
Another variable included for this study is the unemployment rate (UNR) as
published by the Colorado Department of Labor and Employment on a monthly basis.
This is included as another variable to represent the security or stability of income.
The higher the unemployment rate the less secure that households feel in their jobs
and therefore would be less likely to change residences.
Budget constraint
As previously indicated, after tax income is important in reflecting the
amount of disposable income available for housing demand. However, disposable
income also has to be spent on other non housing goods, which is referred to as a
budget constraint. Smith, Rosen and Fallis (1988) point out that the current
18


consumption is subject to a multi-period budget constraint. They therefore would
include not only the prices of current goods, housing and non-housing, but also the
expectations for future prices of housing and non-housing goods.
For this study consumer price index (CPI) as published bi-monthly by the US
Department of Labor Bureau of Labor Statistics for the Denver metro area is
included to represent a budget constraint variable. The data was converted from bi-
monthly to monthly for this study by using the mean of the two surrounding periods.
Income Tax Policy and other Government Subsidies
Governments typically impact housing markets through income tax policy and
through the credit markets. There is a substantial amount of tax policy that impacts
owners of SFR's and substitutes: mortgage interest and property taxes are deductible
for income tax purposes; appreciation in value is tax deferred and possibly not taxed
for owner occupants; for investors, tax deductions are allowed for depreciation and
taxes on appreciation are at favorable rates and are deferred until a sale occurs; and
local property taxes are assessed on owners of residences.
Marginal Income Tax Rates
Allowing for income taxes on income is necessary in arriving at disposable
income, which is a better indicator of the amount of income that is available for
housing. Rosen and Rosen (1980) found that ignoring taxes leads to an overestimate
of the impact of permanent income. He theorized that when gross income is used it
"picks up" the effect of a changing marginal tax rate.
19


The tax policy has changed several times over the time period covered.
Higher income tax rates leaves less disposable income available for housing. Higher
marginal income tax rates increase the demand for home ownership as a result of the
lower user costs due to the income tax deduction for mortgage interest and property
taxes. In 1986, tax policy was substantially changed to provide for a higher standard
deduction for every taxpayer, which reduced the tax savings due to choosing a
financed purchase over renting.
"Millions of taxpayers who had itemized deductions prior to 1986
ceased to itemize and claimed the increased standard deduction after 1986.
For these middle-income taxpayers, the tax code's subsidy to home ownership
was also reduced." Poterba (1992)
For this study, the combined federal and Colorado marginal income tax rate
(MTR) is used as the variable for income tax policy effects. It was computed based
on the marginal income tax rate applicable using annualized manufacturing weekly
earnings (MWE) and average household size, and assuming married filing joint and
no itemized deductions. (By assuming no itemized deductions, this leaves the
marginal taxable income at the level desired to test the marginal income tax rate
benefit on deductions related to ownership.) Social Security tax rates were not
included in this study.
Capital Gain Tax Preferences
In the United States, an income tax is assessed on the gain that is recognized
due to the sale of houses. As will be pointed out later, the appreciation in value is not
recognized when incurred, but rather is recognized when the house is sold.
Therefore, this factor is also evaluated as a transaction cost. There have been several
income tax rates that have applied to these transactions over the time period covered.
20


For most homeowners, the capital gains tax is deferred if they continue to "buy up or
is eliminated or only partially taxed for most owners when they reach age 55. The
capital gains rate has been included in this study in order to reflect its impact on the
investment aspect of housing demand.
Hoyt and Rosenthal (1992) theorized that the impact of changes in marginal
income tax rates could be overstated when capital gains taxation is ignored, finding:
"Simulation results suggest that the Tax Reform Act of 1986 (TRA86)
has enhanced the importance of the capital gains kink by raising the after-tax
cost of housing through lower marginal income tax rates while increasing the
tax rate bn capital gains. As a result, a reduction in the capital gains tax rate
would reduce housing demand as some families currently at the kink would
buy a less expensive home. Our findings also indicate that the level of excess
burden increases with the capital gains tax rate, but the TRA86 reduced the
size of implicit price subsides received by owner-occupiers, and related
deadweight loss, by roughly one-half." Hoyt and Rosenthal (1992)
As transaction costs, higher capital gain taxes have the effect of discouraging
the number of transactions that occur. Englund (1986) pointed out that "It is shown
that higher transaction costs [including capital gains taxes] have lock-in effects,
inducing consumers to keep the same house for both periods.
A variable is included in this study to provide for capital gains {CAP)
preferences in income tax rates. Since taxpayers pay the lower of the regular taxes or
the capital gains taxes on the gain, the amount of preference was computed as the
difference between marginal income tax rates and the capital gain tax rates for the
average income families.
Government Subsidies Through Credit Markets
Previously discussed was one credit related variable, mortgage interest rates,
which is a cost of credit. As a capital good most purchases of housing are financed
21


with credit, which makes the availability of credit a variable that should be
considered. Duca and Rosenthal (1991) point out that a rejection rate in the mid-
1980's of 15% to 20% is in contrast to neoclassical models of competitive markets
where the price is the primary instrument by which scarce supplies are rationed.
Although high mortgage rejection rates are suggestive of non-price rationing, they do
not in themselves provide the reasoning as to why credit may be rationed in the
mortgage market.
Other studies generally discuss the "rationing" of credit due to limited
availability and/or through income qualification practices. Rosen and Rosen (1980)
used the real growth rate in deposits at thrift institutions to represent the availability
of credit. Their results neither strongly supported not refuted the conjecture that
credit rationing and the supply of mortgage funds have an impact on housing
decisions. "The supply of mortgage funds does not generally equal the demand for
mortgage funds at the market interest rate. During these periods many households
and builders are not able to obtain mortgage funds at the quoted interest rate, and
non-price rationing techniques, such as lowering the loan-to-value ratio, tightening
borrower income requirements, imposing a ceiling on loan size, or limiting loans to
larger depositors of long standing, are employed." Smith, Rosen, and Fallis (1988)
The effect of credit on the housing market is theorized to be a short term
effect. Smith, Rosen and Fallis (1988) indicate that a major portion of the literature
agrees that short-run variations in housing activity are due to the overwhelming
dependency of housing on mortgage credit among a few other factors. They go on to
point out that in the long-run credit may not have an impact on housing demand.
The credit market is one of those areas in which the government intervenes in
the housing market. The justification for government intervention is to stabilize the
housing market by stabilizing the mortgage loan credit markets. Smith, Rosen and
Fallis (1988) summarized studies on this issue, indicating that these programs have
22


reduced fluctuations in mortgage credit somewhat; however, government mortgage
loans have not increased total mortgage credit by the amount of the loans. This is
because government loans can be substitutes for private loans.
The government established quasi-public financial institutions to promote a
secondary mortgage market and new issues of government mortgage-backed pass-
through securities, which represented over half of all mortgage originations in 1986
per Smith, Rosen and Fallis (1988). They pointed out that this activity "reached a
peak around 1980 when subsidized housing (Farmers' Home Administration, FmHA)
and public housing (Department of Housing and Urban Development, HUD) starts
accounted for 15 percent of total housing starts, and Federal Housing Administration
(FHA) and Veterans' Administration (VA) programs accounted for an additional 20
percent of starts; this activity then declined to 3.5 percent and 8.7 percent
respectively in 1985. Offsetting these declines in subsidized activity has been a rapid
growth in government mortgage-backed pass-through certificates, which more than
tripled in volume in the five years."
The favorable credit terms are limited to houses costing less than a
predetermined price and they establish an interest rate ceiling. Duca and Rosenthal
(1991) indicated that the FHA rate ceiling may influence the demand for housing and
that due to the spread in interest rates they may have to charge more points than the
market will bear to compensate for the deviation between market rates and regulated
ceilings. They theorize that under these circumstances, as market rates rise, FHA
ceilings may become more binding (affecting FHA share).
The more favorable terms of the government backed loans comes at a price.
FHA loans are government insured by requiring a mortgage insurance premium,
which increases the transaction costs in using a government backed loan. Rosenthal,
Duca and Gabriel (1991) point out that not only are the loans government guaranteed
but FHA requires a minimum down payment of only 3% to 5%. By contrast,
23


conventional loans carry no federal guarantees, but for borrowers with sufficient
down payment, private mortgage insurance is not required.
Government subsidies of mortgage rates occurs in the United States in various
manners: through income tax policy; guaranteeing mortgages through FHA and VA;
and policies related to the transferability of these guaranteed mortgages. For the first
two listed subsidies see previous sections of Income Tax Policy and other
Government Subsides. The transferability of guaranteed mortgages has the biggest
impact when interest rates are rising and when credit is scarce. Rosen and Smith
(1986) addressed this issue as follows: "However, not all mortgages are non-
assumable with the result that the benefits of existing low-rate mortgages are often
acquired jointly with the house. These financing benefits should normally be
capitalized in the price of the house, and this is reflected in the significant positive
coefficient on the difference between the current and eight-quarter lagged mortgage
rates in the price determination regression."
The variable included for this study to represent government subsidies in the
credit markets is the percent of mortgages financed by FHA and VA (FED) as
published monthly in the Federal Reserve Bulletin. There is no variable included to
represent the availability of all credit, which is an opportunity for further study.
Investment Variables
As previously indicated, the SFR market is different than most other markets
in that it is a rare combination of two distinct demand incentives: investment and
consumption. The portion of the price paid for each purpose is not separately
definable. The investment incentive can primarily be represented by the expected
value should the residence be resold or passed on to ones heirs.
24


Appreciation
The expected appreciation in value of a SFR is a topic of much discussion in
recent studies. This represents the investment aspect of the purchase. The studies
have used various methods to arrive at the expected appreciation. Most have
concentrated on the past appreciation in housing value as being representative of the
expectations of future appreciation, especially since this simple method is more
likely to be used by consumers than a more sophisticated prediction model. They
have used anywhere from the last one years appreciation to the last eight years (Since
that represents the time period of the average holding of a housing unit.).
The most extensive study of the different methods for testing the significance
of expected appreciation is the one done by Van-Order and Dougherty (1991).
"This measure uses information from the Livingston survey of
expected inflation discussed in [3], However, these numbers are of general
inflation, and they are for short periods of time (either 6 months or a year).
We adjust the numbers by
(1) Regressing the expected rate on actual past rates (using semiannual
data) to get a behavioral equation.
(2) Assuming that house price expectations are formed in the same
way as general prices, we applied the coefficients from step one to
house prices and used the equation to forecast prices semiannually for
5 years. Our expected inflation number is an average of these 10
semiannual numbers (see[4] for detail). Numbers used here have been
updated and are not exactly the same). We label this measure 1-1.
We also used the following alternative measures:
(1-2) An average of past house price and general inflation rates taken
from Hendershott and Shilling [8],
(1-3) Actual house price inflation over the current and subsequent 31/2
years; i.e., perfect foresight.
25


(1-4) The nominal interest rate, on the assumption that the real rate is
roughly constant, so that the nominal rate is both a forecast of inflation
and a measure of the cash-flow problem.
The best results came from the version using a mechanical distributed lag. 1-2
from Hendershott and Shilling [8] is an average of house prices and general
price level changes over 4 years." Van-Order and Dougherty (1991)
The impact of expected appreciation is directly related to expectations about
inflation.
"Inflation raises the real cost of ownership housing in early periods
and reduces it in later period. The change in current demand reflects the
influence of both cost changes (Robert Schwab 1982). Smith, Rosen, and
Fallis (1988)
This model includes the average rate of appreciation (APPREC) for the past
two years as representative of the expected future appreciation.
"Controlling for the combined effects of employment growth,
population growth, interest rates, income, construction costs and a number of
other variables, the model in Case (1986) predicted a 15 per cent increase in
housing prices between 1983 and 1986. Instead, single-family home prices
virtually doubled. The argument in Case and Shiller (1988, 1989, 1990) is
that home buyers and sellers were significantly influenced by psychology.
That is, reacting to rising prices and generally favorable economic conditions,
home buyers paid inflated prices in anticipation of future price increases and
capital gains." Case (1992)
Transaction Costs
The costs incurred related to a change in housing can be substantial,
especially if the move involves a change in ownership. These costs can be divided
into a separate categories: search costs; transaction costs related to the old residence;
transaction costs related to the new residence; financing costs; capital gains tax;
26


moving costs; and nonmonetary costs. Some of the costs are actual costs incurred
and others relate to time spent, which has an implicit cost.
These costs are important to study since they make up a substantial part of the
cash required up front in order to initiate the change in residences. Transaction costs
are the equivalent of an increase in price to the buyer or a decrease in price to the
seller/supplier. As with any change in price, an increase in transaction costs is a
deterrent to the decision to make a change in housing.
"Because of large search and transaction costs associated with a
housing move, household do not respond to changes in the determinants of
demand such as income, family size, and price until the present value of
the expected benefits from changing the quantity of housing consumed
exceeds the transactions costs associated with a housing adjustment. As an
alternative to moving, homeowners can change their level of housing
consumption by undertaking housing renovations, or by allowing housing
deterioration." Smith, Rosen, and Fallis (1988)
The impact of the transaction costs are so significant that Harmon and
Potepan (1988) found that "adjustment" costs are more important than other demand
factors in influencing mobility decisions. They used a sample of recently moving
homeowners which is best group to test for this hypothesis since they are the
households that were at the point where the benefits of the move exceeded the costs.
Some studies address the effect of the expected length of stay in the residence
to the impact of transaction costs. The theory is that the transaction costs should be
spread over the expected length of stay, which is the benefit period. The studies
showed average lengths of stay of 6 to 8 years. This study does not accounted for the
length of stay, since this information is not available for the Denver metro area for
the period covered by this study.
The amount of time spent searching related to an ownership change is
typically more than the amount of time spent searching related to a change in rental
residences. There have been several studies related to this topic. They put a value on
27


the time at the hourly rate of earnings of the worker doing the search. Since this is a
macroeconomic study, this information is less relevant, in addition to not being
available.
Moving costs are incurred because, as Smith, Rosen and Fallis (1988) pointed
out, the "immobility of the stock... necessitates that housing be physically allocated
between users by the movement of the users rather than the movement of the house."
This study does not included any variable for moving costs under the assumption
would be the similar in amount for households moving to different housing unit
types.
Several of the studies of the SFR market recognized that there are
nonfinancial factors that impact the decision to change residences. The community
in which they are leaving is typically discussed as a restraining influence on the
decision to move.
"Attachment costs stem from the loss of community and familiarity
people experience when moving to a new place. While difficult to quantify in
dollar terms, these costs are undoubtedly important. Their impact on housing
demand has been studied by Synarski [7]." Harmon and Potepan (1988)
However, the community being left could have been a positive influence on
the decision to move due to gentrification or decaying of the community. Similar to
most of the studies with a macroeconomic focus, this study does not have any data
representing transaction costs without associated financial costs. Some studies
discuss the hard to measure variables such as gentrification of the neighborhoods, etc.
They are appropriately not included in this model since it does not distinguish
between neighborhoods within the Denver Metro Area. Gentrification of
neighborhoods represents the increase in the age of the housing, whereby certain
traits begin to appear, such as the housing becomes relatively more affordable, more
of the properties are rented to nonowners, lower income families move in, crime rates
increase, etc.
28


Transaction Costs Related to Change in Ownership
The specific costs incurred to sale the SFRs are recording fees, legal fees,
survey, appraisal, real estate agents fees (paid by the seller in Colorado for both the
buyer and seller), etc. Capital gains taxes paid on the gain from the sale is addressed
elsewhere in this study.
Theoretically, transaction costs that are paid by the buyer should be separated
from that paid by a seller/supplier. Transaction costs that are paid by the
seller/supplier should be treated as either costs of supply or reductions in the price.
The largest transaction costs are typically paid by the seller/supplier in Colorado: the
real estate agents fees and title insurance, both of which are charged as a percent of
the selling price. The officially quoted real estate fee has remained at a constant 7%
over most of the time period studied. Title insurance is less significant and is
typically about 1% of the selling price. For this study, the transaction costs that are
paid by the seller (including the two identified above) are not reflected since they
were a constant percentage of the selling price over the period of this study. Not
including them avoids a simultaneity problem.
Transaction costs that are paid by the buyer have not been separately
identified other than financing costs (see below). They tend to be small in amount
and are fairly constant over time regardless of the price or qualitative characteristics
of the residence. Haurin and Lee (1989) also dropped the transaction cost variable
based on the assumption that it does not vary among households.
Financing Costs
Financing costs for this study have been separated from other transaction
29


costs since they are only incurred if the purchase is financed using credit rather than
cash or if the existing loan is being carried, or the seller/supplier is financing the
transaction. Information on an aggregate basis about the percent of transactions
financed using owner-will-carry terms or qualifying and non-qualifying assumptions
of existing loans for the Denver metro area have been available from June, 1989,
which is too short of a time period for this study1.
Financing costs primarily consist of loan origination fees, points and filing
fees. This study includes a national variable for finance costs under the assumption
that costs in Colorado closely correlate with national costs. Closing fees as a
percentage of the loan amount (FEE) is published monthly in the Federal Reserve
Bulletin.
Inventory Variables
Number of Davs to Sale
The speed at which SFR's are being sold is considered to have some impact on
the supply of SFR's. Topel and Rosen (1988) concluded that the length of time to
sale has a large effect on new construction. Their hypothesis was that a delay in sales
causes forgone interest costs to the builder similar to assumptions by Poterba (1984).
However, they conclude that delay effects are much too large to be interpreted as
forgone interest costs alone, since the incremental cost of a 1-month increase in time
to sale would be less than 1 percent of the price, yet they found that an additional
month's delay reduces investment by 30 percent.
1 There is a lot of variance during the available time period in the percent of transactions financed by
assumptions of existing loans. (1% to 15%)
30


This study includes a variable for the number of days it takes to sale an
existing SFR. The Metropolitan Listing Service of Denver (MLS) publishes a
monthly statistic on the number of days on market (RDM).
Number of New Listings
Also available from MLS is the number of new listings (NEWL) for the sale of
existing SFRs. This information is included in this study to represent information on
the intent to make a sale. (Not all listings result in sales.)
Change in Inventory
In addition to new construction the supply of additional SFR's is affected by a
change in the vacancy rate, properties taken off the market or kept in the market
through renovations and other conversion to or from nonresidential use. In the long
run, the change in demand for SFR's is met through the supply of new SFR's.
However, that is not the case in the short run. Hendershott and Smith (1988) indicate
that net other additions play a major role in the short-run equilibration of the demand
and supply for housing units. They conclude that, on average, a surge in household
formations is half satisfied by reduced losses or non-new construction additions
during the concurrent year. Included in this study to account for an increase in the
supply of new SFRs is the number of single family permits (SFP) taken out in the
Denver metropolitan area as reported by the Homebuilders Association on a monthly
basis.
31


Population and Demographic Variables
Size of the Demand Market
The number of households is the population variable that is important since it
represents the size of the demand market for housing units, whether rented or owned.
The number of households expands and contracts through children leaving home,
marriages, divorces, deaths, net migrations, etc.
In the analysis of Massachusetts, Case (1992) points out that the construction
industry and related industries of finance, insurance and real estate increased during
the expansion period and then decreased during the recession. Thereby the
construction and related industries accentuated the business cycle by amplifying the
multiplier effect in employment demand in the state and the number of households
migrating.
This study includes the size of the labor force (employed and unemployed)
(LAF) for the Denver metro area as published monthly by the Colorado Department
of Labor and Employment as the variable to represent the number of households or
the size of the demand market.
Migrations
Also included in this study is a variable to represent migration into and out of
the Denver metro market for residences. The data used is the net migration (MIG)
into the State of Colorado as published by the Colorado Division of Local
Government on an annual basis, under the assumption that net migration in the
Denver metro area is highly correlated with net migration at the State level. The data
32


was converted to a monthly basis using a linear extrapolation for the intervening
eleven months.
Demographics
Demographic variables usually include variables such as age, sex, race,
education, marital status of the head of household, household size, and number of
children. Goodman (1990) points out that demographic variables can have a
significant impact on housing demand and that the failure to account for these
differences implies that all households, irrespective of demographics, have the same
utility (and hence, demand) functions. This would be a very restrictive assumption.
For example, first time buyers often reflect different demographic characteristics,
such as age, than the population at large. The characteristics and actions of first time
buyers are often studied in order to get a better understanding of what motivated
them to make the choice of ownership.
Although demographic variables can be very informative, they can also be
misleading. Time series data for the United States suggest a strong correlation
between the age of the population and real house prices. Mankiw and Weil (1989),
drew attention to the high correlation between the population age structure and real
house prices, arguing that if the historical correlation persists, real house prices in the
United States could fall substantially during the next three decades. However,
Engelhardt and Poterba (1991) compared the United States to Canada, which have
similar population age structures. They point out that there was a rapid increase in
real house prices in the United States between the mid-1970's and early 1980's which
coincided with the entrance of the Baby Boomers into prime home buying years.
However, they also point out that Canada exhibited a strikingly different pattern of
33


real house prices, with a rapid rise in the early 1970's followed by a deep decline with
a trough in 1985. They conclude that the disparate house price experiences of the
two nations stand in marked contrast to their similar demographic structures. They
found a statistically insignificant and in most cases negative association between
demographic demand and house prices.
This study includes the following demographic variables: median population
age (AGE), percent of population under age 18 (PI8), and percent of population age
50 or over (P50). Average age is considered by most of the studies to be significant
in the choice of ownership. The variable for percent of the population less than 18
was selected in order to separate from the total population the changes in age groups
that are not potential owners and to allow for demand differences that may occur for
families with children under the age of 18. The selection of the age 50 or over
variable is to provide a variable to reflect demand patterns that may differ for an age
group with retirement concerns.
Other Variables
User Costs
Typical user costs that are incurred by owners of SFR's are maintenance and
repairs, utilities and physical depreciation. The following is typical of the equations
that are built to represent user costs for owners versus renters:
"Assuming capital gains are tax-exempt, but otherwise assuming the
income tax system in the United States, the expected user cost over any time
period, Euc, may be defined as in equation (1) where c is expected operating
costs (excluding property taxes), d is the expected nominal cost of physical
depreciation, property tax [rate], m is the expected mortgage interest, Ei is the expected
34


foregone interest rate at rate / on equity E, and *PH is the expected capital
gain on the depreciated unit of stock (see Douglas Diamond 1980):
Euc = c + d+(l Smith, Rosen, and Fallis (1988)
They also indicate that this accounts for both the consumption and investment aspects
of ownership. Physical depreciation represents the decline in value of the property
due to declines in the quality of the housing, or obsolescence. Maintenance and
repairs slows down this process of physical depreciation. Remodeling costs can
create a shift in the time line of physical depreciation, but the trend of depreciation
will continue.
New SFR's are produced using land, labor, and building materials. However,
as Smith, Rosen and Fallis (1988) point out housing services are produced using
housing stock, labor, and other inputs such as heat, light, and the services of furniture
and appliances. They contend that it is housing services that yield utility and are
demanded by households.
Heating and lighting costs are appropriate variables in a study that addresses
the different characteristics of available housing. Over the time period of this study
there was an increase in technology related to building SFRs more energy efficient,
which decreases user costs. Demand for newer homes would have increased during
this time period due to this variable. This study does not have a variable that
represents the utility costs for new SFRs versus existing SFRs since it is not an
appropriate variable for a macro study without characteristics of individual SFRs.
Interest rates and income taxes, referenced in the above user cost equation,
are reflected under other headings in this study.


Physical Depreciation
Engelhardt and Poterba (1991) used a rate for physical depreciation of 0.025
and a rate for the required cost of maintenance and repairs of 0.014. For this study
these rates are not used since they are a percent of the value and therefore would vary
directly with price variations creating a simultaneity problem, and this is not crucial
to this macro-economic study.
Wealth
Wealth has been reflected by many studies to be one of the critical factors
impacting the first time buyer. Generally the equity in the existing residence is
considered to be the largest contributor to the wealth of a family. Jones (1990) finds
that for young Canadian owners, current net worth provides both greater explanatory
power of demand for SFRs and higher elasticities than labor earnings. This study
does not include a variable that is sufficient to represent wealth on a macro level for
the Denver metropolitan area due to unavailability.
36


CHAPTER 3
THE MODEL
Unit Root Tests
All of the variables were tested for unit roots using the procedures
recommended by MacKinnon (1991), applying the process both with and without
allowing for a trend. The computations were computed using four variations:
traditional Dickey-Fuller (DF) computations; DF allowing for seasons; Augmented
DF; and Augmented DF allowing for seasons. These four variations were computed
both with and without allowing for trend.
Significant variables (Appendix 6) using the augmented DF allowing for
seasons and including a trend variable were temporary income (77) and the
unemployment rate (UR). Significant variables using the augmented DF allowing for
seasons but excluding a trend variable were the same two variables of temporary
income (77) and the unemployment rate (UR), and three others: labor force (LAF),
percent of population under age 18 (PI8), and material price index (MPI).
First differences were used for all the variables other than temporary income
(77), unemployment rate (UR), and the variables that were converted from annual to
monthly for this study: marginal income tax rate (MTR), capital gains rate (CAP), net
migration (MIG), average age of the population (AGE), percentage of the population
under age 18 (PI8), and percentage of the population age 50 and above (P50).
(Using monthly differences for annual data converted to monthly data would have
resulted in less viable data.)
37


Serial Correlation
Serial Correlation tests (Appendix 7) were conducted on both of the
dependent variables: number of residential sales (RNS) and price of residential sales
(RP). The results for RNS indicated that two lags of RNS were required, and for RP
no lags were required.
The model was later changed to increase the number of lags for RNS from
two to four in order to reduce the significance level of Q.
Supply and Demand Model
Normally a supply and demand model would consist of two equations being
reduced into one. Most of the previous studies use reduced form equations.
However Haurin and Lee (1989) made the following argument as to why a reduced
form should not be used:
"In our empirical work, we find evidence that supports that hypothesis
that the amount of housing, the loan-value ratio, and the planned length of
stay in the house are chosen simultaneously. The most important new result
is that in our sample we find that the income elasticity of demand for housing
in the structural system is substantially different from the estimate derived
from a reduced-form equation. We conclude that recognition of the
simultaneous nature of choice involved in housing decisions expands the
range of policy tools and may help to avoid a choice of inappropriate housing
policies." Haurin and Lee (1989)
This is an unusual market, sellers are usually buyers in the same market, often
closing on the sale of their old home on the same day as the purchase of their new
home. Therefore, the criteria leading to the decision to sell are the same criteria
leading to a decision to purchase. The only way to separate the incentives would be
to identify first time purchasers and last time sellers (not replacing with a purchase).
38


This study does not have sufficient data to identify these groups of purchasers and
sellers seperately. This is a suggestion for future expansion of this study.
There are independent variables in both equations that may be endogenous.
Price is included as an independent variable in the quantity equation, quantity is
included as an independent variable in the price equation, and two inventory
variables, number of days on the market and number of new listings, are included in
both equations. The two inventory variables would be explained by the same
independent variables as included in the two equations, but for periods prior to the
current one, and therefore were not considered endogenouse for this study.
Preliminary modifications of these equations to use to use the two stage least squares
method indicated very little change in the resulting significance and coefficients.
Future expansion of this study should include more extensive review of which
variables may be endogenous and using the two stage least squares methods.
39


CHAPTER 4
RESULTS
The results from this study explaining the quantity of SFRs sold, allowing for
seasons, using the AR1 process are as follows (coefficients and (t-values) are
indicated below the name of the variable):
(4.1)
RNS = Constant TREND RNS(-I) RNS(-2) RNS(-3) RNS(-4) RPDIFF
692.0429 6.9644 0.5665 0.0272 0.2022 -0.1069 -0.0124
(0.12) (0.79) (7.47) (0.42) (2.97) (-1.60) (-2.06)
MRDIFF CPDIFF CHEDIFF MPIDIFF MWE3ADIFF TY UNR
162.5074 0.0042 3.9050 2.0314 -102.8355 0.8466 34.1628
(3.96) (0.90) (0.03) (0.68) (-1.47) (0.36) (1.93)
CPIDIFF MTR CAP FEDDIFF APPRECDIFF FEEDIFF RDMDIFF
-27.8097 16.7448 -0.3917 7.1558 -17.5249 -29.3863 -8.7814
(-0.52) (1.34) (-0.05) (0.17) (-2.70) (-0.32) (-1.87)
NEWLDIFF SFPDIFF LAFDIFF MG AGE P18 P50
0.2114 -0.0764 0.0081 0.0015 -140.7315 110.6965 -6.7918
(7.64) (-0.98) (2.32) (1.10) (-0.42) (1.89) (-0.05)
The results of the quantity study show that the variables included explain
81.3% (R-Bar squared) of the variation in the quantity of used SFR sales from
February, 1977, to December, 1992. The Durbin-Watson statistic of 2.009897 and a
Q statistic significance level of 0.35 indicate that serial correlation is not a problem.
However, since the quantity equation includes lagged dependent variables, which
biases these tests towards finding no serial correlation, then the Durbin h-test was
computed giving a h-statistic of 0.20 which is not significant and therefore the null
hypothesis of no serial correlation cannot be rejected. (Note: this was the purpose of
the serial correlation tests done prior to establishing the equation in determining how
40


many lagged dependent variables to include.)
The significant explanatory variables at 10%, other than the lagged dependent
variable, are the change in price (RPDIFF), the change in mortgage interest rates
(MRDIFF), unemployment rate (UNR), change in appreciation rate (APPRECDIFF),
change in number of days on the market (RDM), change in number of new listings
(NEWLDIFF), change in size of labor force (LAFDIFF), and percent of population
age 18 or under (PI8). Additional explanatory variables significant at 20% other
than the lagged dependent variable are permanent income (MWE3ADIFF) and
marginal income tax rate (MTR).
The results from this study explaining the price of SFRs sold, allowing for
seasons, using the AR1 process are as follows (coefficients and (t-values) are
indicated below the name of the variable):
(4.2)
Constant TREND RNSDIFF MRDIFF CPDIFF CHEDIFF MPIDIFF
199444.5024 11.6806 -1.3275 646.1804 -0.0440 -338.1553 19.2897
(1.47) (0.06) (-1.93) (1.14) (-1.06) (-0.29) (0.61)
MWE3ADIFF TY UNR CPIDIFF MTR CAP FEDDIFF
-219.6760 67.1626 189.4145 -998.4700 351.9211 301.9580 569.3330
(-0.18) (1.63) (0.49) (0.17) (1.29) (0.50) (1.05)
APPRECDIFF FEEDIFF RDMDIFF NEWLDIFF SFPDIFF LAFDIFF MIG
-67.9634 -87.1549 -26.6880 0.7885 0.0321 0.0390 0.1931
(-1.13) (-0.10) (-0.61) (2.63) (0.05) (1.06) (6.63)
AGE P18 P50
6784.6769 -8848.2134 -4917.0729
(0.89) (-8.26) (-1.51)
The results of the price equation show that the model explains 98.1% of the
variation in the price of SFR sales from February, 1977, to December, 1992. The
Durbin-Watson statistic of 2.089755 and a Q statistic significance level of 0.47
indicate that serial correlation is not a problem.
The significant explanatory variables, at 10%, are the change in the number of
41


residential units sold (RNSDIFF), capital gains tax rate (CAP), change in new listings
(NEWLDIFF), net migration (MIG), and the percent of the population age 18 or less
(PI8). Additional variables significant when the level of significance is increased to
20% are the constant term, temporary income (TY), marginal income tax rate (MTR),
and percent of the population age 50 or more (P30).
(Note: The significant variables at 20% in explaining the variation in both the
quantity and price models include marginal income tax rate (MTR), change in new
listings (NEWLDIFF), and percent of population age 18 or under (PI 8).
Signs of Coefficients
Quantity Equation
The sign of the coefficients in the quantity equation (Table 4.1) significant at
20% were not always as predicted.
An increase in price (RPDIFF) results in a decrease in the number of sales, as
predicted, which is consistent with traditional supply and demand theory.
An increase in mortgage rates (MR) was predicted to have a negative impact
on the quantity of residential units sold, rather than a positive one, since mortgage
rates increase the cost of ownership. One explanation for an increase in mortgage
rates (MR) having a positive effect on the quantity of residential units sold is that
buyers speed up their transactions when anticipating even higher mortgage rates and
delay purchases when they anticipate lower rates in the future. Also, many loans
were assumable, which gave value to the older loans with lower rates as new rates
increased. This value of the lower interest rate loans added incentive to purchase and
to sale.
42


An increase in permanent income (MWE3ADIFF) was predicted to have a
positive impact on the quantity of residential units sold rather than a negative one,
since families could then afford bigger homes. Further study is required in order to
explain this anomoly.
An increase in the unemployment rate (UNR) was predicted to have a
negative impact on quantity of units sold rather than a positive one, since
unemployed heads of households would not qualify for a loan to purchase a
replacement residence. One possible explanation for higher unemployment rates
resulting in more units being sold is that extended unemployment causes families
financially to no longer be able to afford the residence and therefore must sell it, or
that they must move in order to get a new job.
An increase in the marginal tax rate (MTR) was predicted to have a negative
impact on quantity of units sold rather than a positive one, since buyers would have
less after tax income to spend on purchasing a new residence. One possible
explanation for higher marginal tax rates explaining an increase in the number of
units sold is that the income tax deduction for mortgage interest gives incentive to
buy a home or buy a higher priced home.
An increase in the appreciation (APPRECDIFF) was predicted to have a
positive impact on quantity of units sold rather than a negative one, since past
appreciation leads to future expectations of appreciation, resulting in more first time
families purchasing homes. One explanation is that home owners tend to hold onto
their homes during times of appreciation and sell them during times of depreciation.
An increase in the change in the number of days on the market (RDMDIFF)
has a negative impact on quantity of units sold, as predicted, since the longer it takes
to sell a residence the market conditions are such that fewer units are being sold.
An increase in the change in the number of new listings (NEWLDIFF) has a
positive impact on quantity of units sold, as predicted, since an increase in the supply
43


of residences for sale should lead to an increase in the number of sales, either
because prices are adjusted for the oversupply or buyers have more likely to find a
suitable residence from the larger selection.
An increase in the change in the labor force (LAFD1FF) has a positive impact
on quantity of units sold, as predicted, since an increase in the size of the demand
population will result in an increase in demand.
An increase in the percent of the population under age 18 (PI 8) has a positive
impact on quantity of units sold, as predicted, since such an increase would mean
either more families with children or larger families, both of which should increase
the demand for residences.
Price Equation
The sign of the coefficients in the price equation (Table 4.2) significant at
20% were also not always as predicted.
An increase in the number of units sold (RNSDIFF) has a negative impact on
the price of units sold is consistent with the quantity equation which had an increase
in price resulting in a decrease in quantity sold.
An increase in temporary income (77) has a positive impact on the price of
units sold, as predicted, since families would have more income available to spend on
housing.
An increase in the marginal income tax rate (MTR) was predicted to have a
negative impact on the price of units sold rather than a positive one, since buyers
would have less after tax income to spend on purchasing a new residence. As
discussed above in the quantity equation, one possible explanation for higher
marginal tax rates explaining an increase in the price of units sold is that the income
44


tax deduction for mortgage interest gives incentive to buy a home or buy a higher
priced home.
A higher level of capital gains tax rate (CAP) was predicted to have a negative
impact on the price of units sold rather than a positive one, since an increase in tax
rates should be a disincentive to investing in a residence. Further study is needed to
address this anomoly.
An increase in the change in the number of new listings (NEWMLDIFF) was
predicted to have a negative impact on the price of units sold rather than a positive
one, since an increase in the supply over the demand would typically result in lower
prices. One possible explanation is that as prices go up there is incentive to sell
residences.
An increase in net migration (MIG) has a positive impact on the price of units
sold, as predicted, since an increase in the demand population will typically result in
an excess of demand over supply resulting in higher prices being paid.
An increase in the percent of the population under age 18 (PI8) has a negative
impact on the price of units sold, as predicted, since families with more children
spend a larger protion of their budget on goods other than a residence leaving less to
be spent on a residence.
An increase in the percent of the population age 50 or more (P50) has a
negative impact on the price of units sold, as predicted, since older families have less
income to spend on housing and have less of a need for large housing.
Standardized Coefficients
Standardized coefficients (Appendix 4) reflect that of the significant variables
in the quantity equation several had larger impacts on the dependent variable than
45


most of the others. In the quantity equation one standard deviation increase in the
change in new listings (NEWLDIFF) resulted in 207 additional units sold, or 42% of
one standard deviation in the number of units sold; and one standard deviation
increase in the percent of the population under age 18 (PI8) resulted in 169
additional units sold, or 34% of one standard deviation in the number of units sold.
The other significant variables had standardized coefficients ranging from 7% to 14%
of one standard deviation in the number of units sold.
In the price equation, one standard deviation increase in net migration (MIG)
resulted in higher prices by $5,254, or 28% of one standard deviation in the price of
units sold; and one standard deviation increase in the percent of the population under
age 18 (PI8) resulted in lower prices by $13,524, or 72% of one standard deviation of
the price of units sold. The other significant variables had standardized coefficients
ranging from 2% to 12% of one standard deviation in the price of units sold.
Elasticities
The computed elasticities from the quantity equation (Appendix 5) reflects
that of the significant variables the most elastic variable is the percentage of the
percent of the population under age 18 (PI8) which indicates that at its mean a one
percent increase in P18 will result in a 1.68 percent increase in the number of units
sold.
The computed elasticities from the price equation (Appendix 5) reflects that
of the significant variables the most elastic variables are the percentage of the
percent of the population under age 18 (PI8) which indicates that at its mean a one
percent increase in P18 will result in a 2.61 percent increase in the price of units sold,
and the percent of the population age 50 and over (P50) which indicates that at its
46


mean a one percent increase in P50 will result in a 1.10 percent decrease in the price
of units sold.
47


GRAPHS OF VARIABLES
48


Quantity Sold Single Family Residences
RNS
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
49


Quantity Differences Single Family Residences
RNSDIFF
50


Price Single Family Residences
RP
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
J
51


Price Differences Single Family Residences
RPDIFF
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
52


Mortgage Interest Rate
MR
53


Mortgage Interest Rate Differences
MRDIFF
54


Price of Condos
CP
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
55


Price of Condos Differences
CPDIFF
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
56


Construction Hourly Earnings
CHE
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
57


Construction Hourly Earnings Differences!
CHEDIFF
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
58


Material Price Index
MPI
59


Material Price Index Differences
MPIDIFF
60


Manufacturing Weekly Earnings & Permanent Income
MWE & MWE3A
61


Permanent Income -
MWE3ADIFF
Differences
62


Temporary Income
TY
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
63


Unemployment Rate
UNR
10
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
64


Consumer Price Index
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
65


Consumer Price Index Differences
CPIDIFF
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
66


Marginal Tax Rate
MTR
28
26
24
22
20
18
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
67


Capital Tax Rate
CAP
26
24
22
20
18
16
14
CAP
12
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
68


Percent of Mortgages Financed by Federal Government
FED
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
L
69



Percent of Mortgages Financed by Government Differences! FEDDIFF }
70


Annual Appreciation Rate
APPREC
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
71


Annual Appreciation Rate
APPRECDIFF
Differences
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
72


Closing Costs
FEE
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
73


Closing Costs Differences
FEEDIFF
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
74


Days on the Market
RDM
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
75


76


Number of New Listings
NEWL
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
77


Number of New Listings Differences
NEWLDIFF
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
78


Single Family Permits
SFP
79


Single Family Permits Differences
SFPDIFF
80


Size of Labor Force!
LAF
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan87 Jan-89 Jan-91 Dec-92
81


Size of Labor Force Differences
LAFDIFF
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
82


Migration (Net)
MIG
Jan-74 Jan-76 Jan-78 Jan-80 Jan-62 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
83


Average Age of the Population
AGE
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
84


Percent of Population Under Age 18
P18
85


Percent of Population Over Age 50
P50
Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92
Jan-75 Jan-77 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Dec-92
86


APPENDIX A
RATS PRINTED RESULTS
87


*********QUflliTxTY-
AR1(METHOD=HILU,PRINT) HNS / RESID1
CONSTANT THEND RNS{I TO 4} RPDIFF MRDIFF CPDIFF $
CHEDIFF MPIDIFF MWE3ADIFF TY UNR CPIDIFF $
MTR CAP FEDDIFF APPRECDIFF' FEEDIFF RDMDIFF $
NEWLDIFF SFPDIFF LAFDIFF MIG AGE P18 P50 $
SEASONS{11 TO 1}
Dependent Variable RNS Estimation by Hildreth-Lu
Monthly Data From 77:02 To 92:12
Usable Observations 191
Centered R**2 0.851528
Uncentered R**2 0.989608
Mean of Dependent Variable
Std Error of Dependent Variable
Standard Error of Estimate
Sum of Squared Residuals
Durbin-Watson Statistic
<3(36-1)
Significance Level of Q
Degrees of Freedom
R Bar **2 0.813181
T x R**2 189.015
1768.6387435
486.4668327
210.2635779
6675826.5990
2.009897
37.585399
0.35159082
151
Variable Coeff std Error T-Stat Siqni-*'
1. Constant 692.042923 5806.082803 0.11919 0.90528108
2. TREND 5.964431 8.772538 0.79389 0.42850524
3. RNS{1} 0.566552 0.075869 7.46754 0.00000000
4. RNS{2} 0.027170 0.065054 0.41765 0.67679825
5. RNS{3} 0.202202 0.068157 2.96670 0.00350064
6. RNS{4} -0.106398 0.066700 -1.60267 0.11109629
7. RPDIFF -0.012424 0.006035 -2.05863 0.04124806
8. MRDIFF 162.507405 41.029973 3.96070 0.00011483
9. CPDIFF 0.004181 0.004622 0.90454 0.36715160
10. CHEDIFF 3.904991 120.679117 0.03236 0.97422892
11. MPIDIFF 2.031425 2.969923 0.68400 0.49502395
12. MWE3ADIFF -102.835500 70.078315 -1.46744 0.14433703
13. TY 0.846556 . 2.359119 0.35884 0.72021307
14. UNR 34.162798 17.727083 1.92715 0.05583822
15. CPIDIFF -27.809682 53.321583 -0.52155 0.60275027
16. MTR 16.744822 12.455100 1.34441 0.18083042
17. CAP -0.391694 7.227926 -0.05419 0.95685398
18. FEDDIFF 7.155760 41.254478 0.17345 0.86252677
19. APPRECDIFF -17.524920 6.497866 -2.69703 0.00779146
20. FEEDIFF -29.386251 92.841168 -0.31652 0.75204364
21. RDMDIFF -8.781407 4.686270 -1.87386 0.06288211
22. NEWLDIFF 0.211429 0.027671 7.64079 0.00000000
23. SFPDIFF -0.076449 0.078156 -0.97816 0.32955752
24. LAFDIFF 0.008142 0.003514 2.31717 0.02183797
25. MIG 0.001501 0.001367 1.09834 0.27380352
26. AGE -140.731508 332.115449 -0.42374 0.67235644
27. P18 110.696527 58.684833 1.88629 0.06117617
28. P50 -6.791848 137.773257 -0.04930 0.96074753
29. SEASONS{1} -472.548038 126.260093 -3.74266 0.00025823
30. SEASONS{2} -428.984239 88.925967 -4.82406 0.00000341
31. SEASONS{3} -99.537161 97.244618 -1.02358 0.30767306
32. SEASONS{4} 96.531400 102.402561 0.94267 0.34735757
33. SEASONS{5} 73.835259 110.050902 0.67092 0.50329698
34. SEASONS{6} 119.152617 113.907046 1.04605 0.29720891
35. SEASONS{7} 97.483487 111.184241 0.87677 0.38200197
36. SEASONS{8} 104.318635 98.010423 1.06436 0.28886349
37. SEASONS{9} 61.114238 90.495904 0.67533 0.50050149
38. SEASONS{10} -83.596234 85.233121 -0.98080 0.32826257
39. SEASONS{ll} -182.932574 90.085013 -2.03067 0.04404371
40. RHO -0.210689 0.131544 -1.60166 0.11132093
§8


*********PRICE
AR1(METHOD=HILU, PRINT) RP / RESID2
# CONSTANT TREND RNSDIFF MRDIFF CPDIFF $
CHEDIFF MPIDIFF MWE3ADIFF TY UNR CPIDIFF $
MTR CAP FEDDXFF APPRECDIFF FEEDIFF RDMDIFF $
NEWLDIFF SFPDIFF LAFDIFF MIG AGE P18 P50 $
SEASONS{11 TO 1}
Dependent Variable RP Estimation by Hildreth-Lu
Monthly Data From 77:02 To 92:12
Usable Observations 191 Degrees of Freedom
Centered R**2 0.984186 R Bar **Z 0.980615
Uncentered R**2 0.999355 T x R**2 190.877
Mean of Dependent Variable 91426.926702
Std Error of Dependent Variable 18898.718997
Standard Error of Estimate
Slim of Squared Residuals
Durbin-Watson Statistic
3(36-1)
Significance Level of 2631.236725
1073128039.2
2.089755
34.882170
0.47380361
155
Variable Coeff Std Error T-Stat Signif
***** kie-kkickkickirkk'k'kit'tck'k'kic-k'klC'kfe'jfkkle'tcktftT'k
1. Constant 199444.5024 135315.3161 1.47392 0.14253007
2. TREND 11.6806 194.9550 0.05991 0.95230086
3. RNSDIFF -1.3275 0.6386 -1.92779 0.05570935
4. MRDIFF 646.1804 568.8791 1.13588 0.25775852
5. CPDIFF -0.0440 0.0413 -1.06352 0.28919985
6. CHEDIFF -338.1553 1160.4674 -0.29140 0.77113826
7. MPIDIFF 19.2897 31.5172 0.61204 0.54140956
8. MWE3ADIFF -219.6760 1226.7806 -0.17907 0.858-11890
9. TY 67.1626 41.1907 1.63053 0.10502044
10. UNR 189.4145 388.3041 0.48780 0.62638118
11. CPIDIFF -998.4700 785.7469 -1.27073 0.20572960
12. MTR 351.9211 272.2119 1.29282 0.19799691
13. CAP 301.9580 152.5860 1.97894 0.04959484
14. FEDDIFF 569.3330 541.1818 1.05202 0.29442857
15. APPRECDIFF -67.9634 60.3809 -1.12558 0.26208378
16. FEEDIFF -87.1549 848.1406 -0.10276 0.91828626
17. RDMDIFF -26.6880 43.9223 -0.60762 0.54433051
18. NEWLDIFF 0.7885 0.3003 2.62598 0.00950641
19. SFPDIFF 0.0321 0.7039 0.04558 0.96370362
20. LAFDIFF 0.0390 0.0370 1.05622 0.29251207
21. MIG 0.1931 0.0291 6.53379 0.00000000
22. AGE 6784.6769 7617.7791 0.89064 0.37450422
23. P18 -8848.2134 1070.5850 -8.26484 0.00000000
24. P50 -4917.0729 3250.6661 -1.50800 0.13359097
25. SEASONS{l} 1275.2727 1312.3513 0.97175 0.33269069
26. SEASONS{2} -1477.9449 1094.8156 -1.34995 0.17900051
27. SEASONS{3} -722.1522 1123.1276 -0.64298 0.52118502
28. SEASONS{4} -47.2314 1119.7190 -0.04218 0.96640830
29. SEASONS{5} -161.1392 1110.1004 -0.14516 0.88477522
30. SEASONS{6} 3126.1886 1169.7247 2.67258 0.00833233
31. SEASONS{7} 3823.5907 1168.2090 3.27304 0.00131197
32. SEASONS{8} 4340.6081 1079.4597 4.02109 0.00009022
33. SEASONS{9} 2664.0372 1036.4459 2.57036 0.01110116
34. SEASONS{10} 1096.0732 1030.6920 1.06343 0.28923896
35. SEASONS{11} -87.3805 871.9381 -0.10021 0.92030389
*******************************************************************************
36. RHO 0.4447 0.0770 5.77198 0.00000004
89


TABLE 77:02 92:12
Series Obs Mean
CP 191 62720.15133
RNS 191 1768.63874
RP 191 91426.92670
RPL 102 96.59804
RDM 191 76.84293
NEWL 191 3830.76440
LAF 191 840255.47120
UNR 191 5.58848
CHE 191 12.44555
MWE 191 391.38084
MR 191 11.54611
CPI 191 99.29476
SFP 191 1035.52356
TFP 191 17.75393
MFP 191 355.74346
MPI 191 323.95952
REN 139 443.00216
SRP 130 116633.44154
AGE 191 30.57993
pia 191 26.92046
P50 191 20.42858
MIG 191 20491.84381
DED 191 19934.22120
NHU 145 674008.42069
VAC 145 7.72568
HHS 145 2.53556
WDI 191 294.53681
MTR 191 23.31414
CAP 191 20.75393
FEE 191 2.12770
FED 191 40.75651
SEASONS 191 0.08377
APPREC 191 7.78993
TREND 191 133.00000
SUM 191 13087.24319
MWE3A 191 363.53453
TY 191 28.34630
RNSDIFF 191 4.85864
RPDIFF 191 409.37696
MRDIFF 191 -0.00262
CPDIFF 191 199.34555
CHEDIFF 191 0.02853
MPIDIFF 191 0.82476
MWE3ADIFF 191 1.62314
CPIDIFF 19l 0.41937
FEDDIFF 191 -0.35537
APPRECDIFF 191 0.00882
FEEDIFF 191 -0.00042
RDMDIFF 191 -0.05759
NEWLDIFF 191 -1.94764
SFPDIFF 191 -0.26178
LAFDIFF 191 1392.39267
RESID1 191 -0.00000
RESID2 191 0.00001
Std Error Minimum Maximum
10825.97625 32267.00000 79361.00000
486.46683 808.00000 2957.00000
18898.71900 42490.00000 121567.00000
0.78677 95.00000 99.00000
16.90271 36.00000 105.00000
936.50280 1183.00000 6251.00000
76087.48042 643370.00000 930004.00000
0.99714 3.70000 8.90000
1.64953 8.53000 14.39000
94.07659 214.32000 553.37000
2.53917 7.92000 18.45000
22.02556 53.40000 132.80000
537.47862 214.00000 2587.00000
17.35230 0.00000 74.00000
351.51776 0.00000 1604.00000
39.18711 221.33000 388.58000
48.77554 356.00000 599.00000
6014.77893 105186.00000 131433.00000
1.33467 28.46700 33.20000
1.52841 25.40000 30.78300
0.48860 19.50000 21.50000
27210.74962 -24046.00000 64946.00000
1353.51111 17669.00000 22361.00000
51718.05777 577604.00000 728557.00000
2.48704 4.47000 11.-67700
0.04090 2.45600 2.60500
59.30024 175.66000 400.36000
2.79252 20.00000 27.50000
3.40229 14.10000 24.00000
0.48658 1.25000 3.28000
23.34161 11.96400 81.04000
0.27777 0.00000 1.00000
8.42998 -4.07628 28.10181
55.28110 38.00000 228.00000
3475.50101 7275.73000 18400.55000
96.54169 202.10361 511.12917
12.15111 -7.86306 49.06556
406.10185 -1038.00000 848.00000
3418.59206 -9784.00000 9494.00000
0.40916 -2.07000 2.24000
4154.81368 -15556.00000 14121.00000
0.16432 -0.42000 0.56000
5.73585 -19.82000 23.30000
0.49177 0.31139 2.59417
0.34700 -1.40000 1.20000
0.47290 -2.14800 1.80900
2.34571 -7.99584 7.64459
0.19402 -0.58000 0.53000
4.69623 -15.00000 15.00000
979.76050 -2347.00000 3128.00000
257.55522 -359.00000 1087.00000
8652.67353 -26722.00000 25946.00000
192.71796 -525.60024 635.61666
2376.56103 -6590.25070 7253.10133
90


CALENDAR 74 1 12
ALLOCATE 92:12
nppw niTH tttp'ptqi ppw
DATA(MISSING=-999,ORG=OBS,FORMATS((1X,14F14.3))') / CP $
RNS RP RPL RDM MEWL LAF UNR CHE MWE MR CPI SFP TFP
OPEN DATA THESIS2 PRN
DATA(MlSSlNG=-999,ORG=OBS,FORMATS'((IX,10F14.3))') / MFP $
MPI REN SRP AGE P18 P50 MIG DED NHU
OPEN DATA THESXS3-PRN
DATA(MISSING=-999,ORG=OBS,FORMATS'((1X,7F14.3))') / VAC $
HHS WDI MTR CAP FEE FED
SEASONAL SEASONS / 12 1974:12
*
SET APPREC = ((RP{1}-RP{25})/RP{25})/2*100

SET TREND = T

SET SUM s 0
DOFOR I = 0 TO 35
SET SUM = SUM+MWE{I}
END DOFOR
SET MWE3A = SUM/36
SET TY = MWE-MWE3A
*
DIFF RNS / RNSDIFF
DIFF RP / RPDXFF
DXFF MR / MRDIFF
DIFF C? / CPDIFF
DIFF CHE / CHEDIFF
DIFF MPI / MPIDIFF
DIFF MWE3A / MWE3ADIFF
DIFF CPI / CPIDIFF
DIFF FED / FEDDIFF
DIFF APPREC / APPRECDIFF
DIFF FEE / FEEDIFF
DIFF RDM / RDMDIFF
DIFF NEWL / NEWLDIFF
DIFF SFP / SFPDIFF
DIFF LAF / LAFDIFF
91


APPENDIX B
SUMMARY OF VARIABLES
92


SUMMARY OF VARIABLES
APPENDIX B
Variable Description Source Frequency Data Series Start End
Quantity and Price of DeDendent Variable
RNS Number of existing single family residences sold in the Denver Metro area MLS Monthly Jan., 1974 Dec., 1992
RP Average price of existing single family residences sold in the Denver Metro area. MLS Monthly Jan., 1974 Dec., 1992
MR Average Mortgage Rate in Colorado. Professor Monthly Jan., 1974 Dec., 1992
Ouantitv an id Price of Substitutes
CP Average price of existing condominiums and town houses sold in the Denver Metro area. MLS Monthly Jan., 1974 Dec., 1992
CHE Average construction hourly earnings in the Denver Metro area. Colo Dept of Labor and Employment Monthly Jan., 1974 Dec., 1992
MPI Material Price Index for the Denver Metro area. Engineering Record (ENR) Monthly Jan., 1974 Dec., 1992
Income Va riables
MWE Average Manufacturing Weekly Earnings for Denver Metro area. Colo Dept of Labor and Employment Monthly Jan., 1974 Dec., 1992
UNR Unemployment rate for the Denver Metro area. Colo Dept of Labor and Fmnlovment Monthly Jan., 1974 Dec., 1992
93