United States Office of Air Quality EPA-450/5-83-001b
Environmental Protection Planning and Standards August 1982
Agency Research Triangle Park NC 27711
Air
>EPA Benefit Analysis
of Alternative
Secondary
National Ambient
Air Quality
Standards
for Sulfur Dioxide
and Total
Suspended
Particulates
Volume II
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FINAL ANALYSIS
BENEFITS ANALYSIS OF ALTERNATIVE SECONDARY
NATIONAL AMBIENT AIR QUALITY STANDARDS FOR
SULFUR DIOXIDE AND TOTAL SUSPENDED PARTICULATES
VOLUME II
BENEFITS ANALYSIS PROGRAM
ECONOMIC ANALYSIS BRANCH
STRATEGIES AND AIR STANDARDS DIVISION
OFFICE OF AIR QUALITY PLANNING AND STANDARDS
U«S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK
NORTH CAROLINA 27711
r „,•„,,._,.... .1 p;0tGCt!on Agency]
' .s
AUGUST 1982
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FINAL ANALYSIS
BENEFITS ANALYSIS OF ALTERNATIVE SECONDARY
NATIONAL AMBIENT AIR QUALITY STANDARDS FOR
SULFUR DIOXIDE AND TOTAL SUSPENDED PARTICULATES
By:
Ernest H. Manuel, Jr.
Robert L. Horst, Jr.
Kathleen M. Brennan
William N. Lanen
Marcus C. Duff
Judith K. Tapiero
With the Assistance of:
Richard M. Adams
David S. Brookshire
Thomas D. Crocker
Ralph C. d'Arge
A. Myrick Freeman, III
Shelby D. Gerking
Edwin S. Mills
William D. Schulze
MATHTECH, Inc.
P.O. Box 2392
Princeton, New Jersey 08540
EPA Contract Number 68-02-3392
Project Officer:
Allen C. Basala
Economic Analysis Branch
Strategies and Air Standards Division
Office of Air Quality Planning and Standards
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
August 1982
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PREFACE
This report was prepared for the U.S. Environmental Protection
Agency by MATHTECH, Inc. The report is organized into six volumes
containing a total of 14 sections as follows:
Volume I
Section 1:
Section 2:
Section 3:
Volume II
Section 4:
Section 5:
Section 6:
Volume III
Section 7:
Section 8:
Volume IV
Section 9:
Volume V
Section 10:
Section 11:
Volume VI
Section 12:
Section 13:
Section 14:
Executive Summary
Theory, Methods and Organization
Air Quality and Meteorological Data
Household Sector
Residential Property Market
Labor Services Market
Manufacturing Sector
Electric Utility Sector
Agricultural Sector
Extrapolations
Bibliography
Summary of the Public Meeting
Analysis of Pollutant Correlations
Summary of Manufacturing Sector Review
The analysis and conclusions presented in this report are those
of the authors and should not be interpreted as necessarily reflecting
the official policies of the U.S. Environmental Protection Agency.
11
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ACKNOWLEDGMENTS
This report and the underlying analyses profited considerably
from the efforts of Allen Basala, who served as EPA Project Officer,
and V. Kerry Smith, who served as a reviewer for EPA. Allen provided
the initiative and on-going support to conduct an applied benefits
analysis. Kerry's technical insights and suggestions are reflected in
nearly every section of the report.
James Bain and Tom Walton of EPA, and Jan Laarman and Ray
Palmquist, who served as reviewers for EPA, also contributed
substantially to individual report sections through their advice and
comments during the course of the project. Also providing helpful
comments and assistance were Don Gillette, Fred Haynie, Neil Frank and
Larry Zaragosa, all with EPA.
Several other members of the Mathtech staff contributed to the
project during various stages of the work. They included Robert J.
Anderson, Jr., Neil Swan, John Keith, Donald Wise, Yaw Ansu, Gary
Labovich, and Janet Stotsky.
The production of the report was ably managed by Carol Rossell,
whose patience remained intact through countless drafts and deadlines.
Carol was assisted by Sally Webb, Gail Gay, and Deborah Piantoni.
Finally, we extend our appreciation to the many dozens of
individuals, too numerous to list here, who provided advice,
suggestions, and data during the course of the project.
111
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CONTENTS
4. HOUSEHOLD SECTOR
Introduction 4-1
Overview 4-1
Objectives of the Study 4-5
Scope of Analysis 4-7
Summary of Benefits Estimates 4-17
Section Overview 4-19
Summary of Previous Benefits Studies 4-20
Physical Damage Function Studies 4-20
Indirect-Market Studies 4-26
Other Benefits Approaches 4-28
Overall Summary of Previous Air Quality
Benefits Studies 4-29
Model Development 4-30
Utility Maximization 4-34
Demand Functions 4-38
Overview of Service Flow Indices 4-43
Two-Stage Consumer Budgeting 4-46
Alternative Functional Forms 4-60
Inclusion of Environmental/Demographic (E/D)
Variables 4-61
Deviations From Assumptions of the Standard
Utility Maximization Model 4-65
Tests of Hypotheses 4-67
Summary of the Technical Model 4-68
Description of Data 4-69
Scope of Economic Data 4-69
Aggregation 4-77
Empirical Results 4-93
Framework for Empirical Analysis 4-94
Linear Expenditure System 4-99
Linear Logarithmic Expenditure System 4-134
IV
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CONTENTS (continued)
4. HOUSEHOLD SECTOR (continued)
Derivation of Aggregate Price Index 4-147
Estimation of Aggregate Stage Systems 4-154
Calculation of Benefits 4-157
Scenario for Benefits Calculation 4-157
Measures of Benefits 4-162
Economic Benefits of Air Quality Improvements .. 4-166
Summary of Household Sector 4-177
References , 4-180
5. RESIDENTIAL PROPERTY MARKET
Introduction 5-1
General Background 5-4
Methodology 5-7
Literature Review 5-20
Limitations of the Hedonic Technique 5-25
Benefit Estimates 5-32
Conclusion 5-50
References 5-52
Appendix 5-A: Calculation of Benefits 5-55
Appendix 5-B: SMSA Benefits 5-60
6. LABOR SERVICES MARKET
Summary 6-1
Methodology 6-3
Data 6-5
Specification 6-13
Empirical Results 6-14
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CONTENTS (continued)
6. LABOR SERVICES MARKET (continued)
Benefit Calculations 6-24
References 6-32
VI
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FIGURES
Number Page
4-1. Household decision process 4-31
4-2. The consumer's optimum 4-37
4-3. Demand curve 4-39
4-4. Welfare change from air quality improvement 4-45
4-5. Schematic of a "utility branch" 4-55
4-6. Schematic of data development 4-82
4-7. Consumers' surplus 4-162
4-8. Compensating variation 4-164
5-1. Implicit price schedule and bid functions 5-17
5-2. Marginal implicit price schedule and demand
price functions 5-19
5-3. Alternative benefit estimates for a given
change in air quality 5-38
6-1. Alternative benefits estimates for a given change
in air quality 6-25
VII
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TABLES
Number Page
4-1. SMSAs Included in the Analysis 4-16
4-2. Household Soiling and Materials Damage Benefit
Estimates 4-18
4-3. Household Materials Subject to Corrosion/Erosion .... 4-21
4-4. Household Soiling — Cleaning and Maintenance Tasks . 4-22
4-5. Standard Metropolitan Statistical Areas in
Bulletin 1992 4-71
4-6. Expenditure Categories in BLS Bulletin 1992 4-72
4-7. Hypothetical Expenditures on Good XX in Region 1 .... 4-86
4-8. Goods Used in Second Stage of Optimization Model .... 4-88
4-9. Statistical Profile of Expenditure Data — Annual
Household Expenditure by Good 4-89
4-10. Statistical Profile of Price Data 4-91
4-11. Commodities in Demand Systems of the Second Stage
of the Optimization Model 4-104
N
4-12. Glossary of Variable Names 4-105
4-13. LES Food Demand System 4-109
4-14. Own-Price Elasticities of Demand for Food Demand
Category 4-110
4-15. Elasticities of Environmental Variables in the
Shelter Demand System 4-114
4-16. LES Shelter Demand System 4-118
4-17. LES Home Operations Demand System 4-121
4-18. LES Furnishings Demand System 4-124
vui
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TABLES (continued)
Number Page
4-19. LES Clothing Demand System 4-126
4-20. LES Transportation Demand System 4-130
4-21. LES Personal Care Demand System 4-132
4-22. HTL Food Demand System 4-138
4-23. HTL Shelter Demand System 4-139
4-24. HTL Home Operations Demand System 4-140
4-25. HTL Furnishings Demand System 4-141
4-26. HTL Clothing Demand System 4-142
4-27. HTL Transportation Demand System 4-143
4-28. HTL Personal Care Demand System 4-144
4-29. Own-Price Elasticities of Demand 4-145
4-30. Elasticities Between Demand and the Pollution
Variables 4-146
4-31. LES Aggregate Demand System 4-155
4-32. Own-Price Elasticities of Demand for Aggregate
LES System 4-156
4-33. National Ambient Air Quality Standards 4-160
4-34. Household Soiling and Materials Damage Benefit
Estimates 4-167
4-35. Comparison of the Benefits in the Household
Expenditure Model and the Property Value Model in
24 SMSAs 4-171
4-36. Comparison of the Per-Household Benefits of
Attaining the Secondary Standard for TSP 4-172
4-37. Comparison Between SRI Benefit Numbers and the
Present Study 4-175
4-38. Range of Household Sector Benefits for S09 4-178
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TABLES (continued)
Number Page
4-39. Range of Household Sector Benefits for TSP 4-178
5-1. Comparison of the Benefits from Attaining
Alternative Secondary Standards in 24 SMSAs 5-3
5-2. Review of Property Value Studies 5-26
5-3. SMSAs Included in Property Value Study 5-44
5-4. Estimated Benefits of the Reduction in Total
Suspended Particulate Matter to Alternative
Secondary Standards 5-47
5-5. Estimated Benefits of the Reduction in Sulfur
Dioxide to Alternative Secondary Standards 5-47
5-6. Estimated Benefits of the Reduction in Total
Suspended Particulate Matter to Alternative
Secondary Standards 5-48
5-7. Estimated Benefits of the Reduction in Sulfur
Dioxide to Alternative Secondary Standards 5-48
6-1. Comparison of the Per-Household Benefits of
Attaining the Current Secondary Standard for TSP .... 6-3
6-2. Pecuniary Variables 6-7
6-3. Personal Characteristic Variables 6-8
6-4. Work Environment Variables 6-9
6-5. Auxiliary Variables 6-10
6-6. Hedonic Wage Equations 6-16
6-7. Hedonic Wage Equations Estimated for Partitioned
Data Sets 6-22
6-8. Alternative Air Pollution Standards 6-30
6-9. 1978 Pollution Concentrations in Denver and
Cleveland SMSAs 6-30
x
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SECTION 4
HOUSEHOLD SECTOR
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SECTION 4
HOUSEHOLD SECTOR
INTRODUCTION
Overview
In one of the first comprehensive assessments of the benefits of
air quality improvement, Waddell (1) noted:
In urban areas some families spend very little as a result
of air pollution, but many spend hundreds of dollars more
each year than they would need to if the air were clean.
The message is clear, air pollution can be costly to households. The
purpose of this section is to estimate some of those costs and thereby
estimate the benefits of improved air quality.
In the household sector, there are several ways in which an
improvement in air quality can lead to a realization of economic
benefits. First, the improvement may affect individuals directly.
For example, there is evidence that reductions in ambient concentra-
tions of TSP and SOo may have a beneficial effect on the health status
of individuals [Lave and Seskin (2)]. Second, there may be certain
aesthetic benefits attached to living in an environment with cleaner
air (e.g., visibility improvements) [Blank e_t al. (3)]. Finally,
reduced soiling and materials damage to the goods and services
4-1
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consumed by households may result from air quality improvement
[Freeman (4)].
This analysis of the household sector focuses on the benefits
associated with reductions in soiling and materials damage. In
particular, the objective is to provide an assessment of the likely
magnitude of the benefits from attainment of the Secondary National
Ambient Air Quality Standards (SNAAQS) for TSP and S02. The secondary
standards have been established to protect the public welfare and are
companion to the primary standards for protection of public health.
To date, much of the work on household soiling and materials
damage has been devoted to the identification of materials potentially
damaged by air pollution [Criteria Document for TSP and SC>2 (5)].
For example, from these studies, it is known that metal surfaces may
be subject to corrosion, painted surfaces may need more frequent
painting, fibers may deteriorate more rapidly, and various cleaning
and maintenance activities may have to be undertaken with greater
frequency in order to maintain some desired level of cleanliness.
In this analysis of household soiling and materials damage, the
knowledge that particular goods and services may be adversely affected
by air pollution is used as a basis for developing an economic model
which describes how individuals are likely to adjust to changes in air
quality. Specifically, a series of household demand functions are
analyzed and statistical methods are used to assess whether ambient
4-2
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concentrations of S02 or TSP contribute to the explanation of
•
variation in quantity demanded. For example, an increase in TSP
concentrations may lead to an increase in household demand for laundry
and cleaning products. The assumption is that such a relationship
would reflect an attempt by the household to mitigate adverse effects
of TSP through defensive actions. That is, additional laundry and
cleaning products are used by households in order to maintain a
desired level of household cleanliness.
In the above view, air quality improvement generates benefits
because fewer resources are required to produce a given level of
cleanliness. In effect, the unit cost of cleanliness is reduced. To
the extent that a reduction in ambient concentrations can be linked to
a reduction in the unit cost of the service provided by the laundry
and cleaning products (i.e., cleanliness), the monetary benefits
associated with air quality improvements can be identified.
While this effort is not the first to examine the benefits to
households from air quality improvements, the approach adopted is
different from those used in earlier studies. Specifically, this
analysis examines how households reallocate fixed budgets, given
product prices, when air quality improves. The focus is on household
decision makers.
There are several advantages to this approach. First, it
recognizes that individuals can adjust to the adverse effects of air
4-3
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pollution. As the opening quote in this section indicates, air pollu-
•
tion may affect different households to a different extent. People do
make choices, subject to budget and price constraints, and the
adjustment possibilities that can be made should be an integral part
of any benefits analysis.
Second, by giving additional structure to the benefits model, it
is possible to take advantage of the a_ priori restrictions available
in conventional models of consumer behavior. Such restrictions are
important, as they narrow the range of alternative explanations that
might be associated with a particular result.
A third advantage of the household demand approach is that the
data required for analysis may be more easily obtained. For example,
the major type of economic data required are expenditure and price
information for a variety of consumption goods. These data are
available from a variety of government sources. While the collection
of such data can still present a formidable challenge, the require-
ments seem much less burdensome than the materials inventory require-
ments of other approaches to benefits estimation.
Finally, the examination of air quality effects within the
context of an economic demand model leads to an analytically correct
measure of value. In particular, as noted in Section 2, benefits are
correctly defined in terms of the willingness-to-pay concept. In the
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present case, measures of willingness to pay can be identified from
the estimated demand functions.
Objectives of the Study
The main objective of the household sector study is to estimate
some of the benefits of the secondary standards. Given this
objective, it is helpful to have a set of criteria which allow an
informed judgment as to the plausibility of the benefits estimates.
The criteria that are important in an evaluation of the model
structure and ultimately in the degree of confidence one has in the
benefit estimates include:
• The manner in which the household decision model is
structured.
• The manner in which air quality variables are
introduced into the analysis.
• The sensitivity of results to alternative
specifications of functional form.
• The extent to which various assumptions limit the
generality of results and/or impose unrealistic
constraints on the model structure.
Since each of these criteria may have implications for the benefits
estimates to be derived, it is important that some indication of the
sensitivity of the benefits estimates to alternative modeling
decisions be given. A variety of such checks are presented throughout
the analysis reported in this section. While time and resource
constraints precluded an exhaustive analysis of the sensitivity of
4-5
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results, the checks undertaken represent an important part of the
overall analysis plan.
Quite naturally, before one can be concerned about the plausi-
bility of alternative assumptions within a specific model, there must
be some confidence that the general model structure is appropriate for
deriving defensible estimates of benefits. This becomes especially
important in light of comments by two environmental economists. V. K.
Smith (6) summarized his perceptions of environmental benefit analysis
techniques as of 1976 in the following way:
Overall the results of these analyses suggest that the
empirical content of environmental economics, while
growing, is rather weak. Before we can hope to precisely
guide public policy on environmental matters, much greater
attention must focus on the modeling and measurement of the
benefits and costs of these policies.
More recently, Freeman (7) has voiced similar concern. Freeman lists
the following five criteria which he believes a benefits analysis
should satisfy.
The technique must yield measures in monetary value
because the objective of the exercise is the
determination of values.
The technique and estimating procedures must be based
analytically and empirically on individual behavior
and preference, given the utilitarian definition of
benefits.
Benefits estimates must be based on a correctly
specified theoretical model of individual behavior and
the relationships among economic units.
4-6
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The actual measures used in the empirical work should
correspond as closely as possible to the variables of
the theoretical model.
Benefit studies must use the empirical techniques
appropriate to the theoretical model and the data at
hand.
In Freeman's opinion, no benefit study has yet been done which
completely satisfies each of these criteria.
Given these comments, the initial work plan developed for this
study was conditioned by these challenges to provide a more complete
model structure for benefits analysis. Consequently, a second
objective of the analysis has been to try to improve on the manner in
which such analyses are done. We believe the approach adopted for the
present study represents an important step ahead in achieving a more
systematic procedure for identifying defensible benefit estimates in a
variety of areas.
Scope of Analysis
The discussion of the scope of analysis for the household sector
can be conveniently organized in two parts. The first part describes,
in general terms, some of the methodological assumptions inherent in
the model developed. This is followed by a discussion of the scope of
empirical data available for this study.
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Methodological Issues—
At the beginning of this section, three ways in which air
pollution might affect households were listed. These were direct
effects (health), psychic effects (aesthetics), and effects on goods
and services demanded by households (soiling and materials damage).
This study looks only at the latter type of impact. Given that the
primary concern of this study is with the benefits of achieving a
secondary standard, conditional on the primary standard being attained
and maintained, neglect of direct effects such as health do not appear
to be serious. The implicit assumption is that the primary standards
are set at a level consistent with the attainment of an optimum for
health considerations.
It is more difficult to rationalize the exclusion of the psychic
benefits. In fact, the issue takes on importance since researchers
have recently suggested that this class of benefits may be relatively
large in magnitude [Brookshire e_t al. (8)]. Unfortunately, the house-
hold model presented in this section does not identify estimates of
pure aesthetic values. Consequently, the reported benefits estimates
represent only a partial coverage of air quality benefits in the
household sector.*
* One way in which some aesthetic valuations might be incorporated in
a household decision model is to analyze how leisure activities are
influenced by atmospheric visibility conditions. [See, for example,
Horst (9).]
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The next set of methodological issues involves ways in which
households can respond to the damaging effects of air pollution.
These adjustments can occur via several channels. They include:
• Moving to a less polluted environment.
• Engaging in maintenance or replacement activities.
• Substituting more resistant products.
• Doing nothing at all.
Ideally, a complete evaluation of economic benefits would be able to
incorporate each of these adjustment possibilities within the model
framework.
Location Substitutions—
The implication of this adjustment possibility is that
individuals no longer view air quality as something beyond their
control. Consumers can reduce the costly impacts of air pollution by
changing their residence. This location effect can be observed in two
economic measures. First, one can hypothesize that air quality
effects are capitalized into property values. Thus, in an area of
relatively better air quality, the amenities of the site may raise the
price of property. The second economic measure that can be affected
by the locational attributes of air pollution is wages. In this case,
the hypothesis is that jobs in an area with relatively better air
quality will be offered at a lower wage rate (relative to a similar
4-9
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job in a "dirty" area) since residents are compensated (non-
monetarily) through a better "quality of life" in the area.
In order to incorporate these location effects into the household
demand framework described in this section, special assumptions are
required. In the case of property values, one can no longer view the
price of property as being beyond the control of households.
Similarly, for wage rates, one cannot assume that income is fixed. To
date in this analysis, a general model that allows for location
changes has not been constructed. Consequently, assumptions have been
made which permit these location adjustments to be viewed as distinct
categories of benefits.
Maintenance and Replacement Activities—
As mentioned earlier, many benefits studies have been concerned
with identifying the effect of air pollution on the type and extent of
damage to various materials. Given a measure of physical damage,
'estimates are made of repair or replacement costs. Conceptually, the
idea is that if pollution were absent (or lower), these costs of
repair/replacement would not have to be undertaken (or would be
lower). Thus, the dollar number generated represents the potential
cost savings from defensive measures to ameliorate air pollution
impacts. Individuals should be willing to pay at least this amount to
avoid the deleterious effects of air pollution. Note, however, that
this cost-saving measure reflects only the difference in potential
expenditures; the amount "at least" that consumers should be willing
4-10
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to pay. True measures of benefits are couched in terms of "maximum"
willingness to pay and incorporate the notion of consumers' surplus.
This implies that benefits estimates in studies that look only at
cost-savings will provide a lower-bound estimate of some true level of
benefits. In the present study, since a series of household demand
functions is estimated, benefits can be expressed in terms of consumer
surplus measures.
Substitution Possibilities—
One means of adjustment that has often been neglected in earlier
benefits studies involves the notion of substitution. That is, as air
quality improves, an individual has the option of reallocating his
expenditures in a different fashion in order to account for expected
changes in pollution impacts. The decision for the individual
involves choosing that option which he believes will be least costly.
The problem this creates for benefit studies is that failure by the
analyst to consider the range of adjustment opportunities available to
the individual can lead to an understatement of benefits.
One way in which these substitution opportunities can be
incorporated into a benefits study is to consider simultaneously the
various allocation decisions faced by a consumer. This is done in the
current study by analyzing complete systems of demand functions. That
is, a series of demand functions for various goods is estimated as a
single structural system of equations.
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Doing Nothing at All—
While doing nothing at all may not seem very interesting as an
analysis issue, it can be an important part of any benefits study.
There are at least five ways in which the null response may arise:
• The consumer may not be aware of any damaging effects.
• The consumer feels that the cost of an ameliorative
action outweighs the potential benefits to him.
• The consumer may want to adjust to perceived damaging
effects but is constrained by available income.
• The observed data may not be conducive to identifying
the consumer's response.
• The consumer just doesn't care.
The extent to which the household model addresses each of the "non-
response" possibilities is discussed briefly in the following
paragraphs.
Imperfect Information—The lack of complete information may have
important implications for benefits analysis. This is most likely to
be true, however, for the analysis of mortality and morbidity effects.
The present study focuses only on the welfare effects underlying a
movement from a primary to alternative secondary air quality
standards, with a maintained assumption that all health benefits are
captured in the attainment and maintenance of the primary standards.
It does not seem to be as heroic an assumption that all consumers
4-12
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possess perfect information about "welfare effects".* This is the
working assumption in this section.
No Change Warranted—An improvement in air quality may elicit no
response from the consumer because he believes that any adjustment on
his part will be more costly than the benefit to him. This could be
exemplified by the desire of individuals to maintain a habitual
pattern of activity. The costs of changing habits are felt to be very
high. The degree to which this type of non-response is important will
be evident from the statistical analysis.
Constrained Budget—Some consumers may wish to respond to
deteriorating levels of air quality but are unable to do so because of
budgetary requirements in other categories of expenditures. Although
no budget reallocation occurs, there exists a lower level of welfare
relative to the case where the budget reallocation is made.
Part of the problem here may be in the orientation of the
benefits concept toward willingness to pay. That is, it is implicitly
assumed that responsibility rests with the consumers to pay for all
adjustments to pollution impacts. An alternative way to look at
benefits measures is in terms of "willingness to accept". Under this
concept, it is assumed that the property rights to clean air have been
* Potential irreversible changes to the ecosystem represent an
important effect that may be quantitatively significant yet are
areas of great ignorance among most benefits analysts. This type of
effect is neglected in the present study.
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assigned to the public. With this criterion, the budget is no longer
a constraint on response.
Which is the more appropriate criterion? From one point of view,
the existence of the EPA is in part a signal that the property rights
of the air resource belong to the public, so that the willingness to
accept concept may be more appropriate. However, in the promulgation
of selected environmental regulations, EPA recognizes the conflicting
desires of the public in general and the industries or individuals
that pollute. Thus, both parties face some degree of restriction in
terms of property rights to the air resource. Given this situation
and the fact that transactions costs such as information, policing,
and contractural costs make it unlikely that an individual would
attempt to elicit compensation for soiling or materials damage because
of standard violations, operationally, the willingness to pay concept
appears to be the more meaningful benefits measure.
In any case, the difference between the two measures will be
small if the response to damage requires only a small part of income.*
For this project, it would seem reasonable to view the welfare effects
as being of this type. Consequently, it is assumed that willingness
to pay is the appropriate criterion and that changes in expenditures
are small enough so that desired reallocations can be made.
See, for example, Willig (10).
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Non-Observable Changes—The third of the "no action" responses
involves the idea that some change really does occur, but available
data do not allow the researcher to identify changes in welfare.
For example, certain types of aesthetic benefits may not be observed
because it is difficult to identify meaningful quantitative data. As
noted earlier, the present study does not capture such pure aesthetic
values.
Non-Respondents—Finally, some individuals may take no action in
response to changes in air quality because they really don't care.
They make no changes in their allocation decisions because of
increases or decreases in pollution levels, and, in a survey
situation, they (truthfully) respond that they would never be willing
to' pay any amount. If air quality improves, they don't clean less and
their welfare is not affected even though the average level of
cleanliness is higher.
A maintained hypothesis of this study is that better levels of
air quality are preferred to less. Thus, the ultimate test of whether
such individuals constitute a sizeable portion of the general
population will be apparent in the demand relationships estimated and
the benefit numbers that are derived.
Scope of Empirical Data—
The economic data used in our analysis of household demand are
aggregate data for SMSAs (Standard Metropolitan Statistical Areas).
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Expenditure and price data were obtained for approximately 185 con-
sumption items for 24 large SMSAs for the years 1972-73. After aggre-
gation, the dimensionality of the problem was reduced to a more
manageable 20 consumption items. Expenditures for goods included in
the analysis accounted for about 40 percent of total current con-
sumption expenditures in each of the SMSAs. Among the major
categories of goods that have been omitted are recreation and leisure
(data limitations) and payments for property services (methodological
limitations).
Table 4-1 lists the SMSAs included in the study. In 1976, the
population in these SMSAs represented approximately 30 percent of the
total population of the country. The benefit estimates reported in
TABLE 4-1. SMSA'S INCLUDED IN THE ANALYSIS
Region I: Northeast
1. Boston
2. Buffalo
3. New York City
4. Philadelphia
5. Pittsburgh
Region II: North Central
1. Chicago
2. Cincinnati
3. Cleveland
4. Detroit
5. Kansas City
6. Milwaukee
7. Minneapolis
8. St. Louis
Region III: South
1. Atlanta
2. Baltimore
3. Dallas
4. Houston
5. Washington, D.C.
Region IV: West
1. Denver
2. Los Angeles
3. San Diego
4. San Francisco
5. Seattle
6. Honolulu
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this section relate only to the 24 SMSAs included in the table. In
Section 10, estimates are developed for other areas of the country.
Summary of Benefits Estimates
Based on the analysis reported in the following subsections,
estimates of the benefits of air quality improvement have 'been
developed. The estimates represent the incremental benefits of
attaining Secondary National Ambient Air Quality Standards for SO,, and
TSP by 1987, given that primary standards for the two pollutants are
achieved in 1985. Table 4-2 presents the estimates for each of the 24
SMSAs included in the analysis. Entries in the table are discounted
present values in 1980 of soiling and materials damage benefits over
an infinite time horizon. The estimates assume a 10 percent discount
rate and are stated in 1980 dollars. The secondary standards for
which the benefit estimates are derived are 24-hour maximum second-
high standards for both pollutants (150 ug/m3 for TSP and 260 ug/m3
for SG>2).
The benefits numbers shown in Table 4-2 are total benefits for
each SMSA. On a per-household basis, in the two years of standard
attainment, the average level of benefits is approximately $16.25 for
TSP and $16.50 for SO- (in those areas where the SO- Secondary
Standard is exceeded). For a unit change in ambient concentrations
(ug/m3), the per-household benefits are approximately $0.20 and $0.17
for TSP and S02, respectively. Regionally, benefits from the
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TABLE 4-2. HOUSEHOLD SOILING AND MATERIALS DAMAGE BENEFIT ESTIMATES
(discounted present values for 1980 in millions of
1980 dollars)
SMSAS
Region I
Boston
Buffalo
New York
Philadelphia
Pittsburgh
Region Subtotal
Region II
Chicago
Cincinnati
Cleveland
Detroit
Kansas City
Milwaukee
Minneapolis
St. Louis
Region Subtotal
Region III
Atlanta
Baltimore
Dallas
Houston
Washington, DC
Region Subtotal
Region IV
Denver
Honolulu
Los Angeles
San Diego
San Francisco
Seattle
Region Subtotal
Totals
TSP
35.41
47.98
237.05
189.71
83.35
593.50
254.11
21.34
61.59
172.88
39.08
51.92
73.95
85.92
760.79
4.67
7.47
56.00
105.79
152.23
326.16
112.32
*
367.73
86.61
*
53.48
620.14
2,300.59
SO2
*
37.99
302.75
184.45
74.67
599.86
65.45
39.88
52.20
*
*
36.84
56.26
70.06
320.69
*
*
*
*
*
*
*
*
*
*
*
*
*
920.55
* Secondary standard not exceeded; therefore no benefits for attain-
ment of standard.
4-18
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reduction of TSP levels are realized in all but two of the SMSAs —
San Francisco and Honolulu. Cn the other hand, benefits from reduc-
tions in the ambient concentrations of S02 accrue only to households
in the Northeast and North Central regions of the country. Again, we
stress that these estimates of benefits cover only the 24 SMSAs
included in the analysis. A more detailed description of the way in
which these benefit numbers were derived appears in a later part of
this section. Extrapolations to the rest of the nation are presented
in Section 10.
Section Overview
In the remaining parts of Section 4, a complete framework for
performing an air quality benefits analysis in the household sector is
developed. Initially, various benefit studies that have been done in
the past are reviewed. This review is helpful in establishing the
types of benefits that are being analyzed and can also serve as a
point of comparison for the plausibility of the benefits numbers
derived in the present study. Next, a detailed description of the
theoretical model is presented. In this subsection, the structure of
the decision process of households and the way in which air pollution
might affect household decisions are both examined. This is followed
by a description of the available data, and the presentation and
evaluation of the empirical results. Given parameter estimates,
benefit estimates for achievement of the Secondary National Ambient
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Air Quality Standards are calculated. A final subsection briefly
summarizes the major findings of the analysis.
SUMMARY OF PREVIOUS BENEFITS STUDIES
The object of an analytically proper air quality benefits
analysis is to provide an estimate of the income-equivalent change in
welfare for a specified improvement in some measure of air quality.
The purpose of this subsection is to summarize the methods that have
been used to estimate these values and to assess their success at
obtaining meaningful benefits estimates. Additionally, where
possible, estimates are presented of the gross benefits identified in
these studies. The discussion is taken primarily from Waddell (1) and
Freeman (4).
Physical Damage Function Studies
The objective of the damage function approach is to identify
objects at risk from air pollution and to develop statistical
relationships describing the physical damage that may occur. We have
given broad descriptions of the types of effects likely to be observed
in the household sector but, in practice, damage function studies
focus on particular items within the aggregate classifications. For
example, Table 4-3 lists some of the household items that may be
susceptible to corrosion or erosion. Similarly, Table 4-4 describes
those household activities that may be affected by soiling. Clearly,
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TABLE 4-3. HOUSEHOLD MATERIALS SUBJECT TO CORROSION/EROSION
1. Metals
a. Steel structures/products*
i) Exterior lighting equipment
ii) Galvanized roofing, siding, drainage
iii) Prefabricated buildings
iv) Exterior structural steel
v) Exterior gratings, fire escapes
vi) Metal doors, windows
vii) Chain link fencing
b. Aluminum
c. Zinc
d. Electrical components
2. Building materials**
a. Cement and concrete
b. Wood
c. Building bricks
d. Glass
3. Paints (deterioration)"1"
a. Oil-base house paints
b. Latex house paints
4. Fibers
a. Rugs, draperies
b. Furnishings, upholstery
* Source of steel breakdown is Perl (11), who constructed his table
from information in Fink, et al. (12).
**
Source of building materials breakdown is Barrett and Waddell (13).
Breakdown of paint category relies on damage study conducted by
Spence, et al. (14).
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TABLE 4-4. HOUSEHOLD SOILING ~ CLEANING AND MAINTENANCE TASKS
5™~:S^™~™™~~22™™~™™™™™ —ZSZS™ ™S«~~~ ~S —Z —— — — — ™2Z^^ZZ~M«« ™ —— — 3S^^^~ZS "^*"""S'^^~" ~
1. Outdoor
a. Painting walls
b. Painting trim
c. Washing windows
2. Indoor
a. Painting walls and ceilings
b. Wallpapering
c. Washing walls
d. Washing windows
e. Cleaning Venetian blinds
Source: Watson and jaksch (15), Table 1. The authors note that the
tasks described above were drawn from the Booz Allen Hamilton
study (16) which included 15 indoor and 12 outdoor tasks.
The eight tasks listed here represent those activities that
Watson and Jaksch believe to be the most susceptible to
particulate soiling.
if total benefit estimates are to be obtained on an item-by-item
basis, the compilation of benefits would be an onerous task.
Method Requirements—
The development of benefits numbers for a physical damage
function study requires several types of information. First, physical
damage functions relating changes in concentrations of a pollutant to
some measure of damage must be developed. In general, this requires
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laboratory experiments which simulate natural environments, but where
factors other than air pollution can be kept at predetermined levels.
The second step in a damage function analysis involves a transla-
tion of the physical damage function into economic terms. As
suggested in the Midwest Institute Report (17), this requires
knowledge of four items: information on the distribution of
materials; information on the distribution of pollutants; the service
life of products in the absence of pollution; and the value of the
products or structures using the affected materials.
Not only are these information requirements burdensome, but the
process of developing benefits estimates with this type of model
implies some strong underlying assumptions and limitations. For
example, Waddell [(1), p. 24] mentions that extrapolation of
laboratory results to the real world ignores the possibility of
nonconstant marginal products, nonlinearities, and problems of
aggregation and substitution. Freeman (4) stresses the lack of
consideration of consumer adjustments, and the difficulty in assessing
the inventory of materials at risk. Despite these drawbacks, physical
damage function studies have been the most widely used.
Benefits in the Physical Damage Studies—
One must be extremely cautious when reporting gross benefits
estimates from a variety of studies. There are numerous assumptions
underlying the development of any particular estimate, so that
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comparing results of different studies is quite difficult. Among the
more prominent aspects to consider are: the assumed base level of air
pollution and the direction and magnitude of change; the frequency,
averaging time, and collection method of the pollutant; the basis of
the economic dollars (e.g., 1970 dollars vs. 1980 dollars); the social
rate of discount used in deriving the discounted present value (time
stream) of benefits; the statistical sensitivity of the parameters
used in calculating benefits; and the methods of extrapolation to the
general population (i.e., what is the extent of coverage of the
numbers).
As one might imagine, it can be difficult to bring the myriad of
physical damage studies into commensurate terms. Fortunately, both
Waddell (1) and Freeman (4) present a synthesis of many of these
studies.*
In Waddell's case, his best guess estimates of total economic
"damage" in 1970 (for 1970 pollution levels) are: $2.2 billion for
materials damage, $0.2 billion for vegetation, and $5.8 billion for
particulate soiling. We assume that his use of the word "damage" can
be taken to mean the total elimination of pollutant impact.** In
* We will not list the many works that went into the summaries of
Freeman and Waddell. The reader is referred to these two studies
for a complete account of the individual analyses.
** The idea of eliminating pollution is not the purpose of a benefits
study. The rule of cost-benefit analysis is that welfare is maxi-
mized when marginal benefits equal marginal costs. Under quite
reasonable assumptions on the shapes of these curves, it is likely
that this optimum will occur with a positive level of pollution.
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terms of specific pollutants, damages in 1970 attributable to SOX are
$5.4 billion, with TSP damages reported as $5.8 billion. All numbers
in Waddell's study are in 1970 dollars.
Freeman's main scenario involves answering the question: What
are the benefits with/without a particular piece of legislation? For
example, one might compare the actual environmental quality in a given
year (Freeman uses 1978) to the environmental quality in the year the
legislation was adopted (e.g., the 1970 Clean Air Act). In terms of
dollars, Freeman's most reasonable point estimates are $3.7 billion
for materials damage, $0.5 billion for vegetation, and $2 billion for
soiling, all in 1978 dollars. The materials damage number includes
the effects of both TSP and sulfur compounds. The vegetation losses
are calculated for sulfur compound pollution, and soiling damage is
TSP-specific.
In addition to the numbers available in Waddell and Freeman, SRI
(18), in a report recently prepared for the National Commission on Air
Quality, published benefit estimates of attaining the secondary
national air quality standards for TSP and S02. As with Waddell and
Freeman, SRI uses earlier studies as the basis for deriving their
benefit numbers. For soiling and materials damage, a review of their
discussion indicates that S02 benefits for materials damage reduction
are estimated to be about $1.8 billion (1980), while TSP benefits of
reduced soiling are approximately $0.65 billion (1980). Several
things should be pointed out. First, SRI's benefit numbers were
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calculated from a baseline of current (1980) levels of ambient air
quality to the proposed secondary standards. This contrasts with our
approach where the analysis is directed toward measuring the
incremental benefits of going from a primary (or current levels if
below the primary) to a secondary standard. Second, the materials
damage estimates reported by SRI do not distinguish between household
materials exposure and the exposure of commercial buildings,
manufacturing plants, etc. The analysis in this section is strictly
for the household sector. Third, their numbers represent estimates of
total national benefits while the results summarized earlier for the
present study are valid for only the 24 SMSAs included in our basic
analysis. Finally, SRI's benefits numbers appear to be reported in
annual terms, whereas our calculations are based on discounted present
values.
Indirect-Market Studies
A second method that has been used to assess the economic
benefits of air quality improvements is known as the indirect-market
approach. Since a market for air quality does not exist, this
approach relies on the identification of markets in which changes in
air quality may be reflected in production and/or consumption
decisions. The household demand model developed in this section is an
example of the indirect-market approach. Two other applications of
this approach include analyses of residential property markets and the
market for labor services.
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In the residential property value studies, the hypothesis is that
variations in property values (or rents) can be explained not only by
housing attributes, neighborhood characteristics, and availability of
services, but also by site-specific air pollutant concentrations. A
priori, the presumption is that higher levels of air pollution lead to
relatively lower residential property values, all other housing
attributes being the same.
While there have been many empirical studies of property value
differentials, this type of analysis is not well-suited to the problem
of estimating non-health benefits of the secondary standards. This is
because property values are likely to reflect all perceived, at home,
effects of air pollution. Consequently, in addition to coverage of
soiling and materials damage effects implicit for a particular site,
benefits estimates derived from property value studies may also
include values for health and aesthetic benefits. Since it is
difficult to identify the separate influences of the various benefit
types, estimates based on property value differentials are likely to
be larger than those reported for the household demand model developed
in this section.
However, this relationship can provide useful information. In
particular, a benefit estimate calculated from an analysis of residen-
tial property values may be interpreted as an upper-bound plausibility
check on the household demand model benefits. For this reason, a
review and synthesis of the literature on property value analysis was
4-27
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undertaken in this study, and benefits estimates were obtained using
scenarios consistent with those used in other sections of this report.
The results of this analysis are reported in Section 5.
The second application of the indirect-market approach mentioned
above relates to the market for labor services. In this case, the
underlying hypothesis is that wage rate variations can be explained by
attributes of the individual, characteristics of the job, and
location-specific amenities such as environmental quality. Here, the
presumption is that jobs in an area with relatively better air quality
will be offered at a lower wage rate than similar jobs in a more
polluted area.
A benefits analysis based on wage rate variations is likely to
encompass a variety of benefit types, including health and aesthetic
benefits. Thus, as in the case of property values, it may be
difficult to identify non-health benefits directly. As before,
estimates from the wage rate approach become useful as cross-checks on
the plausibility of the household demand model estimates. The results
of an analysis of wage rates is presented in Section 6-
Other Benefits Approaches
For the sake of completeness, several other techniques that have
been suggested for benefits analysis are listed below. These
approaches can, in general, be classified as non-market studies. NO
4-28
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discussion is offered, however, and the interested reader is referred
to Waddell (1) for further elaboration. . These other techniques
include:
• Opinion surveys of air pollution sufferers.
• Litigation surveys.
• political expressions of social choice.
• The Delphi method.
Overall Summary of Previous Air Quality Benefits Studies
In this subsection, some of the ways analysts have approached the
estimation of economic benefits have been discussed. To date, the
most popular methodology has involved an examination of the relation-
ship between pollution and the physical damage to materials thought to
be at risk from exposure. These studies provide a direct link between
air pollution and the objects valued by human beings. While the
studies are important for determining the type and extent of pollution
effects for specific materials, aggregation to more complete
inventories of materials imposes data difficulties.
Economists have found fault with these studies both for data
reasons, and more importantly, for conceptual reasons. In particular,
they point out that a model that does not account for the behavior of
man and his interaction with the environment cannot provide
analytically correct measures of welfare change. One outgrowth of
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this observation has been the development of indirect-market studies,
in which pollution is presumed to play a role in the supply and demand
decisions in various economic markets. Two markets that have received
considerable attention are the property market and the labor services
market. In these studies, the location-specific attribute of air
pollution is highlighted and assumptions are introduced which permit
the analyst to examine locational variations in demand and supply due
to air quality differences.
While the model developed in this section is also of the
indirect-market type, the adjustment mechanisms assumed to be
available to households are different. In particular, location
decisions are viewed as having been made, and reallocations in demand
are assumed to reflect short-run adjustments to changing pollution
levels. This model is discussed fully in the next subsection.
MODEL DEVELOPMENT
It was noted earlier that the manner in which the household
decision process is modeled is one of the important criteria for
judging the plausibility of the analysis. In this section, the model
that will be used to characterize household decisions is described in
detail.
Figure 4-1 outlines the major components of the decision process.
The initial decision facing the household is the allocation of a fixed
4-30
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Environmental
conditions
Relative
prices
I
Soc ioeconomic.
characteristics
Demand for
market goods
I
Index of produced
service flows
Figure 4-1. Household decision process.
budget among the many market goods that may be purchased. In order to
determine these "demands", various factors that are beyond the control
of the household must be taken into account. In particular, the
relative prices of the goods, income, and various demographic factors
all help to shape the pattern of household demand. Furthermore,
environmental conditions such as ambient concentrations may also
influence the demand for certain goods. For example, the demand for
detergents or other cleaning products may be sensitive to the level of
TSP concentrations.
Once the allocation decision has been made, conditional on the
factors mentioned above, the decision-making role of the household is
essentially complete. However, there is a natural extension to the
process that is important for benefits analysis.
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The idea behind the extension is that items like detergents are
not demanded for their own sake, but rather for the services they
provide. Thus, it may be instructive to view the demand for
detergents as a derived demand based on a more fundamental consumer
demand for cleanliness. Viewed in this way, the allocation decision
made by households with respect to detergents and other cleaning items
is consistent with attaining a particular level of household cleanli-
ness. Furthermore, the role of air pollution is clear. In particu-
lar, air pollution increases the cost of cleanliness by increasing the
quantity of detergents and other cleaning items required to obtain a
unit of cleanliness. Conversely, a reduction in air pollution can
lead to a reduction in the unit cost for cleanliness, and consequently
economic benefits are generated.
The underlying relationship between services such as cleanliness
and market goods is also portrayed in Figure 4-1. While households
are not required to make any new allocation decisions in order to
identify the index of service flows, the structure of the link between
the service flows and market demands is crucial. In fact, the
discussion of how this link can be established in a consistent fashion
is a major concern of this subsection.
The nature of this link is formalized by adopting the assumption
that the market goods demanded by households can be grouped naturally
into a series of categories (i.e., final demand service flows) such
that the demands for goods in one group are independent of the demands
4-32
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for goods in another group. Thus, all items that serve to promote
household cleanliness can be grouped together, and because of the
independence assumption, it is possible to analyze budget decisions
for these goods in a decentralized manner. Furthermore, given
appropriate mathematical conditions on functional structure, a well-
defined index for a particular service flow can be constructed solely
from the budgeting information available in the group corresponding to
the service flow of interest.
The model described above is structured to deal directly with
household adjustments to air quality changes. The focus is on the
value households place on certain activities rather than specific
pollution-induced damage. A physical damage function between pollu-
tion and objects that may be damaged is not included in the analysis.
Instead, pollution enters the model as a proxy for damage. It is not
imperative that the type or extent of physical damage is identified
explicitly. The knowledge that is required is the value household
decision makers attach to activities or services that may be sensitive
to air quality changes.
The plan of this subsection is as follows. First, the consumer's
decision problem is described in terms of an optimization model.
Specifically, the notion of a utility function is introduced and the
relationship between the utility function of the consumer and his
demands for various goods and services is developed in a nonrigorous
fashion. Following this discussion, the procedures underlying the
4-33
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development of the link between market demands and household services
is presented. In particular, it will be demonstrated that if house-
holds engage in groups of activities which can be viewed as
independent from one another, then it is convenient to construct a
decentralized decision problem that reflects a two-stage budgeting
problem.
Given the general structure of the theoretical model, the
remaining subsections focus on specific assumptions required for an
empirical study of air quality benefits. The discussion covers the
concepts of aggregation and separability; feasible alternative
functional forms for the utility function; the manner in which
environmental and demographic variables can be introduced into the
analysis; deviations from the assumptions of the standard utility
maximization problem; and a discussion of the hypotheses to be tested.
The section concludes with a brief summary of the advantages and
disadvantages of the developed model.
Utility Maximization
In simplest terms, a utility function can be defined as a
function which measures the level of satisfaction associated with a
particular bundle of goods.* Utility theory can be utilized with
* Our presentation of consumer choice theory relies on the calculus as
a tool of analysis. Modern treatments of the consumer's problem
also use concepts from set theory to characterize preferences. See,
for example, Varian (19).
4-34
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assumptions of different degrees of generality. The assumptions
adopted for the present study require only that the utility function
represents an ordinal index of preferences. That is, the utility
function can be used to rank one bundle of goods as being more pre-
ferred, less preferred, or indifferent to an alternative bundle of
goods, but it does not imply anything about the intensity of prefer-
ences.
If there are only two goods in the world, one can write the
utility function as:
U = U(x1, x2) (4.1)
where U is the utility index and x^ is the ifc good that can be
purchased by the consumer. If another combination of the goods x, and
9 o
x_ [denoted as (x^x^)] is preferred by the consumer, then the utility
index associated with (x?,x^) is greater than the utility index
associated with the bundle (x-, ,x_). The goal of the consumer is to
achieve as high a level of utility as possible. Clearly, if more of a
good implies higher levels of utility, then the consumer would always
opt for more of the good unless a constraint were placed on his
choices.* In fact, people are constrained in their choices among
commodities by the level of their income. In the simplest textbook
* In this general description of utility functions, we have omitted
many details of conditions that are required if consumer preferences
are to be adequately and consistently portrayed. A description of
these conditions can be found in a microeconomic textbook such as
Henderson and Quandt (20).
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version of the utility maximization model the maintained assumptions
are that the consumer views his income as well as the prices of the
products he can purchase as given. Furthermore, it is generally
assumed that he spends his entire fixed income on the available goods.
Thus, we can write a more complete version of the consumer's
decision problem as:
Max U = U(x1, x2) (4.2)
X;
Subject to PIXI + ?2X2 = M
where p. is the price of the ifc good, M is fixed income, and x-, U
are as defined previously. Equation (4.2) states that the decision
problem of the consumer is to find that combination of goods x-, and *2
which maximizes his utility subject to the budget constraint imposed
by his available income.
Before we present a graphical interpretation of the consumer's
decision problem, it is helpful to consider another concept called an
indifference curve. As the name implies, this curve represents a
locus of combinations of the two goods, such that the consumer finds
the combinations of goods equally desirable. In terms of his utility
index, he realizes the same level of utility from any of the combina-
tions, and hence is indifferent to which is selected. Indifference
1 n O
curves corresponding to levels of utility U , U , U are shown in
4-36
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•3 O 1
Figure 4-2 where U > U > U .* In this figure, the quantity of good
x-, is on the vertical axis, while the quantity of good *2 i-s on the
horizontal axis. The budget constraint is represented by the downward
sloping line AC. Thus, any combination of goods inside the triangular
area AGO can be purchased by the consumer, while a combination of x-j_,
Xo to the right of the budget line is unattainable for the consumer
given current prices and income. In the figure, the consumer
X
plxl + p
u
Figure 4-2. The consumer's optimum.
* The curvature properties of the indifference curve are of course
very important. Among the assumptions on the utility function is
one of strict quasi-concavity which will guarantee convex to the
origin indifference curves like the ones depicted in Figure 4-1.
With indifference curves of this shape, consumers must give up some
of one good for each additional unit they gain of another good if
they are to stay on the same indifference curve (i.e., at the same
level of utility).
4-37
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maximizes his utility by obtaining the combination of Xi and x2
represented by point B. With this combination, he achieves utility
o 3 ?
level U . While utility level U is greater than U , the former
utility level is not attainable.
Demand Functions
The mathematical problem represented by Equation (4.2) can be
solved for the utility maximizing values of x-,, x-. The solution of
the problem results in demand functions for x^ and x2- These
functions depend on variables outside of the individual's control.
These are called exogenous variables. In the present case, the
exogenous variables are the prices and income.
xl = fl(Pl' P2' M) (4-3)
P2, M) (4.4)
The demand functions portray the choices made by households given
prices and a fixed budget. Graphically, demand curves can be
illustrated as shown in Figure 4-3. In the diagram, the price of the
good is on the vertical axis while the quantity demanded is on the
horizontal axis.* For a given demand curve, other prices and the
* The placement of price on the vertical axis is counter to the
mathematical representation in Equations (4.3) and (4.4) where price
is an independent variable. However, this has become the standard
way in which economists draw demand curves. In effect, Figure 4-3
can be thought of as portraying an "inverse" demand curve.
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Price
per unit
, D
D
Quantity per
unit time
Figure 4-3. Demand curve.
budget (income) are assumed to be constant. The solid line DD is the
demand curve relating price and quantity for specific levels of these
other variables. If one"or more of these other parameters changes,
the demand curve can shift. An inward shift is shown in the figure as
the dotted line D'D'. This shift might occur because of a price
change in a good related to the good for which the demand curve is
derived. For example, suppose DD represents the demand for butter.
Then if the price of margarine decreases relative to the price of
butter, less butter will be demanded at each price.
Several things can be highlighted from the derivation of the
demand functions shown in Equations (4.3) and (4.4). First, for a
specific utility function form, it may be possible to define a demand
4-39
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curve. This intimate connection between utility and demand makes it
essential that the demand curves we estimate are plausible in the
sense that the utility function from which the curves are derived
conforms to certain mathematical conditions.*
The second point is that Equations (4.3) and (4.4) imply a series
of restrictions which lead to a system of equations. This occurs
because the prices for both goods appear in each of the demand equa-
tions. Thus, in order to take into account the information provided
by all the parameters of the model, the pair of equations should be
estimated as a single structural model.
When there are many goods involved in the analysis, it is
impractical to assume that consumers consider all of these decisions
simultaneously. Instead, it may be more meaningful to assume that
thre is a natural decomposition of household activities into
independent groups which characterize various household activities
(e.g., household cleaning). The budgeting (allocation) decision of
the consumer would then be based only on the characteristics (prices,
etc.) associated with each of the individual activities.
* These conditions require that consumers' preferences are transitive,
reflexive, complete, nondecreasing, continuous, and convex. Thus,
the utility function is nondecreasing, continuous, and quasi-
concave. (It is also assumed that the utility function is twice
differentiable.) For a discussion of these "regularity" conditions,
see Henderson and Quandt (20), Chapter 2.
4-40
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The final point concerns those factors which can lead to
reallocations between goods. As Equations (4.3) and (4.4) indicate,
demand depends on prices and income. Thus, for given tastes (consumer
preferences), reallocations will occur when relative prices change
(i.e., the slope of the budget constraint in Figure 4-2 changes), or
when income is changed (i.e., the budget line in Figure 4-2 shifts).
Of major interest here, however, is the role played by air quality in
reallocation decisions. As currently written, Equations (4.3) and
(4.4) have nothing to say about air quality.
Demand Functions and Air Quality—
If air quality were a private good with a well-defined market
price, then it could be treated as one of the x-. However, air
quality is a predominantly public good rather than a private good, and
generally no market price for air quality exists.* In order to
determine people's demand or willingness to pay for specific levels of
air quality, modifications to the above model are required.
Maler (21) lists four alternatives that may be used to identify
the willingness to pay for environmental services:
* A public good can be defined as a good which can be "consumed" by
one person without reducing the consumption possibilities of the
good by another person, and for which exclusions from consumption
are impossible.
4-41
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• Asking consumers how much they are willing to pay for
some increase in the supply of an environmental
service.*
• Voting on the supply of an environmental service.**
• Indirect methods, based on relations between private
goods and environmental services.+
• Estimating the physical damage from residuals
discharge and evaluating this damage by using market
prices.++
The approach proposed in this section is consistent with the third
alternative mentioned by Maler. Basically, measures of ambient air
quality are incorporated into the demand functions of specific private
goods as additional explanatory factors, the hypothesis being that
changes in the level of air quality shift demand for the private
goods. For example, if air quality improves, the demand for laundry
and cleaning products would be expected to shift inward, so that at a
given price with all other factors held constant, an individual would
demand fewer units of laundry and cleaning products per unit time.
In equation form, one can write:
xi = fl(P].' ?2' AP/ M) (4'5)
* An example of this type of study can be found in Randall et al.
(22).
** An example of this type of study can be found in Fischel (23).
-t- An example of this type of study can be found in Blank e_t a_l_. (3).
-t-f Examples of studies of this type are available in drafts of the
Criteria Document (5).
4-42
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where AP is the ambient concentration of a particular pollutant, and
the other variables are as defined previously. In terms of the
laundry and cleaning products example, one would expect the partial
derivative of x- with respect to the measure of air pollution to be
positive. This occurs because most cleaning expenditures made by
households in response to higher levels of air pollution can be viewed
as defensive expenditures.
Overview of Service Flow Indices
The discussion to this point has focused on the manner in which
the consumer is assumed to allocate his budget among market goods.
The topics that have been considered are pertinent to the decision
process portrayed in the top half of Figure 4-1. Among the issues
covered thus far, one of special interest involves the observation
that it is reasonable to consider that consumer budgeting decisions
are decentralized. That is, market goods that contribute to a
specific household activity (e.g., household cleaning) may be grouped
together.
In the following discussion, this decomposition is used to
describe a process for establishing a consistent link between market
goods and indices of service flow. This is the relation identified in
the bottom part of Figure 4-1. The framework required to formalize
this link can be described heuristically, as follows. Rather than
market purchased goods like detergents yielding utility directly, it
4-43
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is the household cleanliness services they provide from which the
consumer derives utility. The demand for a good like detergents is
more properly viewed as a derived demand based on a more fundamental
consumer demand for cleanliness. The grouping of the derived demands
into classes of activities implies that something is known about the
factors which help to "produce" the utility-generating service flows
like cleanliness. What remains to be established is the exact
structure of this relationship and the role of air pollution in the
linkage.
With respect to air pollution, one can hypothesize that an
improvement in air quality would lead to a lower implicit price for
cleanliness in the sense that it becomes easier to attain the same
level of cleanliness with decreased pollution levels. If such an
effect on the implicit price (cost) of cleanliness is observed, then
the change in price can be used in a meaningful way to identify the
economic welfare change associated with air quality improvements. The
shaded area in Figure 4-4 illustrates this welfare change. The
welfare gain can be split into two parts. First, the consumer reduces
expenditures on the Q-, units of cleanliness originally demanded by the
amount P^ABP2« Then, because of the reduced price of cleanliness, Q2
- Q, additional units of cleanliness are obtained.
With respect to the structure of the link between groups of
market goods and the service flow indices, a general way of viewing
4-44
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Price of
cleanliness
(Price of cleanliness at
~~ pollution level S~)
(Price of cleanliness at
pollution level S, , S.. < S-)
Quantity of
cleanliness
Figure 4-4. Welfare change from air quality improvement.
this relationship can be observed in the concept of a household
production function.
In the economics literature, the idea of household production has
been described in the following way.*
The household purchases "goods" on the market and combines
them with time in a "household production function" to
produce "commodities". These commodities, rather than the
goods, are the arguments of the household's utility
* The concept of household production functions is generally traced to
Lancaster (24), Becker (25), and Muth (26), with subsequent refine-
ments and clarifications discussed by such as Pollak and Wachter
(27), Muellbauer (28), and Hori (29). This approach has also been
used by Griliches (30) and others to analyze questions of quality
differences in products.
4-45
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function; market goods and time are not desired for their
own sake, but only as inputs into the production of
"commodities".
[Pollak and Wachter (27)]
If Z is cleanliness, A is air quality, X is a vector of private
goods that help achieve cleanliness, and T is the time spent in
producing cleanliness, the household's production function for Z can
be written as:
Z = G(A, X, T) (4.6)
Equation (4.6) establishes a relationship between the various
arguments and the unobserved output Z. While we do not have a quanti-
tative measure for Z, if it is possible to add structure to the
character of the relationships among the variables on the right-hand
side of (4.6), we can gain insights into the manner in which
individuals adjust to changes in pollution. This structure is
developed below in the context of a two-stage budgeting decision.
Two-Stage Consumer Budgeting
A way of formalizing the decision process of the consumer that is
consistent with the discussion to this point is to assume that
consumers budget their expenditures in stages. First, consumers are
assumed to allocate their total income (expenditure) among broadly
defined categories such as food and clothing, and given the (optimal)
4-46
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share of expenditure to each broad category, next decide upon the
allocation of category expenditure to each of the goods within the
group.
In equation form, the two stages can be written as:
Stage 1.
Max U = U(Z1/ Z2, ... , Zn) (4.7)
zi
Subject to R-^ + R2Z2 + ... + RnZn = M
where Z^ is the i aggregate good
U is the utility function for the broad (aggregate) group
M is total money income (expenditure)
j_ L_
R^ is the price index for the i aggregate good.
The solution to Equation (4.7) is a system of demand equations
* *
which define optimal levels for the z^ (=Z^). Multiplication of Z- by
R- then yields the optimal expenditure for group i, M..
Given M^_, we can then proceed to Stage 2.
4-47
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Stage 2.
Max Zi = Zi(Xil, ... , Xir) i = 1, ... , n (4.8)
Subject to piixii + ••• + pirxir = Mi
where X^ is the j good in the i aggregate group.
Z- is an aggregate service flow defined by the subfunction of
the Xij.
M^ is the money allocated to the disaggregate stage from the
first stage decision.
P^ is the price of the jtn disaggregate good that appears in
the i aggregate group.
The two-stage budgeting decision presented above makes the
implicit assumption that something is known about the way people
combine various goods, the X-^, in order to obtain a particular flow
of services, the Z^. Although the structure of the process is
formally akin to the utility maximization technique described earlier,
the important aspect of Equation (4.8) for the present study is that
the functions of the X^ variables represent a household production-
like process, where the two-stage budgeting model adds the structure
necessary to define an aggregate index of the Z^. In effect, the
subfunctions of the X' • can be thought of as commodity indices for
each of the Z services.
4-48
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Note that the assumptions made earlier with respect to the
decomposition of goods into classes of activities fits in naturally
with the two-stage budgeting framework. In particular, Equations
(4.7) and (4.8) describe an allocation process in which expenditure
decisions are made first among broad categories using information on
only total expenditures and price indices for each broad category.
Then intracategory allocations are determined with information on only
prices for the specific goods within the broad category. For example,
none of the PjVs appear in the Stage 1 analysis and no P^ appears in
the Z- utility maximization problems where k ^ i. Basically, the
decision problem of the consumer is structured so that each of the
broad categories of service flows is composed of a group of private
market goods that is common to the aggregate activity.
Using the definitions of terms in Equations (4.7) and (4.8), each
Z| can be viewed as a quantity index of private goods. If there are
only two classes of aggregate service flows and five private goods,
one might write:
ZT = l' 1' 2' ^3
(4.9)
Z2 = f2(X4, X5)
Note that an X^ may appear in only one "aggregate" function. This
non-jointness property is necessary for the two-stage optimization
problem to be valid.
4-49
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In terms of the function U of Equation (4.7), this means that one
can write:
U = u(f]_(X1, X2, X3), f2(X4, X5))
In addition to the index Z- price indices R- can also be defined such
that:
or in terms of the example:
Rl = 9l(pl' P2' P3}
(4.10)
R2 = 92(P4, P5)
Given these definitions of aggregate price and quantity indices and
the description of the two-stage budgeting procedure, it is desirable
for the procedure to be consistent in the sense that solution of the
consumers' allocation problem in two stages leads to the same solution
vectors for the private good quantities (the X^) as would be obtained
if one were to solve the larger (in terms of number of parameters)
allocation problem:
4-50
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Max U(f1(X1/ X2, X3), f2(X4, X5)j (4.11
5
Subject to I P.X, = M
1
In order for this process to take place in a consistent fashion,
Strotz (31) and Gorman (32) have shown that the first-stage functions
must be weakly separable and that each of the subfunctions [see
Equation (4.9)] must be homothetic. Furthermore, these conditions are
necessary and sufficient. Before continuing with the outline of the
consumer's decision problem, a discussion of the terms separable and
homothetic is presented.
Separability—
Formally, one can define a group of goods to be (weakly)
separable if and only if the marginal rate of substitution between any
two goods in the group is independent of the quantity of any good
outside the group. With the marginal rate of substitution defined as
the ratio of marginal utilities,* this definition can be represented
mathematically as:
a /au/ax-jX
* Recall that marginal utility is defined as the partial derivative of
the utility function with respect to the good in question.
4-51
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where the definition has been particularized to the division of goods
suggested by Equation (4.9). Green (33) provides a proof that
satisfaction of this condition allows one to write the utility
function
U = U(Xlf X2, X3, X4, X5) (4.13)
like the one shown in Equation (4.11).
The reason that the concept of separability is so important to
economic analysis is that it places specific restrictions on the forms
of the demand functions to be estimated.* In Stage 2 of the two-stage
budgeting problem, by using the notion of separability as a maintained
hypothesis, one can look at the system of demand equations for such
quasi-disaggregate food items as meat, vegetables, fruits, and dairy
products without reference to non-food items like men's pants. Thus,
separability is consistent with the notion that households naturally
group goods into "separable" classes of activities. Furthermore, at
the Stage 1 aggregate level, the concept of separability provides a
rationale for limiting the range of expenditure categories represented
by the %•. An example relevant to the present study comes to mind.
In this study, we ignore labor-leisure decisions of the consumer. We
take income as fixed, and assume that recreational (leisure) expendi-
tures are separable from the group of consumption categories that are
* Note that separability also is important for the household produc-
tion framework discussed earlier. See Muth (27).
4-52
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examined. This is not to say that recreational plans are not affected
by the level of air quality. Rather, the assumption is made that
changes in air quality do not cause reallocations between consumption
and leisure activities. Separability provides the theoretical basis
for making this division.
There are other types of separability besides the weak
separability definition given here. For our purposes, however, weak
separability meets our needs. There are few accessible treatments of
separability in the economics literature, but one source is Beaton and
Muellbauer (34).*
Separability is also a useful concept in the construction of
consistent price and quantity indices. Recalling the first stage of
the two-stage budgeting problem [Equation (4.7)], one might
legitimately ask how quantity indices (Z^) and price indices (R^) are
obtained for the aggregate service flows. The key to answering this
question involves specific mathematical assumptions for the
subfunctions of the budgeting process. In particular, these
subfunctions must be homogeneous of degree one.
* The mathematically sophisticated reader can find detailed
descriptions of separability and functional structure in Blackorby,
et al. (35).
4-53
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Homotheticity and Homogeneity—
A function f(x) is defined to be homothetic if there exists a
homogeneous function of degree one such that
f(x) = 0(g(x)) (4.14)
where 0 is a monotonic transformation. An implication of
homotheticity is that a ray through the origin (in goods space) will
cut all indifference curves at a point of equal slope. This implies,
in turn, that there are unitary income elasticities, and that a change
in demand due to a change in price will be independent of income.
Homogeneous functions are a special case of homothetic functions.
In particular, a scalar-valued function f(x) is defined to be
homogeneous of degree a if it satisfies the relationship
f(tx) = taf(x) .
In the discussion below on consistent aggregation, one of the
conditions required for the existence of a consistent aggregate price
index is that the subfunctions of market goods be homogeneous of
degree one.
Consistent Aggregation—
The notion of separability has been discussed in the context of
reducing the dimensionality of the budgeting problem by adopting
4-54
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assumptions consistent with the grouping of goods into classes of
activities. The use of separability in forming a consistent link
between these groups of goods and the more general classes of service
flows is intimately related to the concept of price aggregation.
The easiest way to understand aggregation across goods is to
construct an example. In particular, consider the aggregate commodity
"food". Figure 4-5 provides a schematic representation of one of the
branches that describes food in the overall "utility tree".* What the
FOOD
DAIRY PRODUCTS
/ \ \
\
\
\
LEAN GROUND
EXTRA LEAN
Figure 4-5. Schematic of a "utility branch".
* The concept of a utility tree is traced to Strotz (31), while Brown
and Heien (36) have discussed "branches" of the tree.
4-55
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tree shows is that goods purchased in the market place are very
individualistic items. In fact, one could define a very specific good
at a specific point in time as being a fundamentally different
consumption good from that same good at a slightly later time. This,
of course, would not be practical. The intuitive test suggested by
economists is that if one good is perceived as being a perfect
substitute for another good, then for purposes of analysis, nothing is
lost by assuming that they are the same good. Thus, in terms of
information needs for the budgeting procedure, one might expect to
obtain the most disaggregated data at the level of "hamburger",
"sirloin", etc. Implicitly, it is assumed that different qualities of
hamburger are reflected as part of an average price obtained from the
sample of observations for hamburger, and that relative prices among
qualities of hamburger remain constant.*
The question to be answered here is how does one move from
hamburger to beef to meats to a price and quantity index for food?
The theory of index numbers can be extremely complicated, and we save
the description of the actual process of aggregation for the DATA
section.
* This latter point is known as the Composite Commodity Theorem of
Hicks. Note that if one believes the theorem holds for higher
levels of aggregation (i.e., that relative prices did not change),
then one could form an aggregate quantity index on the basis of
price proportionality alone. Similarly, if one assumes that goods
in a group are always consumed in fixed proportions, then a
consistent price index for the group can be formed. The form of
aggregation we adopt, based on the notion of functional
separability, does not require these assumptions.
4-56
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In this section of technical details, further discussion of aggrega-
tion is limited to a theorem concerning the existence of an aggregate
price index.
The theorem is taken from Blackorby, et al. (37). In the
notation used earlier, the theorem can be stated:
If the utility function U [see Equation (4.7)] is weakly
separable, then there exist price indices
Ri = gi^Pi^ for a11 i '•see E<3uation (4.10)]
such that R^Z^ = Mi
which implies that
I RiZ* = M
where Zi = Gi[fi(Xi)] = hi(Xi) [see Equation (4.9)]
and G^ is a monotonic transformation of f•
*
Zj_ is the optimal value of 7,^ obtained by placing the solution
values of X^ in Stage 2 into the quantity index represented
by Equation (4.9) ;
4-57
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if and only if
each of the subfunctions fj_(X^) is homothetic. This
implies that we want to choose G^ such that h^(Xj_) is
homogeneous of_ degree one.*
The various concepts underlined in the statement of the theorem are
items that have been discussed in previous pages of this section.
If the conditions of the theorem are satisfied, aggregate price
and quantity indices can be defined, and the two-stage budgeting
problem takes on real meaning. Thus, demand relationships can be
estimated and the link between the two budgeting stages established.
Naturally, of primary concern here is the effect of air quality
changes on demand. Earlier, it was noted that air quality could be
entered as a shift parameter in the demand equation for disaggregate
(market) goods. This approach is retained here and formalized in a
later part of this section. There is also a question as to how air
quality might affect the demand for the aggregate service flows.
There are two possibilities. As with the disaggregate goods, air
quality can serve as a shift parameter to the broad categories of
goods. Alternatively, given the definition of the aggregate price
index, changes in air quality can impact the level of the index.
A proof of this theorem appears in Blackorby, et al. (37)
4-58
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This suggests the following procedure for identifying the effects
of air quality changes on allocation decisions. First, demand systems
for the disaggregate stage are estimated. With the assumption of weak
separability, there will be as many disaggregate systems as there are
categories of aggregate service flows. Furthermore, for some of these
demand systems, air quality may be a statistically significant
explanatory variable.
Given the estimated parameters of a particular disaggregate
demand system, it is possible to use the theorem stated above to
define price/quantity indices for the associated aggregate good. In
particular, for homothetic disaggregate stage subfunctions, the
marginal budget shares can be used to form a subfunction which
satisfies the homogeneity requirements of the theorem. Since this
function depends on the (optimal) quantities demanded of the goods in
a particular disaggregate demand system, it also depends indirectly on
the level of air quality. Thus, air quality effects will show up as
implicit shifters to the price index for an aggregate service flow.
The interpretation is that reduced levels of air pollution reduce the
cost of obtaining a unit of an aggregate service flow such as
cleanliness.
The important point to recognize is that the marginal budget
shares, which are used to ensure the linear homogeneity of the
quantity index, can be obtained from the solution to the Stage 2
decision.
4-59
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This model forms the basis for the estimation procedures used in
this study. However, certain topics must be considered before the
various demand systems are actually estimated. These topics include a
discussion of alternative functional forms; the manner in which air
quality information is included in the analysis; restrictions to the
general model that are specific to an air quality benefits model; and
a brief discussion of hypotheses to be tested.
Alternative Functional Forms
Earlier in this section, it was mentioned that demand systems
should be plausible in the sense that they can be derived from a
utility function which meets various "regularity" conditions. This
can be viewed in two ways. On the one hand, various forms for demand
systems could be estimated first, and if the "Slutsky Conditions" are
met, the "integrability" conditions could be used to define the
utility function up to a constant of integration.* This process can
be extremely messy.
Alternatively, one can assume a specific form for the utility
function, recognizing the implied assumptions for the associated
demand systems, and proceed to the estimation of these systems.**
This is the approach adopted here.
* See Samuelson (38) for a discussion of integrability, and Maler
(21) for an example application of the process described here.
** For a summary of the theoretical constraints of demand systems, see
the review article by Brown and Deaton (39) or Barten (40).
4-60
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Consumer preferences have been characterized by a wide variety of
models in the economics literature. Among those most frequently used
are:
• Cobb-Douglas.
• Linear Expenditure System [Pollak and Wales (41)].
• The Translog form [Christensen, Jorgensen, Lau (42)].
• Quadratic Expenditure System [Pollak and Wales (43)].
• Rotterdam System [Theil (44)] (especially Chapters 6
and 7 ) .
• Linear Logarithmic from the indirect translog with
homogeneity restrictions [Lau, Lin and Yotopoulos
(45)].
The discussion of choice of functional forms is left to the
ESTIMATION section. It should be pointed out, however, that two forms
are chosen for estimation in order to provide some indication of the
sensitivity of the results to alternative structural specifications.
The two forms are the linear expenditure system (LES) and the
homogeneous translog system (HTL).
Inclusion of Environmental/Demographic (E/D) Variables
The model structure for the two-stage budgeting procedure
described in Equations (4.7) and (4.8) is conspicuous in its absence
of an air quality variable. In two recent articles, Pollak and Wales
(41,43) have proposed two ways for including exogenous environmental/
demographic effects in systems of demand equations. While the
4-61
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application of their research has been specific to the linear
expenditure system (LES), the quadratic expenditure system (QES), and
various forms of the translog system, the concepts embodied in
translating and seal ing are appropriate for any plausible demand
system.*
Translating—
As described in Pollak and Wales (43), translating involves
introducing n translation parameters (d-,, ... , d ) into an n-variable
demand system, such that these parameters and only these parameters
depend on the environmental/demographic (E/D) variables.** In
particular, the process of translating replaces each demand function
in the class of demand functions x^ = w1(P,M) by the modified
(translated) system:
ci = £•"•(?,M) = d.j_ + wi(pi,M -
A -j
where w (•) is a demand function, P is a vector of prices; p-^
represents a specific price; the x-'s are quantities demanded; and M
is expenditure. The d.'s are functions which describe the relation-
ship between x- and the E/D variables. For example, d- might be
written as:
* See footnote 7 of Pollak and Wales (43) for a caveat on the
plausibility of "translated" systems.
** As a reminder, recall that the demand systems are the solutions to
the utility maximization problems described by Equations (4.7) and
(4.8).
4-62
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d, =
JL
E
1_ V.^
where a- and S- are parameters and Efc is the t E/D variable (e.g.,
ambient annual 24-hour concentrations of S02).
In terms of the utility function,, the original utility function
of the form U = U(x-,, x2, ... x ) is replaced by a "translated" system
A A
U = U(x1-d-L, x2-d2, ... , xR-dn) (4.16)
Intuitively, the process of translating permits the introduction
of parameters which may increase or decrease demand, such that the
changes are independent of prices and expenditure.
Scaling—
When "scaling" is used to introduce E/D variables into demand
systems, the (scaling) factor is multiplicative. This is in contrast
to translating which relied on an additive (translating) factor.
Thus, n scaling factors (r^, ... , rn) are introduced into a class of
demand functions x^ = w1(P,M) such that the modified system becomes
xt = w1(P,M) = ^iwi(P1r1, p2r2, ... pRrn, M)
4-63
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In this case, each scale factor r^ can be expressed as a function of
E/D variables. A convenient specification of this relationship might
be
T
•••«
t=l
j.
£ aitEt
where again Et is the tfc E/D variable.
The process of scaling is consistent with the notion that the
effects of the E/D variables are principally price dependent. This is
in contrast to the translating process where the E/D parameters are
introduced as additive effects which are independent of prices and
expenditures.
In the present analysis, translating would seem to be the more
appropriate concept. The hypothesis would be that E/D variables act
as shifters to the quantities demanded of the various goods. In
effect, variations in demand are permitted to occur, conditional on
the levels of the E/D variables. With the scaling process, the price
dependent nature of the transformation makes it difficult to isolate
the effect of changes in the E/D variables (specifically air quality)
on the aggregate index of service flows.
Translating and scaling also have implications for the scope of
benefits associated with air quality changes. The introduction of air
4-64
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quality parameters as "shifters" to an original system of demand
equations implies that air quality effects are viewed as affecting the
utility function indirectly through a kind of production process of
service flows. It is possible of course that some effects associated
with air quality changes may be primarily utility effects. An example
would be the amenities attached to simply having a cleaner environ-
ment. While the model presented in this section does not.identify
pure utility effects, it does have the advantage that welfare changes
induced by alternative levels of air quality involve simple price
changes rather than shifts in the utility function.*
Deviations From Assumptions of the Standard Utility Maximization
Model
Two of the maintained assumptions in the standard utility model
are that prices and income are fixed. These assumptions are examined
more closely in this subsection.
The assumption of fixed prices can be interpreted as follows.
The price for a good is determined through aggregate demand and supply
forces in the market for the good. From the perspective of a single
consumer, he is such an insignificant part of the total number of
purchasers that any action he takes will have no affect on the market
* In the Watson and Jaksch (15) article cited earlier, assumptions are
adopted on the demand side that are consistent with observing no
change in expenditures for a given change in air quality. Thus, the
benefits of improved cleanliness identified in their model can be
attributed to a pure utility effect.
4-65
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price he faces. Another way of stating this is that consumers behave
as if they can buy all they desire of a specific good at the market-
determined price.
Does the assumption that price is fixed and beyond the control of
the consumer make sense for the model developed here? For the most
part, the answer is yes. However, for those prices that may be
affected by the location-specific attribute of air pollution, special
assumptions may be required. As an example, people can change the
rent schedule they face by moving to a location with different air
quality attributes. Similarly, wage rates may be dependent on
locational amenities. In this study, all location decisions are
assumed to have been made, and any adjustments observed in the
patterns of demand occur conditional on this decision. Thus, two
plausibly significant means of adjustment are removed from the
analysis.
These adjustment possibilities could be incorporated into the
expenditure model if the model were tailored to reflect dynamic
adjustments. That is, the location adjustment decision is viewed as
occurring only in the long-run. The model developed in this section
is a short-run, static model where long-run decisions are assumed
fixed.*
* A possible way to structure a long-run model would be to employ the
notion of a conditional demand function. See Pollak (46).
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Tests of Hypotheses
The purpose in constructing the elaborate two-stage model is to
be able to estimate the benefits of air quality improvements.
However, if the benefit numbers are to have meaning, they must be
calculated from demand equations that are plausible and for which air
pollution is a statistically significant explanatory variable.
The literature on physical damage functions reports a variety of
products or activities that may be impacted by specific types of air
pollution and this information can provide an a_ priori basis for
including measures of air pollution in selected demand equations.
Given an estimated coefficient for the air pollution variable,
statistical tests must be undertaken to determine if the coefficient
is statistically different from zero. That is, does air pollution
have an effect on demand. Furthermore, one can check if the sign of
the coefficient corresponds to a_ priori notions. In single equation,
linear regression models, the Student t-test is used most frequently
to identify statistical significance. In the present effort,
nonlinearities within or across equations in the demand systems
require the use of more sophisticated tests such as likelihood ratios.
This test is explained more fully in the EMPIRICAL RESULTS subsection.
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Summary of the Technical Model
In this subsection, a model based on individual behavior has been
developed which can be used to identify the benefits associated with
changes in air quality. The principle advantages of the model are
that it is based on established economic theory and explicitly
recognizes the decision-making ability of individuals. In addition,
the estimation of demand systems permits the identification of
benefits in a theoretically sound manner.
Implementation of the model described above requires the
following steps:
Define subfunctions of homogeneous groups of
disaggregate goods.
Estimate demand functions for the goods appearing in
the subfunctions; air quality variables enter the
model directly at this stage.
Utilize the parameter estimates from the disaggregate
demand functions to define aggregate price and
quantity indices.
Estimate the demand functions for the aggregate
service flows.
With the aggregate price indices dependent on air quality, changes in
air quality affect the demand for the aggregate service flows, and
economic benefits can be estimated.
4-68
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DESCRIPTION OF DATA
An empirical analysis of the model requires, at a minimum,
expenditure data and either price or quantity information for a
variety of budget items. Furthermore, the budget information must be
available on a location-specific basis so that the appropriate air
quality data can be merged. The objective of this subsection is to
provide a detailed account of the economic data used in the empirical
analysis. A description of the air quality data is available in
Section 3.
Scope of Economic Data
In 1972-73 the Bureau of Census conducted a Consumer Expenditure
Survey for the Bureau of Labor Statistics (BLS). Approximately 10,000
households from across the country were surveyed in each year, with
expenditure data available for over 2,000 items.
This data set can be accessed via computer tapes created by BLS.
Two tapes in particular — the Interview Survey Detailed Public Use
Tape No. 2 and the Diary Survey Public Use Tape — provide the
expenditure data required for this study. Unfortunately,
confidentiality restrictions prevent the assignment of location
identifiers to individual household records. Since it is imperative
that location-specific air quality data be matched with location-
4-69
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specific expenditure information, the tapes cannot be used as the
primary data source for the analysis.
BLS does, however, publish summary tables of information from the
tapes. These tables report average household expenditures by Standard
Metropolitan Statistical Area (SMSA), and are available in BLS
Bulletin 1992, Consumer Expenditure Survey: Integrated Diary and
Interview Survey Data, 1972-73 (47). In this publication, the data
include average household expenditures by SMSA for approximately 100
items. Unfortunately, for each item, the publication combines
information from the two survey years into a single number.
This latter difficulty was resolved through contact with BLS
personnel. In particular, an unpublished version of Bulletin 1992
data was obtained which distinguished between the survey years.*
However, it was not possible to further augment the data either in
terms of expenditure categories or the number of SMSAs reported.
Table 4-5 lists the SMSAs included in Bulletin 1992. Of the 28
cities listed, four had to be dropped because of data deficiencies
elsewhere. Thus, the data set consisted of observations for 24 SMSAs
in two different years.
* George Weeden and Chuck Bailey of BLS were most helpful in providing
this information.
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TABLE 4-5. STANDARD METROPOLITAN STATISTICAL AREAS IN BULLETIN 1992
New York City Atlanta
Boston Baltimore
Philadelphia Washington, DC
Scranton* Houston
Buffalo Miami*
Kansas City San Diego
Milwaukee Los Angeles-Long Beach
Minneapolis-St. Paul San Francisco-Oakland
St. Louis Denver
Chicago Honolulu
Cleveland Portland*
Cincinnati Seattle-Everett
Detroit Anchorage*
The expenditure categories included in Bulletin 1992 are listed
in Table 4-6. In addition to these items, demographic and income
information is also available. Of course, expenditure information
alone is not sufficient for estimation of the two-stage budgeting
problem. Price or quantity information is also required. Ideally,
this data would have the same regional breakdown as that of the
expenditure data.**
Such data does exist for prices. In 1971, BLS conducted a survey
of average prices in 56 urban areas for approximately 200 detailed
nonfood commodity and service categories. [U.S. BLS: "Average Retail
* Not included in analysis due to data deficiencies elsewhere.
** See Pollak and Wales (41) for a discussion of the estimation of
household budget data with no regional price variation and only two
years of data.
4-71
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TABLE 4-6. EXPENDITURE CATEGORIES IN BLS BULLETIN 1992
Current consumption expenses, total
Food, total
Food at home, total
Cereals and cereal products
Bakery products
Beef
Pork
Other meats
Poultry
Fish and seafood
Eggs
Fresh milk and cream
Other dairy products
Fresh fruits
Fresh vegetables
Processed fruits
Processed vegetables
Sugar and other sweets
Nonalcoholic beverages
Fats and oils
Miscellaneous prepared foods, condiments, and seasonings
Food away from home
Meals as pay
Alcoholic beverages
Tobacco products and smoking supplies
Housing, total
Shelter, total
Rented dwellings
Owned dwellings
Other lodging, excluding vacation
Fuel and utilities, total
Gas, total
Gas, delivered in mains
Gas, bottled or tank
Electricity
Gas and electricity, combined bills
Fuel oil and kerosene
Other fuels, coal, and wood
Water, garbage, sewerage, trash, and other
(continued)
4-72
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TABLE 4-6 (continued)
Housing (continued)
Household operations, total
Telephone
Housekeeping and laundry supplies, total
Laundry and cleaning supplies
Other household products
Postage and stationery
Domestic and other household services
Housefurnishings and equipment, total
Household textiles
Furniture
Floor coverings
Major appliances
Small appliances
Housewares
Miscellaneous
Clothing, total
Male's, 2 and over
Female's, 2 and over
Children's, under 2 years
Materials, repairs, alterations and services
Dry cleaning and laundry
Transportation
Vehicle purchases (net outlay)
Vehicle finance charges
Vehicle operations, total
Gasoline and fuels
Other
Other transportation
Health care, total
Health insurance
Expenses not covered by insurance
Nonprescription drugs and medical supplies
Personal care
Recreation, total
Owned vacation home
Vacation and pleasure trips, total
Food
Alcoholic beverages
[continued)
4-73
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TABLE 4-6 (continued)
Recreational (continued)
Lodging
Transportation, total
Gasoline
Other transportation
All expense tours
Other vacation expenses
Boats, aircraft, and wheel goods
Other recreation, total
Television
Other
Pets, toys, and games
All other recreation expenses
Reading
Education, total
Private
Public
Day and summer camp
Miscellaneous
Personal insurance, retirement, and pensions, total
Life, endowment, annuities, and income insurance
Other personal insurance
Retirement and pensions
Gifts and contributions
Prices of Selected Commodities and Services, Fall 1971" (48)]. In
this survey, prices were collected from a sample of outlets in each
urban area, with particular attention given to identifying different
levels of product quality for pricing purposes. Although the sample
size for each item for each city is small (usually less than 20
observations), these are the best data available for place-to-place
comparisons.
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A question might arise as to the possibility of using a city- and
category-specific Qonsumer Price Index (CPI) as a measure of price.
The CPI measures the value of a particular bundle of goods as it
changes over time. If, for example, a group of goods cost $10.00 in
1967 and $18.00 in 1980 (for the same goods), an index of 1.8 would
describe the fact that prices had risen 80 percent relative to a base
value in 1967. Typically, the base of the CPI is reported in terms of
100, so that in the above example, the CPI in 1980 would be 180.
While city-specific CPI exist, they are reported with each city
indexed to 100 in the same year. Thus, the CPI only reveal changes
across time within the city and cannot be used for place-to-place
comparisons. There is no guarantee that the bundle of goods consumed
in the base year represented equivalent levels of economic welfare
across cities. Naturally, once place-to-place prices have been
developed, the CPI is invaluable for adjusting prices across time.
Such an adjustment process was necessary for the nonfood price
data described above. This occurs because the actual prices are in
1971 dollars, while the available expenditure information is drawn
from 1972 and 1973.* Consumer price indices obtained from U.S. BLS:
"Handbook of Labor Statistics, 1978" (49), Table 124, were used to
bring prices and expenditures into comparable terms. Table 124 of
* In the small number of cases where price data were missing for a
particular item in a particular city, the average price for that
item from cities with data was computed and assigned to the missing
data cell.
4-75
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Reference (50) contains CPI data for 23 of the SMSAs listed in Table
4-5 and six categories of consumer expenditure (All Ite.ms, Food,
Housing, Apparel and Upkeep, Transportation, and Health and
Recreation) .*
As an example of the calculations required for price adjustment
across time, consider the following. Assume that it is reported that
the average price of a man's suit in Atlanta in 1971 is $200.00.
Furthermore, assume that the "apparel and upkeep" CPI in Atlanta was
116.0 in 1971 and 118.7 in 1972. The price of a man's suit in Atlanta
in 1972 can then be determined from:
(118 7
-—-i- J = $204.66
lib . U
Given that the 1973 apparel CPI is also known, the price of a man's
suit in 1973 can be determined in the same fashion. This adjustment
procedure would take place for each good for which actual price data
existed.
The price data available in Reference (49) do not include prices
for food items. Such information is required in order to complete the
match-up with the available expenditure information. Food prices were
* No detailed CPI information is published for Denver. Denver prices
were adjusted with an average of the North-Central and West Regional
CPI.
4-76
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obtained from U.S. BLS: "Estimated Retail Food Prices by Cities, 1973
Annual Averages" (50). This publication contains detailed price
information for nearly 100 food items for 23 of the SMSAs listed in
Table 4-5.* Again, in order to make the 1973 (food) prices comparable
to the 1972 and 1973 expenditure data, the "food" CPI was used to
deflate the 1973 food prices to 1972 terms.
In summary, the economic data consist of expenditure data for 24
SMSAs for each of two years, and actual price information adjusted by
a city- and category-specific CPI. The reader may have noted,
however, that the level of detail available in the price data is
greater than that available in the expenditure data. For example,
expenditure information is available for "beef", while price informa-
tion includes three different types of steak, three different types of
roasts, and hamburger. Thus, adjustments are required to reconcile
the levels of aggregation before estimation is possible.
Aggregation
In the subsection describing the technical model, the issue of
aggregation was discussed briefly. The concern there was with
necessary and sufficient conditions for the existence of a consistent
aggregate price index. The framework within which the aggregation
took place was the two-stage budgeting process, where the
Unpublished data on food prices for Denver were obtained from BLS.
4-77
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(disaggregate) second stage was defined in terms of observed prices
and expenditures.
The issue here is, can the available price and expenditure
information be defined so that the disaggregate stage can be
estimated? One of two alternatives is required. Either a way is
found to disaggregate expenditures to the level of the demand prices
or the observed prices must be aggregated to the level of expendi-
tures. If the former option were possible and carried out, the
econometric burden at the second stage would be severe, since actual
price data exist for over 300 items. On the other hand, aggregation
of the price data would leave a second stage estimation problem that
would involve 50 or fewer goods. The problem with the latter approach
is that the only method described thus far for consistent price
aggregation involves estimation of systems of equations.
Consequently, it would appear that a burdensome econometric problem
still exists.
A Non-Econometric Approach to Consistent Indices—
Diewert (51) shows that it is possible to define consistent price
and quantity indices without having to estimate a series of functions
like those defined in the second stage of the budgeting procedure.
Diewert1 s approach is based on assuming a particular form for the
"disaggregate" stage subfunction. The underlying preferences are
assumed to come from a homogeneous translog specification. That is,
4-78
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if X is a vector of disaggregate goods, then the subfunction can be
written as
N N N
In £(X) = ^o + 13 ai ln xi + 2 E C ^jk ln xj ln xk
i=l =l k=l
where Iiai = 1 i3jk = ,3kj and £k?jk = 0 for j = 1, ... , N. This
function can be viewed as providing a second-order approximation to an
arbitrary twice continuously dif f erentiable linear homogeneous
function [Diewert (51), p. 119].*
If this function is assumed to represent preferences at some
disaggregate level, then a consistent quantity index, the Tornquist
approximation to a Divisia index, can be defined. The index is
written as:
N
TF
n=l
where f(*) is the subfunction over which the aggregate commodity
index is defined.
xr refers to the vector of disaggregate goods in the r
city.
Q(P°,pr,x°,xr) = f(xr)/f(x°) = TT n
* Recall the conditions of the theorem concerning the existence of an
aggregate price index. One of these conditions was that the
subfunction be linearly homogeneous (i.e., of degree one).
4-79
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x is a normalizing factor for the vector of disaggregate
goods. In a time series study, this would be a
particular year. For our cross-section study, we have
normalized on the basis of the average across all cities
in our sample.
n indexes the number of goods in the disaggregate group.
As written, the index defines an aggregate quantity
measure for N disaggregate goods.
Sj; is the, expenditure share of the n disaggregate good in
n. 4- Vt v v v v v
the rcn city. It is defined as s£ = p£x£/pr • x .
S^ is the expenditure share of the nfc disaggregate good for
the "average" SMSA.
Equation (4.19) depends only on disaggregate price and quantity
information. Although the assumptions required to form this index are
comparable to those outlined for the two-stage method, in the present
case there is no need to estimate econometrically a series of
commodity subfunctions in order to define a consistent index. Note
also that, given a consistent quantity index, a consistent price index
can be defined from the following relationship:
P(P0,pr,x0,xr)Q(p0,pr;x°,xr) = pr - xr/p° ' x° (4.20)
where P is the aggregate price index and Q is the aggregate quantity
index defined above; pr • xr is the inner product of prices and
quantities in the r city; and p • x is the inner product of prices
4-80
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and quantities in the base city (i.e., average across SMSAs in the
sample).*
The assumptions underlying construction of the Tornquist-Divisia
(T-D) Index permit consistent price and quantity indices to be
developed based only on price and expenditure information. However,
the form of the index does not allow one to identify air quality
effects. Consequently, the econometric procedure for deriving
aggregate indices must still be used in the second stage of the
budgeting procedure. The T-D index is useful for aggregating market
prices to a level consistent with the "market" goods of this second
stage.
Figure 4-6 outlines the process used to construct the various
data files used in the analysis. The initial data requirement is
price and expenditure information for very specific market goods.
These data are obtained from the ELS tapes and Reference (48). Given
this information, the T-D index is then used to aggregate the price
and expenditure data to a level of 20 goods. This process is
described in detail below.
The 20 goods defined in the T-D aggregation procedure represent
the "market goods" that enter the subfunctions defined for the second
* This relationship is known as the Fisher weak factor reversal test.
It requires that a normalized price index times a normalized
quantity index be equal to normalized total expenditures for all
goods in the disaggregate group. See Diewert (51).
4-81
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BLS tapes
T-D index
Second stage
maximization
First stage
maximization
Prices and expenditures
for 185 goods
Price and quantity
indices for 20 goods
Price and quantity
indices for seven
aggregate goods
Demand system
for aggregate
goods
Figure 4-6. Schematic of data development.
4-82
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stage of the two-stage budgeting procedure. Thus, once the T-D
aggregation has been performed, the procedures described in the Model
Development subsection can be initiated. These steps are shown in the
bottom part of Figure 4-6.
Definition of SMSA Expenditure Data—
As Equation (4.19) shows, disaggregate price and quantity
information is needed to implement the (T-D) procedure. The price
data are available (with SMSA variation) but quantity or expenditure
data are not available at the same level of disaggregation on an SMSA
by SMSA basis. In this case, however, it is possible to utilize the
detailed BLS computer tapes from which the expenditure data were
developed. Earlier, it was noted that the computer tapes could not be
used in the estimation phase because specific location identifiers
were not available. This was crucial when merging air quality data
was an immediate concern. However, specific location identifiers are
less crucial in forming measures of average expenditure for use in the
(T-D) index. The type of location information that is available on
the tapes is a regional identifier (Northeast, South, North Central,
and West), and a code representing the city size of the respondent.
This information can be used in conjunction with city-specific
demographic characteristics to obtain a reasonable approximation to
expenditure allocations on a city-by-city basis.
The following approach was used. First, 185 distinct goods were
identified for which actual price data were available. Then the tape
4-83
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codes corresponding to these 185 items were entered in a computer
program so that expenditure data for these items could be read from
the tapes. In addition to the expenditure information, the computer
program classified each household record by several characteristics:
region of country (four possibilities); city size greater than
1,000,000 (one possibility);* race of family head (two possibilities
— black or non-black); education of family head (two possibilities —
greater or less than high school diploma). Thus, average expenditures
for the 185 items were recorded for 16 different cells (4 regions x 2
race classes x 2 education classes). A typical entry might be
interpreted as: The average non-white household in the West with the
head of family having at least a high-school diploma spent $70 per
year on bread.
Given this stratified information, the 1970 Census of Population
(52) was used to obtain information on the percentage breakdown by
SMSA of racial and educational attainment characteristics.** These
percentages were then used as weights in order to identify SMSA-
specific average expenditures for each of the 185 items.
* The program was restricted to read only those records from house-
holds in areas of more than 1,000,000 people because our 24 SMSAs
fall into this category (with the exception of Honolulu).
** This breakdown includes the cross-comparisons as well (e.g., the
percent blacks with greater than a high school diploma).
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To clarify this weighting process, consider the following
example. Table 4-7(a) records hypothetical expenditure levels for
good number XX in region 1. It is assumed that city A is in region 1
and has population characteristics as shown in Table 4-7(b).
With these data, the average expenditures in city A on good XX
can be calculated as:
$10 x 0.01725 [$10 x % of total population that is black,
>_ 12 yrs. = (0.115 x 0.150)]
+ $12 x 0.26435 (0.26435 = 0.311 x 0.85)
+ $ 6 x 0.13275 (0.13275 = 0.885 x 0.15)
+ $ 5 x 0.58565 (0.58565 = 0.689 x 0.85)
= $7.069 = average expenditures in city A for good XX
This procedure is repeated for each SMSA for each of the 185
items for each of the two years. This procedure yields the
disaggregate expenditure data needed to use the (T-D) index.
Application of the Tornquist-Divisia Index—
Given price and expenditure data for 185 items, the (T-D) index
was employed to aggregate the price data to a level of 20 goods. This
aggregation occurred in several stages. First, a price index for the
185 items was defined for 40 aggregate goods. These 40 goods
corresponded to a level of detail consistent with the expenditure
information available in Bulletin 1992. Next, the 40 item group was
4-85
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aggregated to 20 goods. For this stage of aggregation, the expendi-
ture data found in Bulletin 1992 was used to construct the expenditure
shares needed for the (T-D) index.*
The price and expenditure data for these 20 goods formed the data
set used in the second stage of the budgeting model. Table 4-8 lists
the 20 items that make up the set of goods. Note that they are
grouped into seven categories. This higher level of aggregation
corresponds to data used in the first stage of the budgeting model.
The conditions outlined earlier for the two-stage process to be valid
require that the seven most aggregate goods be weakly separable in
their subsets of goods. Thus, the manner in which the 20 goods are
grouped places restrictions on the possible substitutions, where these
groups reflect prior beliefs about how households make decisions. The
groupings shown in Table 4-8 are consistent with the major classes of
data items listed in Bulletin 1992.**
A statistical profile of the expenditure data is shown in Table
4-9 by category of goods. On average, these items account for 40
* Explicit expenditure information was not available for one of the
40 items. This was home repairs. In Bulletin 1992, home repairs
was lumped into the expenditures by renters or owners of property.
Because of the possible importance of these expenditures in
measuring air quality benefits, data on home repairs were read from
the BLS computer tapes and assignment of an SMSA-specific home
repair expenditure was calculated on the basis of percentages of
home owners/renters in the SMSA.
** See Christensen and Manser (53) for an example of the procedures
required to test separability assumptions. Their application
focuses on the "meat" branch of the utility function.
4-87
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4-88
-------
TABLE 4-9. STATISTICAL PROFILE OF EXPENDITURE DATA — ANNUAL
HOUSEHOLD EXPENDITURE BY GOOD
Variable name
Cereal/bakery products
Meats
Dairy products
Fruits and vegetables
Miscellaneous foods
Repair
Utilities
Laundry/cleaning
Other household products
Textiles
Furniture
Appliances
Housewares
Clothing
Dry cleaning
Vehicle gas and fuel
Other vehicle expenditures
Non-insured medical
Non-prescription drugs
Personal care
Mean
136.33
428.10
184.20
172.73
523.37
129.26
387.17
47.59
47.28
54.65
145.80
85.29
20.46
477.60
89.82
336.45
427.47
273.50
54.59
173.63
Std.
deviation
22.62
89.53
25.47
29.14
58.63
26.70
66.04
8.02
9.16
12.06
37.38
21.69
6.24
77.81
24.70
47.10
50.93
43.15
21.50
24.19
Min
69.04
283.71
126.63
115.70
322.19
76.33
229.40
29.70
26.68
28.06
82.78"
48.48
9.55
397.59
50.64
204.65
327.06
171.09
14.93
107.94
Max
177.23
657.62
230.25
249.92
675.53
179.02
500.64
67.17
68.19
79.30
268.54
154.61
39.05
756.83
158.93
451.88
529.43
353.63
92.63
234.49
4-89
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percent of current consumption expenditures. Statistics for the price
data are given in Table 4-10. The means for the price indices are
unity since all prices are normalized.
Limitations of Data—
The expenditure information drawn from Bulletin 1992 has several
drawbacks. Foremost is the fact that only SMSA averages are reported.
The utility maximization model defined here is based on the actions of
individual consumers (or households acting as a single unit), so that
estimation over SMSA averages presents a new kind of aggregation
problem. Whether or not aggregation across individuals in the data
creates real difficulty depends to some extent on the form of the
utility function and the associated demand system. For example,
Pollak and Wales (41) note that if the demand system is of the Linear
Expenditure type, then no problem arises since the average consumption
pattern of a group is consistent with the consumption pattern that
would be observed given the group's mean expenditure.* Basically, the
assumption made in this study is consistent with the notion that there
exists a composite, representative individual.
The expenditure data could also be improved in terms of the
geographic regions covered and the items defined. Both of these
* Note that aggregation over individuals in the data is fundamentally
different than aggregation across individual utility functions. In
order to be able to aggregate across individual utilities, one must
assume at the least that the marginal propensity to demand out of
income be equal for all consumers. See, e.g., Maler (21), p. 118,
and papers by Lau (54) and Jorgenson, Lau and Stoker (55).
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TABLE 4-10. STATISTICAL PROFILE OF PRICE DATA
Variable name
(price of)
Cereal/bakery products
Meats
Dairy products
Fruits and vegetables
Miscellaneous foods
Repair
Utilities
Laundry and cleaning
Other household products
Textiles
Furniture
Appliances
Housewares
Clothing
Dry cleaning
Vehicle gas and fuel
Other vehicle
Non-insured medical
Non-prescription drugs
Personal care
Min
0.645
0.673
0.636
0.639
0.680
0.443
0.637
0.737
0.655
0.706
0.650
0.796
0.520
0.569
0.642
0.763
0.735
0.631
0.638
0.738
Max
1.638
1.504
1.564
1.736
1.611
1.552
1.696
1.532
1.457
1.370
1.425
1.555
1.450
1.175
1.568
1.451
1.402
1.350
1.734
1.342
Std.
deviation
0.196
0.168
0.177
0.196
0.172
0.266
0.237
0.182
0.163
0.142
0.203
0.153
0.208
0.122
0.236
0.145
0.137
0.174
0.284
0.141
4-91
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limitations could be overcome if it were possible to assign location
identifiers to the BLS tape records. However, confidentiality
restrictions, coupled with project time and resource constraints,
limited further inquiry into these directions. Consequently, at least
for the short-term, the scope of data found in Bulletin 1992 appears
to be the best available.* One recommendation can be made, however.
It is the intention of BLS to conduct continuing annual surveys of
consumer expenditures. If some form of the economic model developed
here is to be used for benefits analysis, it would be to the benefit
of EPA to work with BLS in identifying areas of information needs.
Thus, questionnaires developed for the expenditure surveys could be
structured to obtain the type of data needed by economists to evaluate
air quality welfare effects.
One other point should be mentioned with respect to the
expenditure data. In Table 4-8, seven groups of category expenditure
were listed. While these groups constitute a sizable proportion of
consumption expenditures, they do not represent complete coverage. In
particular, leisure-oriented activities (recreation, reading, etc.)
have been excluded from the analysis. In essence, a separability
assumption has been imposed. This was done for two reasons. First,
many recreation activities take place at some distance from the home,
and since the data do not identify where households recreate, there is
* Some time was spent searching for expenditure data that were city-
specific with an eye towards conducting a detailed intracity
benefits analysis. No good data source was identified.
4-92
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no way to determine air quality parameters at the recreation site.
Second, from a theoretical perspective, if leisure activities are
considered a part of the complete demand system, one must be able to
model the labor-leisure decision of consumers. Data limitations again
precluded this particular extension of the model. While leisure
decisions have been left out of the current analysis, this is
certainly an area where extensions to the analysis should be
considered in the future.
EMPIRICAL RESULTS
In this subsection, empirical results are presented for the two-
stage optimization problem with air quality. Equations are presented
for two alternative demand system specifications in order to get an
idea of the sensitivity of the results to different structural forms.
The demand systems estimated are the linear logarithmic expendi-
ture system which is derived from a homogeneous transcendental
logarithmic (HTL) function [Lau, Lin and Yotopoulos (45)], and the
linear expenditure system (LES) which was developed by Klein and Rubin
(56) and is identified closely with the work of Stone (57).
Prior to a discussion of the results for these two systems, some
general comments will be made on the overall approach to the empirical
part of the study.
4-93
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Framework for Empirical Analysis
For a given functional form, there are two stages in the
estimation process. First, N disaggregate stage systems are
estimated, where N is the number of broad categories identified in the
aggregate stage of the budgeting problem. Given the parameters of the
N disaggregate stage systems, the overall system is then estimated.
As described earlier, the parameters of the disaggregate stage are
important for defining consistent aggregate price indices. In total,
there are N + 1 systems to estimate.
The estimation procedure used is the iterative Zellner technique
(58).* This routine is appropriate for simultaneous estimation of all
the equations in a disaggregate demand system because it allows cross-
equation constraints implied by demand theory to be imposed directly.
Note also that the iterative Zellner estimator is equivalent
asymptotically to a Maximum Likelihood Estimator [Kmenta and Gilbert
(59)1 .
In estimating a system of expenditure share equations, one
equation must be dropped to prevent singularity of the covariance
matrix. Singularity arises because the share equations sum to one, by
definition. Fortunately, since iterative Zellner results in maximum
likelihood estimates, the choice of the equation to be dropped can be
* The Zellner routine in the GREMLIN set of programs of the TROLL
software package was used for estimation.
4-94
-------
made arbitrarily. Note also that if the system contains only two
equations, then only one equation is estimated. In this case, a
restricted version of Ordinary Least Squares (OLS) rather than the
Zellner systems method is appropriate.
In those instances where the Zellner routine was used, the
estimation took place in two phases. First, each equation of the
system was estimated by restricted OLS in order to derive a set of
initial values for the parameters and begin the iterative Zellner
estimation. It should be noted that the optimization algorithm only
guarantees local optimums. Thus, while convergence to similar
parameter estimates with different starting guesses cannot guarantee a
global optimum, it does lend additional credence to the estimates.
For the systems results reported here, alternative sets of starting
guesses typically led to identical results out to the third decimal
place.
The estimation of systems of equations in share form also has
o
implications for the reported R . First, if households consume
approximately constant shares given regional price variation, one can
2
expect a low R . Second, the across-equation parameter constraints
9 9
can result in negative R being reported. Thus, although the R is
reported in later sections, for completeness, it is essentially
meaningless in the context of Zellner estimation.
4-95
-------
The way environmental/demographic (E/D) variables are handled in
the estimation phase is also of concern. The discussion of
translating and scaling indicated how the E/D variables might be
included, but there has been no discussion thus far on the statistical
implications of including alternative sets of E/D variables. In
principle, the procedure of testing combination after combination of
specifications until a "good" one is achieved has implications for the
meaning of the statistical tests of significance. This can be
especially important for the E/D variables since the a priori basis
for including a particular variable may seem essentially arbitrary.
Two things can be done to limit the scope of equation testing.
First, every effort should be made to identify meaningful a_ priori
information. For example, previous consumer budget studies may have
considered the impact of different demographic variables on demand
[Pollak and Wales (41)]. Additionally, while our study is unique in
its approach of embedding air quality information within a complete
demand system framework, information from the Criteria Document (5)
can provide guidance in this area.
The second thing that should be done is to develop a "game plan"
for analyzing the statistical significance of E/D variables. Given
the relatively small number of degrees of freedom, and the extended
parameter requirements for systems of equations, a parsimonious
selection process was adopted for the E/D variables.
4-96
-------
The following procedure was employed. Initially, two demographic
variables were considered for each equation — family size and a dummy
variable for region of the country.* The regional variable was equal
to one for the Northeast and North Central SMSAs, and zero otherwise.
There were also eight air quality and two meteorological variables to
consider. These include:
The maximum annual second high reading for SO2 and TSP
in the SMSA (/ug/m ).
The maximum of annual arithmetic (geometric) means for
SO2 (TSP) in the SMSA (Mg/irT).
The average of annual second highs for reporting sites
in the SMSA for S02 and TSP (/zg/m3).
The average of annual arithmetic (geometric) means
from reporting sites in the SMSA for S02 (TSP)
(/"g/m3) .
Annual average temperature for the SMSA in degrees
Celsius.
Annual total precipitation in millimeters.
While the Criteria Document suggests items that may be affected by SO2
or TSP, information on the appropriate averaging times is more sparse.
Consequently, preliminary testing of alternative pollution measures
was conducted. These tests indicated that the maximum annual second
high readings were the most robust variables in terms of magnitude,
* With two years in the sample, a dummy variable for Year may also
seem to be a worthy demographic variable. We did want to limit the
number of demographic variables, and in a choice between Region and
Year, we felt the cross-sectional variations in Region would likely
be more influential in explaining expenditure allocations.
4-97
-------
sign, and statistical significance. Thus, in the equation results
presented here, only the maximum second high measures are included.
Temperature and precipitation variables were also included in
several of the disaggregate demand systems. Given the definition of
the Region demographic variable, temperature and the region dummy may
be expected to play similar roles. This was borne out in the testing
of alternative specifications, and in some instances the greater
locational specificity of temperature made it the preferred variable.
The precipitation variable was never statistically significant in any
of our test specifications, and has not been included in the results
reported here.
The hypotheses to be tested take the form of restrictions on the
E/D variables. Specifically, statistical tests are conducted to
determine if the coefficients of the E/D variables are significantly
different from zero. The test-statistic we employed for the systems
estimates is based on the likelihood ratio X, where
max LA
A = —• (4.21)
max L
The likelihood ratio is the ratio of the maximum value of the
likelihood function L for the econometric model A (which imposes
restrictions) to the maximum value of the likelihood function for the
model B (which is unrestricted). In practice, a test-statistic is
4-98
-------
used which is based on minus twice the logarithm of the likelihood
ratio. This test statistic is asymptotically chi-square with degrees
of freedom equal to the number of restrictions to be tested.*
Finally, it should be noted that although the series of equations
presented below are termed "final specifications", an important part
of the analysis plan involves identifying the sensitivity of results
to alternative specifications, especially with respect to the role of
the air pollution variables. Thus, an indication of the stability of
the equations for different specifications is provided throughout.
Where possible, these tests of sensitivity are also carried forward to
the derivation of aggregate price indices and ultimately to the
benefits calculations.
Linear Expenditure System
The first functional form evaluated is the Linear Expenditure
System (LES). This system was one of the earliest demand system forms
to be subjected to extensive empirical testing, and has been used
frequently over the last two decades.
* In those systems where there are only two goods, so that only one
equation is estimated, an F-test is used to test for statistical
significance. Note that because different criteria are used in
testing the various specifications, there is a possibility that
conflicts on appropriate restrictions could arise in those cases
where the decision to reject or fail to reject is close [Bernt and
Savin (60)]. With respect to the statistical tests conducted for
the environmental variables of the analysis, the decision was
uniformly clearcut.
4-99
-------
The LES demand equations can be written (in expenditure form) as:
Pixi = Pisi + bi M -
where p^ is the price of the i good, x^ is quantity demanded of the
i good, M is total expenditure for the n goods in the system, and s.j_
and b^ are parameters to be estimated. This system has 2n-l
independent parameters and is generated from a utility maximization
problem in which utility is defined as:
bl b2 bn
U = (xi - si) (x2 - s2) ... , (xn - sn) (4.23)
In most applications of the LES system, the S| are interpreted as
"necessary" quantities. Thus, the term (M - Ep^s^) in Equation (4.22)
can be viewed as representing available expenditure net of committed
expenditure. Note, however, that this interpretation is realistic
only if the s^_ are restricted to be positive. Since there is no
theoretical reason for imposing this restriction, we have left the
signs of the s^ as an empirical question. An implication of this is
that both inelastic demands (s- > 0) and elastic demands (s- < 0) are
permitted.
There are a variety of restrictions or assumptions that are
implicit in the LES system. These include:
4-100
-------
• Each x- must be greater than the corresponding s.j_ if
the utility function is to be well-defined.
• The marginal budget shares are independent of prices
and expenditures.
• The utility function of the LES is additive in the
logarithms. This restricts the types of interactions
permitted among goods.
• The Engel curves are linear but pass through the point
(Sp s2, ... , sn) rather than (0, 0, ... , 0). Thus,
it is possible to observe the share of a commodity in
the budget increase or decrease as the budget
increases.*
• The LES utility function is affinely homothetic. That
is, the function is homothetic to the point (s-,, 32,
•« • i s^}.
• The conditions for consistent price and quantity
aggregation can be satisfied since the LES system can
be written as a "Gorman polar form." [See Blackorby,
et al. (35), Section 5.4.4.]
For estimation purposes, it is convenient to rewrite Equation
(4.22) in share form and to normalize by total expenditure. In
particular, the estimating form can be written as:
p • x •
4.24)
for i = 1, ... , n.
* See Anderson (61) for a discussion of an additive perfect price
aggregate model (APPAM), which is an additive specification with
nonlinear Engel curves.
4-101
-------
The empirical restrictions implicit in the system of equations
represented by (4.24) include:
• With Equation (4.24) expressed in share form, only n-1
equations are estimated. The unestimated b^ can be
obtained from the restriction Ib- = 1.
• Across-equation constraints exist for the $•
parameters. Thus, a system method is required in
order to obtain efficient estimates of the parameters.
• The LES system is nonlinear in the parameters. For
example, the first term includes the product (l-b-)s^
where b^ and s^ are both parameters.
• Environmental/demographic variables can be incorpo-
rated through the translating technique. For the LES
system, this implies replacing each s^ by a functional
expression in the E/D variables. In this study, we
have examined variations of a linear functional
expression. For example, we might write s^ = O.Q +
a^TSP, where TSP is the level of particulate matter
concentration and ctg,a-, are parameters to be
estimated.*
The various empirical and structural restrictions listed above
become important in the evaluation of the strengths and weaknesses of
a particular model. These features have only been summarized at this
point because it is likely to be more instructive to discuss them in
the context of specific equation results.
The first use of the LES is in the estimation of the disaggregate
demand systems of the two-stage budgeting problem. The equation
specifications for each of the seven disaggregate systems are as shown
* Pollak and Wales (43) discuss the importance of retaining an
intercept term (i.e., O.Q) in the functional expression for the
translating parameter.
4-102
-------
in Equation (4.24). Table 4-11 lists the commodities in each of the
demand systems, and Table 4-12 is a glossary of the acronyms used in
reporting the equations. Recall that because the dependent variables
are shares and sum to unity, only n-1 equations for any system are
estimated. The value of the unestimated b> can be easily derived from
the adding-up restriction.
Food—
The estimating form represented by Equation (4.24) can be thought
of as a restricted form in the sense that the necessary quantities,
the Sj_, are introduced as a simple parameter. It was noted that one
way in which E/D variables may be incorporated into the LES specifica-
tion is by replacing each s^ by a function of the E/D variables. For
example, one could let s^ = d^ + e^ FAMSZ. In this case, Equation
(4.24) would be written as:
p • x •
-i-
- bi)(di + ei FAMSZ)(pi/M)
(4.25
for i = 1, ... , n.
A comparison between Equations (4.24) and (4.25) makes clear why
Equation (4.24) is referred to as being restricted. Estimation of
4-103
-------
AGE OF THE OPIIMIZATION MODEL
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TABLE 4-12. GLOSSARY OF VARIABLE NAMES
MFOOD Total expenditure on all food items.
CERBAK Expenditure on cereal and bakery products.
CEBAPI Price of cereal and bakery products.
BEPOUK Expenditure on meats (beef, poultry, pork).
BEPKPI Price of meats.
DREGGS Expenditure on dairy products and eggs.
DREGPI Price of dairy products.
FRUVE Expenditure on fruits and vegetables.
FRVEPI Price of fruits and vegetables.
MISCFD Expenditure on miscellaneous food items.
MI5CPI Price of miscellaneous food items.
MSHELTER Total expenditure on home shelter.
REPAIR Expenditure on home repair.
RPRPI Price of home repair.
UTIL Expenditure for gas and electricity.
UTILPI Price of gas and electricity.
MOPS Total expenditure on household operations.
LAUCLE Expenditure on laundry and cleaning products.
LAUCPI Price of laundry and cleaning products.
OHOUSE Expenditure on other household products.
OHSEPI Price of other household products.
MOUSE Total expenditure on home furnishings and equipment,
HTEXT Expenditure on household textiles.
HTEXPI Price of textiles.
FURN Expenditure on furniture.
FURNPI Price of furniture.
APPLS Expenditure on major and minor appliances.
APPPI Price of appliances.
HWARS Expenditure on housewares.
HWARPI Price of housewares.
MCLOTH Total expenditure on clothing items.
MCLO Expenditure on clothes.
MCLOPI Price of clothes.
DRYCL Expenditure on dry cleaning.
DRYCPI Price of dry cleaning.
MTRANS Total expenditure on transportation.
VEHGF Expenditure on gasoline.
VHGFPI Price of gasoline.
VEHO Expenditure for other vehicle operations.
VEHOPI Price of other vehicle operations.
(continued)
4-105
-------
TABLE 4-12 (continued;
MCARE Total expenditure on health and personal care items.
PERSCR Expenditure on personal care.
PERSPI Price of personal care.
NONINS Expenditure for non-insured medical care.
NINSPI Price of non-insured medical care.
NONPRE Expenditure for non-prescription drugs.
NPREPI Price of non-prescription drugs.
Yll, Y12, Expenditure shares for cereal/bakery products, meats,
Y13, Y14, dairy products, fruits and vegetables, and
Y15 miscellaneous foods, respectively.
Y21, Y22 Expenditure shares for repair and utilities,
respectively.
Y31, Y32 Expenditure shares for laundry/cleaning products and
other household products, respectively.
Y41, Y42 Expenditure shares for textiles, furniture,
Y43, Y44 appliances, and housewares, respectively.
Y51, Y52 Expenditure shares for clothing and dry cleaning,
respectively.
Y61, Y62 Expenditure shares for vehicle gasoline and other
vehicle operations, respectively.
Y71, Y72 Expenditure shares for non-insured medical care, non-
Y73 prescription drugs, and personal care,
respectively.
FAMSZ Number of people in family.
REGION Dummy variable for region of country (1 = Northeast
or North Central; 0 otherwise).
TEMP Average annual temperature in degrees Celsius.
SX2HI Annual average of maximum second high concentrations
of SC>2 / for 24-hour continuous monitors.
TX2HI Annual average of maximum second high concentrations
of PM for 24-hour hi-vol grarametric monitors.
4-106
-------
(4.24) implicitly assumes that the e^ and e^ terms are zero. The
approach adopted in each demand category thus involves a generaliza-
tion of the restrictive (4.24) so that E/D variables can be used to
help explain some of the variation in the expenditure shares.
In the food category, there is no _a priori reason to expect
environmental variables to have an influence on the intracategory
allocation of food expenditures. Thus, the initial specifications
include only the demographic variables family size and region.
The unrestricted counterpart to Equation (4.24) is an equation
system where each s^ is replaced by a function that depends on family
size and region. It is convenient to specify this relationship as
being linear in the demographic variables. Note that because there
are "n" s^ terms appearing in each equation of the LES system, the
linear expression will also appear n times. Thus, 2n parameters are
added to the estimation process when the unrestricted form is
estimated.*
In order to arrive at a final specification, the null hypothesis
that a subset of the demographic variables is zero is tested. This is
done with the test-statistic X described earlier. Specifically, it is
* Note that the system is unrestricted only in the sense that it has
been assumed that the universe of relevant demographic variables can
be limited to family size and region.
4-107
-------
assumed that the error terms of the equations are distributed normally
and write the likelihood ratio as:
-2 In X = N(ln IS"1! - In IS"1)) (4.26)
where N is the number of observations, Is I is the determinant of
the unrestricted estimator of the variance-covariance matrix of the
disturbances, is lr is the determinant of the restricted estimator of
the variance-covariance matrix of the disturbances, and In is the
natural logarithmic function.*
Table 4-13 reports the final specification for the food demand
system. Note that in the equation specifications some of the
demographic variables have been restricted to zero. The likelihood
ratio test between the unrestricted model and the model shown in Table
4-13 yields a test-statistic of 2.699. With four restrictions, the
chi-square critical value at the 10 percent level of significance is
7.78. Consequently, with the test-statistic less than the critical
value, we fail to reject the null hypothesis that the restricted
demographic variables are zero. That is, the restricted model is
adopted.
Additional restrictions were imposed on the food demand system,
but the results shown in Table 4-13 were eventually chosen as the
* See Gallant (62) for a discussion of the use of the likelihood ratio
test for hypothesis testing in nonlinear equations.
4-108
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final specification. As a point of interest, a comparison of the
final specification with the completely restricted model led to a
test-statistic greater than 45. Thus, the inclusion of the
demographic variables does add to the explanatory power of the
equation.
Table 4-14 reports own-price elasticities of demand for the
demand system of Table 4-13.* The elasticities are evaluated at the
means of the variables. The own-price elasticity measures the
responsiveness of quantity demanded of a good to a change in its
price. Demand is said to be elastic if a rise in price leads to a
proportionately greater decline in quantity demanded so that total
expenditure of the commodity declines. This is consistent with the
elasticity measure being greater (in absolute value) than unity.
TABLE 4-14. OWN-PRICE ELASTICITIES OF DEMAND FOR POOD DEMAND CATEGORY
Commodity Elasticity
Cereal and baking products -1.245
Meat products -1.079
Dairy products -1.159
Fruits and vegetables -0.985
Miscellaneous foods -1.041
* Note that the nonlinearities in the LES system make it difficult to
assess the statistical significance of the elasticity measures.
Consequently, the standard errors of the elasticities for the LES
system have not been computed, except in the two-equation systems,
when we consider the pollution elasticities.
4-110
-------
Conversely, demand is inelastic if a price increase leads to a smaller
change in quantity demanded such that total expenditure increases.
For the LES system, the own-price elasticities are obtained by
evaluating the relationship:
ax Pi bi
.M^HHt «•» ~ — ^•••M^
aPi xt PiXi
n
M *^ ) Oi Si
k=l
The demand elasticities for the food items are slightly elastic
for four out of the five goods. We have not found elasticity
estimates in the literature corresponding to the disaggregate
breakdown reported here. However, many authors report elasticities
for an aggregate food commodity. For example, Pollak and Wales (43)
estimate a Quadratic Expenditure System (QES) and a Generalized
Translog (GTL) for different combinations of family size and age
composition for three aggregate goods. The reported elasticities for
the food category range from -0.84 to -1.17 for "middle-level"
combinations of the demographic characteristics, so that our estimates
are representative of food elasticities reported by Pollak and Wales.
One can also examine the responsiveness of demand to changes in
the demographic variables. However, since the major interest relates
to the role of the environmental variables in the demand system, a
discussion of this topic is postponed until the results for the next
commodity group are reviewed. The next group, home services, includes
both TSP and SC>2 in the specifications.
4-111
-------
Shelter—
The disaggregate demand system for shelter is composed of two
goods? materials repair and utilities (gas and electricity). Since
the equations are expressed in share form, only one equation is
estimated.
Hypothesis testing for the two-good systems in the analysis is
based on an F-test rather than the likelihood ratio. In particular,
we test whether specific subsets of additional explanatory variables
are statistically different from zero. The appropriate test statistic
is:
2 2 "
.x - *2 .
*
N
nu
- nu
- nr
~ F
rn -n
u r
N-n
(4-28)
u.
22 22
where R^ is the R of the unrestricted equation, R£ is the R of the
restricted equation, N is the number of observations, nu is the number
of parameters estimated in the unrestricted equation, and n is the
number of parameters in the restricted equation. If the evaluation of
Equation (4.28) leads to a value greater than the critical F-value,
then one rejects the null hypothesis that the (restricted) parameters
are zero.
There were several stages in the analysis of alternative specifi-
cations for this commodity group. First, a series of regressions
which included the two demographic variables in several combinations
4-112
-------
were analyzed. In comparisons between the completely restricted model
and models with FAMSZ and Region, we failed to reject the null
hypothesis in all cases except when Region was used as a shifter
affecting repair. However, when the influence of pollution was
controlled for in the specification, the Region variable did not add
significantly to the explanatory power of the equation. Thus, in the
equations of this demand system, neither of the demographic variables
is included.
The environmental variables are statistically different from zero
when entered in a variety of combinations. As used here, the term
combination refers to the different specifications which can be
generated by restricting certain of the environmental variables to
zero. The unrestricted specification includes TSP and S02 measures in
both of the translating terras. In addition to the unrestricted model,
several other specifications were estimated with S02 and TSP. A
summary of the equations estimated is presented in Table 4-15. In the
table, the entries for the elasticities are presented on an equation-
by-equation basis. For each equation, a description is given for the
combinations of TSP and SC>2 included in the specification. For
example, in equation 4, SO- is restricted to zero as a translating
parameter for utility, while TSP is restricted to zero as a
translating parameter for repair. Note that all entries are reported
for the case in which the dependent variable is "repair".
4-113
-------
TABLE 4-15. ELASTICITIES OF ENVIRONMENTAL VARIABLES IN THE SHELTER
DEMAND SYSTEM (dependent variable repair)
Equation Elasticity
Equation 1 (unrestricted)
S02 included in both translating terms 0.069
TSP included in both translating terms -0.066
Equation 2
SO-, included in repair translating term 0.063
TSP included in repair translating term -0.078
Equation 3
S02 included in repair translating term 0.049
TSP included in utility translating term -0.072
Region dummy included in repair translating term
Equation 4
SO- included in repair translating term 0.061
TSP included in utility translating term -0.075
The elasticities for the environmental variables are defined as
the percent change in demand that occurs for a percent change in air
quality. The elasticities in Table 4-15 indicate that an increase in
S02 concentrations leads to an increase in the demand for home
repairs. Conversely, TSP is seen to have a negative relation with the
demand for home repairs. Given that these estimates are derived for a
two-equation system, this latter result can be interpreted as
indicating a direct relation between TSP and the demand for utilities.
4-114
-------
Given the inherently nonlinear form of the LES system (in terms
of the parameters), the interpretation of statistical significance for
the elasticities must be made carefully. First, it should be noted
that t-statistics reported for individual coefficients do have meaning
since the coefficients are asymptotically normally distributed.
However, in order to talk about significance levels for elasticities
or for variables that appear more than once in the equation, two
intermediate steps must be undertaken.
First, it is convenient to linearize the equation directly. This
is accomplished by replacing products of coefficients by a single
parameter. The equation can then be estimated in linear form. Given
the linearized regression, the statistical significance of the
elasticity can be checked by the formula for calculating the variance
of a linear combination of random variables. This can be written as:
n
Var(a0 + a-^ 4- ... , + ctnxn) = E ai Var(xi.) (4.29)
n n
E E aiaj cov(xi' xj
where the a are constants and the x are random variables.
4-115
-------
When these steps are undertaken for the various specifications
shown in Table 4-15, each of the calculated air quality elasticities
is significantly different from zero.
From the elasticities reported in Table 4-15, one can see that
each specification is fairly stable with respect to combinations of
the environmental variables. In order to choose among the different
equations, elasticities were compared and, where appropriate, the F-
test statistic was used. For example, in a comparison between the
unrestricted model and Equation 4 of Table 4-15, the test-statistic
was 0.415, which is less than the critical F-value. Thus, the
restricted model is adopted in this comparison.
There is one other important point to mention about the manner in
which the combinations of environmental variables are allowed to
appear in the specifications. It turns out that not every combination
is consistent with an aggregate price index that behaves in accord
with _a priori expectations. In particular, we note that the
unrestricted model may be consistent with an aggregate price increase
or decrease depending on the marginal budget shares of the goods
involved in the aggregation. Consequently, this is an instance where
it is helpful to use the prior information available about the types
of goods or services that may be affected by air pollution.
Before choosing a final specification for this demand category,
there was one more check performed for the environmental variables.
4-116
-------
While alternative combinations of S02 and TSP have been considered,
one can also examine different transformations of these variables.
For example, the logarithms of both variables could be entered as
explanatory variables or quadratic terms could be added. The choice
could once again be based on elasticities.
These checks were undertaken, and it was decided to use the
linear specification of the environmental variables. The final
specification for this demand category is shown in Table 4-16.
The dependent variable in the equation of Table 4-16 is the share
of shelter expenditure on home repair. Thus, the parameter estimate
for S02 indicates that as concentrations of SCU decrease, relatively
less will be spent on home repairs. In turn, the equation also shows
that there is a direct relationship between TSP and the unestimated
good, utilities. The demand elasticity for SO^ is 0.0611 in the home
repair equation. This means that a 10 percent decrease in SO2
concentrations leads to a 0.611 percent decrease in the demand for
home repair items. The elasticity for TSP is -0.075 in the home
repairs equation. Elasticities can also be derived for the pollution
variables implicit in the unestimated second equation. These
elasticities are -0.020 and 0.025 for S02 and TSP, respectively.
The observed relation between SCU and home repairs is plausible.
However, there was no a priori expectation that a positive relation
would be observed between TSP and expenditures for utilities. As the
4-117
-------
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results shown in Table 4-16 indicate, a positive.relation does exist.
One explanation for this result is that TSP is picking up regional
differences. That is, TSP is serving as a proxy for the added heating
requirements (and hence higher utility bills) in colder areas. This
was not substantiated in a specification with TSP and region or
temperature variables. Another possible explanation is that
electricity is used in conjunction with other goods to mitigate the
effects of air pollution. For example, in areas where relatively more
vacuuming, air filtering, etc. is required, the demand for electricity
could be expected to be somewhat higher.
With respect to the economic characteristics of the equation
system, the own-price elasticities are -1.126 and -1.067 for home
repairs and utilities, respectively. We have seen no other budget
studies that identify home repairs as a separate item. However, for
utilities, our elasticity estimate is in the range of elasticities
(-0.86 to -1.46) reported by Taylor (63) in a survey of residential
electricity demand studies.
The discussions have been rather extended in both the food and
shelter categories. This was done in order to lay out in some detail
the testing procedures that were undertaken in the evaluation of
alternative models. From this review of the different specifications
of the air quality variables, we feel reassured that the variables are
fairly stable. After a discussion of the remaining demand categories
of the LES, the chosen specifications are subjected to one more
4-119
-------
sensitivity test. Specifically, a different structural model, the
homogeneous translog, is adopted. Estimation of demand equations for
this other system permits a comparison of price elasticities as well
as the marginal effects of the air pollution variables with the
results reported for the LES.
Home Operations—
Table 4-17 presents the final specification for the home
operations demand system. There are two sets of aggregate goods
included in this system — laundry/cleaning products and "other
household products". In the second group, items such as paper
products, air fresheners, and insect sprays are included.
Unfortunately, data limitations did not allow the formation of an
aggregate variable of "household services" which includes expenditure
items like lawn care, gardening services, and appliance repair
services.
The home operations subsystem is a two-good system, so that OLS
procedures are appropriate and testing is based on the F-test. As
expected, TSP has a direct relation with the demand for laundry/
cleaning products and is statistically significant. In alternative
specifications with family size and 202' we cou-'-^ n°t reject the null
hypothesis that the coefficients of these variables were zero.
However, the Region dummy is statistically significant and an
evaluation of the partial derivative of the quantity demanded of
laundry/cleaning products with respect to region results in a direct
4-120
-------
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4-121
-------
relation. A comparison of the specification shown in Table 4-17 with
a model in which the coefficients Cl and Dl are restricted to zero
results in an F-test statistic of 7.295, which is greater than the
critical value of 2.44. Thus, we reject the null hypothesis that the
two coefficients should be restricted to zero.
The elasticities of demand with respect to TSP are 0.079 and
-0.079 for laundry/cleaning products and other household products,
respectively.* The own-price elasticities of demand are -1.182 for
laundry/cleaning products and -1.332 for other household products.
Home Furnishings and Equipment—
This disaggregate demand system includes four goods: household
textiles, furniture, major and minor appliances, and housewares. A
distinguishing feature of the goods included in this demand system is
that they can be thought of as being durable goods. The existence of
durable economic goods often poses a problem for the researcher. In
many instances, an appropriate separability assumption is introduced
so that durable goods can be excluded from the analysis. Other
options include constructing measures of the flow of services provided
by the durable goods, or simply treating purchases of durables as
current consumption items.
* In a model with TSP entered in both translating terms, the
elasticity of laundry/cleaning demand with respect to TSP is 0.089.
Similarly, with the logarithm of TSP entered as a single translating
parameter, the elasticity is 0.063. All elasticities were
statistically significant.
4-122
-------
In the present case, the latter approach has been adopted. In
part, this assumption seemed reasonable since the data consist of
average household expenditures across all households in a particular
SMSA.
Table 4-18 presents the final specification for this demand
'system. As the equations show, higher concentrations of SO- lead to
increased demand for household textiles. This finding is supported by
evidence cited in the Criteria Document (5) that cottons and nylons
are subject to damage by acids derived from SO-. A priori, it also
seemed reasonable to expect that higher levels of TSP would lead to
increased soiling of fabrics and consequently increased cleaning, and
possibly more frequent replacement because of wear and tear. While
the signs of the TSP coefficients were as expected, several specifica-
tions with TSP included did not lead to coefficients that were
significantly different from zero.
The demand elasticity with respect to SO- for household textiles
is 0.100. This implies that a 10 percent reduction in S02 concentra-
tions leads to a 1 percent reduction in the demand for home textile
products.
The equation results recorded in Table 4-18 have several
restrictions imposed on the E/D variables. In particular, note that a
translating parameter for S02 is defined only for household textiles.
Other restrictions involve the appearance of the family size and
4-123
-------
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specification and a model where all E/D coefficients are restricted to
zero results in a test statistic of 9.28. Since this statistic is
greater than the critical value at the 10 percent confidence level, we
reject the null hypothesis and adopt the less restricted model.
The own-price el-asticities of demand are -0.848 for textiles,
-1.284 for furnishings, -1.182 for appliances, and -1.370 for
housewares. As with some of the earlier groups that have been
discussed, we have not seen previous demand studies with a breakdown
like that used here: However, Abbott and Ashenfelter (64) report own-
price elasticities in the range of -0.601 to -1.525 for an aggregate
durable goods category. Our estimates fall within the range of these
elasticities.
Clothing—
The clothing disaggregate demand system is a two-good system
comprised of clothing and dry cleaning. Table 4-19 reports the final
specification for this system. The included E/D variables are family
size and temperature. Temperature replaced the region dummy in this
specification because its more precise locational definition provided
a better fit in explaining the share of expenditures on clothing. The
signs of the family size and temperature coefficients are both
plausible. The estimated equation indicates that as family size
increases, expenditure on clothing increases. Similarly, as
temperature increases, expenditure on clothing decreases.
4-125
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A priori, one might expect TSP to influence the demand for both
of these items. However, this was not substantiated in the
estimation. The best fit achieved was a quadratic specification for
the maximum of annual geometric means for TSP. This specification
indicated that higher concentrations of TSP lead to higher
expenditures on dry cleaning when the equation is evaluated at the
means of the variables. The F-test for the models with and without
the TSP variables resulted in a statistic less than the critical
F-value at the 10 percent level of significance.* Thus, we fail to
reject the null hypothesis that the TSP coefficients should be
restricted to zero.
One possible explanation as to why a pollution effect is not
observed in this demand system is that both goods may be positively
related to TSP or SC^. Consequently, given the expenditure constraint
implicit in the system, the effect for either of the goods may not be
easily identified. In order to test this hypothesis, several single
equation, multiplicative specifications were run that did not include
the constraints mentioned above as a part of the set of maintained
assumptions. Again, no statistically significant relationship was
observed between any of the pollution measures and clothing or dry
cleaning. Consequently, given this data set, one cannot justify
including pollution variables in the clothing demand system.
* The value of the F-test was 1.36, while the critical value with
(2,41) degrees of freedom is approximately 2.44 at the 10 percent
s igni f icance leve1.
4-127
-------
The own-price elasticities for the specification shown in Table
4-19 are -1.027 and -1.283 for clothing and dry cleaning,
respectively. Our elasticity for clothing is lower than that reported
by Pollak and Wales (43) for a generalized translog and quadratic
expenditure system, which were in the range -1.3 to -1.7. However,
our elasticity is also slightly higher than the elasticities reported
by these authors for an LES specification [Reference (41), elasticity
for clothing equal to about -0.90].
Transportat ion—
The sixth disaggregate demand system involves expenditures for
transportation purposes. The two goods included in this system are
gas and fuel, and "other vehicle operations". The latter good
includes items such as lubricants, filters, tires, batteries, body
work, and electrical work.
A priori, one might expect TSP or S02 to affect the demand for
both of these goods. For example, acids from S02 may add to corrosion
of metal surfaces, while high concentrations of TSP may hinder vehicle
performance because of particle accumulations in engine parts.
The demand for gas and fuel may also be directly related to
pollution levels. For example, over time, people may decide to reside
further away from highly polluted central city areas in order to
ameliorate the disamenity affects of pollution at their residence. In
4-128
-------
this case, they exhibit a willingness to trade off increased gas and
fuel costs for a cleaner environment at their homes.*
S0? and TSP were included in several specifications for this
demand system. While the coefficient for TSP was always statistically
insignificant, a significant, positive relation was observed between
S0_ and the demand for gas and fuel.
The final specification for this system is shown in Table 4-20.
The E/D variables included in the equation are the maximum second-high
concentration of S02 and temperature. Alternative models with family
size and region did not support the inclusion of these variables. The
coefficient for temperature is positive, which indicates that there is
a direct relation between temperature and the demand for gas and fuel.
This seems plausible for at least two reasons. First, the use of
automobile air conditioners is likely to increase in warmer areas,
which could result in a loss of fuel efficiency, and consequently more
expenditures for gasoline. Second, warmer temperatures might also
lead to more frequent outdoor, away from home activities.
The demand elasticities with respect to SO2 are 0.038 and -0.034
for gas and fuel and other vehicle operations, respectively.** The
* Note that this effect is consistent with the notion that certain
long-run adjustments have already been made.
** When SCu is entered in both translating terms, the elasticity of
gas and tuel demand with respect to SCU is 0.039. With SO- entered
logarithmically, the elasticity is also 0.039. In each of the
specifications, the elasticities were statistically significant.
4-129
-------
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estimates of own-price elasticity are within the range of elasticities
reported by Abbott and Ashenfelter (64) (-0.571 to -1.439) for
transportation services.
Personal Care—
Table 4-21 reports the results for the final specification of the
personal care disaggregate demand system. The three goods included in
this system are non-insured medical care, prescription drugs, and
personal care items. Since all three of these items are related to
health expenditures, there is a basis for suspecting that increased
levels of air pollutants may lead to higher demands for these items.
However, estimation of the demand system does not support the
hypothesis that TSP or SO- should be included in the equations. For
example, with a translating parameter for TSP added to each
translating expression in the system, the test statistic, relative to
the case where each TSP translating parameter is zero, is 2.37. Since
this is less than the critical value of 6.25, we fail to reject the
null hypothesis. On the other hand, a comparison of the specification
shown in Table 4-21 with a completely restricted model leads to a test
statistic of 9.28, which is greater than the 10 percent chi-square
critical value. Therefore, we reject the null hypothesis.
There are two possible reasons for the statistical insignificance
of the pollution variables in this system. First, if all three goods
4-131
-------
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4-132
-------
are directly affected by TSP or SC^r the constraints imposed through
the system estimation may conceal air pollution effects for any one
good. However, as before, single-equation regressions for each good
did not support this hypothesis. Alternatively, it may be that the
three goods are defined at too aggregate a level so that any air
quality effects for a particular good are not easily identified. This
is a real possibility in this demand system, since personal care items
encompass over 50 items while non-prescription drugs is defined for
about 30 separate items. In each case, some of the goods in the group
may be affected by high concentrations of TSP or S02, while others may
not.
The own-price demand elasticities for the equations shown in
Table 4-21 are -1.256, -1.541, and -1.024 for non-insured medical
care, non-prescription drugs, and personal care items, respectively.
Summary of LES Model—
In this subsection, the empirical results for the LES
disaggregate demand system have been described. Each equation set has
been subjected to a variety of checks in order to gauge the
plausibility of the equations presented as final specifications.
These checks have included alternative specifications of the way in
which the pollution variables are allowed to enter the system,
calculation of elasticities of demand with respect to prices and
pollution, and where possible, comparison with elasticities taken from
4-133
-------
the literature. These checks indicate that our final specifications
are reasonable.
There is one other set of checks that can be made. This involves
estimating a different structural model. In the next subsection, a
demand system using equations generated from a homogeneous translog
(HTL) indirect utility function is estimated. Estimation of this
second system provides another basis for judging the sensitivity of
the results. For example, it would be reassuring if the various sets
of elasticities we have calculated for the LES are not drastically
different from those derived from the HTL model.
Linear Logarithmic Expenditure System
The linear logarithmic expenditure system is derived from an
indirect utility function that is a homogeneous transcendental
logarithmic function:
n n n
In W = a0 + ^ <*i ln Pi + C E pi ln pi ln Pj (4'29)
where W is the indirect utility index, fr^- = |i ^ for all i and j ; p^
*
are normalized prices such that p j_ = p./M (where M is total
n n
expenditure); and I a. =1; H 13^ = 0 for all j.
J
4-134
-------
Individual commodity expenditures can be obtained by using Roy's
identity:
* a in w ^ n, ,
-p^X^ = j for all i.
a in pi
Given the form of In W, this can be rewritten as:
n
-piXi = ai + /_/ ^ij ln Pj f°r a11 i* (4.30)
Lau, Lin and Yotopoulos (45) show that within this framework, E/D
variables can be introduced such that the consumption expenditure
functions become:
n
* ^^ *
-p;X- = a, + ) . !!..: In p.:
m
LJ £ik ^n Sk ^or
k=l
n
with the additional restriction I c^ = 0 for all k, where Sk is the
i=l
k E/D variable and m is the number of E/D variables.
This way of introducing E/D variables into a demand system is
different from the translating technique used with the LES. The
4-135
-------
advantage in specifying the system as in Equation (4.34) is that each
equation of the system is linear so that estimation and hypothesis
•
testing become easier. Unfortunately, the homogeneity restriction on
the E/D variables can lead to difficulties in constructing a
meaningful aggregate price index. This problem is discussed more
fully in the next subsection.
For estimation purposes, it is convenient to make use of the
homogeneity assumption on the indirect utility function. This results
in an expenditure function of the form:
n-1
pj - ln pn
m
L-J eik ln Sk for
k=l
Furthermore, in the reported results, the cross-equation symmetry
restrictions 13 ^. = [3^. for all i,j have been imposed.
The feature that sets the HTL specification apart from more
general translog forms is the homogeneity assumption. While this
assumption is required for the two-stage optimization model to be
valid, it does impose restrictions that have an economic interpreta-
tion. In particular, the total expenditure elasticity of demand for
each good must be unity. Note, however, that because the analysis is
4-136
-------
concerned with disaggregate subsystems, this does not imply that the
income elasticity of demand for each commodity is unity. The latter
would seem to be an even more tenuous assumption.
Tables 4-22 through 4-28 present the final specifications for the
HTL disaggregate demand system. Note that each of the dependent
variables is an expenditure share so that only N-l equations for each
system are estimated. The coefficients of the remaining equation can
be derived from the homogeneity and symmetry constraints.
The discussion of the results for the HTL will be limited.
Instead of providing a detailed account of the steps undertaken to
arrive at a final specification, the emphasis is on comparing the HTL
results with those of the LES. Specifically, comparisons are made for
the various elasticity measures.
Own-price elasticities of demand for the HTL are presented in
Table 4-29. These elasticities are calculated from the relation:
Pi BUM
= -1 - -=— (4.33)
where B^ is the coefficient for the ith price term in the ith
equation, M is total expenditure in the category and x- is the
quantity demanded of the ith good.
4-137
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TABLE 4-29. OWN-PRICE ELASTICITIES OF DEMAND
Category
HTL system
LES system
Food
a.
b.
c.
d.
e.
Cereal and bakery products
Meats
Dairy products
Fruits and vegetables
Miscellaneous foods
-1.260
-1.211
-1.309
-0.981
-1.337
-1.245
-1.079
-1.159
-0.985
-1.041
Shelter
a. Home repair
b. Utilities
Home operations
a. Laundry/cleaning products
b. Other household products
Furnishings and equipment
a. Textiles
b. Furniture
c. Appliances
d. Housewares
Clothing
a. Clothing
b. Dry cleaning
Transportation
a. Gas and fuel
b. Other vehicle operations
Personal care
a. Non-insured medical care
b. Non-prescription drugs
c. Personal care
-1,
-1,
220
074
-1.348
-1.351
-0.792
-1.300
-1.249
-1.462
-1.049
-1.314
-1.128
-1.101
-1.278
-1.412
-1.052
-1.126
-1.067
-1.182
-1.332
-0.848
-1.284
-1.182
-1.370
-1.027
-1.283
-1.220
-1.000
-1.256
-1.541
-1.024
4-145
-------
The own-price elasticities for the LES system are also included
in Table 4-29. As can be seen from the table, there is good agreement
between the calculated own-price elasticities of the two systems.
Another important check that can be made is with respect to the
elasticity between demand and the pollution variables. Since it is
these elasticities which play a crucial role in determining the
benefits associated with an improvement in air quality, it would be
reassuring to find similar results for the two systems. Table 4-30
presents the results for this plausibility check. As with the own-
price elasticities of demand, there was good correspondence between
the results of the two models. In general, the HTL elasticities are
TABLE 4-30. ELASTICITIES BETWEEN DEMAND AND THE POLLUTION VARIABLES
Category HTL system LES system
Shelter
a. Home repairs (SO-) 0.062 0.061
b. Utilities (TSP) 0.039 0.025
Home operations
a. Laundry/cleaning products (TSP) 0.099 0.079
Furnishings and equipment
a. Textiles (S02) 0.078 0.100
Transportation
a. Gas and fuel (S02) —* 0.038
* SO2 not a statistically significant variable,
4-146
-------
slightly larger than those observed from the LES system, but the
differences do not seem extraordinary.
The checks discussed so far use information obtained only from
the estimated parameters of the two disaggregate demand models.
Another component of the plausibility analysis could focus on the
implied effect of the air pollution measures on the price indices
developed for the aggregate stage of the two-stage budgeting problem.
This is the next topic considered.
Derivation of Aggregate Price Index
Once the parameters of the disaggregate demand systems have been
estimated, the next step is to construct consistent aggregate price
indices. In the model development subsection, the assumptions that
are required for the existence of these indices were described. Here,
those results are applied to the specific functional forms that have
been analyzed. The objective in forming these indices is to develop
the information that is needed to estimate the aggregate stage system.
The construction of these price indices also provides another
means of checking the plausibility of the role of air pollution
measures in our models. In particular, air pollution measures have
been found to be statistically significant variables in four of the
disaggregate demand systems. Thus, the four aggregate price indices
developed from these subsystems will be functions of air quality. A
4-147
-------
priori, the expectation is that as air quality improves, the aggregate
price index should fall since the cost of providing a given unit of
cleanliness (or some other service flow) should be lower.
LES System—
In the LES system, outputs are characterized by a function of the
form:
b2 bn
(x2 - s2) ... (xn - sn)
(4.34)
where each of the variables are as defined previously. There are two
characteristics of this function which are important for defining an
aggregate index. First, Equation (4.34) is affinely homothetic. This
means that the function is homothetic to the point (s-^,S2/ ... , sn).
Second, since the b-'s sum to unity, the function is linearly
homogeneous. Given these two characteristics, it is convenient to
define an aggregate quantity index in the same form as Equation
(4.34). With the quantity index defined in this way, the aggregate
price index is defined such that the product of the price and quantity
indices equals total group expenditure. This leads to an aggregate
price index of the form:
pi '
Mi
(xi2~si2).
(x~s
in~in) .
:4.35)
4-143
-------
where P- is the aggregate price index for the i category.
M- is total expenditure in the ifc category.
(x. --s- •) is the quantity demanded net of variations implied by
1 1 the translating parameters for the j good in the ifc"
commodity group.
).j_ is the marginal budget share.
indexes the nun
commod i ty group.
•f* V^
n indexes the number of disaggregate goods in the i
The immediate interest with Equation (4.35) is to identify the
role of air pollution in the price index. Air quality variables enter
Equation (4.35) through the s^. Clearly, if all estimated parameters
for S02 or TSP in a given system are positive, then a reduction in
concentrations will lead unequivocally to a decrease in the aggregate
price index. Will this always be the case?
The manner in which the translating parameters are introduced in
the LES system implies that a positive effect of a translating
variable for one good in a demand system must be counterbalanced by an
equivalent negative effect elsewhere in the system. Thus, in a two-
good system, with TSP entered as a translating variable for both
goods, the estimated coefficients for TSP must have different signs.
Returning to Equation (4.35), this implies that the direction of
change of the price index for an air quality improvement depends on
the relative sizes of the marginal budget shares.
In the LES system results reported earlier, the air pollution
variables are included as translating terms only for those goods whose
4-149
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demands are affected directly by pollution. For example, in the home
operations system, TSP was included in the translating expression for
laundry/cleaning products, while it did not appear for other household
products. The constraint on fixed expenditures is maintained, since
the intercept term of the translating expression for other household
products picks up the required offsetting effect.
The question here is whether TSP in and of itself is expected to
lead to a change in the demand for "other household products". The
basis for an adequate answer is, in part, limited to available prior
information. In particular, the Criteria Document (5) does not
present evidence that the types of goods included in "other household
products" would be affected by changes in air quality. This prior
information provides one rationale for adoption of a restricted model.
Alternatively, it should be noted that specifications with
pollution variables appearing in all translating expressions were
generally not supported by statistical tests. In particular,
comparisons with models in which some of the air quality coefficients
were restricted to zero typically resulted in a failure to reject the
null hypothesis; that is, the restrictions were warranted.
It should be stressed that the observations made above do not
invalidate Equation (4.35) as a meaningful price index. Rather, they
indicate that care must be taken when attempts are made to analyze the
effects of changes in certain variables on the aggregate price index.
4-150
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Given the parameter estimates of the LES system, one statistic of
interest involves the predicted average percent change in aggregate
price per unit decrease in the air quality measures. For TSP, this
value was -0.008 percent for both the shelter and home operations
aggregate categories. Similarly, the average percent change in the
aggregate price index for a unit decrease in S02 concentrations was
-0.002, -0.003, and -0.005 percent for the shelter, furnishings, and
transportation aggregate goods, respectively.* Each of these values
is of the anticipated sign and the magnitudes are not offensive to
prior intuition.
HTL System —
Following Lau, Lin, and Yotopolous (45), an aggregate
price index for the HTL can be defined as:
n
In Pi = ^wk In P* (4.36)
k=l
where PJ is the aggregate price index for the i category, w^. is the
share of the kfc good in the, disaggregate system, p-u is the fixed
price of the ktn good, and n indexes the number of goods in the
disaggregate group.
* The total change in price for a change in air quality consistent
with attainment of the secondary standards generally resulted in
price changes of less than $0.01. The maximum observed change in
price was approximately $0.015.
4-151
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As air quality changes, the shares adjust so that their sum is
always unity. Since the shares are weighted by the fixed prices, the
direction of change in p. for an improvement in air quality depends
solely on the relative prices of the goods in the system. Thus, in a
two-good system, if a decrease in concentration levels leads to a
decrease in expenditures in the first equation of the system, P^ will
decrease only if the price of the first good (i.e., the good for which
the expenditure share in the first equation is defined) is greater
that the price of the second good. The possibility that P^ can move
in any direction with an improvement in air quality runs counter to
our _a priori expectations that P^ should decrease in such a case.
An explanation as to why this may occur is related to the way in
which air pollution variables are introduced in the HTL specification.
In particular, if one looks at the subfunction which generates the
share equations and ultimately the aggregate indices, it is apparent
that the terms involving pollution variables in the share equations
are price dependent. That is, they are generated from price interac-
tion terms in the main subfunction. This subfunction can be written
as:
4-152
-------
u * *•
In w = aQ 4- I a. In p- + E bfc In qfc
-, n n
- I I cjk In p. in pk
+ i I I dtm in q in ^ + £ I e. In p* In qfc (4.40)
z t m 3 t
where the p^ are normalized prices, qfc are E/D variables, and the a,
b, c, d, and e terms are parameters. With the share equations
obtained by taking the partial derivative of In W with respect to In
p*, the parameters a,., b , and d. cannot be identified. Note that
this occurs because the b and d. terms are price independent. The
e-t terms, which are ultimately identified, are price dependent.
In effect, when only the e-. terms are used in the formation of
the aggregate price index, there is an implicit assumption that the bt
and dfc contributions to the subfunction In w are zero. In turn, this
may restrict the interpretation of the aggregate price index.
One way to incorporate these observations is to estimate the
expenditure function of the HTL system as part of a system with the
share equations. While this approach would identify the other para-
meters, it is difficult to implement empirically because the expendi-
ture function depends on the level of indirect utility. Consequently,
the aggregate stage demand system for the HTL specification is not
estimated.
4-153
-------
Estimation of Aggregate Stage Systems
Given the aggregate price indices, it is possible to estimate the
LES aggregate stage system. For convenience, it is assumed that the
form of the utility function in the aggregate stage is identical to
the form of the function used to generate demand curves at the
disaggregate stage. Thus, we again look at demand specifications of
the LES form.
Table 4-31 presents the final specification for the LES system.
As structured, air pollution enters the final stage of analysis only
through its effect on the appropriate aggregate price indices. There
are seven utility-generating "goods" in the aggregate system, so that
six equations are estimated. The parameters Al, Bl, Cl, Dl, El, and
Fl are the marginal budget shares for the services provided by food
consumption, shelter, home operations, furnishings, clothing, and
transportation, respectively. The marginal budget share for personal
care items can be derived from the restriction that the sum of the
budget shares must equal unity. These estimates are all statistically
significant and appear reasonable in magnitude.
Table 4-32 presents estimates of the own-price demand
elasticities for the LES aggregate system. Five of the seven goods
have own-price elasticities less than unity, which indicates that as
prices decrease, quantity demanded increases less than proportionately
so that total expenditure declines. These elasticities are comparable
4-154
-------
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4-155
-------
TABLE 4-32. OWN-PRICE ELASTICITIES OF DEMAND FOR AGGREGATE LES SYSTEM
Category
Food
Shelter
Home operations
Furnishings and equipment
Clothing
Transportation
Personal care
Elasticity
-0.670
-1.110
-0.486
-0.649
-1.021
-0.929
-0.806
to those derived in other studies for similarly defined aggregate
categories. For example, Abbott and Ashenfelter (64) report own-price
elasticities for a linear expenditure system to be: food (-0.605),
housing services (-0.518), durable goods (-1.525), clothing (-0.581),
and transportation services (-0.637). Similarly, own-price
elasticities for food and clothing are reported by Pollak and Wales
(41) to be -0.72 and -0.91, respectively.
Although the food and clothing elasticities from this analysis
match up well with those of Pollak and Wales, there are differences
between some of this study's elasticity estimates and those reported
by Abbott and Ashenfelter. In particular, the housing services and
durable goods (furnishings categories) are quite dissimilar. We
4-156
-------
suspect that much of these differences can be attributed to different
•
definitions of these classes of goods.
CALCULATION OF BENEFITS
Models have been estimated for two structural forms, and measures
of air pollution are statistically significant in several of the
disaggregate demand systems. In this subsection, this information is
used to determine the benefits of attaining the secondary standards.
The first task is to describe carefully the scenario for the calcula-
tion of benefits. If the benefit numbers are to be useful, the scope
of coverage must be made clear. Following the description of the
scenario, the concepts presented in Section 2 are developed further.
In particular, the notion of an expenditure function is defined and
its relation to the compensating variation measure of benefits is
noted. With these discussions as background, benefits numbers
associated with attainment and maintenance of the Secondary National
Ambient Air Quality Standards are presented.
Scenario for Benefits Calculation
There are a variety of scenarios that can be chosen. The
particular set of assumptions adopted here is consistent with the
timeframe for standard implementation used in a companion study of
cost of control and economic impact.
4-157
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Assumptions for Environmental Variables—
There are three environmental variables in the demand systems
estimated in this study. These are the maximum annual second-high
readings for S02 and TSP, and temperature. The temperature variable
included in the benefit calculations is the 30-year annual average for
each of the SMSAs in our sample. No change in the annual average
temperature is assumed to occur because of air quality improvements.
With respect to the air quality data, the objective is to
estimate the incremental benefits of going from a primary standard to
a secondary standard. The assumption is that the primary standard is
attained in 1985 with the secondary standard being met two years
later. Consequently, in order to undertake benefits calculations, it
is necessary to describe the air quality levels in 1985. This is done
by assuming specific changes in 1978 air quality data, the most recent
information available to us. In particular, it is assumed:
Any SMSA above the primary standard in 1978 would be
at the primary standard by 1985.
Any SMSA below the primary standard in 1978 would
remain at the 1978 levels to 1985.
Given attainment of the primary standard, the secondary standard
was assumed to be achieved in the following way:
Any SMSA above the secondary standard in 1985 would
reach the secondary standard in 1987 through two equal
annual reductions in concentration levels.
4-158
-------
Any SMSA below the secondary standard in 1985 would
have no further improvement in air quality.
As an example of the first point, if concentrations of TSP in an
SMSA in 1985 are 200 ^g/m and the secondary standard for 24-hour
second high (150 /ug/m ) is to be achieved in two years, this would
require a decrease of 25 ^g/m in each year. This assumption requires
cities that are further from the secondary standard in 1985 to under-
take more intense cleanup efforts if all cities are to be in
compliance with the secondary standard by 1987.
The second assumption has implications for the magnitude of gross
benefits. This is because it is assumed that cities already in
compliance with the secondary standard experience no additional
improvements. Thus, there are no benefits accruing to individuals in
these cities. This could lead to an underestimate of benefits if, in
fact, attainment of the secondary standard leads to a general
improvement in air quality for all cities.
Table 4-33 lists the National Ambient Air Quality Standards for
TSP and SO,,. The number enclosed in parentheses represents an
alternative standard that is not a part of the current Federal
regulations but that will also be considered in this study (see
Section 3 ).
4-159
-------
TABLE 4-33. NATIONAL AMBIENT AIR QUALITY STANDARDS
Air quality standard (/*g/m )
Pollutant
Primary Secondary
Sulfur dioxide
Annual arithmetic mean 80
24-hour maximum* 365 (260)
3-hour maximum* — 1,300
Particulate matter
Annual geometric mean 75 —
24-hour maximum* 260 150
* Not to be exceeded more than once per year.
Source: Air Quality Data, Annual Statistics 1977 (65).
Assumptions for Economic Variables—
The crucial assumption with respect to the economic variables is
that the parameter estimates derived from 1972-73 data can be used to
describe the allocation decisions of individuals in 1985 and beyond.
This implies that the structure of individual preferences is not
altered by time.
Given the parameter estimates, it is still necessary to describe
how the economic variables themselves change over time. The following
assumptions were adopted.
4-160
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• Projections of family income in constant 1972 dollars
were obtained for 1985 and 1990 from U.S. Department
of Commerce, Regional Economic Projections (66).
These data were currently available by state only, but
were assumed to be appropriate for our SMSA-level
data. The data were converted to 1973 constant
dollars, and the annual average percent change between
1985 and 1990 was calculated. This annual percent
change was applied to the 1985 data to obtain a
measure of family income in 1986 and 1987.
• The projected number of households by SMSA for 1986
and 1987 were derived from state and U.S. projections
in the Bureau of the Census, Current Population
Reports, Series P-25 (67). The calculated percent
change in households between 1986 and 1987 was assumed
to hold into the future.
• All benefits calculations were done in constant 1973
dollars. We assumed that there was no intrinsic
change in the relative prices of our goods across
time. Thus, year-to-year and across-category changes
in price were limited to changes in the CPI.
• The benefit numbers are reported in 1980 dollars. The
benefit calculations were adjusted to 1980 terms using
the annual average percent change in the CPI between
1973 and 1978 as a proxy for CPI changes in any year.
• Benefits are reported as discounted present values in
1980. Three social rates of discount were used: 2,
4, and 10 percent.
• Family size was assumed to remain fixed at 1973 levels
throughout the analysis.
The data described above were developed for the 24 SMSAs in the
sample. Thus, the benefit numbers legitimately represent only these
places. To facilitate comparison with other studies, the scope of
coverage has been expanded to develop an estimate of national
benefits. These results are reported in Section 10.
4-161
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Measures of Benefits
In Section 2, the concept of economic benefits was described in
general terms. The discussion in that section defined consumers'
surplus as the area under a demand curve but above the horizontal
price line. Given changes in price, benefits can be measured as the
change in consumers' surplus. This situation is shown in Figure 4-7,
where an instantaneous price decrease from P~ to P-, leads to economic
benefits equal to the area p ABP,.
In addition to this standard notion of consumers' surplus,
several variations of the consumers' surplus measure have been
defined. Given the structure of the model developed in this section,
it is convenient to use one of these other measures in the calculation
Change in consumers' surplus
Figure 4-7. Consumers' surplus.
4-162
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of benefits. In particular, the compensating variation (CV) measure
is employed.
As was noted in Section 2, the differences among the various
measures of consumers' surplus will be small as long as (1) the
magnitude of the measured surplus is small relative to the consumer's
income, or (2) the income elasticity of demand for the good or service
under consideration is small. These criterion are satisfied for the
analysis conducted in this section.
Compensating Variation (CV)—
Compensating variation (CV) can be defined as the amount a
consumer would be willing to pay (or would have to be paid) in order
to be indifferent between an original situation and a new situation
with lower (higher) prices. Figure 4-8 portrays the CV measure in
terms of an indifference curve diagram. There are two goods, X-, and
X-f with X- assumed to be a numeraire good which can be thought of as
income. Originally, the consumer faces relative prices shown by PQPI«
He maximizes utility along U-, at point A. If the price of X-, falls
due to an improvement in air quality, the new price line is given by
P0P2* W:"-tn tnis lower price for good X-,, the consumer achieves a
higher level of utility (lU)/ and maximizes utility at point B in the
diagram. For a price decrease, CV measures the amount the consumer
would be willing to pay to attain the original level of utility (U-, )
at the new set of prices. Thus, if the amount PQD in income is taken
away from the individual and he is faced with the same relative prices
4-163
-------
X,
cv
U.
U.
X.
Figure 4-8. Compensating variation.
as after the price change, he could consume combination C of goods X^
and X2 and be on U-,. PnD is the measure of CV for the given price
change. This is the measure used in reporting the benefits numbers.*
The Expenditure Function—
The CV measure of welfare change can be made operational with the
concept of an expenditure function. This function shows the minimum
dollar expenditure required to reach a specific level of utility, ~U,
given prices P. It can be obtained through solution of the
For a comparison of CV and other measures of benefits, see Freeman
(7).
4-164
-------
mathematical dual to the consumer's utility maximization problem.
That is, it is a solution to a decision problem in which the consumer
is assumed to minimize expenditures subject to a constant level of
utility.
With this definition of an expenditure function, CV can be
defined as the difference be'tween an expenditure function evaluated
before and after a price change, such that utility remains constant.
CV = E(P1,U) - E(P2,U) (4.38)
-] o
where P is a vector of prices in an initial situation and P is a
vector of prices after a price change. If CV < 0, then the consumer
must be compensated and if CV > 0, the consumer should be willing to
pay the amount CV if he is to be at the same level of utility as
before the change.
The benefits estimates reported below are derived from Equation
(4.38). This requires knowledge of the expenditure function before
and after the postulated change in air quality. The expenditure
function is defined by solving analytically for the compensated demand
curves associated with the Linear Expenditure System. Since the
structural parameters of the ordinary demand equations presented
earlier can be identified on a one-to-one basis with the parameters of
the compensated demand equations, there is no need for additional
estimation. Note also, that the indirect utility function of the
4-165
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Linear Expenditure System can be used to determine the constant level
of utility appearing in the expenditure functions.
Economic Benefits of Air Quality Improvements
Table 4-34 presents the benefit estimates derived from the series
of demand specifications presented earlier in this section. Results
are reported separately for TSP and S0_, and regional subtotals are
given. The benefits are reported as discounted present values in
1980, in millions of 1980 dollars. The estimates shown are for a 10
percent discount rate.
An important assumption implicit in the calculation of these
benefits is that both pollutants are expressed in terms of maximum
annual 24-hour second-high concentrations. While these units are
appropriate for the air quality standards defined for TSP, no such
secondary standard is currently part of the Federal regulations for
SO-. The only current SO- secondary standard is based on a 3-hour
averaging time. In Section 3, assumptions were presented that would
be required to determine the 24-hour second-high concentration that
would be expected to occur when the 3-hour concentration of 1,300
ug/m occurred once per year (i.e., the secondary standard is
attained). This concentration level was termed the 24-hour equivalent
standard. If the appropriate transformations are made and all primary
standards are assumed to be met, none of the 24 SMSAs are found to be
out of compliance with the 24-hour SO- equivalent secondary standard.
4-166
-------
TABLE 4-34. HOUSEHOLD SOILING AND MATERIALS DAMAGE BENEFIT ESTIMATES
(discounted present values for 1980 in millions of
1980 dollars)
SMS As
Region I
Boston
Buffalo
New York
Philadelphia
Pittsburgh
Region Subtotal
Region II
Chicago
Cincinnati
Cleveland
Detroit
Kansas City
Milwaukee
Minneapolis
St. Louis
Region Subtotal
Region III
Atlanta
Baltimore
Dallas
Houston
Washington, DC
Region Subtotal
Region IV
Denver
Honolulu
Los Angeles
San Diego
San Francisco
Seattle
Region Subtotal
Totals
TSP
35.41
47.98
237.05
189.71
83.35
593.50
254.11
21.34
61.59
172.88
39.08
51.92
73.95
85.92
760.79
4.67
7.47
56.00
105.79
152.23
326.16
112.32
*
367.73
86.61
*
53.48
620.14
2,300.59
so2
*
37.99
302.75
184.45
74.67
599.86
65.45
39.88
52.20
*
*
36.84
56.26
70.06
320.69
*
*
*
*
*
•k
*
*
*
*
*
*
*
920.55
* Secondary standard not exceeded; therefore no benefits for attain-
ment of standard.
4-167
-------
As noted in Section 3, this result is not too surprising since the 3-
hour standard is expected to be the "controlling" standard only in
areas with extremely high, strong sources of SO-. Furthermore, given
that the damages analyzed here (soiling and materials damage) are
likely to be more sensitive to longer averaging times, it appeared
reasonable to estimate benefits for an alternative 24-hour secondary
standard such as the 260 ug/m^ value listed in Table 4-33. The
benefits shown in Table 4-34 are for this alternative SO- standard.
Total benefits for the 24 SMSAs, with a 10 percent rate of
discount, are $920 million and $2.30 billion for S02 and TSP,
respectively. With a social rate of discount of 4 percent, benefits
increase to $3 billion for SO- and $7.97 billion for TSP. A further
reduction in the social rate of discount to 2 percent leads to benefit
estimates of $5.17 billion for S02 and $14.1 billion for TSP.
On a regional basis, TSP benefits are realized throughout the
nation, while SO- benefits accrue to households only in the Northeast
and North Central parts of the country.
The aggregate benefit estimates in Table 4-34 can also be broken
down on a per-household basis. For example, in the two years of
standard attainment, the average per-household benefits are about
$16.25 and $16.50 for TSP and SO-, respectively. Furthermore, for a
unit change in air pollution (ug/m ), the per-household benefits
average about $0.20 and $0.17 for TSP and S0« These numbers can be
4-168
-------
interpreted as an indication that the average family in the 24 SMSAs
in this study should be willing to pay $0.37 for a simultaneous one-
unit reduction in ambient concentrations of TSP and S02.
These benefit numbers represent our "most reasonable" estimates
of the air quality benefits that would be realized in the household
sector, for the 24 SMSAs, with attainment of the 24-hour maximum
second-high secondary standards. In the remaining parts of this
subsection, these estimates are compared to those derived via other
models and approaches.
Comparison With Property Value Estimates—
In the organizational stages of this project, an area of concern
was to identify alternative ways of checking the plausibility of the
benefits numbers derived in the household expenditure model. Among
the options considered was to make a comparison with other indirect-
market studies such as the property value models.
These studies were considered appropriate as plausibility checks
since soiling and materials damage benefits are among the benefits
covered by the property value analyses. In addition to coverage of
soiling and materials damage, the property value studies are generally
considered to include health and at-home aesthetic benefits as well.
Unfortunately, it is not possible to identify the separate influences
of the various types of benefits. Consequently, benefits obtained
4-169
-------
from a study of property value differentials should provide an upper-
bound plausibility check on the benefits derived in this section.
With this in mind, a review of property value studies was
undertaken. The results of this review are presented in Section 5.
In developing the benefits estimates in Section 5, assumptions were
adopted which were consistent with the assumptions used in calculating
benefits in this section. A strict comparison of the benefits
estimated using the two approaches is not possible, however, since the
property value studies reviewed in Section 5 generally use the annual
mean of TSP and SCL. Consequently, the benefits reported in Section 5
are based on an alternative secondary standard of an annual mean of 60
ug/m^ for both TSP and SO-. Since the current secondary standard used
to calculate benefits in the household expenditure model is likely to
be more stringent than the alternative secondary standards used in
Section 5, the benefits reported from the household expenditure model
may exceed those reported from the review of the property value
studies. On the other hand, the property value benefits are likely to
exceed the benefits estimated from the household expenditure model/
since the property value benefits include health and at-home aesthetic
benefits. Table 4-35 presents a comparison of the benefits obtained
with the two approaches. As shown in the table, the sum of the
benefits estimated from the household expenditure model fall within
the range of the sum of benefits estimated from the property value
studies. Without additional supporting evidence on the stringency of
the current secondary standard in relation to the alternative
4-170
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TABLE 4-35. COMPARISON OF THE BENEFITS IN THE HOUSEHOLD EXPENDITURE
MODEL AND THE PROPERTY VALUE MODEL (discounted present
values for 1980 in billions of 1980 dollars)
Pollutant/ Household expenditure Property value
Standard model differentials
TSP 2.3 2.08-4.99
SO,, 0.92 0.33 - 0.47
secondary standard used in the property value analysis and the likely
magnitude of aesthetic or health benefits in the SMSAs considered in
this analysis, it is difficult to judge the reasonableness of the
relative benefit levels shown in Table 4-35.
Comparison With Wage Rate Estimates—
A second plausibility check for the household model can be
obtained by analysis of the market for labor services. As with the
property value studies, benefits derived via a wage model cover a
variety of benefit types. In addition to soiling and materials damage
benefits, the wage models include benefits for health and aesthetic
effects. Again, since the separate influences of the health and
aesthetic effects cannot be isolated, benefits obtained from a study
of wage rate variations should provide an upper-bound check on the
benefits derived in this section.
4-171
-------
Section 6 outlines the basic structure of the (hedonic) wage
analysis, and derives benefits estimates for two of the SMSAs included
in the household sector analysis. A comparison of the results between
the wage and household models is presented in Table 4-36. Note that
the benefits estimates are reported on a per-household basis. This is
the appropriate comparison since the wage analysis excludes self-
employed and part-year workers. Thus, a simple comparison across
total population for an SiMSA is not possible.
Like the property value analysis, the benefits estimated from the
wage rate study are based on an alternative secondary standard of 60
ug/m^ annual mean of TSP. In addition, the wage study benefits
include health and aesthetic benefits. Therefore, a strict comparison
of these estimates is not possible without additional information on
these factors.
TABLE 4-36. COMPARISON OF THE PER-HOUSEHOLD BENEFITS OF ATTAINING
SECONDARY STANDARDS FOR TSP (1980 $)*
Household expenditure Hedonic wage
model model
Cleveland
Denver
6.23
7.39
=======================
189.40
212.40
=========================
* 1980 discounted present value of the per-household benefits
occurring in 1987.
4-172
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Comparisons With Damage Function Studies—
In an earlier subsection, three studies were mentioned that
provided an assessment of national benefits for reductions in TSP and
SO.-, [(1), (4), (18)]. In each of these studies, benefits estimates
were developed by using damage relationships from earlier, independent
studies. In fact, many of the damage relationships used are the same
across the three studies. The differences that occur in reported
benefits come about because of differences in the assumptions used to
calculate benefits. These differences also make it difficult to
compare benefits from the damage function studies with those developed
in this section.
One of the few results that appears to be amenable to comparison
with our results is the soiling damage estimates reported by Freeman
(4). Using a model developed by Watson and Jaksch (15), Freeman
concludes that the best estimate associated with achievement of the
secondary standard for TSP (annual mean) is $2.0 billion annually.
This number is expressed in 1978 dollars and covers 122 SMSAs. The
annualized estimate for our discounted present value of TSP benefits
(24-hour second high), in 1980 dollars, is approximately $0.23 billion
for 24 large SMSAs.
While it is a straightforward calculation to convert our dollar
figures to 1978 terms, more detailed procedures are necessary for
geographic extrapolation. However, no extrapolations are undertaken
in this section. Extrapolation issues are addressed in Section 10
4-173
-------
where a summary is provided of the level of national benefits for the
household model.
Despite the intrinsic differences among the various damage
function studies that have been discussed and the present effort, it
may be possible to make rough comparisons by attempting to replicate
the air quality scenario used by one of the other studies. For
example, one of the differences pointed out between the current study
and that conducted by SRI (18) was that SRI's benefits estimates were
calculated from current (1980) levels to the secondary standard rather
than from the primary standard to the secondary standard. If this
difference is removed, it would be possible to make a rough comparison
of the benefit estimates.
Note that even with this change, there are still several
important differences between the two studies which make comparisons
difficult. These include:
• Our "current" year for benefits calculations is 1978.
SRI's is 1980.
• The maximum annual 24-hour second high is used in this
study as the pollution measurement index. SRI uses an
annual mean.
• The geographic scope in this study covers 24 SMSAs.
SRI reports national benefits estimates.
• This study focuses on the household sector. SRI does
not make this distinction.
• In this study, the secondary standard is assumed to be
achieved in the two years 1986-87. SRI appears to
assume instantaneous attainment in 1980.
4-174
-------
• The benefit numbers reported in this study are
discounted present values. SRI appears to report an
annualized number.
Only the last point is relatively easy to address. In Table
4-37, discounted present values are presented for the scenario
described above. The SRI estimates were reformulated as discounted
present values by assuming an infinite horizon for benefits and a 10
percent social rate of discount. As would be expected from the
various differences that remain in the two studies, the SRI estimates
are larger than those reported for the household sector. As with the
property value comparisons, it is difficult to make further judgments
about the reasonableness of the relative magnitudes.
One point that is brought out by Table 4-37 is that there are
welfare benefits to be gained by attainment of the primary standard.
In particular, a comparison of Tables 4-37 and 4-34 reveals that
additional benefits of $3.08 billion for TSP and $1.14 billion for SO-
TABLE 4-37. COMPARISON BETWEEN SRI BENEFIT NUMBERS AND THE
PRESENT STUDY (discounted present values for
1980 in billions of 1980 dollars)
TSP SO,
SRI estimates 6.50 18.00
Current study estimates 5.38 2.06
4-175
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are realized with primary standard attainment.* These welfare
benefits should not be neglected in an analysis of the benefits
associated with attainment of the primary standard.
Sensitivity of Results to Alternative Assumptions—
The benefit estimates presented in Table 4-34 are reported as
point estimates. Given the stochastic nature of the equations that
have been estimated, it is perhaps more realistic to think in terms of
a range of benefits estimates.
With this in mind, an ad_ hoc check based on the statistical
properties of the estimated coefficients in the demand equations was
undertaken. The check devised involves perturbing the estimated
coefficients of the air quality variables by a given amount. For
example, the estimated coefficient for TSP in the home operations
subsystem of the LES specification was found to be 0.01865. This is
the point estimate used in constructing the aggregate price index.
However, this coefficient is a random variable with a standard
deviation of 0.00647. Thus, the coefficient can take on a range of
values. A question of interest might be, how do the benefit estimates
change if the coefficients of all the pollution variables are assumed
to take on values plus and minus one standard deviation from the mean
value? While covariances among variables make such a test
nonrigorous, the results can still be informative.
* These are rough estimates since they do not take into account that
the primary standard is to be achieved in 1985.
4-176
-------
Tables 4-38 and 4-39 present the low, "most reasonable", and high
estimates .for benefits when these changes are made. Table 4-38
reports the results for S02> while Table 4-39 describes the range of
TSP benefits. As earlier, these numbers are discounted present values
in 1980, in millions of 1980 dollars. The social rate of discount is
assumed to be 10 percent. Again, note that these benefit estimates
are only for the 24 SMSAs included in the basic household analysis.
SUMMARY OF HOUSEHOLD SECTOR
In this section, economic benefits of achieving secondary air
quality standards for TSP and S02 in 24 SMSAs have been estimated.
The "most reasonable" estimate of the benefits associated with
attainment of the S02 standard is about $920 million, while the
benefits realized with attainment of the TSP secondary standard are
about $2.3 billion. These benefit estimates are discounted present
values in 1980, in 1980 dollars. A 10 percent social rate of discount
is assumed.
The approach used to obtain these estimates is different from
approaches used in previous air quality benefits studies. In the
present analysis, considerable attention has been given to developing
estimates which: 1) are consistent with the theoretical definition of
benefits, 2) account for household adjustments to air pollution, 3)
are derived from a well-tested model, 4) are based on real world data,
and 5) are plausible in comparison with estimates using other
4-177
-------
TABLE 4-38. RANGE OF HOUSEHOLD SECTOR BENEFITS FOR S02
(discounted present values for 1980 in
millions of 1980 dollars)
Region
Northeast
North Central
South
West
Total benefits
Low
$356.67
191.34
*
*
$548.01
Most
reasonable
$599.86
320.69
*
X
$920.55
High
$ 839
448
*
*
$1,288
.73
.33
.06
* Secondary Standard not violated for SMSAs included in analysis.
TABLE 4-39. RANGE OF HOUSEHOLD SECTOR BENEFITS FOR TSP
(discounted present values for 1980 in
millions of 1980 dollars)
Region
Northeast
North Central
South
West
Total benefits
Low
$ 332.91
430.42
184.77
350.97
$1,299.07
Most
reasonable
$ 593.50
760.79
326.16
620.14
$2,300.59
High
$ 855.67
1,095.26
468.86
893.62
$3,313.41
4-178
-------
techniques. The inclusion of each of these features in a single study
represents an important contribution to air quality benefits analysis.
4-179
-------
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57. Stone, Richard. Linear Expenditure Systems and Demand Analysis:
An Application to the Pattern of British Demand. The Economic
journal, 64:511-527, 1954.
58. Zellner, Arnold. An Efficient Method of Estimating Seemingly
Unrelated Regressions and Tests for Aggregation Bias. Journal of
the American Statistical Association, 54:348-368, 1962.
59. Kmenta, Jan and Ray K. Gilbert. Small Sample Properties of
Alternative Estimators of Seemingly Unrelated Regressions.
Journal of the American Statistical Association, 63:1180-1200/
1968.
60. Berndt, Ernst and N. E. Savin. Conflict Among Criteria for
Testing Hypotheses in the Multivariate Linear Regression Model.
Econometrica, 45(5):1263-1278, July 1977.
61. Anderson, Ronald W. Perfect Price Aggregation and Empirical
Demand Analysis. Econometrica, 47:1209-1230, 1979.
62. Gallant, A. Ronald. Testing a Subset of the Parameters of a
Nonlinear Regression Model. Journal of the American Statistical
Association, 70:927-932, 1975.
63. Taylor, Lester. The Demand for Energy: A Survey of Price and
Income Elasticities. In: International Studies of the Demand
for Energy. W. D. Nordhaus (ed.), North Holland, Amsterdam,
1977.
64. Abbott, Michael and Orley Ashenfelter. Labour Supply, Commodity
Demand and the Allocation of Time. Review of Economic Studies,
43(3) :389-4ll, October 1976.
65. U.S. Environmental Protection Agency. Air Quality Data, Annual
Statistics 1977. Office of Air Quality Planning and Standards,
EPA-450/2-78-040, September 1978.
66. U.S. Department of Commerce News. Projections of Personal Income
to the Year 2000. December 9, 1980.
67. Bureau of the Census. Current Population Reports. Series P-25,
Projections of the Population of the United States, 1977 to 2050.
No. 704, July 1977.
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SECTION 5
RESIDENTIAL PROPERTY MARKET
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SECTION 5
RESIDENTIAL PROPERTY MARKET
INTRODUCTION
Section 4 of this report uses an economic model of household
expenditure decisions to estimate some of the benefits that would
result from attainment of the secondary national ambient air quality
standards for TSP and S02. The benefits estimated by that model
primarily reflect reduced soiling and materials damage within the
household sector. Not included in those estimates are benefits
arising in other sectors (e.g., agricultural benefits), or other
household sector benefits such as improved visibility.
Many previous studies have developed estimates of household
sector benefits by analyzing differences in residential property
values. The underlying hypothesis in those studies is that
residential property values will reflect not only housing quality but
also site-specific attributes such as location, neighborhood
characteristics, availability of services, and environmental quality
including air quality.
The purpose of this section is to draw upon the results of
representative property value studies to provide a cross-check on the
5-1
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magnitude of the benefits estimated by the household expenditure
model. As discussed previously in Section 2, one would expect the
estimates based on property values to be larger than the estimates
from the household expenditure model. This is because the former will
tend to include a broader range of effects such as visibility benefits
and possibly some health benefits. Thus, by comparing the estimates
from these two methodological approaches applied to the same
geographic areas, one can assess whether the household expenditure
model estimates are consistent (i.e., smaller in magnitude) with the
estimates based on property values.
Using the same air quality data employed in Section 4, the
property value technique is used in this section to develop benefits
estimates for the same 24 SMSAs (metropolitan areas) examined in
Section 4. Benefits are estimated for the same air quality scenarios
— attainments of alternative secondary ambient air quality standards
for TSP and SC^. The resulting estimates from the two methods are
compared in Table 5-1. As can be seen in the table, a reduction in
the ambient level of TSP within each of the 24 SMSAs has been
estimated to result in a discounted present value of benefits in 1980
dollars in the range of $2.08 to $4.99 billion.* A reduction in the
ambient level of S02 within each of these SMSAs are estimated to
result in benefits in the range of $0.33 to $0.47 billion in 1980
dollars.* As Table 5-1 shows, the sum of the estimates from the
* Using a 10 percent rate of discount,
5-2
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TABLE 5-1. COMPARISON OF THE BENEFITS FROM ATTAINING ALTERNATIVE
SECONDARY STANDARDS IN 24 SMSAs
(billion $)
Pollutant/ Property value Household expenditure
standard differentials model
TSP 2.08-4.99 2.3
S00 0.33 - 0.47 0.92
household expenditure model fall within the range of the sum of
benefits estimated from the property value studies.
In addition, the benefits estimated in this section should be
considered to be general approximations of the benefits resulting from
the attainment of alternative secondary standards in these 24 SMSAs
for the following reasons: 1) The results of studies on specific
cities in the early 1960's and 1970's are used to estimate the
benefits of pollution reductions occurring in 1986 and 1987 for the 24
SMSAs. If the valuation of air quality improvements has changed
significantly since that time, the use of these study results can only
be considered as approximations of the benefits of attaining alterna-
tive secondary standards. 2) These estimates are based on studies
that generally examine the relationship between residential property
values and the annual average, as opposed to the second highest,
pollution readings. 3) The maximum of the second highest pollution
reading within an SMSA is taken as representative of the level of
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exposure of all households within the SMSA. 4) The marginal
willingness to pay for air quality improvements of households residing
in single-family units is assumed to be representative of all house-
holds.
General Background
The analysis of residential property value differentials has been
widely used for estimating the benefits of reductions in air pollution
levels. This method assumes that the benefits of living in a clean
air environment are capitalized into property values. In other words,
what people are willing to pay for air quality improvements can be
measured by the observed differences in the value of residential
properties that are identical in every, respect except air pollution
exposure.
Since this method focuses on the decisions made in the housing
market, the household does not need to know the technical relationship
between air pollution and physical damage. The household, however,
must be able to perceive the effect of different levels of air
quality, and make decisions in the housing market based on that
perception. Consequently, the types of benefits that are measured
through the property value method are any perceived health, physical
property, aesthetic, or psychic benefits that are the result of
residing in an area with relatively clean air. Because some of the
effects of air pollution are probably not perceived by households, one
5-4
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of the disadvantages of property value studies is that they cannot
provide estimates of all the benefits that result from air quality
improvements. For example, health effects that are not perceived by
the household will not be captured by residential property values.
Another disadvantage is that residential property value studies may
only provide estimates of benefits that occur at home. For example,
benefits of air quality improvements that occur at recreation areas
and the workplace may not be measured by residential property value
differentials.*
One of the major advantages of property value differential
analysis is the ability to capture the value that households place on
the aesthetic and psychic amenities of the place where they reside.
Neither health studies nor dose-response functions measure the
aesthetic benefits of improvements in air quality. In addition,
property value studies can reflect the choice of substitute activities
and goods that are used as a means of offsetting the effects of
pollution. If the members of a household substitute indoor activities
for outdoor activities on certain days because of poor air quality,
this reduced flow of services from the property would be reflected in
a lower property value. It is possible, however, that the purchase of
goods to offset the effect of pollution may result in an enhancement
It is possible that property values, in addition to reflecting the
value individuals place on amenities at the home, may also reflect
the value placed on amenities at the workplace since once an
individual makes a residential location decision, the choice of
other locational amenities, such as those at the worksite, are
limited. See Cropper (1).
5-5
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of the property value in a polluted area. If central air
conditioning, for example, is bought by a household in order to offset
the effects of pollution, the value of that house is higher relative
to an identical home without air conditioning that is exposed to the
same level of pollution. This can be correctly reflected in property
value differentials if air conditioning is identified as one of the
attributes of housing.
Since the purpose of this study is to measure the welfare
benefits of attaining proposed alternative secondary standards, we
have assumed that the primary standards have been met. Although the
primary standard was established to protect human health, there is the
possibility that some health benefits may remain to be captured when
moving from the primary to secondary standard. On the other hand,
some part of the physical property and aesthetic benefits of a cleaner
environment will be captured in achieving the primary standard.
Consequently, the benefits estimated in this section by the analysis
of residential property value differentials will be limited to the
perceived at-home health, physical property, and aesthetic benefits of
the reductions in air pollution from the primary to alternative
secondary standards.*
* The majority of property value studies have estimated air pollution
control benefits based on reductions in pollution over a range that
would most likely include the majority of perceived health benefits.
The appropriateness of using the results of these studies to
estimate the benefits of moving from the primary to secondary
standards is addressed in the Benefit Estimates subsection.
5-6
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As mentioned in Section 4, the household expenditure model, as
currently developed, provides estimates of only the short-run benefits
accruing to the household that result from a change in air quality.
Since the model does not at the present time reflect the long-run
adjustments to changes in air quality, the changes in property value
that result from changes in air quality are not measured. It must be
mentioned, however, that it is not appropriate to add the benefits
estimated by the consumer budgeting model to the benefits that will be
estimated in this section because there certainly will be some
overlapping of the benefits estimated by these two models. For
example, an improvement in air quality that results in a reduction in
expenditures on home repairs probably will be reflected in an increase
in the value of the property.
Methodology
The use of property value differentials as a means of determining
the willingness to pay for air quality improvements has its
underpinnings in the hedonic price technique. This technique was
originally developed by L. M. Court (2). Griliches and Adelman (3),
Griliches (4), Ohta and Griliches (5), Kain and Quigley (6), and
others have used the technique to estimate the value of changes in the
quality of consumer goods. Generally stated, the hedonic technique
examines the functional relationship between the price of a good and
5-7
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its characteristics.* It has been used extensively as a means of
estimating the marginal willingness to pay for environmental quality
[Harrison-Rubinfeld (7); Nelson (8)]. In these studies, housing
values are regressed on a set of housing characteristics which
includes a measure of air quality.
Before explaining the hedonic technique, it is necessary to
address the question of whether predicted changes in property values
are accurate measures of the total benefits of air quality
improvements. Using a model of locational choice, Polinsky and
Shavell (9) have shown that predicted property value changes are
accurate measures of these benefits only under certain rather
stringent assumptions. Their explanation proceeds as follows:
Assume that there is a city inhabited by individuals with
identical utility functions and equal incomes.* People work in the
center of the city and reside in the area surrounding the center city.
Air quality (AQ) at a specific location increases with distance (d)
from the center city. Travel cost (T) to the center city is also an
increasing function of d. Utility in this city is a function of the
* See Chapter 1 of Griliches (4) for a summary of the hedonic price
technique.
** The model can be generalized to reflect the possibility that there
is more than one utility function and unequal incomes within the
city. In this case, there would be i consumer groups (i = l,n)
where each member of the i group would have identical utility
functions and incomes. This would only serve to complicate the
analysis without changing the results. If incomes are endogenous
to the model, however, the following results will be altered.
5-8
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consumption of household services (H), a composite good (X), and the
level of air quality [AQ(d)]:
U = U H, X, AQ(d) (5.1)
The consumer desires to maximize his utility subject to the budget
constraint:
Y = p(d)H + X + T(d) (5.2)
where Y = money income,
p(d) = per unit price of housing services at a location
with distance (d) from the center city,
H = household services,
X = the composite good with price equal to 1, and
T(d) = commuting costs to the center city.
By solving the first-order conditions of the utility maximization
problem, Equation (5.1) can be stated in terms of an indirect utility
function — utility as a function of the demand functions for H, X,
and AQ:
U = I[p(d), Y-T(d), AQ(d)] (5.3)
Under the assumption of unrestrained and costless mobility
throughout the city, and identical utility functions and income, a
5-9
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common equilibrium level of utility, U , will be obtained. At U , no
individual can increase his utility level by moving.
U* = I[p(d), Y-T(d), AQ(d)] (5.4)
Implicit in this relation is the equilibrium housing function:
p(d) = P[U*, Y-T(d), AQ(d)]. (5.5)
It is important to note that the equilibrium price of housing is
a function of U as well as Y-T(d) and AQ(d).
In Polinsky and Shavell's paper, Equation (5.5) is used to
explain the conditions under which a new property value schedule can
be predicted from a change in air quality. If it is assumed that the
city is small and there is perfect and costless mobility among cities,
then U will be the same across all cities and exogenous to the small
city. If air quality improves within the small city, U will not
change and the change in property value is only dependent on the
characteristics of d. A regression equation specifying the relation-
ship between p(d) and d can be used in this case to predict the change
in property values resulting from a given change in air quality. If
the city is either large, or there is imperfect mobility among cities,
then U will be endogenous. If air quality improves within the city, U
will be affected. In this case, the new property value schedule
5-10
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cannot be predicted without first using a general equilibrium model to
determine the new level of U resulting from the change in air quality.
In general, therefore, property value equations that predict the
change in property value for a given change in air quality can be used
to estimate the willingness to pay for air quality improvements only
if the following assumptions are met:
• The geographical area under consideration must be small.
• There must be perfect mobility throughout, and into
and out of, the geographical area.
• There must be no changes in input and output prices.
The hedonic technique, however, does not attempt to predict a new
property value schedule resulting from a change in air quality, but
rather estimates the marginal willingness to pay for air quality
improvements by observing the housing market in equilibrium. In this
method, the implicit price of air quality is identified by examining
the differentiated prices within the housing market that result from
variations in existing air quality. Since the housing market is in
equilibrium, the implicit price of air quality can be shown to be
equal to the marginal willingness to pay for air quality. The hedonic
technique is therefore useful in predicting the benefits of marginal
changes in air pollution. Given certain conditions, the implicit
prices estimated by the hedonic technique and other relevant variables
can be used to estimate the inverse demand function for air quality.
5-11
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Through the estimation of this demand curve, the benefits of non-
marginal changes in air quality can also be predicted.
The general form of a hedonic equation relates the price of a
good to the characteristics of that good. As applied to the housing
market, this can be expressed as:
(5.6)
where R^ = price of the i residential location.
S^ = a vector of structural characteristics of the
itn location.
N- = a vector of neighborhood characteristics of the
itn location.
Q- = a vector of environmental characteristics of
the i location with one element in the vector
being air quality (q-,).
Note that housing price in the hedonic equation is a function only of
the characteristics of the house, not of the household.
The assumptions that are necessary in order for the hedonic
equation to estimate the marginal willingness to pay for air quality
improvements are:
• The housing market must be in equilibrium.
• Individuals must be able to perceive the
characteristics and attributes of housing.
5-12
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• A complete range of houses with alternative
characteristics must be available.
The partial derivatives of property value with respect to the
housing characteristics are interpreted as the marginal implicit
prices or the additional amount that must be paid for a house with one
more "unit" of a particular characteristic, ceteris paribus. Since
one of the assumptions of the property value model is that the housing
market is in equilibrium, the marginal implicit price is therefore
equal to the marginal willingness to pay for that characteristic. In
terms of the partial derivative of property value with respect to air
quality (6Rj/3q-,), an estimate of the equilibrium willingness to pay
for marginal air quality improvements is obtained.
In order to see why the partial derivatives of the housing
equation variables are equal to the equilibrium marginal willingness
to pay for housing characteristics, it is helpful to develop a model
of consumer choice following Rosen (10).*
Let's assume that there is a consumer whose utility is dependent
on the consumption of a composite good (X) and a vector of housing
* Rosen's paper dealt with both the consumption and production of a
good that could be defined in terms of its attributes and
characteristics. Since the hedonic price technique only reveals the
equilibrium outcome of demand and supply conditions and not the
underlying demand and supply functions, and since the purpose of
this paper is to estimate the willingness to pay for air quality
improvements, we will limit our discussion to the consumer
allocative decisions made for housing.
5-13
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characteristics (H) where air quality (h^) is an element in the
vector:
U = U(X, hx, ... , hn) (5.7)
The consumer has income (y) which can be expressed as:
y = X + p(H) (5.8)
where p(H) = price of housing.
X = the composite good with price equal to 1.
Setting up the Lagrangian, the consumer maximizes U subject to
his budget constraint. The first order conditions can be expressed
as:
au/dX = A and dU/3hi = Adp(H)/3hi (5.9)
where A = the Lagrangian multiplier.
By combining equations, we find that in equilibrium the marginal
rate of substitution between each housing characteristic and the
composite good is equal to the partial derivative of the price of
housing with respect to that particular characteristic (i.e., the
implicit price of the characteristic estimated by the housing
equation) :
5-14
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(au/ahi)/(au/ax) = (ap(H)/dhi) . (5.10)
If X is thought of as money (the price of a dollar is equal to $1.00),
equilibrium is achieved when the marginal rate of substitution between
h. and money is equal to the marginal implicit price of h^. Since the
marginal rate of substitution between h.^ and money can also be viewed
as the marginal payment for h- with money, the equilibrium conditions
can be expressed as equating the marginal willingness to pay for h.
(with money) with its marginal implicit price.
The equating of the marginal implicit price and the marginal
willingness to pay can also be explained by viewing equilibrium in
terms of a particular h.^. Assume that there is a level of consumer
utility, u, that can be defined by the function:
U(y - 9; h-j^ ... , hn) = u (5.11)
where y - 9 = X.
For a given u, Equation (5.11) can be thought of as an indifference
curve relating the tradeoff between h^ and X. A bid function:
, hn; u,y) (5.12)
can be derived from Equation (5.11) which relates the alternative
expenditures a consumer is willing to make for h^ given a certain
5-15
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level of utility and income. By totally differentiating (5.11), we
find that:
3U/3X (dy - dQ) + dU/dhl di^ + ... + 3U/3hn dhn = du (5.13)
Given the assumption of a fixed level of utility and income, du = 0
and dy = 0. If dhu = 0 for k /= i, Equation (5.13) reduces to:
i = (3U/3hi)/(3U/3X) . (5.14)
Viewing a particular h.,h-, as air quality, Equation (5.14) shows that
the marginal rate of substitution between air quality and X (money) is
equal to the marginal implicit bid for air quality (39/3h-^) at a given
level of utility and income.
Figure 5-1 shows the bid function of consumer j for air quality
while holding everything else constant, 9^(h,, h2, • •• , hn ; u , y ).
There are a number of different bid functions reflecting the different
levels of tastes, preferences, and income of consumers. This function
shows the willingness to pay (bid) for air quality in terms of the
amount of money (X) foregone, ceteris paribus. The minimum implicit
prices revealed in the market that must be paid for different levels
of air quality while holding )\ through h constant is shown by p(h, ,
}\2' ••• ' nn^* Equilibrium is reached when 03 (h,, h2, ... , hn; u ,
y ) is tangent to p(h^, hj, ... , nn); i.e., where the marginal
5-16
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;h2* ... hn*, u* , y*)
... h*, u*, y*
hu. (air quality)
Figure 5-1. Implicit price schedule and bid functions,
5-17
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willingness to pay for air quality is equal to its marginal implicit
price.
Since the hedonic equation can be expressed by p(h,, ... , h ),
the marginal implicit price schedule for air quality (6p(H)/8h^) can
be easily obtained by taking the derivative of the hedonic housing
equation with respect to air quality (see Figure 5-2). Assuming that
the housing market is in equilibrium and following the above explana-
tion, this schedule will also trace out the loci of marginal
willingness to pay equilibria for different levels of air quality by
consumers with different bid functions. Note that unless all
consumers have identical bid functions (i.e., identical utility
functions and incomes), the hedonic technique yields only the
equilibrium marginal willingness to pay of consumer j with bid
function 9^. This is only one point on consumer j's demand price
function for h^ while holding utility constant (i.e., the inverse
compensated demand function). Consequently, dp(H)/6h-]_ is not the
inverse compensated demand function for air quality and, in most
cases, can only be used to compute the benefits of marginal improve-
ments in air quality. In order to accurately estimate the demand
curve for air quality and predict the benefits of non-marginal changes
in air quality when consumers do not have identical utility functions
and incomes, additional information and steps are needed.
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h, (air quality)
Figure 5-2.
Marginal implicit price schedule and
demand price functions.
5-19
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Literature Review
The first study undertaken to measure the relationship between
property values and the level of air quality was done by Ridker and
Henning (11). Using 1960 cross-sectional census tract data from the
St. Louis metropolitan area, the effect of air pollution levels on
property values was estimated using regression analysis. The
dependent variable was the median value (estimated by owner) of owner-
occupied single-family housing units, and the independent variables
included those reflecting location characteristics (e.g.,
accessibility to highway, travel time to central business district),
property characteristics (e.g., median number of rooms, houses per
mile), neighborhood characteristics (e.g., school quality, persons per
housing unit), median family income, and an air pollution variable (an
index indicating the presence of SCu/ SCu, H-S, I^SO., and in some
cases dustfall). Different linear specifications were tried and a
significant negative relationship was found between the dependent
variable and the air pollution variable. From these results, they
concluded that property values could be expected to rise at least
$83.00 and more probably $245, if the measurement of SCU were to drop
by 0.25 ug/100 cm2/day.*
* Freeman (12) concluded that Ridker and Henning's results were over-
interpreted and could not be used to predict changes in property
values when air quality changed because the demand curve for air
quality had not been identified. This led to quite a debate in the
literature over the proper interpretation of the derivative of the
air quality variables. [See Anderson and Crocker (13); Freeman
(14); Polinsky and Rubinfeld (15); Small (16); and Harrison and
Rubinfeld (17).]
5-ZO
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Zerbe (18) estimated a property value equation for Toronto and
Hamilton, Ontario. Sulfur dioxide and dustfall were the two pollution
measures used. Both linear and log-linear specifications were
employed; in the log-linear specification, the elasticity of property
values with respect to sulfur dioxide ranged from 0.061 to 0.121 for
Toronto and 0.081 for Hamilton.*
Crocker (19), in a study of the relationship between home sale
price and sulfur dioxide and particulates in Chicago, found a
significant negative relationship between sale price and particulate
matter when both pollution variables were entered into the equation.
When each pollution variable was entered separately, they both
exhibited a significant negative relationship with sale price.
Anderson and Crocker (24) estimated the relationship between air
pollution and median property values (estimated by owner) for three
cities: St. Louis, Washington, D.C., and Kansas City. Using separate
equations for owner-occupied and renter-occupied housing, they found a
significant negative relationship between air pollution and property
values while controlling for median family income, percentage of old
units, percent of run-down units, percent of non-white population,
distance to the central city, and median number of rooms. Using a
log-linear specification, they found that the mean property value for
the St. Louis area would be reduced by $300 to $700 for an increase at
* Information on the studies by Zerbe (18), Crocker (19), and Steele
(20) is taken from Freeman (21), Waddell (22), and Appel (23).
5-21
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the mean of 0.1 ug/100 cm2/<3ay in S03 and a 10 ug/m3 increase in
particulates.
Steele (20) did not find a significant relationship between
property values, as measured by mean value per room, and SO- and
particulates.
Wieand (25) regressed per-acre housing expenditures in St. Louis
(a proxy for land values) on property characteristics, neighborhood
characteristics, income, and pollution as measured by annual mean
sulfation and annual mean particulates. Neither pollution variable
was significant.
Deyak and Smith (26), using a log-linear specification, found a
significant relationship between median property values of
representative SMSAs and suspended particulates. Other variables
included in their best equation were median family income and percent
of inferior housing units. In a later study on the owner- and renter-
occupied housing market for 85 cities which included measures of local
public services and taxes, Smith-Deyak (27) did not find a significant
negative relationship between air pollution and property value. A
possible reason for their failure to find a significant negative
relationship between air pollution and property values may be due to
the fact that property value differentials were examined across,
rather than within, cities.
5-22
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Using the data from Anderson and Crocker's St. Louis study (24),
Polinsky and Rubinfeld (28) empirically estimated the equilibrium
housing market function developed by Polinsky and Shavell (9) using a
Cobb-Douglas form of utility function. Log-linear equations were
developed for both owned and rented properties. The suspended
particulate variable was negative and significantly different from
zero at the 0.05 level for both equations, while the sulfur oxide
variable was negative and significantly different from zero at the
0.10 level for the homeowner equation.
The concentration of nitrogen oxides, NOV (used as a proxy for
A
air pollution), was found to be negatively related to median property
values in Boston by Harrison and Rubinfeld (7). Besides air
pollution, the housing characteristics that were included in the
equation were: two structural variables, eight neighborhood
variables, and two accessibility variables. With all the independent
variables at their mean levels, a change in NO of 1 pphm was
X
associated with a change in median housing values of $1,613. They
also estimated a willingness-to-pay equation and found that the
marginal willingness to pay for air quality improvements varied a
great deal depending on the existing level of air pollution and
income.
Nelson (8) also found a significant relationship between air
pollution and median census tract owner-occupied property values in
Washington, B.C. Several different specifications were employed with
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the semi-log and log-linear forms giving the best results. It was
concluded that an increase in the mean level of total suspended
particulates of 10 ug/m^ would reduce the mean value of property by
$576 to $693, and an increase in the mean oxidant level of 0.01 ppm
would reduce the mean value of property by an additional $141 to $152.
The estimated marginal willingness to pay was then used to calculate
the demand curve for air quality.
In a study of single-family owned residences in the Los Angeles
area, Brookshire e_t al. (29) found a significant negative relationship
between the sale price of homes and air pollution measures. Actual
market transactions for individual homes were used as the unit of
observation. Both the linear and nonlinear specifications employed
showed a significant relationship between home sale price and
pollution. The average sale price differential attributable to a
change in the level of pollution from "poor" to "fair" ranged from
$5,793 per home to $6,134 per home.
In a study of the New York metropolitan area, Appel (23) found a
significant negative relationship between suspended particulates and
mean property values. The hedonic equation that performed best was
one in which the pollution variable was entered in exponential form.
This form conforms to a_ priori expectations that the marginal damages
of pollution increase as pollution increases. Other variables
included in the best equation were the mean number of rooms, the crime
5-24
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rate, the percent of non-white persons, and minutes of time to the
central business district.
A summary of the studies that have found a significant negative
relationship between residential property values and air pollution is
given in Table 5-2.
LIMITATIONS OF THE HEDONIC TECHNIQUE
Before proceeding with the calculation of benefits, it is
important to reiterate the limitations of using the hedonic technique
and the effect these limitations have on the ability to predict the
benefits of improvements in air quality. The hedonic technique is
capable of estimating the implicit price of the characteristics of a
good that the consumer is able to accurately perceive. Since most
characteristics of a good are tangible and easily perceived, this is
not unreasonable. Air quality, per se, is not a tangible
characteristic of housing and it is possible that households are
unable to accurately perceive the effect of air quality on their
residential property. Even if households are cognizant of some of the
effects of air quality, it is doubtful that they will be aware of all
of its effects. Consequently, all of the effects of air quality may
not be capitalized into residential property values. Application of
the hedonic technique in order to estimate the effects of air
pollution may therefore result in an underestimate of the "true
5-25
-------
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5-27
-------
benefits" accruing to residential properties.* Although there has
been some criticism that the hedonic technique is invalid for
predicting the benefits of air quality improvement because households
are unable to accurately perceive any of the effects of air pollution,
the studies in Table 5-2 appear to support the hypothesis that
households perceive at least some of the effects of air pollution and
these effects are capitalized into property values.
Benefits estimated through hedonic property value equations may
only provide estimates of the perceived benefits that occur at the
residential property. Some of the benefits from air quality
improvements that occur away from home (e.g., at the workplace,
recreational areas) may not be capitalized into residential property
values. Since a portion of the household's time is spent away from
home, it is possible that only a portion of the total benefits
accruing to a household may be predicted from the hedonic property
value equations. This must be kept in mind when comparing benefits
estimated by the hedonic technique to benefits estimated by other
methods.
* It is also possible, on the other hand, that benefits may be over-
estimated if households, because of their lack of knowledge of the
true effects of air pollution, overcompensate for the effects of air
pollution through their valuations of properties exposed to
different levels of air pollution.
5-28
-------
As mentioned*in the last subsection, the assumptions that are
necessary in order for the hedonic equation to estimate the marginal
willingness to pay for air quality improvements are:
• Individuals must be able to perceive the
characteristics and attributes of housing.
• The housing market must be in equilibrium.
• A complete range of houses with alternative
characteristics must be available.
It is very unlikely that these conditions will hold in the
housing market. In this study, we are mainly concerned with how the
violation of these assumptions will affect the estimated air
pollution-property value relationship. The violation of the first of
these three assumptions has already been addressed in the discussion
on the difficulty of applying the hedonic technique to a good
possessing a characteristic such as air quality.
In order for the second assumption to be met in the housing
market, households must be just willing to hold the existing stock of
housing at the prevailing prices. Equilibrium will be achieved only
if: 1) all households have complete information on the prices and
characteristics of housing, 2) transactions and moving costs are equal
to zero, and 3) housing prices adjust instantaneously to changes in
demand and supply. According to Freeman (32), divergencies from
equilibrium, in most cases, will only result in random errors in
marginal willingness-to-pay estimates. Freeman mentions, however,
5-29
-------
that less than instantaneous adjustment in the housing market to
changes in demand or supply may result in biased estimates of the air
quality variable. For example, if equilibrium is disrupted due to an
air quality change, and transactions and moving costs are non-zero,
households will not move unless the benefit is at least as great as
the costs involved in moving. If air quality is consistently changing
in one direction and households consistently lag in their adjustment
to that change, the observed marginal implicit price will diverge from
the true marginal willingness to pay. In this case, the marginal
implicit price of air quality identified in the hedonic property value
equation is a biased estimate of the equilibrium marginal willingness
to pay.
Freeman also mentions that future expectations on housing prices
may result in biased estimates of the implicit price of air quality.
If households perceive that an improvement in air quality will take
place in the future and housing prices are affected by that
perception, the market has adjusted to the air quality change before
the change actually takes place. If a hedonic price equation is
specified for the housing market in an area that has already adjusted
to a future air quality change, the marginal willingness to pay for
air quality would be underestimated.
It is quite possible that the third assumption may be violated
due to the nature of the housing market. Given the time necessary for
the supply of housing to adjust to changes in demand, it is likely
5-30
-------
that some households will not be able to. find housing with all of the
characteristics that the household finds desirable. In these
households, utility cannot be maximized. Whether this is a problem
that will seriously affect the estimates of the marginal implicit
price of air quality has not been investigated at the present time.
It is doubtful, however, that the existence of an incomplete range of
homes in the study area will make the estimated relationship between
air pollution and property values totally unreliable.
Segmentation in the housing market can also affect the estimates
of the marginal implicit prices of housing attributes. Housing market
segmentation exists when the purchasers of housing participate in
distinctly separate housing submarkets even though the purchasers are
technically participating in the same housing market. The submarkets
may exist because of racial discrimination, cultural differences, or
geographic immobility. Where housing market segmentation exists, the
structure of the prices of housing in each submarket will be
different. The specification of a hedonic price function for one
housing market when submarkets exist will result in incorrect
estimates of the marginal implicit prices of housing attributes. In
order for the implicit prices of housing characteristics to be
correctly estimated, separate equations for each submarket must be
used. Harrison and Rubinfeld (7) have found that separating their
sample into submarkets did affect their benefit estimates for Boston,
while Nelson (33) did not find that stratified samples for the
Washington, D.C. area affected the hedonic price functions. Further
5-31
-------
research investigating this problem is needed before anything
more conclusive can be said regarding the effect of market
segmentation on the hedonic price functions.
Certainly, one should not conclude that the benefits estimated
using the hedonic price technique are meaningless because of the
caveats that must be attached to the technique. A negative
relationship between air pollution and property values has been
consistently shown to exist. In addition, the marginal implicit
prices of air pollution estimated in different studies are consistent
and quite plausible. The technique is definitely useful in providing
approximate estimates of the magnitude of some of the benefits of air
quality improvement.
BENEFIT ESTIMATES
The studies reviewed in the Literature Review subsection provided
estimates of the willingness to pay for marginal air quality
improvements for specific cities. In this section, we will assume
that these studies are representative of the 24 SMSAs examined in this
study and will use the results to estimate the benefits of achieving
alternative secondary standards for these 24 SMSAs. It should be
noted that there are a number of reasons why a strict comparison of
the results of the studies reviewed in the Literature Review
subsection is not possible. These reasons can be explained by
referring to Table 5-2. Although the majority of studies use the
5-32
-------
median property value of a census tract as the dependent variable in
their equations, Crocker (19) and Brookshire e_t a_l. (29) use the sale
price of individual homes. Most studies have concentrated on only the
owner-occupied housing market, while some studies have also estimated
equations for the rental market using median gross rent and median
contract rent as dependent variables.
The pollutants measured also differ among studies. Sulfur
oxides, particulate matter, dustfall, and nitrogen oxides are used in
various studies. Because of the high correlation that tends to exist
among pollutants, it is difficult to tell whether the effect on
property values of a particular pollutant, or just pollution in
general, is being measured. When two highly correlated pollutants are
entered as independent variables in the same equation, it is difficult
to isolate the separate effects of each of the pollutants on property
values. If only one of the highly correlated pollutants is entered
into the property values equation, on the other hand, its coefficient
is probably picking up the effects of both the included and excluded
pollutant. In Zerbe's study (18) on Hamilton property values, for
example, it is difficult to tell whether the coefficient of sulfation
is also measuring the effect of particulate matter on property values.
In addition to the various pollutants measured, the studies in
Table 5-2 also differ in that the pollutants are measured in different
units. Annual means, monthly means, maximum values, geometric means,
and arithmetic means are the units used to measure the pollution
5-33
-------
variables. The techniques used to measure pollution also vary among
the studies. Although most of the studies have used estimates of
sulfation that were measured by the lead candle technique, this
technique is not strictly comparable to the techniques that are
currently in use. In fact, the lead candle technique tends to bias
the sulfation measurements in an unknown direction.*
The results of the studies reviewed in Table 5-2 are based on
data collected in different years (e.g., 1960 and 1970 Census data).
This is not likely to be a problem in comparing the studies because
the demand for air quality probably has not changed significantly over
the years in which these studies were done. However, the benefits
estimated by the studies using data from different years are obviously
not comparable because of the differences in property values due to
increases in the price level. For this reason, the comparison of the
results of the property value studies will be based on the estimated
coefficients and elasticities of the air pollution variables.
As can be seen in Table 5-2, all but one of the studies have used
a nonlinear functional form to estimate the relationship between air
pollution and property values. The choice of a nonlinear
specification in the studies employing the hedonic technique can be
viewed as being twofold. The hedonic equation need not be linear if
costless repackaging of the characteristics of the good is impossible.
* As per phone conversation with John Clements of USEPA.
5-34
-------
In the housing market, it is unlikely that costless repackaging of the
characteristics of housing will be common. For example, two homes
with four sides are not equal to one home with eight sides. In
addition, the hedonic equation may be nonlinear in the air quality
variable depending on the assumptions regarding the marginal implicit
price of air quality. If the hedonic equation is linear in the air
quality variable, its marginal implicit price is constant over the
entire range of air quality. Since there is no variation in the
implicit price of air quality, it is not possible to identify the
demand for air quality. In those hedonic studies where both linear
and nonlinear specifications have been tried in order to measure the
implicit price of air quality within a specific geographical area
(e.g., SMSA), the nonlinear specifications have given more
satisfactory results.
The majority of studies listed in Table 5-2 have used a log-
linear functional form to specify a nonlinear relationship between air
pollution and property values. A significant negative relationship
between air pollution and property values has been found in the
majority of these studies. Unlike the marginal implicit price of air
pollution in a linear specification, the marginal implicit price in
these specifications varies depending on the ratio of the property
value to the pollution level.* Of more interest, however, is the rate
of change of the marginal implicit price schedule. It is positive for
* The first derivative of the log-linear specification, (Property
Value) = a(Pollution)13, is b (Property Value/Pollution).
5-35
-------
a log-linear specification, implying that the marginal implicit price
(a negative) is an increasing function of the level of pollution.
Since pollution is something to be avoided (i.e., a disamenity), this
means that the marginal willingness to pay to avoid pollution becomes
less negative as pollution increases; in other words, the marginal
willingness to pay to avoid pollution is lower as the level of pollu-
tion rises. Intuitively, one would expect that the higher the level
of pollution, the greater the willingness to pay for a marginal
improvement in air quality. Both Harrison and Rubinfeld (7) and
Appel (23) employ specifications that yield negatively-sloped marginal
implicit price curves that conform to the a priori expectation that
the marginal willingness to pay to avoid air pollution is greater for
higher levels of pollution.
Since the hedonic technique examines the equilibrium relationship
between property values and air pollution, it is not clear whether the
positive slope of the marginal implicit price curve results from the
fact that people living in relatively clean air environments may tend
to have larger incomes, and consequently a higher equilibrium marginal
willingness to pay for additional air quality improvements, than
poorer people who may tend to live in relatively dirty air environ-
ments. Not enough empirical research has been done in this area,
however, to justify the hypothesis that the marginal implicit price
curve is negatively sloped.
5-36
-------
As mentioned in the Methodology subsection, the hedonic price
technique yields only the equilibrium willingness to pay for marginal
improvements in air quality. Moving from the primary to secondary
standard, however, will involve non-marginal changes. In order to
accurately estimate the benefits of these changes in air quality, the
demand price function of consumers for air quality must be known.
This function can be calculated using the implicit prices estimated by
the hedonic technique, and information on air quality levels, consumer
income and characteristics. Since such information is lacking at this
time for the majority of the property value studies, we will
approximate the benefits of these non-marginal reductions based solely
on the information yielded by the hedonic price technique.
The benefits of achieving the secondary standard will be
approximated using the results of the studies listed in Table 5-2.
The marginal implicit price curve for air quality for the log-linear
specification is shown in Figure 5.3.* MPV'(P) is a plot of the
derivative of the housing equation with respect to air pollution and
also traces out the equilibrium willingness to pay to avoid air
pollution. D(P) is the true demand curve for air pollution. Since
air pollution is a "bad", a large negative price implies that the
household is willing to pay large amounts to avoid air pollution.
Note that the marginal implicit price curve resulting from the log-
* Since this is the most common specification used in the studies
listed in Table 5-2, it will be used for explanatory purposes.
5-37
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p
*
PoLLu.ti.on
MPV'(P)
D(P)
-$
Figure 5-3.
Alternative benefit estimates for a
given change in air quality.
5-38
-------
linear specification implies that the marginal implicit price of air
pollution increases (becomes less negative) as pollution increases.
The benefits of an improvement in air quality can be estimated by
the area under the demand curve over the range of improvement. For
the improvement in air quality from PQ to p^ that is shown in Figure
5-3, the benefits are estimated by the area APgPj^C. The demand curve
for air quality has not been estimated in this analysis, however, and
it is necessary to rely on information contained in the hedonic price
equations to approximate the benefits of an improvement in air
quality. The benefits of an improvement in air quality from PQ to P^
can be approximated by the area under the marginal implicit price
curve, AP/jP-^B. It must be kept in mind that this approximation
implies that all households' marginal willingness-to-pay functions are
identical and increasing in pollution abatement.* Clearly, this is an
overestimate of the true benefits of improvement.
Freeman (34) has suggested two alternative ways of approximating
the benefits of non-marginal changes in air quality when the demand
curve for air quality is not known. By assuming that the household's
marginal willingness to pay for air quality is constant over the
* The marginal implicit price function will necessarily be increasing
in pollution abatement only for log-linear specifications. The
linear specification of the property value equation will result in a
constant marginal implicit price. Exponential, semi-log
exponential, quadratic, and the Box-Cox transformation may yield
marginal implicit price curves that are decreasing in pollution
abatement.
5-39
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entire range of air quality, household benefits can be approximated by
the area APQP-,E. The benefits represented by this area can be
estimated by:
Benefits = aProperty Value upollution) (5>15)
dPollution
For the log-linear specification, this is equivalent to:
Benefits = b ******* Val"e (APollution) (5.16)
Pollution
where b = the estimated coefficient of the pollution
variable in the hedonic equation.
If the true demand curve for air pollution is D(P), this approxima-
tion technique will result in an overestimate if the marginal implicit
price function is increasing in pollution abatement. However, this
technique clearly will result in a closer approximation of true
benefits estimated by the area APQP,B.
The other alternative is consistent with the a_ priori expectation
that the marginal willingness to pay for air pollution abatement
declines as air quality improves. One point on the household's demand
curve for air quality is known from the hedonic price equation. By
assuming that the household's marginal willingness to pay for air
pollution abatement declines linearly from that point to a zero
5-40
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marginal willingness to pay when air pollution has been completely
abated, benefits can be approximated for a given improvement in air
quality. For the reduction in air pollution from PQ to P^ shown in
Figure 5-3, household benefits can be approximated by the area APQP-^D.
The benefits represented by this area can be easily calculated as the
difference in triangle OPgA and OP-]_D. This area can be approximated
by:
Benefits = i [(PQA • OP ) - (P D • OP.)]
(5.17)
For the log-linear specification, this is equivalent to:
Benefits = -=• Property Value
1 -
(Pollution^2
(Pollution0)2
(5.18)
where Pollution,. = initial pollution level
Pollution-, = pollution level after an air quality change.
Depending on the shape of the actual demand curve for air
quality, the approximation of benefits under the assumption of a
linearly declining marginal willingness to pay curve can result in
either an underestimate or overestimate of true benefits.
Obviously, either of these alternatives will result in closer
estimates of the true benefits of a given air quality improvement than
the benefits estimated by the area under the marginal implicit price
5-41
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curve of the log-linear hedonic property value specification. The
linearly declining marginal willingness-to-pay alternative, however,
is consistent with the a_ priori assumption that the household's
marginal willingness to pay for air pollution abatement declines as
air quality improves. Because it can be assumed that the majority of
health benefits are captured in moving to the primary standard, it
seems reasonable to expect that the marginal willingness to pay for
further air quality improvements will be decreasing. For this reason,
we will calculate the benefits of proposed secondary standards using
the linear to the origin technique.
Assuming the secondary standard will be set in terms of sulfur
dioxide (SO?) an<^ total suspended particulate matter (TSP), we will
concentrate on the studies that have examined the effect of one or
both of these pollutants on property values. Allowing for the
differences among the studies reviewed in Table 5-2, the results of
these studies have been remarkably consistent. The elasticities of
the sulfur oxide variables range from a low of -0.061 to a high of
-0.12, with a more likely range being -0.07 to -0.10.* The
* The elasticity is a measure of the percentage change in one variable
that can be expected from a given percentage change in another
variable. In this case, it is the percentage change in property
value that can be expected from a given percentage change in pollu-
tion. An elasticity of 0.1 means that a 10 percent change in air
pollution will result in a 1 percent change in property values.
5-42
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particulates1 elasticities range from -0.039 to -0.5, with the more
likely range being -0.05 to -0.12.*
As can be seen in Table 5-2, these ranges of elasticities
correspond to the studies employing log-linear specifications.
Household benefits will therefore be approximated using Equation
(5.18).
Benefits of achieving alternative secondary standards will be
calculated for the 24 SMSAs listed in Table 5-3. Household benefits
in a particular SMSA will be calculated for the single-family owner-
occupied household with median property value that is exposed to the
average level of pollution within the SMSA. For the purposes of this
analysis, the benefits accruing to this household will be taken as
representative of the benefits accruing to households residing in
rental and multiple-dwelling units. This may lead to an overestimate
or underestimate of benefits if the willingness to pay for air quality
improvements tends to be different for the households residing in
these types of structures. Similarly, benefits may be under- or
overestimated if the majority of the housing units in an SMSA are
exposed to pollution levels that are different from the average level
* The particulate elasticity of 0.039 reported by Appel (23) is based
on an exponential specification, unlike the elasticities reported
in those studies employing log-linear specifications, this
elasticity varies depending on the level of particulates. For
example, if the mean level of particulates from Nelson's study on
Washington, D.C. is used with Appel's estimated pollution
coefficient, the elasticity increases to -0.067.
5-43
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TABLE 5-3. SMSA'S INCLUDED IN PROPERTY VALUE STUDY
Atlanta
Baltimore
Boston
Buffalo
Chicago
Cincinnati
Cleveland
Dallas
Denver
Detroit
Honolulu
Houston
Kansas City
Los Angeles
Milwaukee
Minneapolis-St. Paul
New York
Philadelphia
Pittsburgh
St. Louis
San Diego
San Francisco
Seattle-Everett
District of Columbia
for the SMSA.* With these qualifications in mind, the benefits of
achieving the secondary standard for the 24 SMSAs listed in Table 5-3
are:**
Benefits =
24
I (No. of housing units in SMSA-) • (Benefits per
i=l housing unit of meeting the secondary standard
in
* In the case of the Chicago SMSA, for example, the benefits of the
reduction in TSP levels will be underestimated using the average
TSP level within the SMSA since 80 percent of the SMSA population
live in areas where the TSP levels exceed the SMSA average.
** Although the national benefits will exceed the benefits estimated
for the 24 SMSAs, we will limit our benefit estimates to these 24
since the purpose of this section is to provide a cross-check on
the benefits estimated by the household expenditure model.
5-44
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The scenario for reaching the secondary standard is identical to
the one used in previous sections; i.e., air quality in the SMSAs will
improve by half of the amount necessary to reach the secondary
standard by the end of 1986 and the remaining improvement by the end
of 1987. It is also assumed that these improvements in air quality
will be instantaneous, occurring on the last day of 1986 and 1987. In
addition, any SMSA that was in excess of the primary standard in 1978
is assumed to be meeting the primary standard in 1985 and benefits
will be estimated for the change in pollution from the primary to
secondary standard. Benefits for any SMSA that had a level of pollu-
tion in 1978 that was less than the primary standard but more than the
secondary standard will be based on the change in pollution from the
1978 level to the secondary standard. Any SMSA that was meeting the
secondary standard in 1978 is assumed to be meeting it in 1985.
Consequently, no benefits are calculated for these SMSAs. This may
underestimate benefits if air quality in these SMSAs has deteriorated
since 1978.
Because the alternative secondary standards used in this study
are couched in terms of the mean and 24-hour maximum, we will
calculate benefit estimates for compliance with these standards:
5-45
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Alternative Secondary
Air Quality Standard*
(Mg/m3)
S02:
Annual arithmetic mean 60
24-hour maximum** 260
TSP:
Annual geometric mean 60
24-hour maximum** 150
Obviously, the benefits estimated from the reduction in the means
and maximum values are not additive and should be viewed as
alternative measures of the benefits in meeting the secondary
standard. A detailed explanation of how the benefits are estimated is
given in Appendix 5-A. Appendix 5-B provides estimates of the
benefits in reducing air pollution, broken down by SMSA.
Tables 5-4 through 5-7 give the benefits, in discounted present
value, of the reduction in air pollution to the secondary standard
using different measures of air pollution. As Tables 5-4 and 5-5
show, the discounted present value of the benefits in reducing the
mean level of TSP and SO2 to 60 Mg/m is in the range of $2.41 to
* The standards listed above are not, in all cases, part of the
current Federal regulations. The source of the standards shown
here is Stern _e_t a_l. (35), p. 159.
** This value is not to be exceeded more than once a year.
5-46
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TABLE 5-4. ESTIMATED BENEFITS OF THE REDUCTION IN TOTAL SUSPENDED
PARTICULATE MATTER TO ALTERNATIVE SECONDARY STANDARDS*
(in discounted present value billions of 1980 $)**
Average benefit
Reduction in: Total benefits per household
(in billion $) (in $)
Annual average to
60 Mg/nv3 $2.08 - $4.99 $ 71 - $170
Average of second
highest values to
150 Mg/m3 $3.53 - $8.47 $120 - $289
* Benefit calculations based on 24 SMSAs.
** Assuming a 10 percent rate of discount.
TABLE 5-5. ESTIMATED BENEFITS OF THE REDUCTION IN SULFUR DIOXIDE TO
ALTERNATIVE SECONDARY STANDARDS*
(in discounted present value in billions of 1980 $)**
Average benefit
Reduction in: Total benefits per household
(in billion $) (in $)
Annual average to
60 /ug/m3 $0.33 - $0.47 $ 14 - $ 19
Average of second
highest values to
260 Mg/m-3 $1.14 - $1.62 $ 48 - $ 69
* Benefit calculations based on 19 SMSAs.
** Assuming a 10 percent rate of discount.
5-47
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TABLE 5-6. ESTIMATED BENEFITS OF THE REDUCTION IN TOTAL SUSPENDED
PARTICULATE MATTER TO ALTERNATIVE SECONDARY STANDARDS*
(discounted present value in 1980 $)**
Average benefit
Reduction in: Total benefits per household
(in billion $) (in $)
Maximum annual
average within
SMSA to 60 M9/mJ $ 7.64 - $18.32 $260 - $ 626
The second highest
value within SMSA
to 150 Mg/mJ $13.40 - $32.16 $457 - $1,098
* Benefit calculations based on 24 SMSA's.
** Assuming a 10 percent rate of discount.
TABLE 5-7. ESTIMATED BENEFITS OF THE REDUCTION IN SULFUR DIOXIDE TO
ALTERNATIVE SECONDARY STANDARDS*
(discounted present value in 1980 $)**
Average benefit
Reduction in: Total benefits per household
(in billion $) (in $)
Maximum annual
average within
SMSA to 60 Atg/m3 $ 3.20 - $ 4.57 $136 - $ 194
The second highest
value within SMSA
to 260 Mg/nr $ 5.98 - $ 8.54 $255 - $ 364
* Benefit calculations based on 19 SMSA's.
** Assuming a 10 percent rate of discount.
5-48
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$5.46 billion for the 24 SMSAs of the study.* Per-household benefits
are in the range of $71 to $170 for the reduction in TSP and $14 to
$19 for the reduction of SCU.** The estimated benefits increase to a
range of $4.67 to $10.09 billion when the reduction in pollution is in
terms of the average of the second-highest values. Per-household
benefits ranging from $120 to $289 for TSP and $48 to $69 for S02 are
also calculated.
Upper-bound benefit estimates are calculated using the maximum
pollution reading within an SMSA as representative of the reduction in
pollution for the entire SMSA. Benefits are calculated for the
maximum annual average and the second highest pollution readings
within each SMSA for both TSP and S02. Tables 5-6 and 5-7 give the
results of these calculations. Benefits in the range of $10.84 to
$22.8 billion are calculated for the reduction in maximum annual
averages of TSP and SCu within an SMSA to the secondary standard.
This translates into per-household benefits of approximately $200 to
$626 for TSP and $136 to $194 for SG>2. Using the second highest TSP
and S02 readings within an SMSA as representative of the pollution
* Data on S02 are available for only 19 of the 24 SMSAs in the study.
SO2 readings were not available for the Atlanta, Baltimore,
Honolulu, Los Angeles, and Seattle SMSAs. The benefits, therefore,
may be underestimates of the total benefits that would be estimated
by the property value analysis if any of all of these SMSAs
exceeded the secondary standard in 1978.
** Per-household benefits of the reductions in TSP and S02 will be
kept separate because these calculations are based on different
numbers of households.
5-49
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level within the SMSA, benefits increase to a range of $19.38 to
$40.70 billion, or per-household benefits of $457 to $1,098 for TSP
and $255 to $364 for SG>2.
Because these estimates are based on studies that generally
examine the relationship between property values and pollution in
terms of the annual average of pollution, benefits in the range of
$2.41 to $5.46 billion are considered to be the best estimates.
CONCLUSION
In this analysis, the discounted present value of the benefits in
reducing TSP and SO^ levels to comply with the proposed secondary
standards has been estimated using the results of past property value
differential studies. The benefits from the reduction in TSP have
been estimated for 24 SMSAs which comprise about 32 percent of the
United States' population. Benefits calculated for the reduction in
S02 are based on 19 SMSAs which comprise about 28 percent of the
population. Using the linear to the origin approximation technique, a
reduction in the annual arithmetic mean of SO2 and the annual
geometric mean of TSP to 60 ng/m has been estimated to result in
benefits of $2.41 to $5.46 billion for the 24 SMSAs in the study.
Viewed in terras of the reduction in the average of the second highest
reading in an SMSA to 260 M9/m3 and 150 M9/™3 for SO2 and TSP,
respectively, the benefits increase to a range of $4.67 to $10.09
billion. These estimates are gross approximations of the benefits in
5-50
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meeting the secondary standard for basically four reasons: (1) the
results of studies on specific cities in the early 1960's and 1970's
are used to estimate the benefits of pollution reductions occurring in
1986 and 1987 for 24 SMSAs; (2) the benefits of the air quality
improvements are approximated without knowledge of the true demand
curve for air quality; (3) the marginal willingness to pay for air
quality improvements of households residing in single-family units is
assumed to be representative of the marginal willingness to pay of all
households; and (4) the average of the air pollution readings in an
SMSA is taken as representative of the level of exposure of all
households in the SMSA. If the majority of households in an SMSA are
located in areas that are exposed to levels of air pollution that are
beneath the SMSA average, benefits will be overestimated. Conversely,
if households are typically located in the "polluted" areas of the
SMSA, benefits will be underestimated. These estimates are useful,
however, because they provide some idea of the magnitude of the
"property value" benefits that will be obtained when moving from the
primary to the secondary standard.
5-51
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Air Pollution Control Benefits. Vol. 4: Studies on Partial
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5-52
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12. Freeman, A. Myrick III. Air Pollution and Property Values: A
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13. Anderson, Robert J., Jr. and Thomas D. Crocker. Air Pollution
and Property Values: A Reply. Review of Economics and
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556, November 1974.
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18. Zerbe, Robert, Jr. The Economics of Air Pollution: A Cost
Benefit Approach. Toronto, Ontario Dept. of Public Health, 1969.
19. Crocker, Thomas D. Urban Air Pollution Damage Functions: Theory
and Measurement. Prepared for U.S. Environmental Protection
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20. Steele, William. The Effect of Air Pollution on the Value of
Single-Family Owner-Occupied Residential Property in Charleston,
South Carolina. Masters Thesis, Clemson University, 1972.
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Improvement: Theory and Practice. Johns Hopkins University
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22. Waddell, Thomas E. The Economic Damages of Air Pollution. U.S.
Environmental Protection Agency, Office of Research and
Development, Research Triangle Park, North Carolina, May 1974.
23. Appel, David. Estimating the Benefits of Air Quality
Improvement: An Hedonic Price Index Approach Applied to the New
York Metropolitan Area. Unpublished Ph.D. dissertation, Rutgers
University, 1980.
24. Anderson, Robert J., Jr. and Thomas D. Crocker. Air Pollution
and Residential Property Values. Urban Studies, 8(3):171-180,
October 1971.
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25. Wieand, Kenneth F. Air Pollution and Property Values: A Study
of "the St. Louis Area. Journal of Regional Science, 13(l):91-95,
April 1973.
26. Deyak, Timothy A. and V. Kerry Smith. Residential Property
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28. Polinsky, A. Mitchell and Daniel L. Rubinfeld. Property Values
and the Benefits of Environmental Improvements: Theory and
Measurement. In: Public Economics and the Quality of Life,
Lowdon Wingo and Alan Evans, eds. Johns Hopkins University Press
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29. Brookshire, David S. et_ al_. Methods Development for Assessing
Tradeoffs in Environmental Management. Vol. 2: Experiments in
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Southern California. Prepared for the U.S. Environmental
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Pennsylvania, 1972.
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Measuring Environmental Benefits: A Survey of the Issues.
Scandanavian Journal of Economics, 1979. pp. 154-173.
33. Nelson, Jon P. Economic Analysis of Transportation Noise
Abatement. Cambridge, Massachusetts, 1978.
34. Freeman, A. Myrick III. Estimating Air Pollution Control
Benefits from Land Value Studies. Journal of Environmental
Economics and Management, l(l):74-83, May 1974.
35. Stern, Arthur C., H. C. Wohlers, R. W. Baubel, and W. P. Lowry.
Fundamentals of Air Pollution. Academic Press, New York, New
York, 1973.
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APPENDIX 5-A
CALCULATION OF BENEFITS
Benefits were calculated in the following manner:
1. Any SMSA that had TSP and/or S02 levels exceeding the primary
standard in 1978 was assumed to be meeting the primary standard in
1985. In these cases, the reduction in pollution was measured in
terms of the movement from the primary to secondary standard. Any
SMSA that had a pollution level beneath the primary standard in 1978
was assumed to remain at this level until 1985 and the reduction in
pollution was measured in terms of the movement from the 1978 level to
the secondary standard.
2. The decrease in pollution necessary to reach the secondary
standard in 1987 was assumed to occur in two stages. Half of the
decrease was assumed to occur on the last day of 1986 and the other
half of the decrease was assumed to occur on the last day of 1987.
For example, the average of the annual geometric means of TSP for the
monitoring stations in the Pittsburgh SMSA was 82.33 /ug/m3*. This
level exceeds the primary standard of 75 /ug/m . Assuming compliance
with this standard in 1985, the reduction in TSP in Pittsburgh
* Throughout this appendix, the Pittsburgh SMSA will be used as an
example of the calculations. Pittsburgh and the Pittsburgh SMSA
will be used interchangeably for the remainder of the example. The
procedure used to measure the benefits from the reduction in the
annual geometric mean of TSP to 60 Mg/m can also be used to measure
the benefits of the reduction in the annual average of S02.
5-55
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necessary to meet the secondary standard is 15 /ug/m or 7.5 /ug/m at
»
the end of both 1986 and 1987.
3. The next step was to estimate property values in 1986 and
1987. Data on the median property value of owner-occupied single-
family dwellings by SMSA were found in the Annual Housing Survey of
the Bureau of Census. Using the Consumer Price Index for the "housing
bundle" specific to each SMSA from 1970 to 1978, the average increase
in the price of the housing bundle was calculated.* The Consumer
Price Index for the housing bundle in the Pittsburgh SMSA was:
1970 118.9 1975 163.4
1971 125.5 1976 174.3
1972 129.7 1977 187.4
1973 134.2 1978 204.6
1974 147.3
An average yearly increase in the price of the housing bundle of 7.05
percent was calculated for the Pittsburgh SMSA. The median property
value of single-family owner-occupied dwellings in Pittsburgh was
$22,400 in 1974. Using the actual yearly percentage increases in the
housing bundle index from 1974 to 1978 and the average increase of
* The housing bundle includes rent, home purchase, mortgage rates,
property taxes, maintenance and repairs, fuel and other utilities,
household furnishings, supplies, and operations. Although this
index is not an exact measurement of the increase in property
values, it is probably more representative of the increase than the
Consumer Price Index for all goods.
5-56
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7.05 percent per year from 1978 to 1987, the median property values
estimated for Pittsburgh were:
1986
1987
Median property value
$49,900
$53,400
4. Using the median property value estimated for 1986 and 1987,
and the changes in and levels of particulate matter in those years,
along with the estimated range of coefficients for particulate matter
(i.e., 0.05 to 0.12), ranges of the dollar benefits for a single-
family owner-occupied household were estimated according to the
following formula:
Benefits = - Property value
1 -
(Pollution-^
(PollutionQ)2
— under the assumption that the household's marginal
willingness to pay for air quality improvements declines
linearly from the equilibrium point revealed from the
hedonic price equation to the origin —
where b = the estimated coefficient of the pollution variable
in a log-linear hedonic equation.
Pollutiong = initial pollution level.
Pollution-, = pollution level after an air quality change.
5-57
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The range of household benefits in the Pittsburgh SMSA are therefore
•
estimated to be:
Year Benefits
1986 $237.03 - $568.86
1987 $280.19 - $672.44
Since the benefits were calculated from the change in property
values, the estimates are in terms of the discounted present value (in
1986 and 1987) of the individual household benefits in reducing TSP to
the secondary standard.
5. The benefits accruing to the household residing in a single-
family owner-occupied residence were taken as representative of the
benefits accruing to all households within an SMSA. Data on the
projected number of households for 1986 and 1987 were not available by
SMSA; therefore, the projected number of households in the United
States and state populations for 1986 and 1987 were used to project
the number of households in each SMSA for these years. These data
were available from the Bureau of the Census Current Populations
Reports, Series P-25. The estimated number of households in
Pittsburgh were projected to be:
December 31, 1986 911,415
December 31, 1987 921,636
5-58
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6. The benefits accruing to the SMSA were estimated by
multiplying the number of households within- the SMSA in 1986 and 1987
by the dollar benefits accruing to the individual household in 1986
and 1987. The benefits of the reduction in the SMSA average of the
annual geometric mean of TSP to 60 Mg/m estimated for the Pittsburgh
SMSA were:
Benefits
Year (in $1,000)
1986 $216,030 - $518,470
1987 $258,230 - $619,750
7. The final step was to express the benefits in 1980 dollars.
This was accomplished by deflating the 1986 and 1987 benefit estimates
by the housing bundle index derived for each SMSA. Using the 7.05
percent average increase in the price of the housing bundle for the
Pittsburgh SMSA and a 10 percent discount rate led to discounted
present value benefit estimates, in 1980 dollars, of:
Discounted present
value benefits in
thousands of 1980 $ $169,782 - $407,478
8. Benefits are calculated in the manner described in Steps 1
through 8 for each SMSA. Benefits are estimated using a 10 percent
discount rate. The aggregate benefit estimates given in the text are
obtained by aggregating across the various SMSAs.
5-59
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APPENDIX 5-B
SMSA BENEFITS
The tables in this appendix list the benefits of attaining
alternative secondary ambient air quality standards within each of the
24 SMSAs examined in this study, Tables B-l through B-4 report the
SMSA benefits of attaining alternative secondary standards for TSP,
while Tables B-5 through B-8 report the benefits of attaining
alternative secondary standards for SCu.
TABLE B-l. ESTIMATED BENEFITS OF THE REDUCTION IN THE AVERAGE OF THE
SECOND HIGHEST VALUES OF TSP WITHIN AN SMSA TO 150 jug/m *
(discounted present value in thousands of 1980 $)
Range
SMSA
Low High
Buffalo
Cleveland
Denver
Detroit
Houston
Kansas City
Los Angeles
Milwaukee
Pittsburgh
St. Louis
San Diego
Total
$ 21,477
150,995
367,127
218,822
579,566
28,173
1,630,070
85,005
253,674
106,326
87,307
$3,528,542
$ 51,546
362,389
881,107
525,175
1,390,950
67,616
3,912,191
204,014
608,819
255,182
209,537
$8,468,526
*Based on 24 SMSAs.
5-60
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TABLE B-2. ESTIMATED BENEFITS OF THE REDUCTION IN THE ANNUAL AVERAGE
GEOMETRIC MEAN OF TSP WITHIN AN SMSA TO 60 Mg/irT*
(discounted present value in thousands of 1980 $)
Range
SMSA
Low High
Cleveland
Denver
Detroit
Houston
Kansas City
Los Angeles
Minneapolis
Pittsburgh
St. Louis
San Diego
$ 37,770
195,366
130,382
137,229
94,885
905,386
4,380
169,782
193,517
209,191
$ 90,648
468,878
312,918
329,351
227,726
2,172,927
10,514
407,478
464,441
502,060
Total $2,077,888 $4,986,941
*Based on 24 SMSAs.
5-61
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TABLE B-3 .
ESTIMATED BENEFITS OF THE REDUCTION IN THE MAXIMUM OF THE
SECOND HIGHEST TSP WITHIN AN SMSA TO 150 Mg/m*
(discounted present value in thousands of 1980 $)
SMSA
Range
Low
High
Atlanta
Baltimore
Boston
Buffalo
Chicago
Cincinnati
Cleveland
Dallas
Denver
Detroit
Houston
Kansas City
Los Angeles
Milwaukee
Minneapolis
New York
Philadelphia
Pittsburgh
St. Louis
San Diego
Seattle
District of Columbia
$ 58,495
48,870
256,875
244,695
1,749,360
126,153
401,921
386,258
411,425
788,352
579,566
228,319
1,905,079
359,749
553,704
1,736,515
824,255
357,159
407,113
501,791
336,970
1,138,968
$ 140,388
117,289
616,500
587,268
4,198,475
302,767
964,612
927,020
987,422
1,892,045
1,390,958
547,967
4,572,190
863,398
1,328,891
4,167,637
1,978,214
857,183
977,072
1,204,300
808,728
2,733,523
Total
$13,401,592
$32,163,847
*Based on 24 SMSAs.
5-62
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TABLE B-4.
ESTIMATED BENEFITS OF THE REDUCTION IN THE MAXIMUM OF THE
ANNUAL GEOMETRIC MEANS OF TSP WITHIN AN SMSA TO 60 /ug/m3*
(discounted present value in thousands of 1980 $)
Range
SMSA
Low
High
Atlanta
Baltimore
Boston
Buffalo
Chicago
Cincinnati
Cleveland
Dallas
Denver
Detroit
Houston
Kansas City
Los Angeles
Milwaukee
Minneapolis
New York
Philadelphia
Pittsburgh
St. Louis
San Diego
San Francisco
Seattle
District of Columbia
$ 230,699
176,811
347,537
116,325
831,578
126,153
191,065
250,668
195,366
374,739
275,413
103,525
905,386
170,983
263,179
1,217,400
404,656
169,782
193,517
238,479
145,699
160,164
541,279
$ 553,678
424,348
834,090
279,180
1,995,788
302,767
458,557
601,603
468,878
899,375
660,992
260,461
2,172,927
410,361
631,630
2,921,762
971,174
407,478
464,441
572,350
349,677
384,395
1,299,071
Total
$7,635,403
$18,324,983
*Based on 24 SMSAs.
5-63
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TABLE B-5. ESTIMATED BENEFITS OF THE REDUCTION IN THE AVERAGE OF THE
SECOND HIGHEST VALUES OF S02 WITHIN AN SMSA TO 260
(discounted present value in thousands of 1980 $)
Range
SMSA
Low High
Buffalo
Cleveland
Milwaukee
Minneapolis
Pittsburgh
$ 84,997
79,185
311,687
529,176
130,910
? 121,425
113,122
445,268
755,965
187,015
Total $1,135,955 $1,622,795
*Based on 19 SMSAs.
TABLE B-6. ESTIMATED BENEFITS OF THE REDUCTION IN THE ANNUAL AVERAGE
ARITHMETIC MEAN OF S02 WITHIN AN SMSA TO 60 /ug/m3*
(discounted present value in thousands of 1980 $)
Range
SMSA
Low High
Buffalo
Cleveland
Pittsburgh
$ 75,100
31,836
218,592
$107,286
45,480
312,275
Total $325,528 $465,041
*Based on 19 SMSAs.
5-64
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TABLE B-7. ESTIMATED BENEFITS OF THE REDUCTION IN THE MAXIMUM OF THE
SECOND HIGHEST S02 READINGS WITHIN AN SMSA TO 260
(discounted present value in thousands of 1980 $)
Range
SMSA
Low High
Buffalo
Chicago
Cincinnati
Cleveland
Milwaukee
Minneapolis
New York
Philadelphia
Pittsburgh
St. Louis
$ 233,879
708,672
193,161
384,152
343,803
529,176
2,041,944
813,595
341,364
389,094
$ 334,113
1,012,389
275,945
548,788
491,148
755,965
2,917,063
1,162,279
487,663
555,849
Total $5,978,840 $8,541,202
*Based on 19 SMSAs.
TABLE B-8. ESTIMATED BENEFITS OF THE REDUCTION IN THE MAXIMUM OF THE
ANNUAL ARITHMETIC MEANS OF SO^ WITHIN AN SMSA TO 60
(discounted present value in thousands of 1980 $)
Range
SMSA
Low High
Buffalo
Cleveland
Milwaukee
Minneapolis
New York
Philadelphia
Pittsburgh
$ 187,274
104,346
181,682
127,309
1,883,070
415,176
296,879
$ 267,535
149,065
259,546
181,870
2,690,101
593,109
424,113
Total $3,195,736 $4,565,339
*Based on 19 SMSAs.
5-65
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SECTION 6
LABOR SERVICES MARKET
-------
SECTION 6
LABOR SERVICES MARKET
SUMMARY
Section 5 of this report reviewed the studies that have analyzed
site differentials in residential property values as a basis for
estimating the willingness to pay for air quality. The results of
that review were used to provide a cross-check on the benefits
estimated by the household expenditure model (Section 4). The basic
approach in most of the residential property value studies reviewed in
Section 5 involved the use of the hedonic price technique. In this
section, the hedonic technique is applied to the market for labor in
order to develop an additional cross-check on the benefits estimated
in the household sector. Like the benefits estimated through the
analysis of residential property value differentials, it is expected
that the benefits estimated from wage rate differentials will be
higher than the benefits estimated by the household expenditure model.
This is because wage rate differentials will tend to reflect some of
the aesthetic and health effects of locational differences in air
pollution, as well as the effects of soiling and materials damage that
are estimated by the household expenditure model.
6-1
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In this section, socioeconomic data from the Panel Study o£
Income Dynamics (1) and air quality data from Air Quality Data —
Annual Statistics (2) are used to estimate hedonic wage equations.
The hedonic wage equation identifies the influence of job
characteristics, worker characteristics and amenities on wage rates in
a local area. Through the estimation of these equations, it has been
found that a significant positive relationship exists between total
suspended particulate (TSP) levels and wage rates. These results
suggest that individuals are paid higher wages in compensation for
working in an area that experiences relatively high levels of TSP.
Consequently, this suggests that reductions in TSP concentrations
could reduce the amount of additional compensation required. The
results described above are used to estimate the benefits of meeting
the current secondary standard for TSP in the Cleveland and Denver
SMSAs. These benefits, along with the benefits estimated for these
SMSAs by the household expenditure model, are reported in Table 6-1.
For Cleveland, the reduction in the level of TSP in 1987 is estimated
to result in a reduction in the annual wage of $189.40 in 1980
dollars. Similarly, the reduction in the level of TSP in Denver will
result in a reduction in the annual wage of $212.40. As Table 6-1
shows, the estimates for both of these SMSAs exceed the per-household
benefits in 1987 estimated from the household expenditure model.
6-2
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TABLE 6-1. COMPARISON OF THE PER-HOUSEHOLD BENEFITS OF ATTAINING
THE CURRENT SECONDARY STANDARD FOR TSP*
Hedonic wage Household expenditure
SMS A model model
Cleveland
Denver
$189.40
$212.40
$6.23
$7.39
* Discounted present value in 1980 of the per-household benefits
occurring in 1987, at a 10 percent discount rate, in 1980 dollars.
Benefits based on alternative secondary standards for TSP of 150
ug/m , not to be exceeded more than once a year, and a 60 ^
annual mean.
METHODOLOGY
The hedonic technique was explained in detail in Section 5 of
this report. The reader is therefore referred to that section for a
complete explanation of the hedonic technique.* In this subsection, a
brief summary of the hedonic technique as applied to the market for
labor will be given.
The general form of a hedonic equation relates the price of a
good to the characteristics of that good. The market for jobs,
however, differs from the consumer goods markets, since employers are
not indifferent to the identity of workers to whom they "sell" their
* See Lucas (8) for an excellent explanation of the application of the
hedonic technique to the labor market.
6-3
-------
jobs (8). Consequently, the hedonic wage equation relates the wage
for a particular job to the characteristics of the job and to the
•
characteristics of the worker. This relationship can be expressed as:
Wj = W(Ei,Pct) (6.1)
where W^ = the equilibrium wage rate for worker a performing job
i.
E^ = a vector of characteristics of job i.
pa = a vector of characteristics of worker oc.
The partial derivative of the wage rate with respect to the job
and worker characteristics can be interpreted as the marginal implicit
prices of these characteristics or the additional amount that must be
paid for a job or worker with one more unit of a particular
characteristic. Since one of the basic assumptions of the hedonic
technique is that the market for the "good" is in equilibrium, the
hedonic equation is a reduced form equation where the marginal
implicit price of each characteristics is equal to the marginal
willingness to pay a worker (in terms of the employer) or marginal
willingness to accept a job (in terms of the employee) with one more
unit of that characteristic. With respect to a job with an
environmental characteristic such as the level of air pollution, the
partial derivative of the hedonic wage equation with respect to air
quality can provide an estimate of the implicit price of air quality
and therefore the equilibrium marginal willingness to accept a job
with one more "unit" of air pollution. The hedonic equation can
6-4
-------
consequently be used to estimate the benefits of marginal improvements
in the level of air pollution.*
DATA
Equation (6.1) expresses the equilibrium wage rate (W^) as a
function of a vector of worker characteristics (Pa) and a vector of
job characteristics (E^). In this study, the vector Pa is assumed to
contain measures of: (1) whether the individual is a union member
(UNION), (2) whether the individual is a veteran (HVET), (3) the size
of the individual's family (FMSZ), (4) the individual's health status
(HLTH), (5) the individual's prior educational achievement (EDC2,
EDC3), and (6) the length of time the individual has spent on his
present job (TOJ2). Next, E.: contains measures of: (1) mean January
and July temperature in the individual's area of residence (COLD,
WARM), (2) the job accident rate in the industry where the individual
works (JACK), (3) average rainfall in the individual's area of
residence (HUMD), and (4) levels of the air pollutants sulfur dioxide
(302), total suspended particulates (TSP), and nitrogen dioxide (NO2).
Unfortunately, this formulation may be subject to a specification
error of unknown severity resulting from the omission of relevant
* Note that in this discussion, no distinction has been made between
indoor air pollution in the work site as compared to atmospheric air
pollution in the area of the work site. Clearly, both of these
characteristics may be appropriate variables in the hedonic wage
equation. In this analysis, however, only atmospheric pollution is
considered. The implications of omitting a potentially relevant
variable are discussed in a subsequent section.
6-5
-------
explanatory variables. While the personal characteristics are fairly
standard for analyses of this type, biased coefficient estimates may
*
result from the exclusion of still other relevant job characteristic
variables. That is, climate, job hazards, and air pollution may not
exhaust the list of job characteristics that may affect the
equilibrium wage rate. [For good surveys of the role other variables
may play, see Brown (12) and Rosen (5).] Proximity to recreational
opportunities and the amount of local social infrastructure are but
two examples of work environment variables that could in principle be
measured and included. Also, the more labor market specific variables
used by Nakamura, Nakamura, and Cullen (7) have been excluded from
consideration here. Because this analysis was done solely for the
purpose of providing a cross-check on the basic household expenditure
model, no efforts were made to collect observations on these
potentially relevant variables.
The variables used to explain variations in the wage rate were
chosen from those that had been collected previously by the Resource
and Environmental Economics Laboratory at the University of Wyoming
for use on other research projects. Specifically, the basic data set
used to estimate the wage equation consisted of observations drawn
from the Panel Study of Income Dynamics (PSID) (1) for the 1971
interview year. This data set gives the head of household's state and
county of residence along with information on the characteristics of
the head of the household. Consequently, data on environmental
variables were collected by county and then matched to the individual
6-6
-------
observations obtained from the PSID. In total, there are observations
for household heads on variables that can be used to construct a
measure of their real wages, together with measures of the variables
in the P^ and E^ vectors defined previously in Equation (6.1). The
exact definitions of all of these variables as well as their sources
are provided in Tables 6-2 through 6-5.
For the variables COLD, WARM and HUMD, the matching process was
quite simple and requires no further elaboration. However, the
matching of the air pollution variables to counties should be
TABLE 6-2. PECUNIAR? VARIABLES
Variable
Definition
HOURS
AWGH
WAGH
BDAL
RWGH
Annual hours working for money by the head of
household. Source: Reference (1).
Annual money income from labor received by the head of
household. Source: Reference (1).
Per-hour money income from labor received by the head
of household (i.e., WAGH = AWGH/HOURS). If HOURS = 0,
then WAGH = 0. Source: Reference (1).
Index of comparative living costs for a four-person
family for various areas within the United States.
The lowest living standard was used for the purpose of
this study. Source: Reference (19).
Real hourly money income from labor received by head
of household (i.e., WAGH/BDAL). Source: Reference
(19).
6-7
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TABLE 6.3. PERSONAL CHARACTERISTIC VARIABLES
Variable
Definition
HLTH If there are limitations on the type or kind of work
that the head of the household can do, HLTH = 1;
otherwise, HLTH = 0.
UNION If head of household belongs to a labor union, UNION =
1; otherwise, UNION = 0.
EDC1 If head of household has completed grades 0-8 or has
trouble reading, EDC1 = 1; otherwise, EDC1 = 0.
EDC2 If head of household has completed grades 9-12 plus
possible non-academic training, then EDC2 = 1;
otherwise, EDC2 = 0.
EDC3 If head of household has completed at least some
college, then EDC3 = 1; otherwise EDC3 = 0.
HVET If head of household is a veteran of the armed
services, HVET = 1; otherwise, HVET = 0.
FMSZ Number of people in each household.
TOJ1 If head of household has been employed at present job
for 3 years or less, TOJl = 1; otherwise, TOJl = 0.
TOJ2 If head of household has been employed at present job
for more than 3 years, TOJ2 = 1? otherwise, TOJ2 = 0.
Source: Panel Study of Income Dynamics. Reference (1).
6-8
-------
TABLE 6-4. WORK ENVIRONMENT VARIABLES
Variable
Definition
WARM
COLD
HUMD
SO-
TSP
NO-
JACR
Mean annual July temperature in °F x 10.0 in county of
residence in 1970. Source: Reference (20).
Mean annual January temperature in °F x 10.0 in county
of residence in 1970. Source: Reference (20).
Mean annual precipitation in inches x 100.0.
Reference (20).
Source:
Annual 24-hour geometric mean of sulfur dioxide as
measured by the Gas Bubbler Pararosaniline-Sulf uric
Acid Method (in /ig/m ) for a monitoring station within
the county of residence in 1970. Source: Reference
(1).
Annual 24-hour geometric mean of total suspended
particulates as measured by the Hi-Vol Gravimetric
Method for a monitoring station within the county of
residence in 1970 (in jug/m ) . Source: Reference (1).
Annual 24-hour geometric mean of nitrogen dioxide as
measured by the Salzman Method for a monitoring
station within the county of residence in 1975 (in
Mg/m ). Source: Reference (1).
Number of disabling work injuries in 1970 for each
million employee hours worked by 2- and 3-digit SIC
codes. Source: Reference (21).
6-9
-------
TABLE 6-5. AUXILIARY VARIABLES
Variable
Definition
AGE
OCCUP
SEX
RACE
REG1
REG2
REGS
REG4
PRX1
PRX2
PRX3
PRX4
PRX5
Age of the head of household.
If head of household is blue collar worker, OCCUP = 0;
otherwise, OCCUP = 1.
If head of household is a female, SEX = 0; otherwise,
SEX = 1.
If head of household's race is white, RACE = 1;
otherwise, RACE = 0.
If head of household lives in a Northeastern state,
REG1 = 1; otherwise, REG1 = 0.
If head of household lives in a North Central state,
REG2 = 1; otherwise, REG2 = 0.
If head of household lives in a Southern state, REG3 =
1; otherwise, REGS = 0.
If head of household lives in a Western state, REG4 =
1; otherwise, REG4 = 0.
If head of household's dwelling unit is within 5 miles
of the center of a city with a population of 50,000 or
more (hereafter referred to as city center), PRXl = 1;
otherwise, PRXl = 0.
If head of household's dwelling unit is within 5 to
14.9 miles of the city center, PRX2 = 1; otherwise,
PRX2 = 0.
If head of household's dwelling unit is within 15 to
29.9 miles of the city center, PRX3 = 1; otherwise,
PRX3 = 0.
If head of household's dwelling unit is within 30 to
49.9 miles of the city center, PRX4 = 1; otherwise
PRX4 = 0.
If head of household's dwelling unit is more than 50
miles from the city center, PRX5 = 1; otherwise, PRX5
= 0.
Source: Panel Study of Income Dynamics. Reference (1).
6-10
-------
explained in greater detail.* The matching process was begun by
listing each of the 669 counties in the 50 states where PSID families
lived during 1970. Outdoor air pollution monitoring data existed for
at least one of the three measures of S02, N02 and TSP for 247 of
these counties. In cases where data from only one monitoring station
in the county were available, those data were automatically assigned
to all PSID families residing there. On the other hand, where data
were available from multiple monitoring stations in the county, data
from the single station that had operated for the greatest portion of
the 9-year period 1967-1975 were selected. The monitoring stations
selected using this rule tended to be at central city locations.
Finally, since no pollution data were available for 422 counties (699
minus 247), values were assigned to the air quality variables for
these counties by replacing the missing observations with either the
means of the observed values for the pollutants or estimated using an
amended version of a technique suggested by Dagenais (22). A brief
discussion of the replacement with means method is outlined in Maddala
(23). The amended variant of the Dagenais procedure would involve
running a regression of each pollution variable on: (1) all remaining
(non-pollution) explanatory variables in Equation (6.1), and (2) any
relevant auxiliary variables that may be selected. The values of the
missing observations are then predicted from these regressions. An
alternative to either the replacement with means or the Dagenais
* The procedure used to assign air pollution measures to the
individual observations is similar to that used by Crocker, Schulze,
et al. (18).
6-11
-------
procedures would be to restrict the sample to only those observations
where actual measurements were available on all variables, including
the pollutants. Even though this restriction reduced the available
data set to 112 observations, it was employed in the estimation of one
equation for illustrative purposes.*
It should also be mentioned that SC>2 data that are obtained using
the Gas-Bubbler Pararosaniline-Sulfuric Acid Method have been shown to
be biased downward. A correction factor was therefore developed in
order to remove the bias from the SC>2 data measured by this method
(see Section 3 for details regarding this correction).
For the purpose of estimating the hedonic wage equation, the data
set was reduced from the roughly 3300 possible observations to 1395
observations after excluding all households where: (1) any family
member received transfer income, (2) the head's annual hours of
working for money were less than 400 hours. The first of these
exclusions was made in order to reduce the statistical problem created
by families that may be facing non-convex budget constraints, while
the second was made in order to eliminate casual workers, who may be
out of equilibrium because their asking wage may exceed the offered
wage, from the sample. Curiously, after making these two exclusions,
there were no families remaining in the sample where the head: (1)
* Additionally, even if the NO-? variable was eliminated from
consideration, there would still have been only 432 families for
whom data on both SO 2 and TSP could have been matched.
6-12
-------
received income from overtime, bonuses or commissions, or (2) was
self-employed.
The restricted sample used here is quite similar to that used by
Wales (24) and Wales and Woodland (6,25) in their numerous papers on
the empirical determinants of labor supply using PSID data. However,
by excluding household heads who worked less than 400 hours, the
estimates reported in the next section cannot be taken as
representative of the general population. Instead, they apply only to
those in the population having the same characteristics as those in
the sample. In short, the estimates say little about the wage rate
that would be paid to an individual working 400 hours or less had that
individual chosen to work, for example, full time.*
SPECIFICATION
The exact specification of the wage equation used in the present
study is:
log (KWGH) = fBUNION, HVET, FMSZ, HLTH, EDC2, EDC3, (6.2)
TOJ2, WARM, JACK, COLD, HUMD, SO2,
TSP, N02, (TSP)2, (S02)2, (N02)2
See Heckman (4,26) for a discussion of sample selectivity bias,
6-13
-------
In Equation (6.2), the function f is linear in the parameters and RWGH
denotes the real wage. Also, note that the squares of the levels of
the three pollution variables are included as regressors in order to
allow for possible nonlinearities in the way that air pollution
affects the real wage. This equation was estimated by ordinary least
squares for both the complete sample of 1395 observations and for
selected partitions of this sample constructed on the basis of age
(AGE), race (RACE), sex (SEX), and occupation (OCCUP). In particular,
there were three age categories (17-29, 30-49, 50-69), two race
categories (white, non-white), two sex categories (male, female), and
two occupation categories (white collar, blue collar). The total
number of possible partitioned regressions was therefore 24. However,
not all of these possible regressions were actually estimated because
for certain partitions the number of available observations was
insufficient.*
EMPIRICAL RESULTS
As previously indicated, three basic versions of Equation (6.2)
were estimated where: (1) the restricted sample of 112 observations
was employed, (2) the replacement with mean procedure was used, and
(3) the amended Dagenais procedure was used to construct values for
* Regressions for partitions containing less than 50 observations were
not estimated. For these cases, the observations from two or more
partitions were pooled and one regression was run on the combined
data set.
6-14
-------
the missing pollutants. All regressions were estimated by ordinary
least squares (OLS).
Equation (1) of Table 6-6 reports the results from estimation
with the restricted data set. In this equation, all of the personal
characteristic variables are significant at the 1 percent level except
HLTH and TOJ2. However, the work environment variables are all
insignificant at conventional levels. In fact, the t-statistics on
the pollution variables in no case exceed 1.1 in absolute value.
Using the replacement with means procedure, the quality of the
estimated coefficients improves considerably. These results are shown
in Equation (2) of Table 6-6. With the increase in the number of
observations (NOB) employed from 112 to 1395, all of the personal
characteristic variables turn out to be significant at the 1 percent
level and have the correct sign.
The estimates of the coefficients on the work environment
variables also tend to be more highly significant and are more
plausibly signed than in the case where the restricted sample of 112
observations is used. Also, they are generally consistent with the
findings of other investigators. As indicated in Equation (2) of
Table 6-6, the variables WARM and COLD enter with a significant
negative sign. In the case of WARM, the negative sign indicates that
the individuals in the sample are willing to accept a lower wage in
order to live in an area with hot summers. That same qualitative
result has been obtained by Rosen (16) where the number of sunny days
6-15
-------
TABLE 6-6. HEDONIC WAGE EQUATIONS (standard
error in parentheses)
Variable
CONSTANT
UNION
HVET
FMSZ
HLTH
EDC2
EDC3
TOJ2
WARM
JACK
COLD
HUMD
so2
Equation 1
-30.473
(37.253)
0.313*
(0.107)
0.265*
(0.089)
0.030**
(0.015)
-0.202
(0.153)
0.205**
(0.096)
0.495*
(0.111)
0.080
(0.084)
0.942
(0.897)
5.94E-05
(0.001)
-0.291
(0.214)
0.010
(0.007)
0.532
(0.594)
Equation 2
1.505*
(0.465)
0.127*
(0.028)
0.187*
(0.026)
0.022*
(0.005)
-0.107*
(0.037)
0.073**
(0.034)
0.491*
(0.039)
0.133*
(0.027)
-0.010*
(0.003)
0.001*
(4.07E-04)
-0.008*
(0.003)
-0.002
(0.001)
-0.003
(0.005)
Equation 3
1.141*
(0.322)
0.128*
(0.028)
0.187*
(0.026)
0.023*
(5.54E-03)
-0.099*
(0.037)
0.075**
(0.034)
0.492*
(0.039)
0.128*
(0.027)
-7.79E-03**
(3.12E-03)
1.41E-03*
(4.07E-04)
-7.39E-03*
(1.80E-03)
-7.84E-05
(1.38E-03)
1.85E-03
(3.34E-03)
* Significant at the 1 percent level (two-tailed test).
** Significant at the 5 percent level (two-tailed '—"'
(continued)
6-16
-------
TABLE 6-6 (continued)
Variable
( so2 ) 2
TSP
(TSP)2
N02
(N02)2
NOB
R2
CTSP
Equation 1
-3.05E-06
(5.67E-06)
-0.832
(0.785)
3.34E-06
(3.13E-06)
0.039
(0.337)
5.26E-07
(2.66E-06)
112
0.59
—
Equation 2
-5.48E-06
(6.81E-05)
0.009**
(0.005)
-5.09E-05**
(2.31E-05)
0.002
(0.008)
-2.52E-05
(8.57E-05)
1,395
0.30
-0.016
Equation 3
-9.71E-05
(6.12E-05)
8.23E-03
(4.40E-03)
-3.74E-05
(2.25E-05)
1.65E-03
(1.94E-03)
-4.05E-06
(1.42E-05)
1,395
0.31
—
* Significant at the 1 percent level (two-tailed test).
* Significant at the 5 percent level (two-tailed test).
6-17
-------
was used as a climate variable with individual data from the Current
Population Survey together with SMSA-specific attributes. Hoch (15)
and Cropper (17) also found that higher temperatures result in a lower
wage. On the other hand, the negative sign on COLD suggests that
individuals must be paid a premium to live in areas where mean January
temperatures are low and winter weather is probably severe. Of the
three studies just mentioned, only the one by Hoch employs a similar
variable. The coefficient on "winter temperature" is positive in his
regressions on Samples I and II and negative in his regression on
Sample III [see Hoch (15), p. 39].
Next, the coefficient on JACR is positive and significant,
supporting Viscusi's (11) result that employers must pay a premium in
order to induce workers to accept jobs where the probability of
accidents is higher. Also, this result is consistent with the
findings of other investigators who measured other dimensions of
working conditions. For example, Lucas (8), Hamermesh (9), and Thaler
and Rosen (10) consider the effect of variables on wages, including:
(1) a generalized measure of poor working conditions, (2) the presence
of hazardous materials and/or equipment, and (3) deaths per 1,000 man-
years of work. All three of these variables have been found to be
positively and significantly related to dependent variables that are
similar to the one used in the present study.
With respect to the HUMD variable, Equation (2) shows that its
coefficient is negative but statistically insignificant at the 5
6-18
-------
percent level. Although this negative sign is intuitively
implausible, that same sign was obtained for the precipitation
variable in Hoch's (15) regressions on each of his three samples.
Rosen (16), however, obtains the more appealing result that increases
in precipitation are positively associated with real wages. The
precipitation variable that Rosen uses, which is defined as number of
rainy days, was always positive and usually statistically significant
in each of 29 different equation specifications [see Rosen (16) p.
94] .
The pollution variables do not perform quite as well as the other
variables in the equation. Both the linear and quadratic terms for
SCU and NCU are statistically insignificant at the 5 percent level.
The result for S02 conflicts with those of Cropper (17). In her
regression for all earners and in four of her eight occupation-
specific regressions, a measure of SCU turned out to be positively and
significantly related to median earnings of males who were employed
full time. However, in the Cropper study, SCU was the only pollution
measure used and, therefore, this variable could also be proxying the
effects of other pollutants. Rosen's (16) results show that this
conjecture is a real possibility. His SC>2 measure occasionally has
the right sign, but is more frequently negative. Particulates, on the
other hand, exhibit superior performance in Rosen's equation. This
variable was positive in each of the 32 cases where it was used and
had a t-statistic exceeding 2 in 27 cases (again, see Rosen (16), p.
94). The results on the TSP variable used in the present study
6-19
-------
compares favorably with the findings of Rosen. As Equation (2) of
Table 6-6 shows, the linear TSP term has a positive and statistically
significant coefficient and the quadratic TSP term has a smaller
negative but significant coefficient.
The elasticity of the real wage with respect to a change in TSP
can be computed from the estimates presented in Equation (2) according
to:
3RWGH TSP 9
' ' + 2S TSP <6-3'
where £TSP denotes the elasticity of the real wage with respect to
TSP, a denotes the estimated coefficient on the linear TSP term, and 3
denotes the coefficient on the quadratic TSP term.* Evaluated at the
mean of the values for TSP in Equation (2), the elasticity is equal to
-0.016. In the neighborhood of the mean value of TSP, this elasticity
indicates that an increase in the level of TSP will result in a
decrease in the offered wage. Although this is contrary to our a_
priori expectations regarding the relationship between the wage rate
and the level of air pollution, this negative elasticity results from
the relatively high value for the mean of TSP. This high mean can be
attributed to a number of counties in the data set where the annual
* The elasticity is a measure of the percentage change in the
dependent variable that can be expected from a percentage change in
the independent variable.
6-20
-------
averages of total suspended particulates were considerably in excess
of 100 Mg/m . For annual average TSP readings beneath 92.83, £TSp is
positive and indicates that at TSP levels beneath 92.83, an increase
in the level of TSP will have a positive effect on the wage rate.
This is consistent with our hypothesis that workers must be paid a
premium in order to work in areas with polluted air.
The results from the estimation using the amended Dagenais
procedure to construct the missing observations on the pollution
variables are reported in Equation (3) of Table 6-6. The coefficients
on the personal characteristic variables reported in Equation (3) are
very similar to those reported in Equation (2). However, both the
linear and quadratic terms for all three pollutants enter the pooled
regression insignificantly at the 5 percent level using a two-tailed
test.
Various partitions of the hedonic wage equation based upon age,
race, and sex were also estimated. In total, 16 partitioned equations
were estimated. In these regression equations, the air pollution
variables are seldom significantly different from zero. More
specifically, there are five of these regressions where one of the
pollution variables entered significantly. The results of these
regressions are reported in Equations (1) through (5) of Table 6-7.
Respectively, the equations reported in this table are based on the
partitioned data sets of:
6-21
-------
TABLE 6-7.
HEDONIC WAGE EQUATIONS ESTIMATED FOR PARTITIONED
DATA SETS (standard error in parentheses)
Variable
CONSTANT
UNION
HVET
msz
HLTH
EDC2
EEC3
TOJ2
WABM
JACK
COLD
HUMD
SO,
(S02)2
TSP
(TSP)2
N02
(NO,)2
NOB
R2
£S02
^TSP
Equation 1
-1.944
(1.220)
0.076
(0.089)
-0.090
(0.080)
-9.59E-03
(0.022)
-0.069
(0.084)
0.273*
(0.106)
0.518**
(0.107)
-0.032
(0.073)
^3.017
(8.71E-03)
-1.47E-03
(1.20E-03)
3.85E-03
(6.36E-03)
5.09E-04
(4.47E-03)
6.72E-03
(0.013)
-5.03E-05
(2.48E-04)
0.010**
(0.030)
-5.21E-04**
(1.S8E-04)
-6.61E-03
(6.40E-03)
3.20E-05
(4.38E-05)
126
0.38
—
4.844
Equation 2
0.197
(1.460)
0.143
(0.102)
0.115
(0.082)
-0.011
(0.023)
-2.20E-03
(0.119)
-0.065
(0.097)
0.066
(0.162)
0.283**
(0.086)
7.386
(0.015)
1.80E-03
(1.49E-03)
5.02E-03
(8.53E-03)
4.37E-04
(5.62E-03)
-0.013
(0.012)
1.71E-04
(2.27E-04)
0.026*
(0.012)
-1.10E-04
(5.58E-OS)
4.85E-03
(6.12E-03)
4.88E-05
(3.S8E-05)
74
0.43
—
1.420
Equation 3
1.904*
(0.793)
0.165*
(0.071)
0.135*
(0.064)
0.020
(0.019)
-0.018
(0.097)
6.95E-03
(0.083)
0.026
(0.100)
0.359**
(0.070)
-0.012
(7.38E-03)
2.91E-04
(1.01£-03)
-8.95E-03
(5.14E-03)
-9.97E-04
(3.62E-03)
-0.024"*
(8.41E-03)
4.68E-04**
(1.69E-04)
8.56E-03
(0.010)
-2.90E-05
(5.26E-05)
1.89E-03
(S.24E-03)
-2.41E-05
(3.47E-05)
178
0.35
-0.313
•~
Equation 4
-0.406
(0.907)
0.347**
(0.063)
-0.060
(0.064)
0.026*
(0.011)
-0.200*
(0.094)
-0.049
(0.063)
-0.032
(0.112)
6.21E-03
(0.065)
-7.91E-03
(8.16E-03)
2.27E-03*
(9.50E-04)
3.95E-03
(4.55E-03)
6.38E-03*
(3.08E-03)
0.019
(0.010)
-3.13E-04*
(1.46E-04)
0.011
(9.76E-03)
-2.33E-05
(4.96E-05)
-1.99E-05
(4.30E-03)
7.44E-06
(3.69E-05)
127
0.53
0.296
•"™
Equation 5
3.795**
(1.236)
0.149
(0.132)
-9.42E-03
(5.39E-02)
-0.169
(0.166)
0.157
(0.204)
0.393
(0.213)
-0.013
(0.105)
5.50E-03
(0.012)
-1.07E-04
(1.92E-03)
-0.012
(8.91E-03)
-7.08E-04
(5.40E-03)
2.39E-03
(0.013)
-2.72E-04
(2.49E-04)
-0.051**
(0.018)
3.01E-04**
(1.05E-04)
-0 .015
(8.49E-03)
7 .18E-05
(5.57E-05)
67
0.39
—
-2.158
* Significant at the 5 percent level (two-tailed test).
** Significant at the 1 percent level (two-tailed test).
6-22
-------
(1) The Male, White, White Collar Worker, Age 50-69,
(2) The Male, White, Blue Collar Worker, Age 30-49,
(3) The Male, White, Blue Collar Worker, Age 17-69,
(4) The Male, Non-White, Blue Collar Worker, Age 30-49, and
(5) The Female, White, White Collar Worker, Age 17-69.
Neither the linear nor the quadratic term on NCU was
significantly different from zero at the 5 percent level in these
partitioned equations. In the five cases where a pollution variable
was significant, the elasticity of the real wage with respect to a
change in the pollution was computed using the method shown in
Equation (6.3). All of these elasticities were evaluated at the mean
(computed over all 1395 observations) of the pollution variables.
Finally, the results of the elasticity calculations are presented
beneath the coefficient estimates for the equations to which they
pertain. As indicated in Table 6-7, three of the calculated
elasticities are positive while two are negative.
The relatively weaker performance of the pollution variables in
the equations estimated using the amended Dagenais procedure can
perhaps be attributed to several factors. First, although this method
produces consistent prediction of the missing observations, this
asymptotic property may say little about the finite sample properties
of such a procedure, particularly when a large fraction of the
observations are missing. Second, the consistency of this method
depends upon the use of a generalized least squares procedure to
6-23
-------
estimate the hedonic wage equation that requires the solution of a set
of simultaneous, nonlinear equations. Because of computational
difficulties, OLS was used instead. In this setting, it is not clear
what statistical properties can be claimed for this approach. Two
other reasons for weak performance, which are also common to the
replacement with means procedure, can be offered: (1) observations
that do exist on the air pollutants may be measured with so much error
that they provide a great deal of misinformation, and (2) after
adjusting for the other factors included in each regression, air
pollution, even if measured perfectly, may not appear to be an
important determinant of wages paid for these equations.
BENEFIT CALCULATIONS
Like the hedonic property value models reviewed in Section 5 of
this report, the hedonic wage equation estimated in this section
yields the equilibrium valuation of air quality. As such, it can be
used to estimate the change in the real hourly wage resulting from a
marginal improvement in air quality. Moving from alternative primary
to secondary standards, however, will involve non-marginal changes.
In order to estimate accurately the changes in the real hourly wage,
and hence the benefits, resulting from these changes in air quality,
the supply price function of workers for air quality must be known.
Since this supply price function is not known, the benefits of these
non-marginal reductions are approximated in this section based solely
on the information yielded by the hedonic price technique.
6-24
-------
The derivative of the hedonic wage function with respect to TSP
corresponding to Equation (2) of Table 6-6 is shown in Figure 6-1.
This derivative, RWGH'(TSP), traces out the equilibrium marginal
implicit wage that different heads of households will accept in order
to work in environments with varying levels of TSP. Each point on
RWGH'(TSP) corresponds to one point on each head of household's supply
price function for TSP. A hypothetical supply price function of head
of household i is shown in Figure 6-1 as S(TSP)-. The positive slope
of the supply price function indicates that worker i must be paid
higher wages in order to induce him to work in an environment with
0
S(TSP) .
RWGH1(TSP)
TSP
Figure 6-1. Alternative benefits estimates for a given
change in air quality.
6-25
-------
higher levels of TSP. As can be seen in Figure 6-1, RWGH'(TSP) is
negatively sloped for values of the annual average of TSP within the
range we are considering. Consequently, the equilibrium marginal
implicit wage that workers are willing to accept decreases as TSP
increases over this range. Intuitively, since pollution is a
disamenity, one would expect that the equilibrium marginal implicit
wage that workers would be willing to accept would be greater for
higher levels of TSP. It is not clear, however, whether there are
other factors not controlled for in the hedonic wage equation that may
be correlated with TSP and hence may cause the plot of the equilibrium
marginal wage to be negatively sloped.
The benefits of an improvement in TSP can be estimated by the
area under the supply price function for air quality, S(TSP)^. For
the improvement in TSP from a primary standard, P^, to a secondary
standard, P^r shown in Figure 6-1, benefits are estimated by the area
PiACP2« The supply price function for air quality has not been
estimated in this analysis, however, and it is necessary to rely on
information contained in the hedonic wage equation in order to
approximate the benefits of the improvement in TSP from the primary to
the secondary standard. The benefits of the improvement in TSP from
P-t to ?2 can be approximated by the area under the marginal implicit
wage curve, RWGH'(TSP). Using this approximation technique, benefits
are equal to the area P-,ABP2. This technique implies that all the
heads of household's marginal implicit wage functions are equal and
6-26
-------
increasing as TSP decreases. This may result in an overestimate of
the true benefits of improvement.
Freeman (27) has suggested two alternative ways for approximating
the benefits in the property value market of non-marginal changes in
air quality from hedonic property value equations when the demand
curve for air quality is not known. These approximation techniques
can also be used to estimate the benefits to wage earners of an
improvement in air quality when the supply price function for air
quality is not known. For this study, we will use the approximation
technique that is consistent with the a_ priori expectation that the
supply price function of the head of the household for TSP decreases
as TSP decreases. One point on the head of household's supply price
function for TSP is known from the hedonic wage equation. This
approximation technique assumes that the supply price function of the
head of household declines linearly from that point to a zero marginal
implicit wage for TSP when TSP has been completely abated. This
linearly declining supply price function is shown as the line OA in
Figure 6-1. For the reduction in TSP from P-^ to P2, the benefits to
the head of household can be approximated by the area P-.ADP2- The
benefits represented by this area can be easily calculated as the
difference of triangle OAP-j_ and ODP2. This area is equal to:
Benefits = - [(KP1 • OP1) - (DP2 • OP2)] (6.4)
6-Z7
-------
For the serai-log hedonic wage specification estimated in this
section, this is equivalent to:
Benefits =
(a + 22 TSP)RWGH TSP
TSPi ' SF7 <6'5
where a = estimated coefficient of the linear TSP term.
(3 = coefficient of the quadratic TSP term.
= initial TSP level.
= TSP level after the implementation of the alternative
secondary standard.
TSP = original TSP level predicted from the hedonic wage
equation.
RWGH = the real wage predicted from the hedonic wage
equation.
Depending on the shape of the actual supply price function for
air quality, the approximation of benefits using this alternative may
result in either an underestimate or overestimate of true benefits.
Clearly, this alternative will result in a closer approximation of the
true benefits of a given change in TSP than the benefits that would be
estimated by the area under the derivative of the semi-log hedonic
wage equation.
Illustrative calculations of the benefits of achieving secondary
national ambient air quality standards (SNAAQS) are presented for two
Standard Metropolitan Statistical Areas (SMSAs), Denver and Cleveland.
These calculations are derived using the derivative of RWGH with
6-Z8
-------
respect to TSP of the pooled regression estimated in Equation (2) of
•
Table 6-6 and the approximation technique just discussed.*
For TSP, it is assumed that neither community would have TSP
levels higher than the primary standards for TSP by 1985 and that the
secondary standards for TSP would be met by 1987. It is also assumed
that air quality in these SMSAs will improve by half of the amount
necessary to reach the secondary standard by the end of 1986 and
improve by the remaining amount by the end of 1987. These
improvements in air quality are assumed to be instantaneous, occurring
on the last day of 1986 and 1987. Table 6-8 reports the alternative
primary and secondary standards for TSP assumed to take effect in 1985
and 1987, respectively, and Table 6-9 reports 1978 annual average
concentrations for the Denver and Cleveland SMS As.
Annual benefit estimates from the abatement of TSP in the two
cities are positive according to the calculations made here. For
Denver, meeting the national secondary standard for TSP results in a
reduction in the real wage from $4.1182/hour to $4.0120/hour. A
similar calculation for Cleveland reveals that meeting this standard
causes the real wage to fall from $3.8670/hour to $3.7723/hour.
* Benefit calculations are not derived for the reductions in SCu and
NC>2 to the secondary standard since the coefficients of these
variables were not significantly different from zero in Equation (2)
of Table 6-6.
6-29
-------
TABLE 6-8. ALTERNATIVE AIR POLLUTION STANDARDS*
(annual average in ^g/m )
Primary standard Secondary standard
so2
TSP
N02
75
75
100
60
60
100
* The source of the standards shown here is Stern et al. (28).
TABLE 6-9. 1978 POLLUTION CONCENTRATIONS IN DENVER AND CLEVELAND
SMSAs (annual average in ^g/m )
Denver Cleveland
S02 16.9 61.49
TSP 86 72.2
N00 100 65.0
6-30
-------
Projected benefits for these two SMSAs are obtained by
multiplying the change in the hourly real wage by the annual hours of
full time work and then multiplying this result by an estimate of the
number of affected household heads in each SMSA. Annual hours of full
time work were assumed to be 2000, and it was estimated that there
would be approximately 458,000 household heads in Cleveland and
392,439 household heads in Denver in 1987 with the hours of work and
employment characteristics required for inclusion in the sample used
to make the pooled regression estimates. Since the secondary standard
will be maintained in the future, it is necessary to project the
future number of heads of household that will benefit from the
attainment of the secondary standard for TSP. For the purposes of
this study, it is assumed that the number of households in Denver and
Cleveland will grow at an annual rate of 2.6 percent and 1.1 percent,
respectively.* Using a 10 percent discount rate, benefits of $1.34
billion in 1980 dollars are estimated for the Denver SMSA. Benefits
of $1.17 billion in 1980 dollars are estimated for the persons
affected in Cleveland.
* Annual growth rate estimated from information contained in Reference
(29).
6-31
-------
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u.r. r —
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