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A benefit-cost analysis of the Clean Air Act amendments

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A benefit-cost analysis of the Clean Air Act amendments an application of the hedonic pricing technique
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Moore, Patrick W
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v, 72 leaves : illustrations ; 29 cm

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Master's ( Master of Arts)
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University of Colorado Denver
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Department of Economics, CU Denver
Degree Disciplines:
Economics

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Subjects / Keywords:
Air -- Pollution -- Law and legislation -- United States ( lcsh )
Air quality management -- Economic aspects -- United States ( lcsh )
Air -- Pollution -- Law and legislation ( fast )
Air quality management -- Economic aspects ( fast )
United States ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Includes bibliographical references (leaves 70-72).
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Submitted in partial fulfillment of the requirements for the degree, Master of Arts, Department of Economics.
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by Patrick W. Moore.

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Full Text
A BENEFIT-COST ANALYSIS
OF THE CLEAN AIR ACT AMENDMENTS:
AN APPLICATION OF THE HEDONIC PRICING TECHNIQUE
by
Patrick W. Moore
B.A., University of Colorado, 1986
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Arts
Department of Economics
1990


This thesis for the Master of Arts degree by
Patrick W. Moore
has been approved for the
Department of
Economics
by
Esmail Noori
Date

/??&


Ill
Moore, Patrick W. (M.A., Economics)
A Benefit-Cost Analysis of the Clean Air Act Amendments
Thesis directed by Assistant Professor Steven G. Medema
The purpose of this thesis is to apply the
techniques of benefit-cost analysis and hedonic pricing
to evaluate the efficiency with which the Clean Air Act
Amendments allocate society's resources. More
specifically, this thesis attempts to determine whether
society is willing to pay for the costs of the
legislation.
The form and content of this abstract are approved. I
recommend its publication.
Steven G. Medema


iv
CONTENTS
CHAPTER
I. INTRODUCTION................................... 1
II. THE THEORY OF PUBLIC GOODS AND EXTERNALITIES 7
III. BENEFIT-COST ANALYSIS......................... 14
The Benefits................................ 18
Hedonic Price Theory...................... 19
The Model................................. 31
The Data................................ 3 6
The Results............................... 43
The Costs................................... 56
Benefit-Cost Comparison..................... 58
IV. CONCLUSIONS................................... 65
BIBLIOGRAPHY....................................... 70


V
TABLES
Table
1. Estimated Pollutant Reductions................. 6
2. Annual Estimated Reductions.................. 40
3. % Reduced from Present Levels by Year......... 41
4. Annual Changes in Concentration Levels........ 44
5. Variable Definitions.......................... 45
6. Region Definitions............................ 46
7. Hedonic Price Estimates....................... 47
8. Inverse Elasticity Estimates.................. 51
9. Variable Estimates............................ 54
10. Estimated Annual Benefits..................... 57
11. Estimated Annual Costs........................ 59
12. Discounted Present Values of the Benefits.... 60
13. Discounted Present Values of the Costs........ 61
14. Net Present ValuesAverage Costs.............. 62
15. Net Present ValuesGradual Costs.............. 63


CHAPTER I
INTRODUCTION
The Clean Air Act was originally passed in 1970
and substantially amended in 1977. The Act is generally
believed to have been successful at limiting emissions of
certain air pollutants. (Reilly, 1989, p. 76) However,
serious air pollution problems persist. Acid rain, urban
smog and the emission of toxic air pollutants continue to
pose significant public health and environmental risks.
(Reilly, 1989, p. 76) It is these three problems which
the Clean Air Act Amendments address.
The Clean Air Act Amendments were introduced by
President Bush in June of 1989. The proposals passed the
Senate as Senate Bill 1630, and the House as House Bill
3030. Presently, both bills are under consideration in
joint committee.
Both the House and Senate versions of the
Amendments are more comprehensive and expensive than the
President's proposals. (Wall Street Journal. April 4,
1990, p. A13) Unfortunately, there is considerably less
information available on the Senate and House versions.
Consequently, given the limited information available at


2
this time, this paper will evaluate the President's
proposals rather than their Congressional counterparts.
If the President's version were enacted, it has
been estimated that most cities would attain national air
quality standards for ozone and carbon monoxide by the
turn of the century, and that all cities would attain
those standards by 2010. (Reilly, 1989, p. 77) Also,
emissions of toxic air pollutants would be cut
substantially, and acid rain would be cut nearly in half
by the turn of the century. (Reilly, 1989, p. 77)
The President's proposal is organized under
seven titles. Title I addresses the problem of non-
attainment of the National Ambient Air Quality Standards
(NAAQS) in some areas of the country. This Title
requires the EPA to promulgate revised NAAQS. Once these
are implemented, the Title establishes a set of general
requirements, in the form of emission reduction targets,
to apply to the air quality plans for all areas of the
country. This Title also requires the EPA to issue
guidelines on control technology for industrial
facilities, as well as guidelines with respect to
controlling emissions of volatile organic compounds
(VOC's) from consumer and commercial products. (Reilly,
1989, p. 82)


3
Title II of the Amendments targets air pollution
generated by mobile sources, calling for the introduction
of clean-fuel automobiles, as well as tougher vehicle and
fuel measures, including, among other things:
1) tighter standards for hydrocarbon and nitrogen
oxide emissions for passenger vehicles and tighter
hydrocarbon and carbon monoxide standards for light
duty trucks;
2) tighter controls on vehicle evaporative
emissions;
3) reductions in gasoline volatility;
4) a requirement for improved inspection and
maintenance controls in many areas;
5) a requirement that all new buses in large cities
use clean fuels;
6) a requirement that oxygenated fuels be used in
areas with the worst carbon monoxide problems.1
(Reilly, 1989, p. 85-86)
Additionally, this Title allows automobile
manufacturers to use emissions averaging to meet
standards. The EPA is also authorized to issue a rule 1
1 These areas include Los Angeles, Houston, New York,
aukee, Baltimore, Philadelphia, Greater Connecticut, San Diego
Chicago.


4
that would allow auto makers to engage in "emissions
trading" and fuel refiners to engage in "fuel-pooling".2
Title III of the Amendments targets air toxics
by authorizing the EPA to mandate the application of
maximum achievable control technology (MACT) for source
categories. MACT is an approach which will require
existing sources to achieve the same emissions standards
as obtained by the best performing plants currently in
operation. (Reilly, 1989, p. 88)
Title IV of the Amendments further defines the
role of states in implementing the Amendments. Among
other things, states will be required to submit to the
EPA a comprehensive program for licensing stationary
sources. (Reilly, 1989, p. 90)
Title V of the Amendments focuses on the acid
rain problem. The President's proposal uses a
combination of an S02 (sulfur dioxide) and NOx (nitrogen
oxides) emissions cap, along with a program which allows
2 Emissions trading refers to allowing emitters to buy and sell
sion permits. Under this program emitters will be issued
sion permits which allow them to emit a specified quantity of
(llutant. In some cases, it may be cost-effective for an
ter to buy or sell an emissions permit to or from another
ter. In fact, some economists have argued that this approach
missions reduction is the most efficient, (e.g., Tietenberg,
, p. 278) Fuel pooling refers to permitting fuel refiners to
reductions of certain pollutants across a spectrum of the
s they produce, rather than be requiring reductions in the
entration of those pollutants in specific fuels.


5
utilities to trade reductions of sulfur oxides and
nitrogen oxides. It has been estimated that this market
approach to pollution reduction achieves the same results
as the command and control approach for $1 billion a year
less. (Reilly, 1989, p. 93)
Title VI of the Amendments addresses the EPA's
role in the implementation of the Amendments. The EPA
will be authorized to issue field citations and conduct
other enforcement and administrative penalty actions.
Title VII of the Amendments addresses miscellaneous minor
issues.
If enacted, the President's proposals will
substantially reduce air pollution. Table 1 contains
estimates of the primary projected reduction in
emissions. As can be seen in the table, the primary goal
of the Amendments is to effect reductions in Air Toxics,
VOC's (to reduce ozone smog), and S02 and N0X (to reduce
acid rain).


6
Table 1
Estimated Pollutant Reductions
Pollutant Current Output (106 tons) Proposed Reduction (percent) Estimated Reduction (106tons)
Air Toxics (191 pol- lutants) 1.35 82.5 by 2005 1.14
VOC's from Mobile Sources 6 77 by 2005 4.62
VOC's from Stationary Sources 6 37 by 2005 2.22
S02 NA 50 by 2000 10
NOx NA 10 by 2000 2
TOTAL 19.96
Source: Reilly, 1989.


CHAPTER II
The Theory of Public Goods and Externalities
Air pollution is a classic example of an
external diseconomy. The latter occurs when the activity
of one or more parties diminishes the well-being of other
parties without the first party or parties compensating
the affect party or parties for their losses. (Boadway
and Wildasin, 1984, p. 105) In the case of air
pollution, factory and automobile operators convert
relatively clean air into relatively dirty air, thereby
diminishing the overall air quality. Diminished air
quality leads to myriad social damages,3 including:
1) reduced public health;
2) reduced productivity of ecological systems used
for economic purposes (i.e. agriculture, fisheries
and forests);
3) reduced benefits from the recreational use of
ecological systems, due to increased damage to
those systems;
3
The following list comes from Freeman,1982.


8
4) reduced option and existence value, due to the
loss of species and ecosystem stability;
5) corrosion of materials;
6) increased uncertainty, due to climatic change;
7) reduced visibility and tranquility.
Therefore, the benefits accruing to factory and
automobile operators of engaging in activities which
pollute the air appear to come at the expense of the
well-being of others. Furthermore, these operators are
allowed to engage in those activities without
compensating the affected parties. Consequently, the
emitters do not take the external costs of their
operations into consideration when deciding upon the
optimal level of their activity. This leads to a
suboptimal allocation of society's resources.
Emitters optimize their level of polluting
activity by equating their marginal private benefit with
their marginal private cost. (Boadway and Wildasin, 1984,
pl06) In mathematical terms,
MCi=MBi (1)
where MC; is the marginal private cost to the ith emitter
and MB; is the marginal private benefit to the ith
emitter. However, for the socially optimal level of
polluting activity to occur, i.e., one which assures an


9
efficient allocation of resources, the emitter should
take the damages to others into consideration, (ibid, p.
107) That is, output should be set at the level where
marginal social benefit is equal to marginal social cost.
Mathematically,
n
MCt+Y^MD-MBi (2)
3=i
where MDj is the marginal external damage to the jth firm
or the jth individual, and the summation MDj is the total
marginal external damage. The term on the left-hand side
of the equation thus represents marginal social costs,
while the term on the right side represents marginal
social benefits. j
Unfortunately, in the case of air pollution,
there is no market-driven incentive system for emitters
to take the damage to others into consideration when
deciding upon the optimal level of their polluting
activity. A market failure occurs as individual decision
makers in a market economy fail to arrive at an optimal
allocation of resources (i.e. someone's gain comes at
another's expense).
The principal cause of this external-diseconomy-
generated market failure is improperly defined property
rights. In the case of air pollution, air cannot be


10
divided into distinct units and marketed by sellers like
a private good. Indeed, the fact that individuals cannot
be excluded from consuming air is the primary reason that
the market fails to generate well defined property rights
for air. The owner of a private good who could not
exclude people from consuming it would not be successful
at extracting a price from consumers of the good.
Similarly, if an individual could own the air, s/he would
have no method by which to prevent us from consuming the
air freely. Consequently, emitters are allowed to
consume the air as they wish without concern for costs.
Market failure is often a precursor to
government intervention. Indeed, it is widely recognized
as a legitimate role of government to intervene in such
cases. In the case of market failures generated by
external diseconomies, governments attempt to internalize
the externality by requiring the emitters to take the
marginal external damage to others into consideration.
Theoretically, at least, the purpose of
government intervention in attempting to internalize an
external diseconomy is to improve economic efficiency.
This may mean different things to different people. To
economists, however, economic efficiency has a very
precise meaning. Economists' view of economic efficiency
has its origins in the works of Vilfredo Pareto, Walras'


11
successor at the University of Lausanne. The following
definitions, drawn from Pareto's work, have been
extremely useful in discussions of economic efficiency:4
1) A Pareto optimum is the state of affairs where
no one can be made better off without at the same
time making at least one other person worse off; in
other words, a Pareto-optimal allocation of
resources exists in an economy when it is not
possible to reallocate resources without reducing
the utility or welfare of at least one person;
2) A Pareto improvement is a situation where a
reallocation of resources leads to at least one
person becoming better off and no one becoming
worse off.
By definition, a Pareto-optimal allocation of
resources is an efficient allocation of resources.
Furthermore, if a Pareto-optimal allocation exists, then
there is no possibility for a Pareto improvement. In
other words, if a Pareto improvement is possible, then a
gain in economic efficiency is possible.
Unfortunately, many changes in the economy do
make some people worse off. Therefore, in order to
determine whether such changes improve economic
4 The following definitions are drawn from Boadway and
iasin. (1984, p. 14-16)


12
efficiency, one must compare the magnitudes of the
improvements to some people's well-being with the
magnitudes of the deterioration to other people's well-
being. This would involve making interpersonal utility
comparisons. Since this endeavor is beyond the means of
an economist, economists discuss such changes in the
economy in terms of potential Pareto improvements. A
potential Pareto improvement occurs when the monetary
value of the increased well-being to those who gain from
an economic change exceeds the monetary value of the
decreased well-being to those who lose from an economic
change, such that the gainers could potentially
compensate the losers and everyone would be made better
off. This is also known as the Kaldor-Hicks Rule.
Therefore, if an economic change results in some members
of society becoming worse off, then the effect of those
changes on economic efficiency can be evaluated in terms
of potential Pareto improvements. Moreover, an economic
change which results in a potential Pareto improvement
also results in a gain in economic efficiency.
In the case of the economic changes proposed by
the Clean Air Act Amendments, the government is
attempting to internalize the external diseconomies
imposed on society by the emitters of air pollution.
However, policy makers do not seek to cause more harm


13
than already exists, and therefore like to have an idea
of the proposal's impact on efficiency. Economists have
developed a technique known as benefit-cost analysis to
provide such a view.


CHAPTER III
BENEFIT-COST ANALYSIS
The purpose of benefit-cost analysis is to
evaluate and compare the discounted monetary value of the
streams of benefits and costs generated by an economic
change. The benefits of an economic change refer to the
improvement in well-being to those who gain from the
change. The costs of an economic change refer to the
deterioration in the well-being to those who lose from
the change. If the benefits exceed the costs, then that
economic change is said to result in a potential Pareto
improvement and a gain in economic efficiency. Thus, the
decision rule for going forward with a policy which
results in economic changes is a positive net present
value. (Boadway and Wildasin, 1984, p. 194) Of course if
there are policy options, the decision rule is to
maximize the gain in economic efficiency by choosing the
policy with the highest net present value.
In order to conduct a benefit-cost analysis, it
is often necessary to make a few assumptions. First, we
assume that individual decision makers are in
equilibrium. In other words, individuals know what is


15
best for themselves and they've allocated their resources
in the most efficient way in order to maximize their
satisfaction, however that may be measured (e.g. utility,
profits, revenues, etc.)* Second, we assume that
observable market prices reflect social values. This
occurs due to the efficiency with which individuals
exchanging in a market economy satisfy their wants and
needs. While these assumptions are not absolutely
necessary, they simplify a benefit-cost analysis
considerably.
Beyond this, there are several difficult issues
involved in any benefit-cost analysis. Perhaps the
greatest problem is that of monetizing all the benefits
and costs. Fortunately, for the purposes of this paper,
the EPA has already monetized the costs of the Clean Air
Act Amendments, and the technique used herein to estimate
the benefits is relatively straightforward.
Another problem with benefit-cost analysis is
the choice of a discount rate. Discounting enables one
to compare future benefits and costs with those occuring
in the present. In essence, the role of the discount
rate is to reflect the opportunity cost of spending a
dollar on a project now in order to obtain benefits in
the future. The discount rate problem arises due to


16
disagreement over what the actual opportunity costs might
be.
Some economists (e.g., Baumol, 1978) argue that
the discount rate should reflect the opportunity cost of
not putting a dollar to its most productive use: private
investment. From this perspective, then, the discount
rate would be equal to the rate of return on investment.
Other economists (e.g., Feldstein, 1964) argue
that the discount rate should reflect the opportunity
cost of putting off consumption. According to this view,
the discount rate should reflect the social rate of time
preference.
Still others (e.g., Bradford, 1975) argue that
the discount rate should be constructed in such a way as
to take into consideration who benefits and who loses
from an economic change, as well as market imperfections.
The resulting discount rate would be a weighted average
of the rate of return on capital and the social rate of
time preference, depending on the percentage of the
benefits and costs that flow from or into private
investment.
In the case of environmental regulation, where
private firms take actions to reduce pollution as
mandated by the government, it has been argued (Kolb and
Scheragacited in Lind, 1990, p. S-24) that the discount


17
rate should reflect the shadow price of capital, which
can be approximated by the higher costs of a regulation
passed on to consumers in the form of higher prices.
Lind (1990, p. S-24), however, argues that such
calculations are not necessarily clear and accurate. He
proposes that policymakers should be given information on
the annual costs and benefits over the lifetime of a
policy. In his opinion, this approach is not necessarily
less informative than the discounted version of the
benefits and costs.
Governmental agencies, in implementing discount
rate policy, seem to follow different paths. For
example, the Office of Management and Budget uses a 10%
real discount rate, the General Accounting Office uses
the average nominal yield on marketable Treasury debt,
and the Congressional Budget Office uses a 2% real
discount rate. (Lyon, 1990, p. S-30-S-31) Additionally,
the Congressional Budget Office suggests doing
sensitivity analysis of plus and minus two percentage
points around their "official" discount rate of 2%; i.e.
analyzing rates of from 0% to 4%.(Hartman, 1990, p. S-4)
Consequently, attempting to emulate governmental discount
rate policy could lead to choosing a discount rate
anywhere from zero to twelve percent.


18
In order to avoid the confusion over the
discount rate issue, this paper will first employ Lind's
suggestion of simply comparing undiscounted benefits and
costs on a year-by-year basis. Following that, the
present value of the benefits and costs will be
calculated using a discount rate of 6%, and doing a
sensitivity analysis of plus and minus 6 percentage
points. If the Clean Air Act Amendments pass all of
these tests, it is reasonable to assume that
implementation would enhance economic efficiency.
Yet another problem with benefit-cost analysis
is the consideration of distribution. Theoretically, a
net present value greater than zero means that the
proposed economic change represents a potential Pareto
improvement. With such a result, the gainers from the
economic change could compensate the losers and everyone
would be better off. However, such compensation rarely
occurs and would be difficult to administer if it were to
occur. Consequently, distribution considerations are
rarely included in a benefit-cost analysis and will not
be included here.
The Benefits
In order to estimate the benefits to society of
the Clean Air Act Amendments, one must have a good idea


19
of society's demand for clean air. Unfortunately, no
market exists for clean air. Hence, there are no
observable market prices, which are assumed to reflect
social values, to use in deriving the demand function.
Economists have developed several techniques to
help overcome the problem of estimating demand for public
goods. Prominent among these are the hedonic pricing
technique, contingent valuation, voting models, and
experimental studies. The technique employed in this
paper is hedonic pricing.
Hedonic Price Theory
A hedonic price is the imputed price of a good.
Hedonic prices are derived through other observable
market prices. Once the hedonic price of a good is
determined, it can be used in conjunction with the
observed market quantities of that good to derive the
price elasticity of demand for the good, from which the
demand function can be derived. Once we have obtained
the demand function we can derive the benefits of an
economic change by calculating the change in consumer's
surplus. All of this will be carried out below, but
first we must discuss the theoretical background of the
hedonic pricing technique.


20
Hedonic pricing takes its theoretical foundation
from the insights on consumer theory of Kevin Lancaster
(1966, 1971). In his seminal works, Lancaster proposed
that goods and services can be viewed as differentiated
products possessing bundles of attributes. It is these
attributes which consumers respond to when purchasing a
good. Consumers, for example, purchase food for the
calories, nutrition, and taste, among other things, that
it possesses. This approach changes the basic arguments
of traditional consumer theory. Instead of utility being
a function of products, utility becomes a function of the
attributes of these products. Therefore, according to
this approach, consumer behavior in the market is a
process of utility-maximizing choices in terms of bundles
of attributes. Products are distinguished by their
combinations of attributes, and the demand for products
is derived from the demand for the attributes they
possess.
Methodologically, demand functions for
attributes are difficult to derive, because the
observable transactions take place among the buyers and
sellers of products, not their attributes. The hedonic
pricing technique, first formalized by Sherwin Rosen
(1974), is a method which allows one to derive hedonic or


21
implicit prices of the attributes of products, from which
the demand functions for these attributes can be derived.
The hedonic price of an attribute is the
equilibrium imputed price of the attribute. For example,
take two homes with identical characteristics, except
that one home has air conditioning and the other does
not. The observable difference between the property
values of the two homes, which should be explained by the
possession of air conditioning in one of the homes, is
the hedonic price of air conditioning, assuming that the
respective housing markets are in equilibrium.
Hedonic prices are derived by regressing the
price of the differentiated product against the
observable quantities of the attributes of the product
and other significant variables. The resulting
coefficient estimates are the hedonic price estimates of
the respective regressors (i.e., the corresponding
attribute). (Freeman,1979) For example, let X represent
a differentiated product, Cj represent the jth
characteristic of X and Y represent the vector of other
significant variables. Then for any X,
P=P(Ct,C2.....Cn, Y) (3)
where P, the price of X, is a function of the
characteristics of X and other significant variables.


22
Moreover, if variations in P can be explained by the
variations in the attributes and the other significant
variables, then the hedonic price of an attribute can be
found by differentiating P with respect to that
characteristic:
dP/ dCj=HPj (4)
where HPj is the hedonic price of the jth characteristic.
This gives the increase in expenditure on X that is
required to obtain a unit of X with one more unit of Cj,
ceteris paribus. (Freeman, 1979)
Assuming that the differentiated products market
is in equilibrium, the hedonic price is the equilibrium
price of the characteristic. The hedonic price, however,
is simultaneously determined by bids for the
characteristic by consumers of the product and the offer
prices for the characteristic by sellers of the product.
Consequently, equation (4) becomes;5
ap/ac Wij=B0+B1C1+B2I1+B3D0+eij (5)
for the household marginal bid function, and
5 The following equations are linear versions of
Rosen's (1974) model provided by Timothy Bartik (1987a).
Some of the variable names have been changed to maintain
the previous variable usage in this paper.


23
dP/BC^G^A^C^S^u^ (6)
for the firms marginal offer price function,
where: P is the price of the differentiated product,
the partial of P with respect to Cj is the
hedonic (equilibrium) price of the jth
characteristic of the differentiated product,
Wy is household i's marginal bid for the
characteristic Cj,
Gy is firm i's marginal offer price for the
characteristic Cj,
C; is the vector of product i's characteristics
(including Cj) ,
I; is household i's expenditures on items other
than the characteristics Cu
Do; is a vector of demander traits affecting W^,
Sq; is a vector of supplier traits affecting G:i.
Therefore, the determination of the hedonic price becomes
similar to the determination of any other price.
Consequently, in order to derive the demand function, we
must first address the identification problem inherent in
any attempt to derive a demand function from observable
market prices.
The identification problem occurs when the
demand and supply functions are simultaneously


24
determined. In most cases, observable market prices and
quantities reflect the interaction of decision making by
the buyers and sellers of products. If one has no other
way of knowing, it is difficult to identify whether
movements in prices and quantities reflect changes in the
decisions of buyers, sellers, or both. In this case, our
model is said to be identified if consistent parameters
can be estimated for equations (5) and (6). (Pindyck and
Rubinfeld, 1981)
Myrick Freeman (1979) has pointed out four cases
in which the parameters for the bid function can be
consistently estimated, and therefore allow for the
identification of a demand function. First, if all
consumers are assumed to have identical utility functions
and incomes and all consumers are in equilibrium, then
equation (5) represents the inverse demand function for
Cj, because all consumers have identical demand curves.
The estimated HPj equals Wy, which is a point on each
consumers' inverse demand curve. Since all consumers
have the same inverse demand curve, all observations of
HPj lie on that demand curve.
A second case pointed out by Freeman obtains
when the supply of the differentiated product is
perfectly elastic at the observed prices. Under this


25
assumption, equation (3) (the hedonic price function) is
exogenous to the consumer, which allows for
identification of the bid function. Under these
conditions, an ordinary demand curve can be derived by
estimating the hedonic price function to obtain HPj and
then regressing the observed quantities of Cj against HPj,
income, and other significant variables. The resulting
coefficient estimates should be the respective elasticity
measures (assuming a nonlinear relationship between the
dependent variables and the independent variables exists,
which justifies using the log-linear functional form).
A third case pointed out by Freeman occurs when
the available quantity of the differentiated product is
fixed. This implies that consumers will be bidding with
one another to obtain the product with the desired bundle
of attributes. In this case, in equation (6) (the
suppliers offer price function) is fixed and therefore
exogenous to the consumer. Consequently, a regression of
HPj against Cj, income, and other significant variables
will identify an inverse demand function for Cj.
Finally, Freeman pointed out the case advocated
by Rosen (1974), where equations (5) and (6) are
simultaneously determined. Rosen argued that
exogenously shifts the supplier's marginal offer price


26
function, which allows for the identification of the
household's marginal bid function, which in turn becomes
the inverse demand function.
Once a demand function has been obtained, the
benefits (losses) of changes in Cj can be derived by
integrating the demand function with respect to the
changes in Cj. This provides an estimate of the benefits
(losses) to society of the changes. It should be noted,
however, that Robert Willig (1976) has warned that this
procedure is only applicable as long as the expenditures
on the characteristic are relatively low, and the income
elasticity of demand for the characteristic is also
relatively low.
Many economists have employed either Rosen's or
Freeman's approach to estimate the demand for the
attributes of housing. For example, David Harrison and
Daniel Rubinfeld (1978) implemented Freeman's third case
and assumed that the supply of housing characteristics
was fixed (and thus perfectly inelastic), in an attempt
to estimate the demand for clean air in Boston. Another
instance of this approach is the attempt by Bruce Bender,
Timothy Gronberg, and Hae-Shin Hwang (1980) to estimate
the demand for clean air in Chicago. An example of
Rosen's simultaneous determination of the household


27
marginal bid function and the firm's marginal offer price
function is Ann Witte, Howard Sumka and Homer Ereksons's
(1979) attempt to estimate the supply and demand
parameters for housing characteristics in North Carolina.
Rosen's approach is also followed by Jon Nelson (1978) in
his attempt to estimate the demand for air quality in
Washington D.C.
Raymond Palmquist (1984), on the other hand,
suggested another tack, one which is something of a
hybridization of Freeman's second case. In attempting to
estimate the demand for housing characteristics in
several markets, Palmquist assumed that each consumer is
a price-schedule taker, thereby having no influence on
market prices. In this way, the supply of
characteristics, C;, is important in determining the
hedonic prices, but is exogenous to a given consumer.
This allowed Palmquist to identify an ordinary demand
curve for Cj.
Palmquist also suggested that there is an
endogeneity problem in using the hedonic price estimates
to derive the demand function, as suggested by Freeman in
his second case. In Freeman's second case, the price of
a differentiated product is regressed against the
observed quantities of the characteristics it possesses.


28
The resulting coefficient estimates are the hedonic
prices of their respective characteristics. These
characteristics are regressed against the hedonic price
estimates to derive the respective elasticities.
Palmquist maintains that using the coefficient estimates
derived in the first step as independent variables in the
second step presents an endogeneity problem.
To overcome this problem, Palmquist suggests
using hedonic price estimates from several cities as the
independent variables in the second stage. For example,
in his study he estimated a hedonic price regression for
seven cities, resulting in seven different hedonic prices
for each independent variable. He then pooled a random
sample of the data from the seven cities. From this data
set, he regressed observed quantities of characteristics
against the estimated hedonic prices from the first
stage. The difference in Palmquist's approach lies in
the fact that he used a different hedonic price estimate
for each observed quantity of a characteristic, depending
on the area in which the characteristic was observed.
Bartik (1987a, 1987b), Robert Ohsfeldt and
Barton Smith (1988), Dennis Epple (1987) and George
Parsons (1988) have reaffirmed Palmquist's suggested use
of multi-market data to overcome the endogeneity problem
in Freeman's second case. However, Bartik (1987a, 1987b)


29
identified another endogeneity problem with estimating
hedonic prices.
Bartik observed that there is an endogeneity
problem with Rosen's approach. Rosen suggested that
supplier traits would exogenously shift the firm's price
function, thereby allowing the bid function to be
identified. Bartik argues that this will lead to biased
results because supplier traits are correlated with the
error term in the household's bid function. To see this,
imagine the error term divided into an unobserved tastes
component, Dui, and a purely random component, R^ (which
might consist of errors in measuring the marginal price
or household optimization errors). Equation (5) then
becomes,
^ij=Bo+B1Ci+B2Ei+B;iD0:i+Dui+Rij (7)
Bartik claims that household i's expenditures on
items other than characteristic j, E;, and the household
choice of product j's characteristics, C;, are correlated
with the unobserved tastes term, Dui. For example, a
household with a significantly large unobserved taste for
a characteristic will choose greater quantities of the
characteristic. Likewise, a significantly large
unobserved taste for any other good will lead to a
greater expenditure on that good. Furthermore, supplier


30
traits, Sq;, are correlated with product characteristics.
For example, wealthier home owners may offer bigger homes
for sale. Consequently, the correlation between supplier
traits and product characteristics, the latter of which
are in turn correlated with the error term in the
household bid function, results in supplier traits being
correlated with the error term in the household bid
function. Bartik maintains that this results in biased
parameter estimates.
To overcome this problem, Bartik suggests that
any variable that exogenously shifts the household budget
constraint will correct for endogeneity, because the
budget constraint is uncorrelated with the unobserved
tastes component of the error term. Moreover, he
suggests that the budget constraint will be exogenously
shifted by changes in income. This is really a self-
correcting problem; since income is already contained in
the bid function, it is equal to the expenditures on C;
plus the expenditures on everything else, E;.
Additionally, Bartik suggests that using multi-market
data or time-series data should overcome the endogeneity
problem, as long as one assumes that while the hedonic
price function varies across cities and time, unobserved
tastes do not.


31
To summarize the literature surrounding the use
of the hedonic pricing technique to estimate a demand
function for air quality, it seems that the technique is
effective as long as one deals with the identification
and endogeneity problems appropriately. Several
solutions to the identification problem have been
proposed. However, most of these solutions do not take
the endogeneity problem, as identified by Palmquist and
Bartik, into consideration. Therefore, it seems that the
most appropriate approach to follow is Palmquist's and
Bartik's suggestionestimating separate hedonic price
functions for several cities and then pooling those
estimates with their respective characteristic
observations to derive the demand function for that
characteristic.
The Model
As previously mentioned, the purpose of this
paper is to evaluate the effect of the Clean Air Act
Amendments on economic efficiency. The method employed
in this evaluation is benefit-cost analysis. In order to
estimate accurately the benefits of the Amendments, we
need to have a clear picture of society's demand for
clean air, as well as an understanding of the benefits of
the Amendments themselves. For the reasons given above,


32
the approach followed in this paper is the hedonic
pricing technique.
Again, the hedonic pricing technique was
developed to estimate the implicit prices of, and demand
functions for, the attributes of differentiated products.
Since air quality is an attribute of housing, the
technique can be applied to estimate the implicit price
of, and, the demand function for, air quality by
analyzing the housing market.
The hedonic price of air quality is determined
by regressing a vector of property values against a
vector of the attributes of housing and homeowner traits.
The resulting coefficient estimates are the hedonic
prices of their respective attributes.
Following the estimation of the hedonic prices
of the attributes of housing, of which air quality is
one, the demand functions for those attributes can be
derived. However, as noted above, Rosen (1974) argues
that there is an identification problem inherent in
estimating the demand functions for the attributes of
housing by using the hedonic price estimates. Along
these lines, Freeman (1979) has pointed out four cases in
which the identification problem can practically be
solved (see previous section).


33
This paper will follow Freeman's third case,
where it is assumed that the supply of characteristics is
fixed at any point in time. Consequently, the firm's
marginal offer price function is perfectly inelastic.
This allows for the identification of the household's
marginal bid function for any attribute of housing, which
in turn is the household's inverse demand function for
that attribute.
As also noted above, Palmquist (1984) and Bartik
(1987a, 1987b) have pointed out that there is an
endogeneity problem involved in the estimation of demand
functions for the attributes of housing using hedonic
price estimates. They argue that hedonic prices should
be estimated for multiple markets. Then, the vector of
the log of the hedonic price estimates for an attribute
should be regressed against the vector of the log of
household demand variables for that attribute to derive
the inverse demand function for the attribute. In this
way, the exogenous variation of hedonic prices across
space (i.e. across different cities) is sufficient to
overcome the endogeneity problem.
To summarize, assuming that housing markets are
in equilibrium, variations in housing values can be
explained by variations in the attributes that the houses
possess. Thus, a regression of housing values against


34
those attributes results in coefficient estimates which
represent the marginal amount the mean household would be
willing to pay (accept) to have a home with an
incremental increase in the respective attribute.
Therefore, the coefficient estimates are imputed
equilibrium marginal prices of housing attributes, also
known as implicit or hedonic prices. Mathematically,
HVij-f (Cij, C2j, . Cnji C-iji C2^r ... Cnj) (8)
where: HVy is the ith home value in city j,
Cy is the ith attribute of the ith home in the
jth city, and
c;j is the ith attribute of the buyer of the ith
home in city j .
Specifying a linear econometric equation,
ifVv,-=a/,,-+a1 C. +a, C, +.
-u
oj
+aniCi+b. c. +b7 c, +
nj nj lj 2j
+^nj Cnj
(9)
where: a;j is the hedonic price of C; in city j, and
by is the hedonic price of Cj in city j .
The ay.s and by's are simultaneously determined
in the market by the bids and offers of the buyers and
sellers of homes in each city. However, since we are
assuming that the supply function is perfectly inelastic,
we can estimate the household's bid function for each
attribute by regressing the hedonic price of an attribute


35
against the quantity consumed of the attribute, income,
and the quantity consumed of other attributes.
Furthermore, if we assume that a non-linear relationship
exists between the hedonic price and the independent
variables, we can specify a log-linear functional form to
estimate this relationship:
1na =Ins^+lnCi:/+p2 ci;f+g31 d)
where: My is household i's income in city j, and
g; is the elasticity of willingness to pay with
respect to changes in C;, c;, or Mj.
Following this, the inverse demand function for
a; can be derived by taking the antilog of both sides of
equation (10) and assuming that the elasticity estimates
are constant,
^i9q^ i
(ID
where is the mean household's willingness to pay
(accept) for an incremental increase in attribute i.
Finally, given an estimate of equation (11) for
air quality,
aAO=g0AQ ^C^c/m/3 (12)
the benefits to society of changes in air quality can be
estimated by integrating the right hand side of equation


36
12 with respect to changes in air quality (dAQ),
AO0
aA0= f 9Qcl'c?2M?3AQ g&0dAQ (13)
AQX
where: AQ0 is the original air quality, and
AQX is the new air quality.
The resulting estimate for aAQ is the mean household's
willingness to pay for improvements in air quality. The
benefits to society of changes in air quality are
determined by simply multiplying the number of households
by the mean household's willingness to pay for those
changes (aAQ) .
The Data
In order to arrive at the most accurate
estimates of the benefits of the Clean Air Act
Amendments, the following data should be obtained:
1) a random sample of the recent selling prices
of homes in many different cities,
2) a corresponding sample of the attributes of
those homes and their buyers,
3) a corresponding sample of the air quality
surrounding those homes, and


37
4) estimates of the projected amount of annual
reductions of each pollutant due to the Clean
Air Act Amendments.
Unfortunately, such data are not readily available.
Therefore, this paper has had to rely upon somewhat less
than ideal data.
The best data available for air quality are
contained in a report by the EPA on the concentration
levels of six different pollutants (lead, ozone, CO, C02,
N02, TSP) for selected counties of the US. (U.S.E.P.A.,
1988) However, only 49 observations are available for
the four pollutants (lead, ozone, C02, N02) being
considered under the Clean Air Act Amendments. However,
707 observations are available for the concentration
levels of total suspended particulates (TSP). Therefore,
in order to use a sufficient number of observations for
the analysis which follows, it is necessary to assume
that measurements of the annual arithmetic mean
concentration levels of TSP in a county act as a proxy
for the air quality of the county.6 Inasmuch as this is
6 Total suspended particulate (TSP) concentration
levels are often taken as a proxy for air quality (e.g.,
Palmquist 1984, and Graves, et al. 1988), because it is
a highly visible pollutant with significant variation
across an urban space. For these reasons households are
usually observed to respond to TSP. Additionally,
Graves, et al. argue that TSP is positively correlated


38
the best available data set for air quality, these 707
observations became the limiting factor for the
collection of the rest of the data.
For information on housing and household
characteristics, two data sets from the census bureau are
used. The City and County Data Book provided county-
based information on median housing values, crime rates,
local government expenditures, median income, educational
attainment, and minority concentration. (U.S. Dept, of
Commerce, 1988) The Detailed Housing Characteristics
volumes of the 1980 Census of Housing provided
information on the percentage of new homes, homes with
air conditioning, homes with central heating, and homes
with three or more bedrooms. (U.S. Dept, of Commerce,
1983)
The important variables which were included in
Palmquist's paper, but not included in this paper due to
data constraints, include median lot size, median home
size, percentage of homes with swimming pools, percentage
of homes with full basements, and the median household's
distance to the Central Business District. The variables
included in this paper which were not included in
with S02 and N02, which provides further justification for
its use as a proxy for those pollutants.


39
Palmquist's paper are crime rate and local government
expenditures per capita.
The best available information on the annual
reductions of air pollutants due to the Clean Air Act
Amendments is Reilly's estimate of the reduction goals by
the year 2005. (Reilly,1989) Therefore, it was necessary
to estimate the annual percentage reductions of the
primary categories of the pollutants under consideration
by assuming that those reduction goals will be met
gradually, and more specifically, that each year's
reductions will be equal. Table 2 contains estimates of
the annual percentage reductions of emissions in the
primary categories of pollutants. Table 3 contains the
estimates for the cumulative percentage reductions of
emissions for those pollutants.
The hedonic price estimates derived below rest
on several assumptions. The first concerns which
pollutants society is willing to pay to reduce. Data
limitations, detailed above, mandate that the only air
quality variable included in the following analysis is
the concentration level of TSP. The Clean Air Act
Amendments primarily target reductions in the emissions
of S02, NOx, VOCs and air toxics. Therefore, it is
necessary to assume that society's willingness to pay for


40
Table 2 Annual Estimated Reductions
Pollutant Proposed Annual Reductions Estimated (percent) Reductions (percent)
Air Toxics 82.5 by 2005 5.5
VOC's 57 by 2005 3.8
S02 50 by 2000 5
NOx 10 by 2000 1
Source: Reilly, 1989.


41
Table 3
% Reduced from Present Levels by Year1
Pollutant 91 92 93 94 95
Air Toxics 5.5 11 16.5 22 27.5
VOC's 3.8 7.6 11.4 15.2 19
S02 5 10 15 20 25
NOx 1 2 3 4 5
96 97 98 99 00
Air Toxics 33 38.5 44 49.5 55
VOC's 22.8 26.6 30.4 34.2 38
S02 30 35 40 45 45
N0X 6 7 8 9 10
01 02 03 04 05
Air Toxics 60.5 66 71.5 77 82.5
VOC's 41.8 45.6 49.4 53.2 57
S02 50 50 50 50 50
N0X 10 10 10 10 10
1. We assume here that the appropriate time analysis goes up to the point where Bush reductions. However, the benefits of clean certainly continue to exist past the year 2005 frame of proposes air will


42
a one percent reduction in the concentration level of TSP
is equal to its willingness to pay for a one percent
reduction in the concentration level of any pollutant.
Furthermore, since the willingness to pay estimates in
this paper are in terms of concentration levels, while
the pollution reduction estimates of the Amendments are
in terms of emission levels, it is necessary to assume
that a one percent reduction in emission levels leads to
a one percent reduction in concentration levels.7
Moreover, the selected data set has information
on the concentration levels of six pollutants (TSP,
carbon monoxide, ozone, lead, S02 and N02) while the
Clean Air Act Amendments target reductions in the
emissions of air toxics, VOC's, S02 and N0X. In order to
calculate projected annual concentration levels of air
toxics, VOC's, S02 and N0X, it will be necessary to assume
the following:
1) N02 concentration levels may act as a proxy
for N0X concentration levels;
2) ozone concentration levels may act as a
7 This assumption is not necessarily accurate,
because emissions reductions will occur in a different
space and time than the corresponding concentration
reductions. Also, different areas will experience
different degrees of concentration reductions, due to
different geophysical and atmospheric conditions.


43
proxy for VOC concentration levels (VOC's are
the precursors to ozone formation); and
3) lead concentration levels may act as a proxy
for air toxic concentration levels.
Given these assumptions and data on present
concentration levels, we can estimate the annual
concentration levels of all pollutants due to the changes
proposed by the Clean Air Act Amendments. Table 4
contains those estimates.
The Results
Table 5 contains a list and description of the
variables used in the hedonic price estimation. A
separate hedonic regression was run for each of the eight
regions of the country. Table 6 contains a list of the
states included in each region. Table 7 contains the
hedonic price estimates for the variables listed in Table
5.
The Rocky Mountain region is the only region of
the country that did not have a significant estimate for
the hedonic price of air quality. In fact, the Rocky
Mountain hedonic price estimate for air quality has the
wrong sign. This might be explained by the fact that
there is an excess supply of housing stock in that
region. Thus, the Rocky Mountain housing market may


44
Table 4
Annual Changes in Concentration Levels1
Pollutant 90 91 92 93 94 95
Air toxics .136 .129 .121 .114 .106 .099
VOC's .0547 .0526 0505 .0485 .0464 . 0443
so2 10.18 9.67 9.16 8.65 8.14 7.64
N0X .0239 .0237 0234 .0232 . 0229 . 0227
96 97 98 99 00
Air toxics . 091 .084 . 076 . 069 . 061
VOC's .0422 .0401 .0381 . 0360 . 0339
S02 7.13 6.62 6.12 5.60 5.09
NO, . 0225 . 0222 . 0221 . 0217 . 0215
01 02 03 04 05
Air Toxics . 054 . 046 . 039 .031 .024
VOC's . 0318 .0298 . 0277 . 0256 . 0235
S02 5.09 5.09 5.09 5.09 5.09
NO, . 0215 . 0215 .0215 . 0215 .0215
1. The present concentration levels were calculated by
estimating the mean concentration level for each
pollutant contained in the EPA report. (U.S.E.P.A. 1998)
Concentration levels for lead (air toxics), ozone (VOC's)
and N02 (NO,) are in terms of micrograms per cubic meter.
Concentration levels for S02 are in terms of parts per
million.


45
Table 5
Variable Definitions
Variable
MV
CRT
MI
LGE
ED
NW
AC
CH
BD
YR
AQ
HP
______________________Description______________
Median home value (occupied units).
Crime rate (serious crimes reported to the
police).
Median income.
Local government expenditures per capita.
Percent of population with 16 or more years of
education.
Percent of population which is non-white.
Percent of homes with air conditioning.
Percent of homes with central heating.
Percent of homes with three or more bedrooms (a
proxy for home size).
Percent of homes built between 1970 and 1980.
Air quality proxy: concentration level of total
suspended particulate (annual arithmetic mean).
The hedonic price of air quality.


46
Table 6
Region Definitions
Region 1 Region 2 Region 3 Region 4
Northwest Rockies N. Midwest Northeast
n=35 n=46 n=109 n=92
Alaska Colorado Illinois Connecticut
Idaho Montana Indiana Maine
Oregon New Mexico Iowa Mass.
Washington Wyoming Michigan Minnesota Wisconsin N.Hampshire New Jersey New York Pennsylvania R. Island Vermont
Region 5 Region 6 Region 7 Region 8
S. Central Southeast S. Midwest Southwest
n=66 n=102 n=56 n=45
Kentucky
Tennessee
West Virginia
Alabama
Florida
Georgia
Louisiana
Mississippi
North Carolina
South Carolina
Arkansas
Kansas
Missouri
Oklahoma
Texas
Arizona
California
Nevada


47
Table 7
Hedonic Price Estimates1,2
Variable R1 R2 R3 R4
Intercept 24614.10 (1.29) 9483.47 (0.96) -49482.64* (-3.90) 27132.25** (2.43)
CRT 173 6.81** (2.47) -16.78 (-0.03) -210.92 (-0.44) 1107.45** (2.54)
MI 1.68** (2.12) 1.97* (4.36) 1.21* (3.45) 3.69* (10.43)
LGE -8.56*** (-1.73) -2.85 (-0.97) 0.09 (0.20) -5.60* (-2.87)
ED 645.33** (2.16) 829.87* (6.32) 204.49** (2.26) 95.56 (1.60)
NW 796.90 (1.55) 148.38 (0.69) 6.06 (0.05) 99.88 (1.17)
AC 56.85 (0.96) 19.92 (0.43) -7.68 (-0.73) -23.77 (-0.47)
CH -209.91 (-1.46) 217.01** (2.20) 679.42* (3.75) -8.09 (-0.06)
BD -63.29 (-0.15) -791.95* (-3.27) -13.11 (-0.25) -666.50* (-6.76)
YR 558.36* (4.60) 391.96* (3.46) 515.69* (4.14) 149.49 (1.36)
AQ -245.48** (-2.59) 62.04 (1.46) -101.76** (-1.71) -235.64* (-2.91)


48
Table 7 fcont.)
Variable R5 R6 R7 R8
Intercept 10375.74** (2.31) 11510.45** (2.11) -21816.97* (-3.05) 6709.91 (0.40)
CRT -5.37 (-0.01) -61.51 (-0.22) -174.50 (-0.52) 339.30 (0.33)
MI 0.51** (2.14) 1.06* (4.36) -0.11 (-0.67) 3.69* (3.57)
LGE 1.47 (0.71) -0.35 (-0.86) 6.17* (1.78) 8.16 (1.28)
ED 934.51* (5.27) -8.78 (-0.27) 456.70* (2.93) 1060.46** (2.60)
NW -158.59 (-1.60) 43.53 (1.45) 69.14 (1.25) -122.82 (-1.08)
AC -4.60 (-0.13) 21.89 (0.79) 138.31*** (1.76) -151.67** (-2.30)
CH 190.54* (3.17) 254.80* (4.33) 262.58* (4.34) 234.58 (1.34)
BD 23.20* (3.45) -231.87* (-3.66) 220.32 (1.31) -603.77** (-2.16)
YR 68.95 (0.98) 199.71* (3.27) 459.88* (4.59) -35.85 (-0.31)
AQ -171.37* (-3.33) -81.00*** (-1.78) -140.56** (-2.15) -144.00** (-2.63)
1. The dependant variable is MV.
2. t-statistics are in parentheses.
* refers to significance at the one percent level.
** refers to significance at the five percent level.
*** refers to significance at the ten percent level.


49
still be approaching equilibrium. Therefore, the use of
housing values in that region will not lead to accurate
estimates of the value of the attributes of housing.
Additionally, there may be an insufficient number of
observations in the region to generate significant
coefficient estimates.
For the nation as a whole, several states
behaved as outliers. No matter how these states were
grouped, they reduced the significance of the results.
These states include Nebraska, North Dakota, South
Dakota, Hawaii, Ohio, Maryland, Delaware, Washington D.C.
and Virginia.
In spite of these problems, seven regions of the
country had hedonic price estimates for air quality which
were significant and possessed the correct sign. Of all
80 hedonic price estimates, 52 had the expected sign, and
of those, 28 were significant at the five percent level.
The variables which consistently possessed the expected
sign and were usually significant were median income,
educational attainment, percent of homes recently built,
and air quality. Of the hedonic price estimates for air
quality, five were significant at the five percent level
and two more were significant at the 10 percent level.
These results indicate that air pollution significantly
affects property values.


50
To reiterate, the correct interpretation of a
hedonic price is that, for an individual to have a home
with an incremental increase in an attribute, s/he would
have to pay the value of the corresponding coefficient in
dollars, ceteris paribus. The correct interpretation of
the air quality coefficient is that if the concentration
level of air pollution were to rise by one unit, then the
mean property value would fall by the value of the
coefficient, ceteris paribus. Alternatively, the
negative of the coefficient represents what the mean
household would be willing to pay for a home with an
incremental reduction in air pollution, ceteris paribus.
To estimate the inverse demand function
(equation 11) the log of the significant hedonic prices
(i.e. all of them except Region 2) for air quality from
the hedonic regression were regressed against the log of
their respective observations of median income, air
quality, educational attainment, ethnic composition, and
number of bedrooms. The resulting coefficient estimates
are the elasticities of the mean household's willingness
to pay with respect to changes in the respective
variables. Table 8 contains these results. 8
8 Actually, regressions were run with various
combinations of variables. The regression results
discussed here seem to make the most intuitive sense.


51
Variable Table 8 Inverse Elasticitv Estimates1 t-statistic
Coefficient
Intercept 0.97 1.01
LMI 0.23 2.43
LED 0.14 2.88
LNW CTl O o -6.12
LBD 0.10 1.38
LAQ 0.29 3.98
1. The dependant variable is LHP. An L before a defined
variable indicates that that variable has been logged.


52
The correct interpretation of the coefficient
estimates in Table 8 is as follows:
1) the coefficient estimate for LMI indicates
that a one percent increase (decrease) in the
median income of a county leads to a 0.23
percent increase (decrease) in the county's
willingness to pay for air pollution
reductions, this can also be interpreted as the
inverse of the income elasticity of demand;
2) the coefficient estimate for LED indicates
that a one percent increase (decrease) in the
percentage of people in a county who have
obtained 16 or more years of education leads to
a 0.14 percent increase (decrease) in the
county's willingness to pay for air pollution
reductions;
3) the coefficient estimate for LNW indicates
that a one percent increase (decrease) in the
percentage of non-white people in a county
leads to a 0.09 percent decrease (increase) in
that county's willingness to pay for reductions
in air pollution,
4) the coefficient estimate for LBD indicates
that a one percent increase (decrease) in the
percentage of homes in a county with three or


53
more bedrooms leads to a 0.10 percent increase
(decrease) in that county's willingness to pay
for reductions in air pollution, and
5) the coefficient estimate for LAQ indicates
that a one percent increase (decrease) in the
concentration level of an air pollutant in a
county leads to a 0.29 percent increase
(decrease) in that county's willingness to pay
for air pollution reductions; this can also be
viewed as the inverse of the price elasticity
of demand.
In order to calculate the benefits of the Clean Air Act
Amendments, we need to estimate equation 13 for the
willingness to pay for improvements in air quality. The
elasticity estimates from Table 8 provide the g/s for
equation 13. Equation 13 then becomes,
AOq
aA0= f 2.64MI*1EDMIMJaBDMAQMdAQ (14)
aol
Next, we have to insert values for the variables in
equation 14. For this, we use the mean estimates from
the data set for each variable, as well as high and low
estimates for each variable. Table 9 contains these
estimates. For the mean variable estimates, equation 14
then becomes,


54
Table 9
Variable Estimates1
Variable Mean S.D. Hiah Low
MI 16104.15 3432.32 19536.47 12671.83
ED 14.65 8.29 22.94 6.36
NW 10.86 2.56 13.42 8.30
BD 52.71 26.72 79.43 25.99
1. The high estimates consist of the mean estimates plus
the standard deviation and the low estimates consist of
the mean estimates minus the standard deviation.


55
AO0
aAQ= f 2.64 (16104.2)'Z314.7'1410.9OS52.8 MAQMdAQ (15)
AOi
which reduces to,
AO0
aAQ= J43 .YlAQ^dAQ (16)
A(?!
Then, solving equation 16 for dAQ yields,
aAQ=22.l {AqI^-AQI**) . (17)
Then, by substituting the 1990 concentration level of a
pollutant from Table 4 for AQ0 and the concentration
level of that pollutant in 1991 for AQj, we can solve
equation 18 for the mean household's willingness to pay
for the reduction of that pollutant in the first year of
the legislation. By repeating this procedure for each
pollutant considered and summing the willingness to pay
estimates for each pollutant, we arrive at an estimate
for the mean household's willingness to pay for the first
year's reduction in air pollution due to the Clean Air
Act Amendments. Furthermore, by multiplying the number
of households in the U.S. (94,240,838) by the mean
household's willingness to pay, we can obtain an estimate
of society's willingness to pay for the first year's
reductions, which can also be interpreted as the benefits


56
of the Amendments.9 (U.S. Dept, of Commerce, 1989)
Likewise, the benefits to society from each year's
reductions in air pollution due to the Clean Air Act
Amendments can be calculated by substituting the
concentration level of each pollutant in each year for
AQj in equation 18, and repeating the procedure detailed
above. Table 10 contains the undiscounted annual
estimated benefits of the Amendments, as calculated in
the preceding manner. Table 10 also contains high and
low estimates of the benefits of the Amendments. These
are calculated by plugging the high and low variable
estimates from Table 9 into the variables in equation
(16), and then calculating the benefits in the same way
as the mean estimates.
The Costs
Unfortunately, specific data regarding the
annual costs of the legislation are not readily
available. However, William Reilly (1989, p78) has
estimated that the costs of the Amendments to society
will average $15 billion per year. It is difficult to
determine whether the costs
9 Here we assume that the number of household's does
not change. This is an unlikely scenario and this
assumption might tend to bias the estimates downward.


Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
57
Table 10
Estimated Annual Benefits ($10sl Low
Hicrh Mean
6574.1 5838.9 4703.2
13162.5 11690.5 13923.1
19499.8 17296.5 13923.1
25886.1 22971.9 18496.7
31970.2 28387.4 22848.5
38082.2 33820.6 27245.5
44121.3 39163.3 31545.6
49835.9 44205.9 35636.0
55720.7 49485.7 39840.3
61292.0 54437.9 43830.3
62953.5 55886.1 45001.7
64492.5 57279.2 46114.7
66047.2 58661.3 47233.1
67608.7 60035.9 48340.6
69069.3 61339.7 49387.0


58
will be bunched in the early years, bunched in the later
years or spread out evenly. Therefore, for a first
approximation, it is necessary to assume that the
estimated annual costs are $15 billion. Following that,
it is assumed that the costs increase gradually. Table
11 contains the annual cost estimates. It is difficult
to ascertain the effect these assumptions will have on
the benefit-cost analysis, because reliable estimates of
the annual costs are not readily available.
Benefit-Cost Comparison
Table 12 contains the discounted present values
of the benefits of the legislation for various discount
rates. Table 13 contains the discounted present values
of the costs of the legislation for the same discount
rates. Table 14 lists the net present values of the
benefits (the discounted benefits minus the discounted
costs) of the legislation, under the average cost
scenario, at the various discount rates. Lastly, Table
15 contains the net present values of the benefits of the
legislation, under the gradual cost scenario, for the
various rates. The net present values under the average
cost scenario indicate that the Clean Air Act Amendments


Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
59
Table 11
Estimated Annual Costs ($106)
Averacre Gradual
15000 1875
15000 3750
15000 5625
15000 7500
15000 9375
15000 11250
15000 13125
15000 15000
15000 16875
15000 18750
15000 20625
15000 22500
15000 24375
15000 26250
15000 28125


60
Table 12
Discounted Present Values of the Benefits f$106)
Discount Rate (%) High Mean Low
0 676316.1 600500.8 483562.4
1 613121.8 544387.0 438377.3
2 557107.1 494648.6 398325.9
3 507350.9 450467.8 362749.5
4 463061.7 411141.5 331082.1
5 423557.4 376064.2 302836.0
6 388249.7 344713.3 277590.6
7 356629.5 316636.9 254981.9
8 328256.2 291443.6 234694.7
9 302746.8 268793.3 216455.4
10 279768.5 248390.6 200025.8
11 259031.3 229978.0 185198.7
12 240282.1 213330.5 171792.9


0
1
2
3
4
5
6
7
8
9
10
11
12
61
Table 13
Discounted Present Values of Costs
Average
225000.000
207975.788
192738.953
179069.026
166775.811
155694.871
145683.735
136618.710
128392.180
120910.326
114091.193
107863.044
102162.967
($106)
Gradual
225000.000
203148.900
183846.300
166758.900
151601.000
138129.900
126125.200
115413.600
105834.600
97251.600
89546.370
82615.900
76370.690


0
1
2
3
4
5
6
7
8
9
10
11
12
62
Table 14
Net Present Values
Average Costs
($106)
High Mean Low
451316.1 375500.8 258562.4
405146.0 336411.2 230401.5
364368.2 301909.7 205586.9
328281.9 271398.8 183680.5
296285.9 244365.7 164306.3
267862.5 220369.3 147141.1
242566.0 199029.6 131906.9
220010.8 180018.2 118363.2
199864.0 163051.4 106302.5
181836.5 257883.0 95545.1
165677.3 134299.4 85934.6
151168.3 122115.0 77335.7
138119.2 111167.6 69630.0


0
1
2
3
4
5
6
7
8
9
10
11
12
63
Table 15
Net Present Values
Gradual Costs
($106)
Hicrh Mean Low
451316.1 375500.8 258562.4
409972.9 341238.1 235228.4
373260.8 310802.3 214479.6
340592.0 283708.9 195990.6
311460.7 259540.5 179481.1
285427.5 237934.3 164706.1
262124.5 218588.1 151465.4
241215.9 201223.3 139568.3
222421.6 185609.0 128860.1
205495.2 171541.7 119203.8
190222.1 158844.2 110479.4
176415.4 147362.1 102582.8
163911.4 136959.8 95422.2


64
will lead to an improvement in economic efficiency under
any benefits scenario. The same results hold for the net
present values under the gradual costs scenario.


CHAPTER IV
CONCLUSIONS
Several assumptions were indispensable in the
effort to arrive at estimates of the benefits and costs
of the Clean Air Act Amendments. As is often the case,
some of these assumptions somewhat distort the reality
which the subsequent analysis seeks to portray.
Perhaps the most problematic assumption is that
the sum of all households7 willingness to pay for
reductions in air pollution approximates society's
willingness to pay for those reductions. It is quite
unlikely that households take all of the damages of air
pollution into consideration when purchasing a home. The
most unreasonable expectation is that they take the
damages to firms and governments or the damages to
ecological systems into consideration. Obviously, it is
unlikely that households are completely aware of the
extent of air pollution in the area of the home they are
buying, or the extent of the damage that may be caused by
that pollution. Therefore, the assumption that
households' willingness to pay equals society's


66
willingness to pay leads to downwardly biased net present
value estimates.
Other problems arise from the assumption that
the concentration level of total suspended particulate
acts as a proxy for the air quality of an area; this is
the basis of the contention that the elasticity estimate
of willingness to pay for reductions in the concentration
levels of TSP reflects the elasticity of willingness to
pay for reductions in the concentration levels of any
pollutant. The difficulty with these assumptions is that
TSP is only one of myriad air pollutants. The effects of
particulate pollution on society differ substantially
from the effects of other pollutants. Particulate
pollution is generally associated with problems of
visibility, soot deposition, eye irritation, etc.
However, many other pollutants have even more of an
impact on public health. Consequently, the use of TSP
concentrations as a proxy for overall air quality may not
reflect the actual situation in terms of extent or
severity. Hence, the TSP elasticity estimate may not be
a good proxy for the elasticities of willingness to pay
for reductions in the concentration levels of all air
pollutants. However, it is difficult to determine the
precise quantitative effect of these assumptions on the
net present value estimates computed above.


68
It is likely that the conservative approach
taken herein to estimating average annual costs
downwardly biases the net present value estimates
associated with those costs. Therefore, it is reasonable
to expect that estimated gradual annual costs come closer
to approximating reality than estimated average annual
costs.
Overall, it is difficult to ascertain how
accurate the above benefit-cost evaluations are.
However, it seems that the assumptions made in this paper
would tend to downwardly bias the benefits estimates.
This suggests that the high benefits estimates are
probably more accurate than the mean and low estimates.
Therefore, taking the high benefits estimates and the
average annual cost estimates as closer representations
of reality, the economic changes caused by the Clean Air
Act Amendments lead to a substantial improvement in
economic efficiency. Under this scenario, if the
President and Congress were to make a decision on the
Amendments based on economic efficiency, Congress would
pass the legislation (because the CBO uses a two percent
discount rate) and the President would pass the
legislation (because the OMB uses a ten percent discount
rate).


69
However, if reality is more closely approximated
by the high benefits estimates and the gradual costs
estimates, as is argued in this paper, then the economic
changes caused by the Clean Air Act Amendments lead to an
even greater improvement in economic efficiency.
In conclusion, given the assumptions made in
this paper, it seems likely that the economic changes
brought about by the Clean Air Act Amendments would lead
to an improvement in economic efficiency. However, a
more accurate picture of society's valuation of these
changes may be drawn by the use of better data and
additional techniques. For example, the employment of
the contingent valuation technique would enable us to
capture society's valuation of the reduction in damages
to ecological systems. Likewise, an estimate of the
avoided costs to commercial, agricultural and
governmental entities due to the reductions in air
pollution brought about by the Amendments would also
provide a more complete picture of society's willingness
to pay for such changes. It is likely that the use of
additional techniques will only serve to bolster the
results detailed above: reductions effected by the
Amendments will result in an improvement in economic
efficiency.


70
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