FINAL REPORT JUNE 15,1971
URBAN AIR POLLUTION DAMAGE FUNCTIONS:
THEORY AND MEASUREMENT
A Report On The Statistical Association
Between Air Pollution And Single Family
Residential Property Values in Chicago, Illinois
Prepared For
Environmental Protection Agency
Office of Air Programs
By
Thomas D. Crocker
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Urban Air Pollution Damage Functions:
Theory and Measurement*
by
Thomas D. Crocker
Department of Economics
University of California, Rivexside
*This paper is the final report for Research Contract CPA 22-69-52 of
the National Air Pollution Control Administration with the Regents of the
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PREFACE
Doctors, lawyers, merchants, and chiefs all.suspect that air pollution
is unhealthy and damaging and that something should be done about it.
Unfortunately, the exact extent of the damages due to polluted air
I *
has not been determined. Consequently, economic evaluations of damages
;have been more in the nature of informed guesses than anything else.
Until the doctors and ethers have more definitive information,
considerable reliance will have to be placed on multivariate statistical
analyses. Ideally, such studies would be able to draw on consistent and
reliable data over a long enough period of time to allow for study of
time lags in the pollution-damage relationship.
This study by Professor Crocker is an important step in the direction
of establishing a statistically significant inverse relationship between
levels of air pollution and residential property values in the City of
Chicago. Hopefully, investigators will recognize the problems and
opportunities inherent in the methodology. Perhaps, they can both im-
prove on the methodology and apply it to even better data. The fact that
Professor Crocker did, on the basis of multivariate analysis, find sta-
tistical significance between elevated pollution levels and depressed
i
property values comes as no surprise. What is impressive is the manner
and thoroughness with which the analyjjis^has proceeded.
Ji
-~{i ,
Paul H. Gerhardt
Chief Economist
Office of Program Development
Air Pollution Control Office
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Acknowl ed g emen t s
Several people have devoted extensive time and effort to
putting together the data employed in this study. Foremost among
these is Mr. Rudi Winzinger, whose imaginativeness, understanding of
the econaaic form of the problem being studied, and attention to
tedious detail were mainly responsible for putting the data in a
form suitable for empirical analysis. In a completely nontrivial
sense, he is responsible with the principal investigator for
whatever merit the empirical results may have.
Mr. William F. Shaw, Chief of the Statistics Section of the
FHA's Division of Research and Statistics made the FHA data
available to the project. His friendly and generous cooperation
and assistance is most gratefully acknowledged. Paul Tsao of the
University of Wisconsin-Milwaukee's Social Science Research Center
devoted many long hours to the writing of programs for compiling
the data and performing the empirical analysis. R. J. Anderson,
Jr. of Purdue University provided encouragement and assistance in
the project's initial stages.
The author and the paper have benefited from an association
with the Program in Environmental Economics of the University of
California, Riverside.
Mr. Paul Gerhardt and Mr. Brian Peckham have been the project
officers. In many respects, the study's initial conception was
Mr. Gerhardt's. Both gentlemen have always made the study a welcome
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ABSTRACT
This study is an extension of previous work done by the
present author and others on the covariation between air pollution
dosages and property values. Data employed consist of the structural,
site, purchaser, sale, and neighborhood characteristics for each
of,1,288 FHA-insured single family residential property transactions
in Chicago, Illinois, from 1964 through 1967. Arithmetic mean
dosages of suspended particulates and sulfur dioxide for each of
the forty-eight months in this period were calculated for each
transaction's location from basic point measurements. The analysis
of this data served two purposes: (1) the testing of new economic
hypotheses about the relation between property values and air
pollution; and (2) to remove possible sources of statistical bias
present in previous studies.
Results conform to previous studies in that on the average
roughly ten percent variations in air pollution dosages yield
approximately $450 variations of the opposite sign for residential
property values. A comparison of regressions employing the
disaggregated FHA data with regressions using Chicago census tract
data gave no support to the hypothesis of the presence of aggregation
bias in the latter regressions. Nor was there any conclusive
evidence that the discrepancies between years of property sale
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studies introduced any serious statistical bias. Local tax
assessments were found to be poor proxies for act;ual market sales
prices, though FHA assessments were good proxies.
The hypothesis that residential property values decline at a
decreasing rate with respect to increasing air pollution dosages
was subjected to several different tests. No grounds were discovered
justifying the hypothesis' rejection. The hypothesis that land
values are more sensitive to air pollution dosages than are the
values of landed improvements was also supported by the results.
Finally, the skewness of the annual distribution of monthly air
pollution dosages was found to contribute to property values,
though no support was found for the contribution of the distribution's
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GENERAL SUMMARY
Introduction
There have been many diverse attempts to provide some
quantitative indication of the willingness of urban air pollution
sufferers to pay for reductions in air pollution dosages. Scattered
not very liberally among all the interview surveys, the speculations
about health related costs, the outright guesses, and the questionable
extrapolations from materials damages studies are studies which
venture to establish quantitatively the extent of covariation
between residential real estate values and air pollutant dosages.
The results of all those studies with which the writer is familiar
are synthesized in Appendix B. With one single exception, a
summary of which is presented in Appendix A, these studies have
universally found an inverse relation between property values and
air pollution which, for residential properties, amounts to an
average marginal capitalized loss of between $100 and $1,000 per
residential unit. An attempt is made in Appendix B to comprehend
why the results of Appendix A do not complement the findings of
other studies.
Employing the same fundamental economic-theoretic rationale as
have all previous studies except that in Appendix A, the purposes of
the present investigation are tyro: (1) to test empirically
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than have been previously tested; and (2) to test the previously
tested and the new hypotheses with data certainly more complete
and probably more accurate than in previous studies. A general
idea of the extent to which the main body of this investigation
fulfills these two purposes is presented in this summary.
The Data
a) The data consists of structural, site, purchaser, sale,
and neighborhood characteristics of each of 1,288 FHA-insured single
family residential properties in the City of Chicago, Illinois, from
January, 1964, through December, 1967. Excluding transformations,
297 separate bits of information were collected and collated for
each of the 1,288 transactions.
b) Dosages of suspended particulates and sulfur dioxide were
calculated for the location of each transaction from monthly
arithmetic means of samples collected by the Chicago Air Pollution
Control District.
Hypotheses Derived from Economic Considerations
a) To the extent that air pollution effects are relevant
considerations to the 'selector of a residential property, the value
of the effects of pollution is embodied in a single entity,
residential property values, and cet. par., differences in the
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In short, air pollution effects are capitalized into property
value:;, and, if disutility is on the average derived from air
pollution effects, an inverse relation will exist between air
pollution dosages and these values.
b) Hints have appeared in earlier studies that the aggregate
air pollution damage function may be increasing at a decreasing
rate over a fairly wide range of dosages. An attempt is made here
to provide a rationale for a declining marginal air pollution
damage function.
c) All previous studies of the covariation between air
pollution and urban property values have been devoted to the
entire property, land and improvements. Thus no attempt has been
made to distinguish between the effects of air pollution upon land
and upon landed improvements. A hypothesis is derived in this
study to the effect that the marginal damage function for land will
decline at a rate more rapid than the marginal damage function for
landed improvements; and that land values will be more responsive
to air pollution dosages than will the values of landed improvements.
d) When future air pollution dosages are uncertain, the
features of the air pollution frequency distribution relevant to
the receptor may not be adequately described by the distribution's
mathematical expectation. In particular, the market may evaluate
the variance and the skewness of the distribution.
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dosages can imply a preference ordering over possible future states
based upon a decision criterion in which the sufferer's objective
is to make his maximum possible losses as small as possible.
f) For given supply conditions, the market price of a
residential property is determined by the market's expectations
about the future values of it structural, site, purchaser, sale,
and neighborhood characteristics. These expectations can be formed
in many ways. In the case of air pollution, it seems likely these
expectations are formed almost entirely on the basis of a history of
past air pollution dosages. One can therefore inquire into the
influence the various parts of this history have upon property
values.
Hypotheses Derived from Statistical Considerations
g) All previous studies of this sort have employed property
characteristics and property value data in which the air pollution
data postdated the property data by anywhere from four to seven
years. This discrepancy can cause the air pollution coefficients
to be understated. The data available to this study permit one to
test for this source of bias by matching property value data for
any one of four years.
h) It can be shown that unless all households in a group
suffer the same marginal damages from air pollution and unless the
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viii
described by a stable linear model, then air pollution coefficients
calculated from such aggregated data can be biased. By comparing
results obtained with completely disaggregated data with results
obtained using grouped data from the U. S. Census, one can ascertain
\l
whether the results with the census data exhibit aggregation bias.
i) Records on FHA assessed property values are perhaps more
readily available than are records on actual market sales prices.
The data permit the comparison of estimated air pollution damages
when FHA assessments are used as property values and when actual
market sales prices are used.'
j) Local assessments of property values are widely collected
and are readily accessible throughout the country. The data used
here permit the comparison of estimated air pollution damages when
FHA assessments are used as property values and when actual market
sales prices are used.
k) It is to be expected that air pollution dosages and
property maintenance outlays will be positively related. The
• presence in the FHA data of a measure of maintenance costs allows a
test of this possible relation.
The Results
a) Results support the hypothesis of an inverse relation
between air pollution dosages and residential property values.
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average the sum of the damage elasticities for sulfur dioxide and
suspended particulates in the City of Chicago is between -.30 and
-.40. Average marginal capitalized damages appear to be about
$450 for an additional ten micrograms per cubic meter per twenty-four
hours of suspended particulates plus an additional part per billion
by volume per twenty-four hours of sulfur dioxide. These results
have been .obtained employing the completely disaggregated FHA data.
No solid evidence of serious multicollinearity of the pollution
variables with other explanatory variables was discovered.
b) Eleven different partitions of the disaggregated FHA
data were carried out so as to run separate regressions on samples
whose annual arithmetic mean pollution dosages differed. In no
case were there any grounds for rejection of the hypothesis that
willingness to pay to avoid air pollution dosages increases at a
decreasing rate.
c) As hypothesized, land values appear to be more sensitive
to air pollution dosages than do landed improvements. Average
marginal capitalized reductions in land values were about half the
average marginal capitalized damages to property values, though,
on the average, land values constituted substantially less than
one-quarter of property values. Similarly, the sum of the damage
elasticities in the property value regressions is always less than
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d) At no time did the inclusion of the second moment of a
calendar year's air pollution distribution yield a statistically
significant result, though the signs of the coefficients for the
variable representing variance were consistently negative. Results
for the third moment were only slightly ambiguous. In two cases
significant results with a negative sign were obtained when the
mean of the skewness variables was positive. In that third case
where statistically insignificant results were obtained, the mean of
the skewness variable wae nearly zero.
e) A meaningful test of the minimax decision criterion was
inhibited by serious multicollinearity between minimum, maximum,
and mean suspended particulate dosages as well between maximum and
mean sulfur dioxide dosages.
f) Because of a relative lack of success in constructing a
computer program capable of estimation when two or more variables
in a cross-sectional regression are distributed lags, no meaningful
estimates were obtained of the contribution the various parts of
an air pollution history make to current air pollution damages.
g) Using the same set of FHA transactions from one regression
to another and permitting the regressions to differ only in the
years in which air pollution dosages occurred, it was difficult
on intuitive grounds to discern any important differences in the
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statistical bias in the air pollution damage estimates due to
discrepancies in the year of property sale observations and the
year of air pollution dosage observations is not immediately
obvious from inspection of the air pollution coefficients. However,
this intuitive identity of the coefficients can not be supported
on statistical grounds.
h) An intuitive comparison of the air pollution coefficients
obtained using census tract data and those obtained using the
disaggregated FHA data failed to reveal any significant "common sense"
differences. However, the hypothesis of the statistical identity
of the two sets of coefficients could not be accepted. When the
level of aggregation was increased to include in each observation
"averages" known as community areas constructed from several
census tracts, there was neither any common sense nor any statistical
identity of the two sets of coefficients.
i) A comparison of the air pollution coefficients obtained
when actual market sale price is employed as the regressand with
the coefficients obtained using FHA assessed value as the regressand
reveals an intuitive identity of the coefficients and at least a
partial statistical identity.
j) A comparison similar to that in i) above for actual market
sales prices and local assessed values reveals no intuitive and
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Was discovered, the difficulty of locally obtaining data on
individual householder attributes would seem to preclude the
use of data obtained from local,assessments. The importance of
this bias is evidence in the fairly substantial changes which occur
in the standard errors of the air pollution coefficients whenever
some measure of householder income is not included as a regr.essor.
k) The air pollution coefficients obtained when maintenance
expenses were included as a regressand had negative signs. It is
therefore concluded that the maintenance measure employed was an
inadequate measure of actual maintenance expenses. To assert
otherwise is to conclude that air pollution dosages have no
effect upon maintenance expenses. This latter assertion is
incompatible with the other results of this study.
Research Extensions
The study concludes with suggestions about possible extensions
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TABLE OF CONTENTS
Section Page
Acknowledgement i
Author's Abstract ii
General Summary iv
Table of Contents xiii
List of Tables xv
List of Figures xvii
INTRODUCTION 1
THE THEORETICAL FRAMEWORK 4
Basis of the Offer Function 5
The Marginal Air Pollution Damage Function 11
Relative Damages to Land and Improvements 18
Air Pollution Damages Due to Uncertainty 21
Householder Decision Criteria under Uncertainty 26
The Formation of Air Pollution Dosage Expectations 31
THE EMPIRICAL BACKGROUND 38
General Nature of the Data 38
The Air Pollution Data 41
Simultaneity of Air Pollution and Transactions Data 46
Aggregation Bias 47
Use of Actual Market Sales Prices 51
Possibilities in^the Use of Assessed Property Values 52
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THE VARIABLES 54
Dependent Variables . 54
Explanatory Variables 56
THE RESULTS , 71
Statistical Attributes of the Data 72
The Inverse Relation Between Air Pollution Dosages 76
and Property Value
Effect of Discrepancies Between Dates of Air Pollution 83
and Property Data
The Use of Assessed Property Values 88
Maintenance Expenditures 91
Effects of Dosages Upon Site Values 91
Declining Marginal Damages 93
The Minimax Decision Criterion 97
The Cubic Utility Function 97
Adaptive Expectations 101
SOME DESIRABLE RESEARCH EXTENSIONS 103
Theoretical Issues lOh
Estimation 112
Empirical Issues 118
Summary and Conclusions 121
FOOTNOTES 12U
BIBLIOGRAPHY 131
APPENDICES
Appendix A. "Property Values and the Demand for Clean A-l
Air", by Kenneth F. Wieand.
Appendix B. "A Comment on Wieand", by R. J. Anderson, B-l
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XV
LIST OF TABLES
Table Page
1. Annual Arithmetic Mean Pollution Dosage by Station 43
and Year.
2. Stations Having Differences in Annual Air Pollution 45
Distributions.
3. Arithmetic Means and Standard Deviations of Original 73
Values of Nonpollution Variables.
4. Arithmetic Means and Standard Deviations of Original 74
Values of Representative Pollution Variables.
5. Simple Correlation Coefficients for 1967 Observations 75
6. Initial Regressions. Dependent Variable, In(COSTS). 77
7. Initial Regressions with One Pollution Variable. 78
8. initial Regressions without In(DISSM) and In(DLAKE). 80
9. Regressions for DISSM and DLAKE Partitions. 81
10. Simple Correlation Coefficients for DISSM and DLAKE 81
Partitions.
11. Regressions for INDUT, BLK66, and INC66 Partitions. 83
12. Regressions Exhibiting Discrepancies in Air Pollution and 84
.Property Sale Data.
13. Analysis of Covariance of 1967 Disaggregated FHA Data. 85
14. Regression Results for Census Data. Dependent Variable, 87
ln(MVAL6).
15. Analysis of Covariance of Disaggregated FHA and Census 87
Data.
16. Regressions with In(FHAVL), In(TAXES), and In(MAINT) as 90
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xvi
17. Regressions for Site Values. Dependent variable, 92
.Ln(PSITE).
18. Regressions with ln(SUL65) Partitioned. Dependent 94
variable, In(COSTS).
19. Comparison of Logarithmic Means and Pollution 95
Coefficients.
20. Regressions for Minimum and Maximum Pollution Dosages. 98
21. Regressions on Second and Third Moments of Pollution 99
Dosages.
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LIST OF FIGURES
Figure Page
1. Possible Householder Losses from Errors in Forecasting 29
Air Pollution Dosages.
2. Comparison of Kinimax z, z , and Expected Utility z, "z, 32
under Uncertainty about Air Pollution Dosages.
3. Locations of Air Pollution Monitoring Stations and 40
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Introduction
In the past five or ten years, the attention which air
pollution problems have received has generated a wide variety of
proposals for their alleviation. Present in all these proposals
has been some notion of a damage function relating air pollution
dosages to the market value of the foregone production and
consumption opportunities suffered by receptors. Most academic
discussions of these proposals have proceeded in a world of
certainty, a world in which the values of all variables relevant
to the decision process can always be consistently and
costlessly predicted with zero probability of error. Most of
the time property rights in the air resource are assumed to be
assigned to a control agency whose tremendous clairvoyance
and omniscience enables if. to select effortlessly or cause to
occur that level of pollutant emissions synonymous with ambient
air concentrations minimizing the sum of sufferer damage and
emitter control costs. Under these conditions, discussions of
optimal control instruments become trivial exercises in which
the only matters of interest are value-loaded statements about
whose judgments are to count. Questions of real economic
interest would occur only when it is supposed that the control
agency knows of no systematic way to put its perfect information
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However, once it Is recognized that the discovery of that
pollution program minimizing the sum of emitter and receptor
costs is itself costly, important differences among alternative
control instruments become apparent. Ultimately, the criterion
for selection of a control instrument must be the minimization
of the sum of emitter and receptor costs and all parties',
including regulatory bodies', informational, contractual and
policing (ICP) costs. Even assuming all property rights to the
air resource are always initially vested in a control agency,
the ICP costs of alternative control instruments can differ
widely. For example, the use of the effluent charge as the sole
instrument of control requires an intimate knowledge of the
behavior of the air pollution damage function. But when the
effluent charge is employed along with an already established
ambient air standard, knowledge of neither the receptor damage
function nor the emitter control cost function is required. All
the agency need do is vary the charge in a manner causing the
ambient air standard not to be exceeded. Of course, though ICP
costs are relatively low in this latter case, the ambient air
standard may be identified with substantial permanent or periodic
deviations from minimization of the sum of receptor and emitter
costs. The probable costs of this deviation must be weighed
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minlmizing effluent charges as well as against the costs of
employing a suboptimal effluent charge as the sole control
instrument.
The formal consideration of the preceding statements
immediately leads one into the formidable quicksands of
problems in decision-making under uncertainty. In this paper
the intent is not to enter these sands but instead to provide an
input which in the context of air pollution concerns can assist
in this decision-making. The particular purpose is to
investigate the urban air pollution damage function as it is
registered in differential market prices of residential property.
This will by no means be the first time this function has been
studied in this manner, e.g., Anderson and Crocker [l]; Ridker
and Henning [2]; Ridker {3, pp. 141-151] ; Zerbe [4]; Wieand[5];
and Peckham [6]. By using sopewhat more complex specifications
and a set of data appearing to have greater informational
content, this study's purpose is to ascertain the sensitivity
of damage functions derived by means of differential land values
to differences in specifications and differences in data. If
results do not appear overly sensitive to data and specification
differences, then simpler and less costly specifications and
daca sets can be used to obtain the damage function with little
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control instrument more likely to approach a continuing
, minimization of the sum of emitter control costs and receptor
damage costs can then be employed. Less obtusely stated, the
question being asked here is whether any additional worthwhile
information about urban air pollution damage functions can be
obtained by working with property value models having somewhat
more complex specifications and more complete data than in
previous studies.
The Theoretical Framework
Lind [8], building upon the work of Strotz [ ?], has shown,
given certain simplifying assumptions, that the difference in
the market price of two sites represents the difference in the
aggregate willingness to pay for the sites net of any difference
in profits or consumer surplus. Thus if two sites are similar
in all respects except air quality, the difference in their
values represents the markets' willingness to pay for reductions
in air pollution dosages. When all consumers do not regard two
sites as perfect substitutes in all respects except air quality,
then some air pollution damages will be capitalized into durable
and immobile improvements and losses in consumer surplus.
However, if the characteristics of these sites and other assets
enter individual utility functions in an additive manner, then
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bound on air pollution damages. Furthermore, when sites are not
viewed as perfect substitutes by consumers, a substantial portion
of damages will still be registered in differential property
values, where a property includes the site and the immobile and
durable improvements thereon.
For each time period dealt with in this study a long-run
equilibrium is presumed to exist in all housing characteristics.
Thus no supplier of housing characteristics is presumed to be
able to increase his net revenues by adjusting the stock or the
location of housing characteristics. Similarly, no individual
buyer of housing 'characteristics can increase his utility by
purchasing a different package of characteristics or by changing
';he location of his residence. ; In short, given the market
structure, all locations are presumed to be held by those
participating in activities yielding the highest property values.
Our task is to explain the differences in these values. Assuming
that all suppliers of housing characteristics face the same
capitalization rates and cost structures in the locale of interest,
these value differences are accounted for by consumer evaluations
of differing locational characteristics.
Basis of the Offer Function. The point of departure
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consume.r behavior. The consumer is represented as the
embodiment of a well-behaved utility function, U [z(x)], where
z is an mxl vector of quantities of characteristics and x is an
nxl vector of the quantities of the goods in which the
2
characteristics are found. Thus housing is a bundle of
characteristics households produce with their own time and skills
using purchased inputs which include buildings and space. In
short, the consumer ranks characteristics, and because he ranks
characteristics, he indirectly ranks goods, which in this essay
will be housing locations. The consumer's problem is therefore
to maximize U subject to the conditions
c'x = y
z = Bx
Zj x >_ 0
where c .is the nxl vector of prices associated with the goods,
B is an raxn matrix, and y is income. It is proved in Anderson
and Crocker [l] and restated in Appendix B of the present essay,
that the utility maximizing quantities of the various
characteristics are functions of the prices of the various goods
in which they reside and consumer incomes. That is, one is
justified in writing c = c(z ) y) where c (.) is the consumer's
offer function.
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consumer evaluate all goods in which a characteristic entering
his utility function is found. Since a house may embody
characteristics found in a wide variety of other goods, a
complete empirical specification of this offer function would
require the simultaneous specification of offer functions for
all those goods also embodying some of the characteristics
embodied in housing. For example, if the individual at some set
of relative prices for the goods in which they are found is
willing to substitute clean air for enclosed three dimensional
space, there is no ji priori reason why his search for clean air
must be limited to housing locations. It would therefore appear
that a study of housing demand would also require a simultaneous
study of the demand for mountain recreation.
Actually, as Lancaster [14] emphasizes, the characteristics
embodied in some goods, for given relative prices of goods, will
represent inefficient consumer choices and can therefore be
disregarded. But in any empirical application the elements of
the B matrix must be specified, an ambiguous task for which there
is little if any theoretical guide. Neither the researcher nor
the consumer are likely to possess the skills and willingness to
survey and count completely and simultaneously all characteristics
to be found in housing. If one introduces, as we shall, dated
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required for the researcher to perceive all gradients of the
consumption technology are indeed astounding. The same point
can be made for. the consumer. Though it is true a great many
things can be measured if the urge for measurement is strong
enough, the very fact that some urging is required implies a
cost. One can therefore reasonably presume the consumer strives
to satisfy a craving for simplicity by means of some aggregation
procedure which reduces at some stage the rank of the B matrix he
must confront.
Consider the following scheme which in certain of its
fundamentals is similar to that presented by Green [15, pp. 9-32],
In order to conserve his means of surveying and counting, the
consumer completely disregards some commodities and aggregates
over others having collections'of characteristics intended to
serve a more or less broad function, e.j;., housing, food,
entertainment. In the first decision stage, the allocation of
the consumer's budget on the basis of price indices of the
commodities forming such broad groupings does not make an
intolerable difference in the decision problem with which the
consumer is confronted. We assume his demand for the broad
grouping "housing" or any other broad grouping to be altogether
independent of air pollution considerations. Only after this
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housing characteristics evaluated. One of these evaluated
characteristics is the presence of air pollution.
It is well known that if the utility function U tz(x)] is
strongly separable in the sense of Goldman and Uzawa [16], the
quantity of each commodity purchased with the consumer operating
under ft. two-stage procedure will be identical to the quantity
purchased if the consumer's purchases had all been made in' one
stage. That is, if we assume the commodities embodying
characteristics entering the utility function are divided into
three groups of commodities, H, I, and J, where H is housing,
then strong separability is defined as:
heH
= 0 for
D xh ici
Rnln J - ft
where i; j , and h are commodities having at least one
characteristic not in common. Given this restriction upon the
utility function, if the consumer allocates his budget in the
first stage so as to maximize a utility function having groups
of characteristics embodied in groups of goods as its arguments,
then the consumer can maximize his overall utility by maximizing
a utility function in the second stage having characteristics
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a utility maximizing allocation of the consumer's budget among
housing locations is therefore not inconsistent with a utility
maximizing allocation of this budget among all goods. This
result dotes not necessarily imply that groups of characteristics
interdependent in demand do not exist. It only implies that the
»
individual property buyer groups all interdependent
characteristics so that he makes his final house purchase decision
in terms of the mutually independent groupings which we are
presumed to be able to describe. Conceptually, these
separability notions imply that air pollution damages to housing
will be relatively greater because they permit the consumer to
respond to changes in air pollution dosages only by a
redistribution of his expenditures among characteristics in the
housing group rather than among all groups. However, in terms
of estimating the effects of air pollution upon the demand for
housing, the failure of these separability notions to be
fulfilled means that the characteristics of certain goods which
contribute to the explanation of variations in offer prices for
housing are not being included. If these characteristics are not
orthogonal to air pollution dosages and if they contribute
positively to offer prices, then air pollution damages will tend
to be biased downward. Similarly, if they contribute negatively,
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On the basis of the above statements, the offer function to
be estimated is a quantity weighted average of implicit prices
for combinations of characteristics embodied in a commodity or
bundle making up something called a housing location. It should
be emphasized that each price observation is presumed to be
attached to one unit of a unique commodity, a housing location
which is objectively distinguishable by its combination of
characteristics. The c^ are therefore observations on the
market prices of distinct goods. They represent T observable
prices of T different goods. Each refers to one and only one
house. Therefore, making the not unreasonable assumption that
each residential property owner owns only one house and that
each residential property is owned by only one owner, the offer
price for housing and consumer expenditures for housing are
4
identical.
The Marginal Air Pollution Damage Function. This essay's
prime concern is the connection between air pollution and land
and property prices, and between land and property prices and air
5
pollution damages. The notion that air pollution damages are in
fact registered in differential property values is quite comforting
to anyone who has ever experienced the theoretical and empirical
difficulties associated with the employment of alternative
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pollution damages. Nevertheless, the ability of an approach to
provide insight into one question makes one wonder whether it
might also provide insight into related questions. In
particular, can anything be said about the form of the relation
between air pollution dosages and property values? Furthermore,
given that some insight can be acquired into the form of this
relation, are there any inferences which can be drawn about the
form of the relation between air pollution dosages and air
pollution damages apart from any capitalization of the latter
into property values? In an earlier effort of the writer and
R. .1. Anderson, Jr. til, empirical results over some interval
of increasing air pollution dosages pointed to the possibility
of a declining marginal property damage function as well as a
declining property damage elasticity. No explanation of the
phenomenon was offered however.
In accordance with the Lancaster formulation, the
household is viewed in the following as a firm selling a bundle
of housing characteristics to itself for a price equal to its
maximum willingness to pay for that bundle. For simplicity, all
households are treated as identical. The bundle of housing
characteristics and the goods used to obtain these characteristics
are each assumed to fulfill the conditions for a composite good.
-------
-13-
that x and y can each be defined by a scalar rather than a vector.
Given the above conditions, the householder's problem is to
maximize
(1) U = cz - c^x
subject to
z = z(x) ,
where U is the householder's utility, z is the bundle of housing
characteristics, and x is the collection of housing location goods.
The unit cost of the collection of goods is c_, and the unit cost of
X,
the bundle of characteristics is c. U can thus be regarded as a measure
of the Marshallian consumer surplus. The first order condition
for a maximum is
(2) ajL- c£5.- cx=o.
Air pollution dosages are specific to location. For locational
equilibrium to prevail, it is necessary and sufficient that each
household occupy the most expensive available property it is
willing to buy and that each available property be occupied by
that household willing to pay the highest price. The change in
the bundle of characteristics resulting from any change in the
household's location is given by
-------
-14-
The condition of (2) implies
(4) cx = c i£
and the change in consumer surplus accompanying such a change in
location is
(5) dU « (zdc - xdCx) + (cdz - cxdx)
The first-order condition of (4) is always fulfilled. Therefore,
upon substituting (3) and (4) into (5), we have
(6) dU - (zdc - xdcv) + (c |5. dx - c |5. dx)
* oX oX
= dc - xdc
x x
If there is to be locational equilibrium, dU = 0. Thus (6)
becomes
i
(7) dc = dc z .
x x
By hypothesis, c = c(p) and ££ 0, where p refers to air
pollution dosages. Therefore, from (7)
(8) dcx _ dc z < 0
dc dp x '
since a positive quantity of housing characteristics can be
obtained only from a positive quantity of housing location goods.
The difference between dc /dp and dc/dp is obviously dependent
upon the ratio of z to x. In general, it is to be expected that
0 < z/x 1. 1, since the number of housing locations the consumer
at least initially chooses among seems likely to exceed the
-------
-15-
to be relevant. One can therefore conclude that the marginal
air pollution damages to goods from which housing characteristics
can be obtained can exceed the marginal damages to bundles of
housing characteristics.
(9) ,
and
(9a)
Furthermore,
dp
d2c
z d2c
x dp
dc
dp
dc d(z/x)
dp dp
dc d(z/x)
x
dp dp
As previously noted, z/x is positive and dc/dp is negative. One
of the major economic features of air pollution is that it
reduces the output (characteristics) to be obtained from any
given mix and magnitude of inputs (goods). Thus d(z/x)/dp
is also negative. It is therefore immediately obvious that if
• 7 9 ? 2
either d c/dp or d cx/dp is positive, the sign of one cannot
be inferred from the sign of the other. However, if either can
be shown to be negative, then it follows that the other must also
be negative. That is, if air pollution damages to housing
characteristics increase at a decreasing rate, then air pollution
damages to goods capable of generating housing characteristics
-------
-16-
o
In location theory, it is widely acknowledged that d c is
negative with respect to any variable which dxffers in magnitude
from one location to another and to whose increased presence
disutility is attached. The reasoning goes as follows.
Locational equilibrium requires that households be unable to
increase (U = cz - ex) by any move. Given that air pollution
X
and property values are inversely related, the household can
increase the quantity it can purchase of the goods embodying
any bundle of housing characteristics for a particular money
outlay by moving to an area subject to greater pollution dosages.
However, the household's willingness to pay, for a given bundle of
housing characteristics at the higher pollution location has
declined. This implies that in equilibrium
(10) dcx dc
dp dp
In short, in locational equilibrium a change due to pollution in
the price of goods embodying a given bundle of housing
characteristics is exactly offset by the change in the
-------
-17-
if this equilibrium is to be maintained, it is necessary that
with increased air pollution, householder willingness to pay
decline at a rate less rapid than the decline in the market
prices of goods embodying housing characteristics. If differences
in willingness to pay are interpreted as the air pollution
damages the householder perceives to be imposed upon a given
bundle of housing characteristics, this implies that the
marginal air pollution damage function is declining with
increased dosages and is declining at a rate less rapid than the
decline in the price of housing goods. Otherwise the location of
each householder would be indeterminant or each householder
could alwayn increase U(z) by moving to locations having the
highest pollution dosages. This is because the incremental
householder benefits implicit in the rate of decline of the
price of housing goods would ultimately exceed the additional
/<
householder damages implicit in the rate of the reduction in
householder willingness to pay.
If households are now permitted to differ in their
sensitivity to air pollution dosages, the above implies that
those households for whom dc/dp is relatively high will tend to
locate where air pollution dosages are relatively low; and those
, !»
households for whom dc/dp is relatively low, will tend to locate
I
-------
-18-
of (10) states that when dc/dp is high, dcv/dp must also be high.
X
Pollution sensitive people bid the most for low pollution locations
because these people attach greater disutility to a little bit
of pollution than does anyone else. Sites are thus assigned on
the basis of the individual's pollution sensitivity, with the
most pollution sensitive being assigned to the low pollution
sites and least pollution sensitive being assigned to the high
pollution sites. The absolute magnitude of dc/dp thus declines
over an array of locations ordered on the basis of the magnitude
of the air pollution dosages to which they are subject. One
would therefore expect to find when comparing marginal property
damage Junctions for high pollution locations to those for low
pollution locations that the absolute magnitude of the latter is
less than the former. If the "production function" z(x) is
homogeneous of degree one so that changes in x lead to identical
percentage changes in z, then this conclusion also holds for the
elasticity of the value of a bundle of housing characteristics
with respect to air pollution dosages.
> Relative Damages to Land and Improvements. Additional
interesting results can be obtained by retaining the same assumptions
but revising the simple formulation beginning with (1) so that land
and nonland goods embodying housing characteristics are
-------
-19-
permanent features of a location. For practical purposes, they
can include such features as utilities and man-made changes in
topography as well as the unimproved space associated with the
site. Jsing the land-non]and distinction, (1) becomes
(11) U = czC^, y - ^ XL - CN XN,
where U, c, and z are defined as before. Land and nonland goods
are represented respectively by :e and x , while CL and c
represent their prices. The first-order conditions for a
maximum are
(12) JMJ = c 3z_ _ CL =0
3xL 9xL
9U _ c 3_z _ Cjj = 0.
3xN 8xN
Performing the same set of operations as in (3) - (7), one obtains
(13) z dc - ^ dcL - Xjj dcN = 0
and
(14) dcL zdc XN
__ __ ^
Thus, in value terms, given that z ^_ x^ + x^ and dc > 1, it
follows that (30) will be greater than unity. That is, marginal
air pollution damages to a bundle of housing characteristics will
be registered to a greater extent in land than in the nonland
goods which contribute to housing characteristics. In general,
-------
-20-
value of the characteristics it produces, the greater will be
the do, caused by a change in air pollution dosages. Again, if
the "production function" Z(XL, Xjj) is homogeneous of degree one
so that equLproportional increases in XL and XN lead to identical
percentage increases in z, then marginal rates of substitution
between land and nonland good remain unchanged and a conclusion
similar to (14) holds for the elasticity of land values and
nonland values with respect to variations in air pollution
dosages. If the elasticity of substitution between land and
nonland goods is positive and if the supply elasticity of land
goods is less than the supply elasticity of nonland goods, the
conclusion of (30) is strengthened, for the magnitude of dc
Li
relative to variations in dc will be accentuated. However, as
land goods are substituted for nonland goods because of the
change in relative prices, nonland goods will exhibit the
greatest relative decline in .quantity employed as a consequence
of an increase in air pollution dosages. In other words, given
the correctness of the preceding assumptions, for a given
population air pollution increases what is typically known as
"urban sprawl," the spreading out over the landscape of streets,
huge signs, and one story buildings.
A number of reasonable offhand estimates about the likely
-------
-21-
First, land goods probably contribute less than one-third of the
value of a typical bundle of housing characteristics, if that
much. Second, the elasticity of substitution of land for
nonland goods in housing is generally acknowledged to be slightly
less than unity, e.g., Muth [27, p. 82 ]. Finally, it is
intuitively obvious that the supply elasticity of residential
land in an urban area must be substantially less than the supply
elasticity for nonland residential goods. There are thus strong
2. priori empirical as well as theoretical grounds for expecting
land values to be more responsive than nonland values to variations
in air pollution dosages whenever any statistical tests are made.
Contrary test results would more likely justify dismissal of the
test on grounds of specification or measurement error rather than a
failure to accept the hypothesis.
Air Pollution Damages Due to Uncertainty. To this point, the
discussion has implicitly assumed that for those variables whose
future values are not largely subject to the householder's control, only
the expected value of the variable's frequency distribution is relevant
to the householder's decisions. In other words, certainty equivalence
has been assumed such that the first moment of the air pollution
frequency distribution at a particular site adequately summarizes the entire
-------
-22-
dosages has been treated as identical in situations where perfect
foresight is lacking and in situations where it is present. The
householder's behavior at a point in time is therefore viewed as
invariant with respect to the probability of error in his forecast
of expected air pollution dosages.
In the following, we continue to express the multivalued
t
expected results associated with alternative time-states as
probability distributions rather than assuming that the
O
householder sets these states out in extensive form. That is, we
add to the set of air pollution characteristics relevant to the
property buyer various derivative statistical measures of air
pollution frequency distributions. In particular, by assuming;
U(z) to be cubic in air pollution dosages, we show the relevance
of the first three moments of the air pollution frequency
9
distribution to air pollution damages. However, this demonstration
does not assert that only the first three moments count, for, as
Richter [22] has shown, an nth degree polynomial for U(z) implies
and is implied by the assumption that only the first n moments are
to count. In short, by assuming a utility function of the proper
degree one can justify the use of any number of moments (until
their values tend to zero).
Assuming a one to one correspondence between the implicit
-------
-23-
householder"s utility, U, we can rewrite c = c (p) as
(15) U = U(p) , and 3.U < 0 uniformly,
given that fewer air pollution dosages are preferred to more.
Expanding (15) in a Taylor series about a mean value, p, ignoring
moments above the third, and taking the expected value yields
(16) E [ U(p*)] = U(p) +
! _2/ \e j _3;
VaP / V3P /
As a random variable, p = p*, and
a2 = E(p* - p)2
a3 - E(P* -p)3
As noted above, taking the utility of dirtier air to be a
function of the first three moments of p*'s distribution about
its mean is equivalent to assuming U(p*) to be a cubic of the
form
(17) U(p*) = p* + bp*2 4- gp*3
Upon .taking the expected value of (17) we obtain
2 3
(18) E U(p*) = E(p*) + bE(p*) + g E(p*)
where
(19) E(p*)2 = o2 + [E(p*)] 2
and
(20) E(p*)3 =a - 2 [E(p*)] 3 + 3E(p*)2 E(p*).
Substitution of (19) and (20) into (18) gives
(21) E [U(p*)l - E(p*) + b [E(p*)J 2 + g [E(p*>] 3 +
-------
-24-
Taking the partial derivative of (21) with respect to E(p*), we
get
(22) 9 E [l)(p*) 3 = 1 + 2bE(p*) + 3g fE(p*) I2 +3g a2
3 E(p*) „ .
- 1 + 2bE(p*) + 3g [E(p*)T + 3g(E(p*r - [E(p*)]ZJ-
- 1 + 2bE(p*) + 3g E(p*)?
This is a quadratic having roots
-2b 1 [2b2 - 4(3g) ]2
6g
Thus if the marginal utility of dirtier air is always to be
negative, then
2b2 < 4(3g).
That is, for (22) to be negative, it is required that
(23) b2 < 3g
o
Since b is always positive, g must also be positive if (23) is
to hold true. Given that g must be positive, the sign for
2 —2
3 U/3 p comes from (16) and (21) where
(24) 9E [U(p*)l . 32U/9 p2 = 3gE(p*) + b
803 2
= 3g"p + b
— 2 —2
Clearly, if p £ -b/3g, then 3 U/3 p 10, which is consistent
with the statements about the sign of the marginal air pollution
damage function in (9a). The assumption of p 1 -b/3g amounts
-------
-25-
3 —3
The correct sign for 3 U/8 p can also be obtained from (16) and
(21) since
(25) 9E [U(p*) ] _ ( 93U/9 p3) = g.
-
The requirement from (23) that g be positive therefore assures
that 33U/9 p3 < 0.
Our conclusion from (24) and (25) above is that the
householder attaches disutility to increasing uncertainty, as
measured by variance, of air pollution dosages. Furthermore,
given equivalent expected values and variances, he prefers those
air pollution frequency distributions skewed toward the lower
range of dosages. Treating these derivative statistical
measures as distinct characteristics, we therefore view each
residential property as giving rise to at least three air
pollution characteristics, the mean, the variance, and the
skewness of the property's air pollution frequency distribution.
As we earlier noted, there is no particularly defensible
reason other than investigative convenience to assert that only
the first moment, or, for that matter, the first three moments
of the distribution of air pollution dosages enter as arguments
into the housing consumer's utility function. In effect, the
problem of discovering what these arguments are with respect to
-------
-26-
Investigator can therefore hope to do is to specify models
capable of being empirically evaluated.
Householder Decision Criteria Under Uncertainty. There
exist several alternative decision criteria conceivably
applicable to a householder faced with uncertainty about the future
pollution dosages to which he will be subject. Each of these
alternatives implies a preference ordering over possible future
states based upon a criterion other than the maximization of
10
expected utility. Many of these criteria cannot be meaningfully
described in probability terms. One often cited criterion of
this sort is the minima* decision criterion of Wald [24]where
(in our context) the householder is presumed to know with zero
probability of error that future air pollution dosages will fall
within a given range. The sufferer's objective is then to make
his maximum possible loss as small as possible, where the loss is
defined in terms of the discrepancy between the realized
consequence of an act and the utility which would have been
obtained if the future state of nature had been correctly forecast.
As Hildreth [25] notes, the common sense appeal of a criterion
of this sort depends directly on how small this maximum possible
loss can be made. If this maximum possible loss is likely to be
small relative to the costs of acquiring that information
-------
-27-
for air pollution situations even when increased risks of health
effects are accounted for -- then the criterion would appear to
be reasonable. If, for example, with wide fluctuations in air
pollution dosages and damages a sufferer employing this criterion
can come within $100 of his minimum possible losses under perfect
•
certainty, then the criterion might arouse the sufferer's interest.
But if the discrepency results in his death or even damages of
$1000 he might display no interest whatsoever.
The article of Hildreth [25] referred to above derives an
expression from a Cobb-Douglas production function for a firm's
demand for an input where the firm employs a minimax decision
criterion. A somewhat more general development applicable to
the minimax decision criterion of an air pollution sufferer can
be obtained with the aid of some easily interpreted diagraramatics.
Assume that the sufferer acts as if air pollution dosages
over whatever time period is deemed relevant are bounded above
and below by fixed values. Let U(p+) in Figure 1 represent the
upper bound of these dosages and U(p-) the lower bound. The
householder would act as if any dosage, p, in the interval
(u(p+), U(p-)l could occur. Since 3U/9 p < 0, movement up the U
axis represents increasing utility levels and decreasing air
pollution dosages. From the sufferer's point of view, any
-------
-28-
increase in dosages is presumed to be utterly independent of any
activities the sufferer might undertake. Thus on the U axis, each
utility level is associated with a unique dosage of air pollutants
over whose presence or absence the sufferer knows he can exercise
no influence.
With any given level of air pollution dosages, there can be
t
combined various quantities of ei bundle, z, of housing characteristics.
The additional utility to be obtained at a given dosage level
with the consumption of an additional unit of the bundle of housing
characteristics is given by dUi/d z, i - 1, 2, 3. The marginal
costs and average costs of obtaining an additional unit of the
bundle of housing characteristics are given respectively by
dc/3 z and c/r. As before, a one to one correspondence is
assumed between utility and dollars. The increasing 9U/3 z
associated with declining pollution dosages implies that
pollution affects the utility obtainable from the elements of
the bundle of housing characteristics. The sufferer's problem
is to select that quantity of the bundle of housing
characteristics minimizing his maximum possible loss from air
pollution dosages.
Temporarily assume the householder acts as if the pollution
dosage to which he will be subjected is to be p where p lies
-------
-29-
Figure 1. Possible Householder Losses from Errors in Forecasting
-------
-30-
z units of the bundle of housing characteristics, where z is
someplace in the interval Jz+, z-1 . If p+ rather than p is
ultimately realized, the householder has purchased ab = z+z units
of the bundle of housing characteristics whose cost outweighs the
additional utility these units provide him. This total loss is
represented by the area a e b. On the other hand, if p- rather
than p is ultimately realized, the householder has failed to
consume fg = zz- units of the bundle of housing characteristics
whose cost does not outweigh the additional utility these units
could have provided him. The loss he suffers by overestimating
future pollution dosages is given by the area e f g. Clearly,
the rainimax rule amounts to selecting a p such that the quantity
of the bundle of housing characteristics associated with that p
is expected to result in a b e - e f g. Thus the minimax
pollution dosage to expect is a function of the maximum and the
minimum expected dosages and the costs of obtaining additional
units of the bundle of housing characteristics.
It is interesting to compare the damage implications of the
householder's use of a minimax criterion with the implications
when an expected utility criterion is employed. Assuming for
simplicity that only the first moment of the air pollution density
function is relevant, the expected utility criterion leads to a
-------
-31-
with information p-f, p- uses the minimax criterion but with
additional information might switch to the expected utility
criterion. Now assume that if he had this additional information,
the mean of the probability distribution of future dosages would
prove to be j>, the midrange of the interval/p+, p-J Thus
E(U) = E [E(p)l = f(p) with the additional information. Given
these assumptions, it is easily seen with the aid of the diagrams
in Figure 2 that the quantity consumed of the bundle of
characteristics and thus the losses due to any errors in forecasting
pollution dosages are Identical regardless of the decision criterion
employed only when 9c/3 z is linear. Otherwise, the loss will
3 3
differ according to the sign of 3 c/9 z and the magnitude of the
ultimately realized pollution dosage. In other words, the losses
householders suffer due to uncertainty about future air pollution
dosages can be the joint result of their expectations about these
dosages and their decision criteria under conditions of uncertainty.
The Formation of Air Pollution Dosage Expectations. From the
immediately preceding material on decision criteria, it is
apparent that householder damages from air pollution dosages are
by no means independent of the accuracy with which expectations about future
dosages are formed. That is, realized householder damages
-------
u *
-32-
u .
Figure 2. Comparison of Minimax z, z', and Expected Utility z, z,
-------
-33-
householder predictions. Realized damages are but present
representations of positions taken in the past in response to
expected air pollution dosages.
It seems likely that the householder will act as a more or
less passive observer of air pollution events. He can have little
knowledge of future events other than the inferences he can draw
from already realized events, for an active search by him for
information on future events is likely to be far too costly.
This cost could be less if the planned emissions of pollution
perpetrators were not entirely independent of individual
householder decisions. It would also be less if ambient air
standards were imposed with some stringency or if distinct
contingent claims markets in air pollution events were available
for the individual receptor. The scale economies of information
production and risk-spreading characteristics of these markets
could make information about future air pollution events much
less costly to the individual householder. Though contingent
claims markets do in fact exist for durable assets affected by
air pollution, e.g., life, medical, and property insurance, the
householder must still make the costly .effort to distinguish
between air pollution risk's contribution to premiums and the
contribution of other risks. Thus in spite of the losses
-------
-34-
dosages when purchasing a residential property (moving or
selling is costly, particularly if done a year or two after
purchase), the seemingly even higher costs of most alternative
informational sources on future air pollution events make
predictions based almost entirely on realized dosages economically
viable. It is therefore a reasonable approximation to assume,
as this study shall, that the major and perhaps the only argument
in the householder expectation generating function is some history
of realized air pollustion dosages.
With one unsuccessful exception [3, pp. 141-151 1, previous
studies of the covariation between air pollution and urban
residential real estate values have been strictly cross-sectional.
That is, observations have been assumed to be drawn from time periods
having similar initial and terminal dates and in which the
effects of time's passage are presumed to be neutral. A dynamic
stability has been assumed in which according to Samuelson
[9, p.26lj ". . .from any initial conditions all the variables
approach their equilibrium values in the limit as time becomes
infinite, i.e.,
0
lim x (t) =• xt
t -*• »
regardless of the initial conditions." This means that the
difference between the ultimately realized or equilibrium value
-------
-35-
for a sufficiently long interval of time, t, and that this
difference tends to zero as it becomes large. The present essay
is also strictly cross-sectional. However, in previous studies,
large has come to mean an annual average of air pollution dosages
for whatever single twelve or eighteen month period for which
the investigators happened to possess air pollution observations.
The expectations about air pollution dosages, on the basis of
which economic adjustments to the presence of air pollution are
made, are presumed to be formed solely within the single year
for which information on dosages is available. In some studies
the result has been that the expectations implicit in property
values are assumed to have been formed on the basis of air
pollution not occurring until anywhere from four to seven years
later! In addition to the possibility of introducing some
statistical biases, this assumes what would seem an inordinate
amount of prescience in the residential property market.
As earlier noted, a more appealing hypothesis is that
expectations about future air pollution dosages adapt to changes
in present air pollution dosages only after some lag in time; so
that if such a change has any permanent effect at all, the
effect is not registered all at once over a fairly short interval
of time but it instead distributed over several time periods.
-------
-36-
only of air pollution dosages,
(26) cik = a± + bE/ J m k pltdt + uik (i - l,...,n)
where a and b are coefficients to be estimated, c is the
m
property's current market value, E/t»k p-ttdt is the expectation
of the stream of air pollution dosages at the ith property at the
end of the current period k, and u is an error term. All variables
are expressed in logarithms throughout. In order to make (26)
tractable in terms of the standard analysis of distributed lags,
we assume
(27) plt = f (E/ t-k pltdt)
*
where p^t is an observable scalar quantity of air pollution
dosages. Expected values of this scalar quantity of air pollution
dosages can be related to observable values by specifying an
expectation generating function such as
(28) E(p*t +1) - ECpJt) = x[Pit - E (Pit -1 >]
or
(28a) E(plt +1) - xptt + (1 - A ) E(pit _x )
This states that air pollution dosage expectations are revised
in proportion to the error associated with previous levels of
12
expectations.
If (28a) is linear in logarithms, A. can be interpreted as an
elasticity coefficient showing the responsiveness of current
-------
dosages and the dosages expected in the previous period for the
current period. In the case where the coefficient is unity, air
pollution damages as registered in the offer prices for bundles '
of housing characteristics are simply a function of current dosages.
That is, if dosages were previously expected to remain constant, '
implying that property values were at long-run equilibrium levels,
they are now expected to remain constant, at the level of current
dosages. A new long-run equilibrium in the property market is
therefore established. In contrast, an elasticity coefficient j
of zero implies that changes in current dosages have no effect
upon the property market's existing long-run equilibrium. Changes
in current dosages have no effect upon future dosages.
The expression (28a) can be solved for expected dosages as
a function of m (m 0) past values of realized dosages.
* * * 2 *
(29) E(pit + i) - At pit + (1 - \±) Pit - 1 + (1 - V Pit - 2
i m *
+ ... + (1 . A£) Pit - m
which reduces to
(30) . E( Pit + i) - Ai * (1 - Ai)t plt _ m.
t - k
This is simply a moving average with geometrically declining
weights on past values of p*. Muth [ill has demonstrated that
(30) minimizes the mean square error in forecasts of dosages if
-------
-38-
realizsd dosages are first-order moving averages of random
deviates . Even when the changes caused by the process are not
a first-order moving average of random deviates so that mean
square error of forecasts is not minimized, Cox [12] shows that
(30) may still be a highly efficient predictor of realized
dosages.
Making the obvious substitution of (30) into (26), the
cumulative effect upon property values of a change in realized
dosages under our assumptions is
(31) cik = ai + b At * (1 . Xj* p*t . m + uik
t=k
if and only if 0 <. X± <_ 1.
The Empirical Background
General Nature of the Data. The city from which the data
used in this study come is Chicago, Illinois, a city which,
according to Babcock [31] , possesses the distinction of having
the dirtiest air of any large city in the United States.
Histories of monthly ambient air concentrations of suspended
particulates and sulfur dioxide at twenty or fewer sampling
stations were provided by the Chicago Air Pollution Control
District for each month from January, 1964, through December,
1967. A history of average annual dustfalls was obtained for each
-------
-39-
sampling stations ig given by the circled capital letters on the
i
city map of Figure 3.
The air pollution data were combined with.data on 1288
individual single family residential property transactions
whose mortgages had been insured by the Federal Housing
Administration over the January, 1964 - December, 1967 interval.
A rough idea of the approximate locations of these transactions
is given by the dotted lines of Figure 3. The small arrows
found occassionally on these lines indicate the direction from
the line in which the transactions are to be found. A clear
majority of the transactions are on the city's south side.
Excluding transformations, 297 distinct bits of information
on the air pollution history and the transaction, buyer,
improvement, site, and neighborhood characteristics were collected
for each individual transaction. In the original FHA records,
the individual transactions were grouped only by the time of
their entry into these records. Assuming a more or less constant
lag between time of sale and entry into the records, the
observations were thus originally grouped by a sequence of dates.
From this population, an initial sampling selected every third
entry. In a subsequent sampling every fifth remaining record was
taken. The FHA records ultimately used for this analysis thus
-------
-Uo-
Figure 3. Locations of
Air Pollution
Monitoring
Stations and
Property
-------
-41-
insured by the FHA in the City of Chicago from 1964 through 1967.
The completely disaggregated and highly detailed nature of this data
allows one to ascertain whether the several possible sources of
statistical bias present in previous studies might indeed be
actual.
The Air Pollution Data. Perhaps the major advantage offered
by the detailed nature of the data is the relative (relative to
that of previous studies) fineness with which air pollution
dosages at each residential location could be determined. For
example, the air pollution data employed in Anderson and Crocker
[ l] were taken from rather crude isopleth maps of the cities
t
studied and transferred by hand to census tract maps. The
isopleths distinguished only between four or five broad intervals
of air pollution dosages and the uppermost interval was unbounded
in the real numbers. Thus the lower bound of each interval had to
be employed as the scalar quantity of air pollution dosages. An
interval's lower bound was assigned to a census tract by "eyeballing"
the overlay of the isopleth map upon the tract map in order to
ascertain whether more than half the tract was located inside or
outside a particular interval's isopleth.
In the present study, the raw data from each of the Chicago
Air Pollution Control District's twenty sampling stations
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-42-
per billion by volume per day and suspended particulates in
micrograms per cubic meter per day. According to Stanley
[37, p. 7 ] , these means were constructed from daily arithmetic
means of three day sampling periods at each of the twenty
sampling stations. Dustfall measures were provided in terms of
annual arithmetic means of the basic sampling unit, monthly tons
11
per square mile.'' Table 1 presents the annual arithmetic means
from 1964 through 1967 for sulfur dioxide and suspended
particulates at each of the twenty sampling stations. It should
be noted that the records are not complete on a month by month
basis for each and every sampling station. Dustfall is
disregarded in Table 1, as it will be henceforth, since in the
empirical analysis its presence did not yield any estimates
amenable to economic interpretation or statistical inference.
Employing the above data, and assuming equal variances in the
monthly air pollution distribution from one year to another at
each of the twenty sampling stations, the hypothesis was tested
by means of the "t-test"that the distributions for every year
at any given sampling station were drawn from the same
population. In addition, an "F-test" was applied to each set of
distributions at each station to test that assumption of equal
variances among distributions required for the validity of the
-------
-43-
Table 1. Annual AriChmeCic Mean Pollutant Dosages by Station and Year
Station Sulfur Diox
A
B
C
D
F
C
H
I
J
K
L
M
N
0
P
Q
R
T
W
V
1964
SO3
80
503
80
a
170
70
iooa
60
40
50
120
203
a
20
a
40
a
40
a
40
20
1303
203
1965
31
79
36
76
102
65
78
b
53
43
46
92
25
32
20
20
33
21
71
38
.de* ;Sus
1966
34
66
28
55
73
64
83
c
52
42
50
90
44
54
33
39
38
37
71
57
1967
26
53
26
23
82
56d
71e
f
35
40
68
42
45
25
24
28
24
59
44
196.4
94
134
101
186
178
163
139
157
146
125
173
114
119
132
124
138
123
124
1348
142g
ended Particulates**
1965
98
128
100
166
173
155
135
146
132
127
164
112
117
125
118
147
130
118
130
147
1966
100
132
111
175
174
165
143
176
147
136
177
125
127
145
131
156
135
144
138
162
1967
82
117
93
167
172
142
132
f
132
118
147
113
115
133
117
142
128
125
120
139
Source: Chicago Air Pollution Control District
*In parts per billion by volume per twenty-four hours.
**In micrograras per cubic meter per twenty-four hours.
a)Does not include January 1 through September 30.
b)Does not include November 1 through November 30.
c)Does not include October 1 through December 31.
d)Does not include February 1 through March 31.
e)Does not include June 1 through July 31.
f)No data available.
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-44-
stations having complete monthly records for at least two calendar
years in the 1964-67 period. Table 2 below shows by pairs of
I
calendar years for those stations having complete monthly records
the number of stations whose means and variances exhibited
statistically significant differences at the .05 levels of the
two-tailed t-test and the F-test. The column labeled n
indicates the number of complete record stations, t indicates the
number of complete record stations not having equal means by the
t-tcst, F is the number of complete record stations not having
equal variances by the F-test, and t & !F is the number of complete
record stations appearing in t and F simultaneously. From Table 2
it would appear that only 1966 and 1967 exhibit statistically
significant differences in dosages of suspended particulates at a
substantial number of stations. However, except for 1964 and
1965, a fair number of stations have significant differences in
sulfur dioxide dosages for each possible pair of years. Given that
suspended particulates and sulfur dioxide have widely recognized
synergic properties, the results in Table 2 provide fairly strong
grounds for asserting that air pollution dosages did display
substantial variation from year to year during the 1964-67 time
interval. A causal inspection of the spatial distribution of
-------
-45-
air pollution sampling stations gave no cause to assert that the
air pollution dosages at the residential locations behaved any
differently than those at the station locations.
Table 2. Stations Having Differences in Animal Air Pollution Distributions
Years
Sulfur Dioxide
Suspended Particulates
1964/65
1964/66
1964/67
1965/66
1965/67
1966/67
n
7
7
6
18
15
15
t
<—>••••••
1
4
3
9
5
6
. F .
0
1
1
2
2
1
t&F
«••*«•••••
0
1
1
1
0
0
n
18
17
17
19
19
19
t
0
0
2
3
1
11
F
2
0
2
0
0
0
t&F
0
0
0
0
0
0
The data on month by month suspended particulate and sulfur
dioxide dosages at each sampling station were used to calculate
similar dosages at each sample residential location. The
calculations finally employed in the empirical analysis of air
pollution damages were made separately for each of the two
pollutants according to the following expression:
1*
E
2
i=l
Di
Pi
i=l Di
4
I
4
Z
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-46-
where p is the calculated arithmetic mean monthly dosage of
suspended particulates or sulfur dioxide at a. specific sample
residential location, D. is the distance from the location to the
ith air pollution sampling station, and p^ is the pollution
dosage registered at the ith sampling station. Stations used for
this calculation were selected so as to enclose the residential
location in question. No more than four stations were ever used
for this purpo.se. The calculated residential location dosage, p,
therefore amounts to a weighted index of suspended particulates
or sulfur dioxide, with the weight consisting solely of straight
line distances from the residential location to each of no less
than three and no more than four sampling stations. No attempt
was made to account for variations in meteorology, topography, or
other factors which could contribute to differences in pollution
14
dosages between sampling stations and residential locations.
The nature of the measurement error, if any, introduced by
failing to account for these factors is unknown.
Simultaneity of Air Pollution and Transactions Data. The
relative crudeness of the air pollution measures employed in
previous studies has not been limited solely to the use of broad
dosage intervals. As was earlier noted, this relative crudity
has extended to attempts to explain differential property values
-------
-47-
number of years. In Anderson and Crocker til, it is shown under
fairly weak conditions that such discrepancies can cause the
negative influence of air pollution dosages to be understated. ;
Clearly, there is no reason to think that the air pollution
dosages to which householders in year t are responding necessarily
correspond to the dosages prevailing in t + m (m > 0). There
is no reason to think that the householders at a given location
were the same in the two sets of years, nor is there any reason
why the air pollution dosages must be the same. If the marginal
air pollution damage function is not constant over increasing
dosages or if locations are assigned among householders on the
basis of relative air pollution sensitivities, any change in
absolute or relative dosage magnitudes from t to t + m gives
cause for a good deal of scepticism about the meaningfulness of
estimates. The data available to the present study allow me to
ascertain whether such scepticism is justified, since disaggregated
property value data for any one of four years can be combined with
air pollution data for any one of four years.
Aggregation Bias. The possibility of measurement error has
been present in the transactions data used in previous studies as
well as in the air pollution data. With the sole exception of
Ridker's inconclusive study [3, pp. 141-151 J, previous studies
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-48-
property values have exclusively employed census tracts as the
fundamental unit of observation. Tract boundaries usually contain
within them at least several hundred housing units. These areas,
according to the compilers of the census [32, p.l ], are supposed
to be relatively uniform with respect to population characteristics,
economic status, and living conditions, so that measures of central
tendency for the individual tracts presumably characterize closely
all units in the tract. In the empirical analysis, group averages
of residential unit values are customarily regressed upon group
averages of the residents*, residential units', and tract's characteristics,
The aggregation thus precedes analysis and the researcher therefore
has had no basis upon which to evaluate the tolerability of any
bias which the aggregation may introduce. Of necessity, it has
been assumed that a knowledge of the aggregate relation (the
function relating the aggregates) leads to the same value of the
dependent variable (offer price) as does a knowledge of the
disaggregated relation.
Aggregation bias can arise because the assumption of
considerable homogeneity among the residents and residential
locations within a single census tract may in fact not be
fulfilled, and because the air pollution dosages to which each
residential location is subjected may not be linearly related to
-------
-49-
Assumc the disaggregated offer function for bundles of housing
t
t
characteristics is given by |
(1) cij = ai + bipij + uij i = l>-">n
j = 1 » • • • »r
n r
where i refers to residential location, j to census tracts, a and
b are coefficients to be estimated, and u is an error term having
the customary properties. For simplicity, we assume that air
pollution, p, is the only argument of offer price, c, which differs
across residential locations.
Average tract offer prices and pollution dosages are clearly
n n
(2) I Ci, *
C4. _i=! _ - _ ' and P,- _i=!
J n J n
Under aggregation, the intercept and the error term are
n n
(3) I a ^
u
n n
The aggregate relation is therefore
(4) C. = a + bP. + u
where b, the coefficient of P.,, is apparently
I b<
(5) b „ 1-1 £ .
n
In other words, the average offer price depends on the pollution
dosages suffered by the tract's n residential locations. This
-------
-50-
linear and Includes an error term whose expected value is zero
for all Cjj. Disregarding a and u * , note, however, that both
b and P are aggregated. Thus
^ n n n
(6) E b . l . P. I
bP .
l . Pl.
j-i J
j n n n
Therefore
(7) z b
-------
-51-
whose sensitivity is less than a census tract's average. In this
latter case, however, the coefficient in (4) would be biased
toward zero. The conclusion is the rather dismaying one that the
measure of air pollution dosages in those studies employing the i
census tract as the fundamental unit of observation has differed
from one census tract to another. There could conceivably have
been as many unique measures employed as there are census tracts.
i
The simultaneous availability to this study of disaggregated |
FHA data and census tract data for the City of Chicago enable one
to ascertain the importance in Chicago of this bias.
Use of Actual Market Sales Prices. A perhaps somewhat more
mundane advantage of the disaggregated FHA data available to this
study is the presence of the actual market prices at which
transactions were concluded. Except for rental properties, the
offer prices set forth in the census volumes are defined as
owners' estimates of what their properties would sell for if
offered for sale at the tine of the census. The errors in these
estimates could be large, though it is generally agreed the errors
are random and on the average tend to be offsetting. It is
therefore thought that the traditional errors-in-variables
specification yields reliable estimates, particularly when some
prior aggregation occurs on the basis of census tracts. Nevertheless,
-------
-52-
solitary 1954 article by Klsh and Lansing [33] which showed that
owners' estimates of offer prices in the 1950 census exhibited
random variation around the "true" assessed values. Though the
data employed in the present study can neither confirm nor deny
this finding, they do provide the opportunity to avoid such
errors as may be present in the census responses.
Possibilities in the Use of Assessed Property Values. In
spite of the extent to which previous studies have depended on it,
census data is, of course,not the only readily available
information on the offer prices for and the components of various
bundles of housing characteristics. In particular, a vast
storehouse of information of this sort is readily available in
the property tax assessment records of nearly every municipality
in the country. Its usefulness for the problem being studied
here hinges largely upon the linearity of the relation between
the weights assessed valuations assign air pollution dosages and
the weights actual market valuations assign them. If there is a
linear relation between these weights, then assessment records
could validly by employed for determining air pollution damages
to residential properties. The presence in the FHA data of annual
property taxes as well as actual market prices for each residential
property observation permits a test of this hypothesis for the
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-53-
value for each observation permits a similar test between this
assessed value and actual market price. In this last case, if no
significant differences are apparent, one could conceivably use
some combination of FHA assessed values and tax assessment
records to estimate air pollution damages to residential properties.
Miscellaneous Advantages of the FHA Data. Finally, the
extremely detailed nature of the disaggregated FHA data introduces
a further but rather disconnected set of advantages. First, the
availability of data on residential property maintenance costs
provides a basis for comparisons with the results obtained in
Booz, Allen and Hamilton, Inc. [34] , Michelson and Tourin [35 ],
and similar studies. Second, previous atudies because of data
limitations have had to employ rather crude measures of several
variables which can be expected to determine offer price. For
example, median number of rooms has been used as a measure of
available housing space, number of housing units per acre as a
measure of lot size, and the number of housing units older than
some arbitrarily specified age as a measure of the age of site
improvements. It can be shown, e.g., Goldberger [36, pp. 284-286 ],
that unless the proxies are contemporaneously uncorrelated with
the disturbances but correlated with the true regressors, the
use of a proxy can introduce an asymptotic bias into estimates.
Except for permanent resident income, the great detail in which
-------
-54-
USP of any proxies. Finally, the available detail and number
of observations allows the partition of the sample on the basis
of factors which might reflect differential responses to air
pollution dosages. Thus one might expect and therefore test for
differential responses to similar air pollution dosages by
resident income, age of improvements, and neighborhood characteristics,
for example.
The Variables
As earlier noted, information was collected on an extremely
wide variety of factors which are measures of and influences upon
offer prices for bundles of housing characteristics. Presented
below are exact definitions of those measures of offer prices and
those explanatory variables which appear in the ordinary least
squares regressions reported in the next section. Inclusion of
variables for which information was available but which are not
defined below did not ever change appreciably any of the next
section's results. Furthermore, the coefficients for those
variables not defined here were almost uniformly nonsignificant.^
Dependent Variables. Seven dependent variables are to be
used in this study. Unless otherwise noted, all are defined in
accordance with standard FHA definitions .
COSTS is the sale price of the residential property plus
-------
-55-
are borne by the purchaser. It is equivalent to the mortgage
amount plus the mortgagor's actual cash outlay. The inclusion
of these incidental costs is entirely consistent with our view
of goods as generating housing characteristics. For example, the
improvement in tenure security to which a costly title search
contributes can be a valued characteristic of the residential
property.
PSITE is the FHA-estimated market price of the site.
Neighborhood characteristics, street improvements, utilities,
rough grading, terracing walls, and retaining walls are all
included as part of the site.
FHAVL is the "FHA-estimated price that typical buyers would
be warranted in paying for the (whole) property for long-term
use or investment."
MAINT is the "FHA-estimated average yearly cost of
maintaining the physical elements of the property to prevent
acceleration of deterioration, and to assure safe and comfortable
living conditions."
TAXES includes annual property taxes and any continuing
nonrepayable special assessments, as estimated by the FHA. These
taxes are thus the result of Chicago's assessment ratio and the
property tax rate per thousand dollars of assessed valuation. In
-------
-56-
median assessment ratio (gross assessed value as a percentage of
market value) was 35.80 percent and its median nominal property
tax rate (annual tax billed as a percentage of taxable assessed
value) was 5.43 percent.
MVAL6, as defined by the Census Bureau [32, p. 7 ], is the
median of the owners' estimates on each census tract of what
their properties would sell for if offered for sale in April,
1960.
MVL66, according to De Vise [44, pp. 151-152 ], is the
"average value of homes'* in 1966 in each "community area" of
Chicago. A community area is a collection of several census
tracts. No indication of how MVL66 was established could be
discovered. A reasonable but vague guess would be that it is
some simple extrapolation of 1960 census figures combined with a
more or less intuitive knowledge of community area trends between
1960 and 1966.
explanatory Variables. The list of explanatory variables
used at one point or another in the next section is long. An
effort to justify in detail the use of each of these variables
could require several separate essays. The justification for the
use of each variable is therefore limited to a very short
explanation of the sign one can expect for its coefficient and,
-------
-57-
can be expected to vary with variations in dependent variables.
A few references where more thorough explanations of the
variables' behavior can be found are offered. Unless otherwise v
noted, all variables are defined in accordance with standard
FHA definitions. Statements about the sign:? coefficients can be
expected to assume refer to offer price as a dependent variable.
When other dependent variables are relevant, explicit note will '<
I
be taken. In order to facilitate reference, the explanations
are presented in the alphabetical order of the acronyms assigned
the variables.
ALMNM is a dummy variable having a value of one if the major
living unit upon the residential property has aluminum siding and
zero otherwise. This variable was employed only to explain the
variation in maintenance costs. If advertisements of the
aluminum industry are to be believed, aluminum's properties are
such that maintenance costs are less relative to alternative
types of siding.
BLK66 is the percentage of total population that was black
in a community area as of April, 1966. This variable, the data
source for which is De Vise [44, pp. 145-146] , was used to
partition the disaggregated FHA data and as an explanatory
variable when MVL66 was employed as a dependent variable. As is
-------
-58-
variable Is not at all clear; nor is the meaning of the coefficient
itself. Under some assumptions, a positive sign attached to a
statistically significant coefficient can be taken as evidence
of housing discrimination.
BRICK is a dummy variable having a value of one if a brick
frame it employed to support the floors and roof of the major
improvement upon a residential location and zero if not. This
variable was used only when maintenance costs were the dependent
variable. Since factory fabricated frames are the type of frame
for which no variable is provided, it is probably the case that
BRICK will take on a negative sign where MAINT is the dependent
variable.
CRIMX is an index of the rate of commitment to prison of
male community area residents from 1963 through 1966. The index,
which was taken from Shaw and McKay [52, p. 355],is the four year
rate in the community area divided by the mean four year rate for
the Chicago metropolitan area. If the probability of criminal
attacks against one's person or property increases with the
absolute number of criminal offenders inhabiting one's
neighborhood, then the coefficient for this variable must take on
a negative sign. Or, even if criminal offenders carry out their
activities beyond the neighborhood, they may have life styles
-------
-59-
DILP6 is the proportion of all residential units in a
census tract classed as dilapidated in 1960. This variable, as
was noted in Anderson and Crocker flK is a composite
of a neighborhood's physical appearance and the attitudes of its
inhabitants about that appearance. Its influence upon offer price
is clearly negative.
OISSM is the distance in tenths of miles to the intersection
of State and Madison Streets in the Loop area of downtown Chicago.
Given that the disamenities of residential locations near the
center of the city don't outweigh the savings in travel and
communication costs, the coefficient for the variable must be
negative.
DLAKE represents the distance in tenths of miles of the
residential location from Lake Michigan. Since this lake is
widely acknowledged to be one of Chicago's prime esthetic and
climatic amenities, the coefficient for this variable will be
negative.
DTTYP is a dummy variable having a value of one if the major
living unit was completely detached from any other living unit
and zero otherwise. The sign for the coefficient for this
variable is expected to be positive, given that a nondetached ,
structure offers less privacy and requires agreement with
-------
-60-
characteristics can be undertaken.
FRAME is a dummy variable having a value of one if a wooden
frame is employed to support the floors and the roof and zero if
not. Given that wooden frames typically cost more to maintain
and have shorter expected lives than most other frames, the
coefficient for this variable is expected to be negative in sign.
USAGE is the age in calendar years of the major living unit
at the residential location. It was calculated as the difference
between the year of sale and the year in which the major living
unit was built. Because of depreciation and obsolescence, the
coefficient for this variable is expected to be negative. It is
generally acknowledged by most writers on housing, e.g., Grigsby
[45] , that rates of depreciation and obsolescence tend to decline
with age.
INCM6 is the median family income on'a census tract in April,
1960. Given that bundles of housing characteristics are not
inferior goods, the sign of the coefficient for this variable
must be positive. Since each observation of this variable is a
measure of central tendency, it is probably a fair measure of
permanent income.
INC66 is the "average income" in April, 1966, in each
residential location's community area. Since a community area
-------
-61-
made up of a broad and heterogeneous collection of occupational
groups who, when considered together, have transitory incomes
averaging out to zero. This measure of income, given that it <_
does not contain other sources of measurement error, should thus
be better than INCM6 as a measure of permanent income.
INDUT is the hundredths of square miles devoted to industrial
uses within the square mile whose center is the residential
location. Data for this variable was obtained from maps published
in the several volumes by the Chicago Department of Development
and Planning [54] . The variable is intended to account for the
presumed disamenities of noise, unsightliness, etc., of residing
adjacent to or within an industrial area. Dirt disamenities are
registered in the air pollution variable. If expectations of a
shift of residential uses to industrial uses are not predominant,
this variable has a depressing effect upon offer price. Partitioning
the sample by this variable permits the consideration of the
effects of air pollution in areas where the confounding influences
of industrial disamenities other than air pollution are minor.
LIVAR is "the total square foot area of a house appropriately
improved for the intended use and in compliance with the minimum
property standards for new homes and with generally accepted ;
criteria for existing homes. It includes family rooms, improved
recreation and attic rooms, cantilevered overhang of rooms and
-------
-62-
spacc permits a greater variety of activities and houses a
greater number of people. The sign of the variable's coefficient
can therefore be expected to be positive.
LOTSZ is simply the number of square feet in the lot. Since
greater lot size permits a greater variety of positively valued
activities to be undertaken, the covariation between offer price
and lot size should be positive. Alonso [ 28] and Muth [ 27 ]
devote substantial energies to the explanation of the theoretical
significance of this variable in markets for bundles of housing
characteristics. No information was available for this variable
in the 1964 disaggregated FHA d.ita.
MASON is another dummy variable. This variable has a value
of one if the frame of the major improvement at the residential
location is masonry and zero if not. Its proper sign where
factory fabricated frames are excluded has not been investigated
by the writer.
MODUR is the term of the mortgage in years. All mortgages in
this study appeared to be of the straight term type such that the
mortgagor pays a fixed sum toward principal and interest each
month. The cost per dollar of the mortgage to the mortgagor is
viewed as the discounted value of his future interest payments
less the discounted expected value of the asset he possesses
-------
-63-
if the mortgagor's subjective rate of interest is greater than
the mortgage rate of interest will the mortgage actually be
taken out. Thus, either an increase in the mortgage term or a
decrease in the mortgage rate of interest would reduce the costs
of purchasing bundles of housing characteristics relative to the
costs of purchasing alternative characteristics bundles. The
i
quantities demanded of and offer prices for housing bundles
would therefore increase. In the present study, market interest
rates were almost completely invariant for the sample within any
one year and, for that matter, did not change greatly over the
four year period being considered. Accordingly, only mortgage
duration, whose sign is expected to be positive, is employed as
an explanatory variable.
At this point, two peculiarities of FHA-insured mortgage
loans relative to conventional mortgage loans should be recognized,
First, the FHA requires that issuers of FHA-insured notes receive
cash payments equal to the full face value of the note. That is,
the cash payment cannot register any discount or premium which
may be attached to a note when the note specifies a rate of
interest below or above the prevailing market rate of interest.
If, for example, a discount is in order, the mortgagor absorbs it
because the seller inflates the price of the house by an amount
-------
-64-
the note. Therefore to the extent that interest rates on FHA
loans in Chicago from 1964 through 1967 were less than those on
conventional loans, the observed price of a given bundle of
housing characteristics in this study's data would be greater
than the observed price of a similar housing bundle financed by
a conventional loan. A cursory survey of prevailing rates during
the period makes it appear that FHA rates after 1965 were about
one-half of one percent less than those for conventional loans.
Thus, for a given bundle of housing characteristics, the absolute
magnitudes of marginal changes in the original values of the
explanatory variables in this study's results are somewhat
greater than would be the case if the house purchase was financed
by a conventional loan. In particular, the absolute magnitudes
of the marginal damages are somewhat greater.
The above tendency is reenforced by the fact that FHA-insured
loans typically have only a small or nonexistent prepayment
penalty', whereas conventional loans often have penalties amounting
to as much as six months' interest. One would expect the positive
value of the lack of an FHA prepayment penalty to be capitalized
into the sale price of the property. However, it must be
emphasized that neither this peculiarity nor that pointed out in
the previous paragraph introduce a statistical bias to our
-------
-65-
property sold on FHA terms, but some slight downward revision
must be made in the absolute magnitudes of the marginal damage
estimates obtained from the disaggregated FHA data if inferences
are to be made about properties sold on conventional terms.
NHAGE is the average age of the residential properties in
the 160 acre quarter section in which the residence is located.
Values for this variable were calculated from Olcutt & Co. [53] |
where typical ages in each quarter section are presented. In
cases where more than one typical age was presented, the weight
each ago. received was the inverse of the number of "typical" ages.
Given that bundles of housing characteristics generally provide
less utility as they age, the demand for these bundles tends to
decline. Price thus decreases and by the filtering process the
bundles are thought to become available to households having
relatively low incomes. This variable for the disaggregated
FHA data is therefore a representation of the same phenomena as
DILP6 is for the census data.
NWPP6 is the percentage of total population that was
non-white in census tract as of April, 1960. As was explained
for BLK66, the meaning of the coefficients obtained for this
variable is not clear.
OLDER is the percentage of residential units in a census
-------
-66-
as a measure of Che same phenomenon as HSAGE is in the disaggregated
FHA data.
PMM refers to the minimum arithmetic mean monthly dosage
during a given year of suspended particulates in micrograms per
cubic meter per twenty-four hours. As is the case for all the
air pollution variables, the two digits following the acronym
refer to the year in which the air pollution dosages occurred.
Thus, PMM64 is the minimum arithmetic monthly mean dosage of
suspended particulates in 1964.
PMX is the maximum arithmetic mean monthly dosage during a
given year of suspended particulates.
PRT is the annual arithmetic mean monthly dosage of suspended
particulates during a given year.
PSK is the third statistical moment or skewness of the
distribution of arithmetic mean monthly suspended particulate
dosages during a given year divided by the annual arithmetic mean.
PVR is the second statistical moment or variance of the
distribution of arithmetic mean monthly suspended particulate
dosages during a given year divided by the annual arithmetic mean.
SMM is the minimum arithmetic mean monthly dosage during a
given year of sulfur dioxide in milligrams per one hundred square
centimeters per twenty-four hours.
-------
-67-
dioxide during a given year.
SQIDX is an index of public elementary school quality in
the residence's school district. The scale of the index has s
four factors with the digit 1 representing the highest quality
and 4 the lowest. The source of the index and the explanation
of its construction is to be found in Havighurst [55, p. 146 ].
Generally speaking, the index is a composite of student performance,
i
teacher quality, funding, and similar factors. If householders
do attach positive utility to "good" schools, this variable's
coefficients will assume negative signs.
STORY is the number of full stories in the major improvement
at the residential location. This variable was employed only
when MAINT was the dependent variable. Its influence upon
MAINT is undefined, and it was included in the MAINT regressions
only because it proved to have a statistically significant
coefficient.
SSK is the third statistical moment or skewness of the
distribution of arithmetic mean monthly sulfur dioxide dosages
during a given year divided by the annual arithmetic mean dosage.
SVR is the second statistical moment or variance or the
distribution or arithmetic mean sulfur dioxide dosages during a
given year divided by the annual arithmetic mean.
-------
-68-
k'. d i ring a given year.
TCINC, defined as the current monthly family income of the
residential property's owners, is the income variable always
employed in the empirical analysis of the next section. Unfortunately,
it is at best an imperfect proxy for the permanent income measure
properly used as an argument in the offer function for bundles of
housing characteristics. In broad terms, the use of current
rather than permanent income can bias downward and make
inconsistent the estimate of the positive effect upon offer price
of additional income. Fundamentally, a measurement error is
introduced because lagged income variables which would affect
offer price are not included as regressors. If, as seems
reasonable, negative transitory incomes appear more frequently
in groups with low current incomes and if positive transitory
incomes appear more frequently in groups with high current
incomes, then the variance of measured income exceeds that of
permanent income. Cross-sectional least squares estimates of
the responsiveness of offer price to income that are based upon
current income would therefore exhibit a downward bias.
The income elasticity estimates appearing in the next
section are generally slightly greater than .30. This is less
than half the most widely accepted estimate of about .90 found,
-------
-69-
tt nearly duplicates the .35 cross-sectional estimates for measured
income elasticity reported by Reid [46, p. 9] and Malone [48] ,
and approximates that of .41 found by Atkinson [49] . If FHA- \
insured mortgages are more likely to be obtained by better
"credit risks" and if these individuals have lower measured
income elasticities of demand for bundles of housing characteristics
than does the population of residential property buyers, then :
such differences as remain between the current income elasticities
obtained here and elsewhere could be accounted for.
Measures of what the FHA terms "effective income" — the
FHA estimate of the household's earning capacity before
deduction for Federal income taxes that is likely to prevail
during the first third of the mortgage term — are present in the
data. When these measures of what at first appearance looks
like permanent income were substituted for current income as
regressors, an income elasticity of about .20 was obtained. This
is to be expected since without exception the effective income
measures when viewed as measures of permanent income implied
that the transitory component of current income for 1,288
families was negative! None of the income elasticity results
reported here are peculiar to the City of Chicago, for similar
results were obtained with disaggregated FHA data in Chicago's
-------
-70-
Faced with these results, a search was then undertaken to find
an instrumental variable, but no variable could be found which
could reasonably be said to be correlated with permanent incomej
I
independent of the measurement error admittedly present in
TCINC, and orthogonal to other explanatory variables.
In and of itself, the measurement error involved in TCINC is
of no particular relevance to this study. It is of concern only
because such error can also bias the estimates of the effects of
air pollution dosages upon offer price. If, for example, permanent
income and damages are strongly and positively correlated and if
the estimated effect of permanent income is biased downward,
then the air pollution damage estimates will tend to be biased
upward (closer to zero) because least squares procedures will
cause the air pollution coefficients to register some of the
positive impact of permanent income upon offer price. More or
less economic theoretic arguments, e.g., Crocker [50, pp. 238-243] ,
appear at several places in the pollution economics literature
purporting to show that air pollution damages and (permanent)
income are positively related. However, none of the previous
work dealing with the covariation between air pollution dosages
and residential property values perceived any collinearity
between air pollution and permanent income requiring substantial
18
-------
-71-
Furthermore, current and permanent income are quite strongly
and positively correlated. Thus if one income measure is
collinear with air pollution dosages, it is not unreasonable to j
expect the other to be. However, employing the Farrar-Glauber
[5] Lests, no statistically significant collinearity was
apparent between TCINC and the air pollution variables in the
present study. We therefore proceed as if the admitted bias '
present in the estimated income coefficients does not affect the
air pollution coefficients.
The Results
All ordinary least squares regressions reported in this
section are multiplicative. The coefficients of the explanatory
variables are therefore elasticities showing the percentage
change in the dependent variable associated with a one percent
change in the explanatory variable. The assumption is made
throughout that the marginal cost of supplying bundles of housing
I
characteristics is constant. We assume unless otherwise noted
that the householder employs an expected utility decision
criterion.
The wide variety of economic-theoretic and empirical hypotheses
raised in the previous sections makes organization of this section
around a central theme rather difficult. Accordingly, an attempt
-------
-72-
dcal with the estimation problems associated with these
formulations, and only then move on to the less familiar. That
is, the sequence of the presentation of results in this section
does not march along in lock step fashion with the sequence
of the presentation of the economic-theoretic and statistical
hypotheses of earlier sections.
Statistical Attributes of the Data. In order to facilitate
evaluation of the results presented in this section, Table 3
immediately below presents the arithmetic means and standard
deviations (in parentheses) of the original values of all the
variables except the air pollution variables listed in the
previous section. Table 4 presents the same thing for the
various air pollution variables. In both tables, the columns
refer to the year in which the property sale occurred. For
certain of the variables, a column thus provides an idea of
year to year variations in a variable or variables for a given
set of residential locations, while the rows show how a given
variable changes with changes in the set of residential locations.
Table 5 presents simple correlation coefficients for the natural
logarithms of some of the variables playing an important role
-------
-73-
Table 3. Arithmetic Means and Standard Deviations of Original Values of
Nonpollution Variables
Year
Variable
Number of
observations
COSTS
PSITE
FllAVL
MAINT
TAXES
MVAL6
MVL66
ALMNM
BLK66
BRICK
CRIMX
DLAKE
DILP6
DISSM
DTTYP
FRAME
HSAGE
INCM6
INC66
1NDUT
LTVAR
LOTSZ
MASON
MODUR
NHAGE
NWPP6
OLDER
SQIDX
STORY
TCINC
1964
245
15789
3256
15534
9.63
25.84
16490
18379
.03
37.21
.67
.80
42.52
.09
DO. 15
.90
.22
28.27
7622
8821
5.31
1181
NA
.76
287
44.08
12.39
65.47
2.52
1.36
788
(2896)
(1104)
(2771)
(2.34)
(8.23)
(3309)
(3586)
(.18)
(25.48)
(.471
(.73)
(22.23)
(.22)
(20.92)
(.30)
(.41)
(16.43)
(1153)
(1302)
(6.21)
(293)
(.43)
(52)
(13.57)
(19.32)
(51.79)
(.87)
(.51)
(232)
1965
212
16208
3402
16203
9.46
26.11
16528
18139
.02
28.06
.70
.77
45.86
.09
100.20
.95
.43
30.85
7714
9004
4.72
1213
4620
.56
289
46.34
10.86
71.36
2.27
1.36
806
(3276)
(1237)
(3198)
(2.54)
(8.59)
(2718)
(3905)
(.14)
(21.97)
(.46)
(.54)
(18.67)
(.21)
(19.51)
(.21)
(.50)
(13.75)
(1202)
(1107)
(5.69)
(334)
(3142)
(.50)
(44)
(13.43)
(17.26)
(57.45)
(.73)
(.51)
(222)
1966
16495
3310
16446
9.02
26.42
16174
18056
.06
28.78
.71
.83
44.56
.08
98.78
.95
.29
32.40
7697
8892
4.85
1194
4347
.69
293
47.31
10.35
72.83
2.30
1.41
864
345
(3295)
(1031)
(3203)
(2.31)
(8.32)
(3071)
(3531)
(.23)
(21.65)
(.45)
(.58)
(18.82)
(.21)
(19.70)
(.22)
(.46)
(15.80)
(990)
(1190)
(6.50)
(279)
(2871)
(.46)
(46)
(12.95)
(17.04)
(59.85)
(.74)
(.49)
(271)
1967
17154
3272
17038
10.25
25.71
15695
17274
.15
34.24
.60
.90
47.18
.27
100.94
.95
.39
31.56
7112
8496
5.87
1268
4154
.60
292
49.68
20.05
76.77
2.39
1.40
918
386
(3910)
(946)
(3730)
(3.22)
(7.77)
0020)
(4230)
(.35)
(26.09)
(.49)
,(.62)
(16.22)
!(.48)
(20.04)
(.22)
(.49)
(21.34)
(1372)
(1539)
(6.90)
(312)
(1168)
(.49)
(56)
(12.69)
(26.88)
(59.61)
(.71)
'(.50)
(245)
-------
-74-
Table 4. Arithmetic Means and Standard Deviations of Original Values of
Representative Pollution Variables
Year
Variable
PRT64
PRT65
PRT66
SUL64
SUL65
SUL66
PMM64
PMM65
PMM66
SMM64
SMM65
SMM66
PMX64
PMX65
PMX66
SMX64
SMX65
SMV6ft
1964
131.43 (11.38)
32.74 (17.54)
90.67 (6.98)
11.01 (4.61)
155.37 (15.73)
64.89 (36.46)
1965
128.05 (10.51)
32.90 (17.47)
91.20 (7.10)
11.17 (4.58)
156.30 (15.40)
64.10 (35.24)
1966
130.22 (10.75)
125.72 (9.59)
33.89 (19.76)
37.38 (15.06)
92.01 (7.11)
98.99 (8.63)
11.14 (4.60)
16.19 (5.60)
158.30 (16.91)
155.20 (8.35)
66.20 (39.85)
63.84 (24.97)
1967
130.09 (10.24)
126.04 (9.94)
138.54 (10.24)
33.43 (20.22)
37.30 (16.82)
50.70 (11.59)
93.38 (8.14)
98.94 (8.0r>
99.09 (15.21)
11.45 (5.44)
15.83 (7.22)
15.80 (3.36)
157.32 (18.15)
157.79 (12.20)
160.32 (14.57)
63.27 (40.28)
63.98 (28.53)
-------
Table 5. Simple Correlation Coefficients for 1967 Observations.
PSITE
COSTS .578
PSITE
BUC66
DISSM
DLAKE
HSAGE
INC66
iNDirr
LOTSZ
MODUR
TCINC
PRT64
PRT65
PRT66
SUL64
SUL65
SUL66
PVR66
PSK66
SVR66
BLK66 DISSM DLAKE HSAGE INC66
,140 .398 .283 ,561 .357
,130 .328 .080 .234 .111
.010 ,029 .129 ,182
.231 ,515 ,001
.304 .234
.168
'*
JflPJff
.128
.140
.238
.147
*020
.078
.167
LOTSZ
.326
.700
.271
.298
.109
.160
.085
.098
MODUR
.716
.355
.111
.420
.170
.660
.089
.039
.058
TCINC
.513
.297
.122
.014
.059
.234
.221
.128
.256
.240
PRT64
.282
.179
.020
.461
,522
.119
.464
.152
.164
,237
.129
PRT65
.305
.115
.001
.371
.431
.044
.654
.198
,112
.190
.044
.952
PRT66
.314
.128
,003
.296
,284
.038
,636
.091
.114
,190
.163
.960
.967
SUL64
.249
.163
r034
,713
,480
.348
,373
.131
,225
,378
,139
.793
.784
.708
SUL65
.242
-201
.028
.806
.376
.441
.300
.131
.238
,415
,120
.720
.712
.609
.963
SUL66
.369
,262
.163
.792
.530
.511
,126
.112
,226
,426
,142
.604
.542
.457
.811
.913
PVR66
.303
,654
.236
.438
.079
.068
,480
PSK66
.376
.425
,099
,331
,162
.523
.712
,296
SVR66
.329
,430
.099
.383
.070
,435
,968
.348
.663
SSK66
.233
.028
.515
.043
.058
,081
,080
.045
.024
.085
COSTS
PSITE
BLK66
DISSM
DLAKE
HSAGE
INC66
INDUT
LOTSZ
MODUR
TCINC
PRT64
PRT65
PRT66
SUL64
SUL65
SUL66
PVR66
PSK66
SVR66
-------
-76-
Thc Inverse Relation Between Air Pollution Dosages and
Property Values. Table 6 presents the results when, except for
the 1964 observations, the annual arithmetic mean air pollution
dosages of the immediately preceding year are regressed on the
FHA-insured sales taking place during a given year. Thus, for
example, that pollution dosage assumed to influence the offer
price of a bundle of housing characteristics purchased at any
time in 1966 is the annual arithmetic mean dosage of 1965. Only
for 1964 do the calendar year of the dosages and the transactions
coincide. The figures in parentheses are the associated
_2
coefficients' standard errors. R is the portion of unexplained
variance adjusted for degrees of freedom, S is the equation's
standard error, n is the number of observations, and ADAM is the
marginal capitalized damages to the representative residential
property due to air pollution dosages. The latter number is
evaluated at the arithmetic means of the original values of the
dependent variable and the air pollution variables. It thus
represents the marginal capitalized damages for each additional
annual average of ten micrograms per cubic meter per twenty-four
hours of suspended particulates plus an additional annual average
of one part per billion per twenty-four hours of sulfur dioxide.
The sum of Table 6's air pollution coefficients has the
-------
-77-
Table 6. I
Year
Variable
Constant
ln(PRT64)
ln(SUL64)
ln(PRT65)
ln(SUL65)
ln(PRT66)
ln(SUL66)
In(TCTNC)
In(LlVAR)
In(HSABE)
In(MODUR)
In(LOTSZ)
In(SQIDX)
In(NHAGE)
In(DISSM)
In (D LAKE)
FRAME
DTTYP
1T2
S
n
DAM
nitial
Regressions. Dependent variable, In
1967
5.3568
T3537
.0296
.3570
.2634
r0438
.3889
.0483
r0648
rll06
.0471
T0236
r0761
.1383
.7711
.1126
388
$428.18
(.9143)
(.1051)
(.0593)
(.0336)
(.0385)
(.0080)
( .0448)
(.0200)
(.0205)
(.0318)
(.0372)
( .0069)
(.0149)
(.0288)
1966
5.0227
T5025
.1298
.3396
.2694
»0490
.3796
.0744
rO 808
»1361
.0453
T0214
*0955
.1228
.6819
.1155
.345
$601.45
(1.1631)
(.1569)
(.1291)
(.0636)
(.0265)
(.0107)
(.0479)
(.0229)
(.0208)
(.0635)
(.0368)
(.0093)
( .0164)
(.0312)
(COSTS)
1965
4.8396
»2207
T1304
.2732
.1873
»0448
.3350
.0489
,1169
T1252
.0543
.0291
T0818
.1347
.7034
.1133
212
$344.12
(1.0461)
(.1616)
(.0270)
(.0366)
(.0388)
(.0157)
(.0627)
(.0258)
(.0317)
(.0574)
(.0420)
(.0234)
(.0188)
(.0405)
1964
5.4809 (
.4343
.0552
.3393
.2726
r0474
.2029
r0609
»1458
»0150
r0186
r0796
.1432
.6022
.1147
244
$510.79
1.1126)
(.1242)
(.0191)
(.0291)
(.0372)
(.0133)
(.0533)
(.0229)
(.0531)
(.0595)
(.0101)
(.0203)
(.0261)
-------
-78-
glance at Table 5, the two pollution variables are highly
correlated in each year. .Application of the Farrar-Glauber [50]
test to each of the pairs of pollution coefficients in Table 6
always revealed statistically significant multicollinearity.
Further statistical evidence of serious multicollinearity in the
pollution measures is presented in Table 7 below, where each of
the pollution coefficients refers to regressions in which the
other pollution variable was not included. For example,
ln(TRT66)refers to a regression similar to that for 1967 in Table
6 except that In (SUL66) was dropped. Similarly In (SUL66) refers
to a regression in which In (PRT66) is excluded. As is to be
expected, standard errors, s, of the estimates, b, in Table 7
_2
tend to decrease relative to those of Table 6, R decreases
very little, and the signs of the SUL coefficients change from
positive to negative.
Table 7. Initial Regressions with One Pollution Variable.
b
s
K2
1967
ln(PRT66} J.nfSIJL66^
-.5337
.0975
.7683
-.1920
.0472
.7555
1966
-.4163
.1438
.6792
-.2739
.1105
.6781
1965
-.3172
.1249
.7006
lnfsm.641
-.1795
-.0267
.7003
If one has inspected the simple correlation coefficients
of Table 5, it would appear that the existence of multicollinearity
-------
-79-
pollution measures. In particular, the high simple correlation
coefficients between In(DISSM) , In(DLAKE), and the pollution
measures almost guarantee that dropping the former two variables
from the initial regressions will affect the air pollution
estimates. Table 8 shows what happens when this is done. As
expected, the standard errors of the air pollution coefficients
in Table 8 differ from those in Table 6. However, nowhere is ,
the change so drastic as to justify acceptance of the null
hypothesis that air pollution has no statistically significant
19
effect on residential property values. Furthermore, the air
pollution damage elasticities change relatively little so that
the conclusions to be drawn from Table 6 suffer no serious harm.
It is, of course, possible that the regressions of Table 8
are biased and inconsistent because variables which should be
included, In(DISSM) and In(DLAKE), are not included. By
partitioning these two variables, it is perhaps possible to avoid
simultaneously the problem of the improper exclusion of a variable
as well as the problem of multicollinearity. Accordingly, using
1966 sales, Table 9 presents regression coefficients for the air .
pollution variables where In(DISSM) was partitioned on the basis
of whether or not the residential location was more than ten
i
miles from downtown Chicago. In(DlAKE) was partitioned according
-------
-80-
Table 8.
Year
Variable
Constant
ln(PRT64)
ln(8UL64)
ln(PRT65)
ln(SUL65)
ln(PRT66)
ln(SUL66)
In(TCINC)
In(LIVAR)
In(HSAGE)
In(MODUR)
In(LOTSZ)
In(SOIDX)
In(NHAGE)
FRAME
DTTYP
K2
S
n
DAM
Initial Regressions Without
1967
5.4928
.3625
.0828
.3258
.2492
.0469
.4008
.0544
.0640
.1568
.0878
.1112
.7664
.1140
388
$476.86
(.6914)
(.1057)
(.0441)
(.0254)
(.0386)
(.0061)
(.0439)
(.0239)
(.0220)
(.0457)
(.0148)
(.0299)
In(DISSM)
1966
5.7158
.5587
.1489
.3105
.2259
.0475
.3611
.0664
.0750
.1683
.1004
.1348
.6731
.1171
345
$667.30
(.8441)
(.1674)
(.1106)
(.0570)
(.0240)
(.0109)
(.0486)
(.0232)
(.0205)
(.0802)
(.0165)
(.0320)
and In(DLAKE) .
1965
4.5587
.3560
.0306
.2919
.2318
.0426
.3434
.0598
.0716
.1498
.0850
.1406
.6853
.1161
212
$435.54
(.6042)
(.1097)
(.0192)
(.0302)
(.0334)
(.0072)
(.0540)
(.0220)
(.0267)
(.0619)
(.0190)
(.0 97)
-------
-81-
Lake Michigan. The specifications of the equations in Table 9
are identical to those of Tables, 6, 7, and 8. If simple
correlation coefficients can be taken as an indicator of the
i
severity of multicol linearity, those of Table 10 would make it
appear that the regression results of Table 9 are not severely
stricken. This judgment is confirmed when In(DISSM) and In(DLAKE)
Table 9. Regressions for DISSM and DLAKE Partitions. '
Partition
Variable
ln(PRT65)
ln(SUL65)
In(DISSM)
In (DLAKE)
2
R
S
n
DISSM
-.2781
.0816
.0892
-.0388
.6807
.1159
185
(
(
(
(
<100
.0874)
.1147)
.0665)
.0194)
DISSM >.
-.5428
.1752
-.0164
-.0422
.6941
.1147
160
(
(
(
(
100
.1974)
.0810)
.0099)
.0266)
DLAKE <30
-.7247
.1594
.0186
-.0583
.6583
.1342
78
(
(
(
(
.1781)
.0297)
.0197)
.0178)
DLAKE
-.4971
.2117
.0716
-.0042
.7110
.1085
267
>. 30
(.1579)
(.0530)
(.0643)
(.0097)
are dropped from the regressions of Table 9. The exclusion of
these variables has no meaningful effect upon the standard errors
of the air pollution coefficients.
Table 10. Simple Correlation Coefficients for DISSM and D1AKE Partitions
PISSM < 100" DISSM -S100 DLAKE < 30 DLAKE 2. 30
In(DISSM) In(DLAKE) In (DISSM) In (DLAKE) In (DISSM) In (DLAKE) In (DISSM) In (DLAKE)
In(PRT) -.2912 -.5136 -.0331 -.6464 -.3026 -.3290 -.4187 -.2556
In(SUL) -.5481 -.3534 -.4251 -.1313 -.6194 -.0915 -.4813 -.1679
On the basis of the immediately preceding manipulations, we
-------
-82-
and the air pollution variables and between In(DLAKE) and the air
pollution variables does not justify acceptance of the null
hypothesis that air pollution dosages have no impact upon residential
property values. However, simple multicollinearity is not the
only ground on which the initial results of Table 6 might be
attacked. For example, In(NHAGE) is supposed to be a composite
measure registering the effects of neighborhood disaraenities
other than air pollution dosages. Yet it is quite possible that
this variable does not register those disamenities which are
correlated with air pollution dosages. If, for example, air
pollution dosages tend to be higher where a substantial proportion
of the sirrounding land area is devoted to industrial uses and if
4
these uses generate residential disamenities unrelated to air
pollution, then the air pollution results of Table 6 may reflect
the presence of these disamenities. Similarly, if air pollution
dosages tend to be heaviest in areas populated by blacks or by low
income people, and if others attach greater disutility to being
near these groups than the utility the group members obtain being
close to each other, then the air pollution variables would
register the net negative effects upon the polluted area.
In Table 11, tests of these hypothesis are made by partitioning
the sample. The first regression employs all 1966 property sales
-------
-83-
flve porcenl of its area devoted to industrial uses. The last
three regressions employ 1966 and 1967 transactions. Except
perhaps for the regression for 1966 and 1967 transactions in which
BLK66 75, the air pollution coefficients of Table 11 are not at
Table 11. Regressions for INDUT, BLK66, and INC66 Partitions
Partition
Variable
Constant
ln(PRT65)
ln(SUL65)
In(TCINC)
In(LIVAR)
In(HSAGE)
In(MODUR)
In(LOTSZ)
In(SQIDX)
In(NHAGE)
In(DISSM)
In(DLAKE)
FRAME
DTTYP
In(CRlMX)
R
s
n
INDUT
6.9438
-.5174
.1297
.3113
.2177
-.0475
.3673
.0446
-.0792
-.0227
.0689
-.0387
-.1039
.1308
.6265
.1190
227
< 5
(.9718)
(.1810)
(.0385)
( .0344)
(.0455)
(.0155)
(.0651)
(.0288)
(.0243)
(.0295)
(.0571)
(.0199)
(.0218)
(.0386)
BLK66
8.0918
-.7331
.2077
.2835
.2015
-.0521
.3783
.0167
-.0291
.0446
-.0346
-.0736
.1578
-.0456
.7186
.1199
254
< 25
(.9804)
(.1633)
(.0457)
(.0302)
(.0399)
(.0092)
(.0517)
(.0268)
(.0288)
(.0577)
(.0196)
(.0178)
(.0299)
(.0177)
BLK66
6.7449
-.5388
.2434
.1600
.1066
-.0283
.5955
.0301
.0162
.1151
-.1582
-.0440
.0713
-.1954
.7005
.1288
76
>. 75
(2.2473)
( .6278)
( .3618)
( .0724)
( .0799)
( .0227)
( .1371)
( .0899)
( .0899)
( .2105)
( .0984)
( .0492)
( .1054)
( .1770)
BLK66
and
INC66 1
9.5894 (1
-.8263 (
.2781 (
.3537 (
.2401 (
-.0561 (
.3388 (
-.0091 (
-.0063 (
.0520 (
-.0462! (
-.0793 (
.1378 (
-.0459 (
.7082
.1159
194
25
8495
.2727)
.2167)
.0704)
.0357)
.0483)
.0116)
.0632)
.0288)
.0406)
.0501)
.0269)
.0218)
.0320)
.0225)
all inconsistent with those of previous tables. The results for
BLK ,1 75 can easily be due to the relatively small degrees of
freedom and the fact that within this partition the standard
deviation of ln(PRT65) was only one percent of its mean while the
standard deviation ln(SUL65) was only six percent of its mean.
-------
-84-
l'ropi!rL> Data. MulCicollinearity and the improper exclusion of
variables have not greatly bothered previous studies of this sort.
Instead, as was earlier noted, concern has been exhibited about
measurement error caused by discrepancy between the years of
observed property transactions and observed air pollution dosages.
Table 12 below compares the results for 1967 property transactions
when the years to which the air pollution dosages differ. The
individual regresssions therefore differ only in the year to
which the air pollution dosages refer. The specifications of
Table 12 as did three of the four regressions of Table 11 differ
slightly from those of Table 6 in that In(CRIMX) was included as
an explanatory variable while In(NHAGE) was excluded. These two
variables, having a simple correlation coefficient of .68 for 1967
transactions, are collinear. The inclusion of both in the same
equation has a substantial impact upon their standard errors.
Table 12. Regressions Exhibiting Discrepencies in Air Pollution and
I'rrjner tV S ll f T)af"J*
onstant
In(PRT)
In(SUL)
IT
S
ADAM
!"• ' ' * linn.
1966
4.1532 (1.0984)
-.3998 ( .1509)
.0601 ( .0501)
.7763
.1116
$474.96
1965
4.1426 (1.1272)
-.4258 ( .1223)
.1223 ( .0345)
.7815
.1103
$601.45
1964
4.1837 (.9626)
-.4557 (.1407)
.0808 (.0226)
.7836
.1098
$541.93
Employing a method proposed by Tiao and Goldberger [56] , an
-------
-85-
oqualIty among years in the air pollution coefficients of Table 12.
Table 13 presents the results of this test, where the columns
refer to the combination of years for the air pollution dosages,
F is the value of the F-test, and Z(T-K) is the sum of the
transactions employed in the regressions less the number of
variables. Only for ln(PRT64) and ln(PRT65) can the null hypothesis
be accepted. However, on strictly intuitive grounds, it is
difficult to discern any very important differences in any of the
sums of the two pollution coefficients. An awareness of our inability
to describe with exactitude the synergic properties of the two
pollutants can neither deny nor fail to deny one's intuitions about
these results. Nevertheless, such an awareness does raise doubts
about the validity of using a statistical procedure which presupposes
that the coefficients being compared are measured in identical
units. A similar caveat applies to all analyses of covariance set
20
forth in this study.
Table 13. Analysis of Covariance of 1967 Disaggregated FHA Data
(T-K)
F
I
ln(PRT65,66)
742
13.08
ln(PRT64,65)
742
.78
ln(PRT64,65,66)
1113
12.80
ln(SUL65,66)
742
43.17
ln(SUL64,65)
742
33.70
ln(SUL64,65,66)
1113
26.21
>/Aggregation Bias. A test similar to that above can be
-------
-86-
acquired as to whether or not census results tend to exhibit
aggregation bias. Table 14 presents regression results using
census data. The air pollution dosages for each census tract
correspond to the dosages found at an individual FHA-insured
residential property near the center of the,tract. Each column
indicates the year to which the air pollution dosages refer.
An analysis of covariance of the air pollution coefficients
of Table 14 yielded not a pair fulfilling the null hypothesis of
equality of the coefficients for different mean annual pollution
dosages. Again, however, the differences do not appear
particularly important to the eye, if one again bases his judgment
upon the sum of the coefficients.
More interesting perhaps is a comparison of the air pollution
coefficients obtained using the census data of Table 14 to the air
pollution coefficients obtained using the disaggregated FHA data
of Table 12. If the air pollution coefficients obtained using
each of the two data sets are statistically equivalent, then the
null hypothesis of an aggregation bias being present in the air
pollution estimates obtained employing census data cannot be
21
accepted. The results of an analysis of covariance to test
this hypothesis are presented in Table 15. The columns refer to
the variables common to both the FHA and the census regressions
-------
-87-
Table 14. Regression Results for Census Data. Dependent variable, ln(MVAL6).
Constant
In(PRT)
In(SUL)
ln(INCM6)
ln(DILP6)
In (OLDER)
ln(NWPP6)
In(DISSM)
In(DLAKE)
In(SQIDX)
E
S
n
ADAM
1966
4.9049
-.5515
.1839
.6182
.0068
-.0269
.0103
.1458
-.0425
-.0769
.5763
.1391
156
$418.73
(1.5794)
( .2307)
( .1066)
( .1180)
( .0050)
( .0133)
( .0054)
( .0670)
( .0298)
( .0400)
1965
5.1712
-.5740
.2410
.6036
.0069
.0220
.0112
.1294
-.0067
-.0820
.5820
.1352
156
$604.64
(1.3420)
( .1841)
( .0560)
( .0980)
( .0049)
( .0119)
( .0041)
( .0583)
( .o:>74)
( .0408)
1964 |
4.6524
-.3754
.0654
.6124
.0039
-.0240
.0127
.1390
.0089
-.0751
.5902
.1339
156
$426.19
(1.2799)
( .1485)
( .0336)
( .1176)
( .0049)
( .0125)
( .0042)
( .0588)
( .0301)
( .0301)
Table 15. Analysis of Covariance of Disaggregated FHA and Census Data.
(T-K)
F
ln(PRT66)
514
1.39
ln(PRT65)
514
8.69
ln(PRT64)
514
1.97
ln(SUL66)
514
6.60
ln(SUL65)
514
16.60
ln(SUL64)
514
2.17
In Table 15, ln(PRT66), ln(PRT64), and ln(SUL64) have values
of F suitable for failing to reject the hypothesis of equality
of the coefficients for these variables in the two data sets. The
values of F for ln(PRT65), ln(SUL66), and ln(SUL65) do not fulfill
the customary statistical criterion. Nevertheless, though the
results of Table 15 do not entirely justify it, the writer is
inclined to dismiss the practical importance of any aggregation
-------
-88-
If any aggregation bias is in fact present in the census data, on
the basis of these results one must attach a rather high value to
the complete absence of bias in order to justify the effort
required to compile and analyze disaggregated FHA or similar data.
The available data permitted a higher level of aggregation
to community areas, a collection of several census tracts.
Observations on forty-six community areas were used in regressions
where MVL66 was the dependent variable and the natural logarithms
of PRT65, SUL65, INC66, SQIDX, DISSM, DLAKE, and BLK66 were the
explanatory variables. The sum of the air pollution coefficients
was -.2527 and marginal capitalized damages were $438.54. However,
the natural logs of the air pollution variables and In(DISSM) were
collinear. When the forty-six observations were partitioned by
DISSM, both air pollution coefficients became statistically
insignificant, though their sum continued to be negative. The
question of whether or not meaningful air pollution damages
estimates can be obtained when the unit of observation is larger
than a census tract therefore remains open.
The Use of Assessed Property Values. Census data and
disaggregated FHA data are not the only data sources from which
air pollution damages to residential properties could conceivably
be estimated. For example a wide variety of local and state
-------
-89-
0
structural characteristics. In its first three columns, Table 16
prescntt1. results for 1967 FHA-insured property sales when In(FHAVL)
and In(TAXES) serve as dependent variables. An analysis of
covariance of the air pollution coefficients in the first column
of Table 16 and the 1967 column of Table 6 reveals no statistically
significant difference in the coefficients for ln(PRT66), though
the coefficients for ln(SUL66) do exhibit such a difference.
In(FHAVL) would thus appear to be fairly satisfactory proxy for
In(COSTS). !
*
Of the explanatory variables employed in the first column of;
Table 16, only In(TCINC) or a similar measure of individual
household income is unlikely to be obtainable from publicly
accessible records. Though it has been shown in Anderson and
Crocker [l], that a failure to include an income variable :
in an offer price equation results in a misspecification and its
attendant biases and inconsistencies, it is of interest to obtain
an empirical indication of the direction and magnitude of this
bias. The second column of Table 16 therefore duplicates the
specification of the first column except that no income variable
has been included. Though increases in the pollution variables
0
and decreases in the income variable tend to have a depressing
effect upon offer price, they are inversely correlated in the
-------
-90-
Table 16. Regressions with In(FHAVL). In(TAXES). and In(MAINT) as Dependent
Dependent
Independent In(FHAVL)
Constant
ln(PRT66)
ln(SUL66)
In(TCINC)
In(LIVAR)
In(HSAGE)
In(MODUR)
In(LOTSZ)
In(SOIDX)
In(NHAGE)
In(DISSM)
In(DLAKE)
FRAME
DTTYP
MASON
BRICK
ALMNM
STORY
£
S
n
ADAM
4.7574
-.3218
-.0088
.3420
.2115
-.0371
.4047
.0924
-.0659
-.0942
.0285
-.0219
-.0800
.0997
.8007
.1001
386
$399.12
(.6285)
(.0927)
(.0472)
(.0219)
(.0250)
(.0052)
(.0392)
(.0217)
(.0176)
(.0351)
(.0111)
(.0121)
(.0131)
(.0268)
In(FHAVL)
5.5620
-.4185
-.0090
.2094
-.0407
.4382
.0904
-.0856
-.1213
.0574
-.0539
-.1201
.1496
.7244
.1121
386
$505 . 75
(.5133)
(.1192)
(.0506)
(.0313)
(.0058)
(.0411)
(.0234)
(.0175)
(.0709)
(.0502)
(.0152)
(.0178)
(.0330)
In (TAXES)
-1.2340
-.2638
.1069
.3515
.2011
-.0299
.0784
.1164
-.0564
.0256
-.0263
-.0901
.0418
.6611
.1051
386
$ .44
(.6601)
(.0974)
(.0496)
(.0230)
(.0263)
(.0055)
(.0412)
(.0228)
(.0184)
(.0133)
(.0142)
(.0137)
(.0282)
In(MAINT)
1.8061
-.3081
-.0179
.3910
-.0305
-.0818
-.0438
.0620
.0455
-.0461
.5719
.0975
386
(.5247)
(.1101)
(.0221)
(.0246)
(.0046)
(.0459)
(.0472)
(.0219)
(.0203)
(.0115)
the negative magnitude of the pollution coefficients. As is
evident in the second column of Table 16, the bias that is
introduced appears to be rather substantial.
The third column of Table 16 employs monthly payments of
locally assessed property taxes as the dependent variable. Since
the coefficients are elasticity measures, one would expect them
to be identical to those found in the 1967 column of Table 6 if
property taxes constitute the same proportion of the sale price
-------
-91-
eye says the coefficients differ. What the; naked eye says is
confirmed by an analysis of covariance. It would seem that the
City of Chicago's residential property assessors understate the
effects of air pollution.
Maintenance Expenditures. In the fourth column of Table 16
is presented the results for a regression in which In(MAINT) is
employed as the dependent variable. These results are totally
contrary to expectations since the air pollution coefficients have
negative rather than positive signs attached to them. If one
considers only the maintenance the FHA's "average resident" would
undertake, it seems unlikely that increased air pollution results
in reduced maintenance outlays upon a given bundle of housing
characteristics. Nevertheless, reduced expenditures on maintenance
with increasing air pollution dosages are not inconsistent with
our earlier hypothesis that householders In locations experiencing
relatively heavy dosages have revealed a lesser willingness to
pay for a clean environment.
Effects of Dosages Upon Site Values. One of the major
hypotheses presented in the section dealing with the theoretical
framework for this study was the greater sensitivity of site
values than property values to variations in air pollution
dosages. A test of this hypothesis is available in Table 17,
-------
-92-
transactions took place. In each year, the sum of the air
pollution coefficients has the expected negative sign, and
In(PRT) is always statistically significant at the generally
accepted levels. When one or the other of the air pollution
variables is dropped from the regression, the remaining variable
always assumes a negative sign and is always statistically
Table 17. Regressions for Site Values. Dependent Variable, In(PSITE).
1967
Constant
ln(PRT64)
ln(SUL64)
ln(PRT65)
ln(SUL65)
ln(PRT66)
ln(SUL66)
In(TCINC)
In(LOTSZ)
In(SOIDX)
ln(INC66)
In(DISSM)
In(DLAKE)
In(CRIMX)
In(NHAGE)
^
S
n
DAM
9.8624
-.7915
.0183
.2719
.3633
-.1265
.2650
.1937
-.0847
- . 1088
-.0510
.6194
.1751
386
$191.09
(1.8545)
( .2691)
( .0920)
( .0380)
( .0329)
( .0392)
( .0883)
( .1142)
( .0270)
( .0328)
( .0457)
1966
7.0144
-1.7651
.4516
.2231
.3750
-.0514
.2730
.2156
-.1102
-.0312
-.0343
.4983
.1954
345
$323.85
(2.0440)
( .3112)
( .0786)
( .0387)
( .0367)
( .0385)
( .1176)
( .1004)
( .0268)
( .0233)
( .0345)
1965
-2.1833
-.7128
.1507
.2581
.2565
-.2101
.4391
.1879
-.0529
-.0012
-.0043
.5138
.2264
188
$167.00
(2.9518)
( .2896)
( .0551)
( .0416)
( .0496)
( .0607)
( .1367)
( .0984)
( .0470)
( .0332)
( .0603)
significant at the .05 level of the one-tailed t-test. As was
the case in the initial regressions of Table 6, In(DISSM) and
In(DLAKE) tended to be somewhat correlated with the air pollution
variables. The exclusion of In(DISSM) and In(DLAKE) had no
-------
-93-
variables however; nor did the dropping of In(PRT) and In(SUL)
have any appreciable effect upon the standard errors of the two
distance variables.
The important feature of Table 17*s air pollution coefficients
emerges when the marginal capitalized damages falling from them ,
are compared to the marginal capitalized damages falling from the
air pollution coefficients of Table 6. In each of the three
years for which regressions were run, the ratio of average
marginal site damages to average site value was greater than the
ratio of average marginal property damages to average property
value. Similarly, the sum of the air pollution elasticities in
the site value regressions is always greater than the sum of the
same coefficients in the property value regressions. This
outcome is consistent with our hypothesis that land or site
values are more sensitive to air pollution dosages than are
property values.
Declining Marginal Damages. Results consistent with another.
earlier stated hypothesis are set forth in Table 18 where the :
1966 property sale observations are partitioned by three distinct
intervals of sulfur dioxide dosages. Thus, the observations
included in the regression for the column headed SUL65 ^25 include
all those 1966 property sales from the disaggregated FHA data
-------
-94-
per billion or less of sulfur dioxide. The other two columns
have analogous meanings.
ln(PRT65)
ln(SUL65)
ADAM
n
SUL65
-.6938
.2001
$802.83
74
<25
(.2219)
(.0610)
, 25 < SUL65 <-45
-.4938
.1135
$574.56
149
( . 1874)
(.1372)
SUL65
-.3892
.1521
$427.31
122
>45
(.1062)
(..0610)
Without bothering to resort to statistical tests to ascertain
whether the observations for the three regressions of Table 18
were drawn from the same population, the above results appear to
be consistent with our hypothesis of declining aggregate marginal
damages. This assertion is statistically confirmed by the failure
of an analysis of covariance to find a significant difference in
the populations of the first and second columns. However, the
covariance analysis rejected the hypothesis that the observations
of the third column came from the same statistical population as
the observations of the first two columns. Thus one cannot
claim that all three sets of pollution coefficients correspond to
different points on the same damage function. Nevertheless, the
fact that this claim can be made for two sets of the coefficients
provides some evidence that the aggregate marginal damage function
declines at least over low and intermediate ranges of air pollution
dosages.
Some further more or less impressionistic support for the
hypothesis of a declining aggregate marginal damage function is
-------
Table 19. Comparison of Logarithmic Means and Pollution Coefficients
Dependent
.Variable
In (COSTS)
In(COSTS)
In (COSTS)
In (COSTS)
In (COSTS)
In(PSITE)
In(PSITE)
In(PSITE)
In (COSTS)
In (COSTS)
In (COSTS)
In (COSTS)
In (COSTS)
In (COSTS)
In(COSTS)
In (COSTS)
In(COSTS)
In(COSTS)
In(COSTS)
T YEAR
67
67
66,67
66,67
66.67
66,67
66,67
66.67
66
66
66
66
65,66,67
65,66,67
65,66,67
65,66,67
65,66^67
65
65
Partition
MODUR > 300
200 < MODUR <300
BLK66 >75
BLK66 <25
BLK < .25 and
INC66 >8495
BLK66 > 75
BLK66 £25
BLK <25 and
INC66 >8495
DISSM 1100
DISSM >100
DLAKE >30
DLAKE <30
HSAGE > 40
20 1 HSAGE £40
HSAGE < 20
None
TCINC > 850
None
INDUT <5
In(PRT)
4.9206
4.8746
4.9160
4.8322
4.8163
4.9160
4.8322
4.8163
4.8638
4.7936
4.8593
4.7810
4.8640
4.8681
4.8455
4.8593
4.8639
4.8553
4.8464
In(SUL)
3.8521
3.5282
3.7983
3.5091
3.4053
3.7983
3.5091
3.4053
3.8110
3.2438
3.5174
3.2516
3 .4438
3.4107
3.0848
3.3343
3.3049
3.3467
3.3010
bPRT
-.2376*
-.6913
-.5388*
-.7331
-.8263
U2390*
-2.1870
-2.4939
-.2781
-.5428
-.4971
-.7247
-.3795
-.2447
-.7665
-.3560
-.4475
-.2207*
-.5174
bSLJL
.0172V
.0866-v
.2434*
.2077
.2781
-.0914*
.3670
.5108
.0816*'
.1752
.2117
.1594
.0217*
-.1506
.1075*
.0227
.0374
-.1304
.1297
I
\0
Ui
-------
-96-
partitions of the data set can be compared. The regression is listed
i
in the dependent variable column. Reading across the rows, the columns
refer respectively to the year in which fhe property sales occurred,
the nature of the partition, the arithmetic mean of the natural logarithm
of average annual monthly suspended particulates in the year preceding
the earliest year of the regression's property sale observations, the
arithmetic mean of the natural logarithm of average annual monthly
sulfur dioxide in the year preceding the earliest year of the regression's
property sale observations, the regression coefficient for In(PRT),
and, finally, the regression coefficient for In(SUL). The horizontal
double lines are intended to separate partitions of different variables,
while the starred regression coefficients indicate nonsignificance
at the .05 level of the one-tailed t-test.
Since arithmetic means were not calculated for the original values
of the variables in each of Table 19's partitions, the presentation
can neither confirm nor deny the hypothesis of a declining aggregate
marginal damage function. In addition, since no analyses of covariance
were performed upon the coefficients of the regressions for the partitions,
one cannot know whether observations were drawn from the same statistical
population. Nevertheless, a cursory view of Table 19 makes it appear
that damage elasticities tend to decline with increasing air pollution
dosages. If the ratio of property value to air pollution dosages remains
fairly constant throughout, a declining damage elasticity is consistent
with a declining marginal damage function. The earlier results of
-------
-97-
the aggregate marginal damages of Table 19 would also tend to
a
decline.
The Minimax Decision Criterion. If it is in fact the case
that marginal damages are greater at low than at high levels
of pollution dosages, one would expect differential property
values' to be more sensitive to differences in minimum dosages
than to differences in maximum dosages. Table 20 shows six
regressions for 1966 and 1967 property sale observations, where,
except for the air pollution variables, the specifications were
identical to the initial regressions of Table 6. The results
presented in Table 20 are again fully consistent with the
hypothesis of a declining aggregate marginal damage function.
It should be recognized, however, that PMM and PMX are highly
correlated with each other anc with PRT, while SMX and SUL are
also highly correlated. The regressions of Table 20 in which
both minimum and maximum pollution dosages are included as
regressors obviously exhibit this collinearity. Its presence
inhibits any meaningful test of the hypothesis of the receptor's
use of a rainimax decision criterion in response to uncertainty
about future pollution dosages.
The Cubic Utility Function. In another of the hypotheses
developed in a previous section about receptor responses to
-------
-98-
Table 20. Regressions for Minimum and Maximum Air Pollution Dosages
ln(PMM66)
ln(SMM66)
ln(PMX66)
ln(SMX66)
£*
S
n
ADAM
1967
-.2267 (.0527)
-.1194 (.0350)
.7722
.1123
388
$522.40
1967
-.2071 (.0719)
-.0209 (.0349)
.7641
.1143
388
$224.89
1967
-.3139
-.1283
.0383
.0607
.7721
.1124
388
(.0936)
(.0397)
(.0954)
(.0457)
ln(PMM65)
ln(SMM65)
ln(PMX65)
ln(SMX65)
£
S
n
ADAM
1966
-.4333 (.0919)
-.0557 (.0258)
.6916
.1141
345
$778.78
1966
-.4629 (.1301)
.0643 (.0223)
.6669
.1182
345
$474.72
1966
-.3758
-.0370
-.3642
.1132
.6915
.1143
345
(.1101)
(.0399)
(.1436)
(.0375)
utility function in air pollution, then the second and third
moments of the annual distribution of pollution dosages become
relevant to damages. Table 21 presents regression results for
1965, 1966, and 1967 property sale observations when various
combinations of the first, second, and third moments of the
distribution of air pollution dosages are included as regressors.
Again, except for the air pollution variables, the specifications
were identical to the initial regressions of Table 6. All air
pollution measures in Table 21 refer to the dosages occurring in
-------
-99-
1 is tied in the columns.
Table 21. Regressions on Second and Third Moments of Pollution Dosages
In(PRT)
In(SUL)
In (PVR)
In(SVR)
In(PSK)
In(SSK)
2
I
S
n
1967
-.4453 1
-.1784 <
-.0195 I
-4
- . 14x10 1
-4
- . 73x10 1
.3
-.25x10 <
.7761
.1121
388
M133)
M525)
(.0248)
_4
;. 16x10 )
-4
(.36x10 )
-3
(. 12x10 )
1967
-.4570 1
-.0407 (
-4
.68x10 <
-3
-.24x10 I
.7756
.1122
388
(.1084)
(.0459)
-4
(.36x10 )
-3
(.12x10 )
1966
-.5793
.1835
-.0112
-5
.13x10
-5
-.64x10
-4
.74x10
.6831
.1149
345
(.1700)',
(.0515)
( .0304)
-5
(.49x10 )
-4
(.19x10 )
-4
(.85x19 )
i
In(PRT)
In(SUL)
In (PVR)
In(SVR)
In(PSK)
In(SSK)
_2
R
S
n
1966
-.6495 (
.1290 <
-5
-.87x10 <
.68xlO"4 (
.6827
.1150
345
M491)
(.0295)
-4
M9xio )
;.79xlo"4)
1965
-.3163 (
-.1521 1
-.0265 (
-. 14x10 "4 |
-4
-.72x10 <
-.31x10" <
.7258
.1124
212
(.1693)
(.0351)
(.0294)
(.21xlO~4)
-4
(.31x10 )
-3
(.14x10 )
1965
-.3206
-.0692
-4
-.75x10
-3
-.31x10
.7188
.1125
212
(.1517)'
(.0276);
-4
(.32x10 )
-3
( . 13x10 )
The results presented in Table 21 are rather ambiguous.
Nowhere does the inclusion of the second moment divided by the
mean yield a statistically significant coefficient, though the
-------
: -100-
fnr "he measure of air pollution variance does not appedr to
be due entirely to multicollinearity problems for only ln(SVR66)
and ln(SUL66) have an extremely high simple correlation coefficient.
The drastic changes which always occur in the standard errors of
In(SUL) whenever In(SVR) is added or dropped are strong evidence
22
of multicollinearity however.
The results for the skewness measures in Table 21 are
somewhat more meaningful. In two of the three years, 1967 and
1965, each of the skewness variables is statistically significant.
In ttvj third year, 1966, where the skewness variables are not
significant, the arithmetic means and standard deviations of the
natural logarithms of the variables were no more than one-half
the values of the other two years. In fact, the mean of ln(SSK66)
was so small as to be practically nonexistent. Further support
for the meaningfulness of the skewness variables is offered by
the fact that their signs, except for ln(PSK66), are in accord
with expectations. For example, the sign of the arithmetic
mean of ln(SSK66) is positive, implying that the air pollution
distribution of 1966 for the locations of the 1967 property sale
observations was skewed toward the higher pollution dosages.
Given that disutility is attached to a greater density of pollution
at the higher dosages, the sign of the coefficient for ln(SSK66)
-------
-101-
ln(PSK66) is negative, implying a greater density for suspended
particulates in 1966 at the lower dosages. As expected, the sign
of ln(PSK66)'s coefficient is positive.
Adaptive Expectations. The results presented in Table 21
constitute the last of this study's economic-theoretic and
statistical hypotheses which were tested by suitable estimation
i
procedures. The one hypothesis, the adaptive expectations
hypothesis, for which no meaningful results have been or will be
i
presented, was originally viewed as one of the study's major .
objectives.
The intent of the study was to test the adaptive expectations
hypothesis by means of a nonlinear distributed lag regression
program capable of carrying out estimation where at least two
variables in a cross-sectional expression were vector-valued
23
while others were scalar-valued. In conjunction with those
transactions taking place in 1967, two different forms of the
air pollution data were used. First, monthly observations of
the mean daily dosages of each pollutant starting at the month of
sale and in some regression runs extending as far back as January,
1964, were employed. Second, only the mean annual concentrations
for 1966, 1965, and 1964 were used. Whatever the air pollution
data, moderately different results were obtained according to ;
-------
-102-
f\t
the complete lag expression and the lag term of this expression.
Never were statistically meaningful results obtained when the
monthly air pollution data were introduced. However, results
having moderate degrees of statistical significance were
occasionally encountered when the annual air pollution data were
entered.
In terms of statistical significance and intuitive
reasonableness, the "best" results with these annual air pollution
data are presented in Table 22. Except for the lag expressions
introduced for the pollution variables, the specification was the
same as in the initial regressions of Table 6. Separate lag
expressions were specified for suspended particulates and sulfur
dioxide. The coefficients for all other explanatory variables
closely approximated those of Table 6. The percentage of variation
explained in the dependent variable was also similar.
Table 22. Example of Distributed Lag Results.
PRT SUL
b -.0019 (.0010) .0005 (.0004)
A .5094 (.0024) .2966 (.8378)
At no time did APRT or ASUL approach unity. Thus one can
be fairly safe in asserting that some lag effect does appear to
exist in the formation of expectations about future air pollution
dosages. If one insists upon accepting the results in Table 22
-------
-103-
between fifty and eighty percent of the expectations held about
air pollution dosages in any following twelve months are accounted
for by the air pollution dosages of the previous twelve months.
The fifty percent figure applies when one dismisses the
statistically insignificant for sulfur dioxide. It should again
be strongly emphasized, however, that results having a degree of
statistical resolution even approximately like those of Table 22!
were obtained in only a minority of cases. In short, though its
other results can be viewed as useful, this study contributes no!
trustworthy empirical insights into the relation between residential
property values and histories of air pollution dosages.
Some Desirable Research Extensions
Whenever one constructs a formal model of a real situation,
one is attempting to express in an internally consistent manner
a conviction as to which of the situation's elements are trivial
and which are essential. A bounded rationality requires that one
pick and choose. It is a commonplace of statistical inference
that these convictions can be rejected but never completely
accepted by comparing their implications with observations on
real situations. The best one can do is fail to reject the
convictions. It is worth noting, however, that even a rejection
must rest upon some self-convincing interpretation of one's
-------
-104-
In order to secure reality somewhat more closely, this
paper's primary focus has been upon an expansion of the elements
to be regarded as nontrivial in air pollution damage contexts.
Inevitably, this means a more detailed economic-theoretic
framework and the development of a greater number of testable
hypotheses, the empirical implications for each of which are more
visible for critical scrutiny by those whose notions of the
trivial and the nontrivial vary. However, if the number of
elements to be regarded as essential is continually expanded,
some agreement on criteria for rejection must ultimately occur.
Given the results of this paper and its author's implied convictions,
this section attempts to suggest some elements of air pollution
damage contexts which might now be regarded as essential. The
section deals in turn with theoretical, estimation, and empirical
elements of air pollution damage investigations.
Theoretical Issues. During his reading of the theoretical
framework of this paper, the perceptive reader will have noted
that the movement from the derivation of the offer function for
bundles of housing characteristics to the derivation of the form
of the marginal damage function was made via a one sentence
application of the composite goods theorem. In short, once the
offer function had been dealt with, it was assumed thereafter that
-------
-105-
in a bundle of housing characteristics were invariant. This not
innocuous step permitted the variables in all later theoretical
developments to be treated as if they were scalar rather than
vector-valued. A subsequent investigation should attempt to
ascertain whether such conclusions as the declining marginal
damage function and the greater sensitivity of land than improvement
values to air pollution dosages can be maintained under the same
derivation of the offer function but without resorting to the
composite goods theorem.
With the one minor exception of the minimax decision criterion
where constant marginal costs of supplying bundles of housing
characteristics had to be assumed, any consideration of the supply
function for these bundles was avoided by assuming the stock of the
bundles to be always in a long-run equilibrium. There exist four
ways of adjusting the stock of housing characteristics: (1) a
positive replacement demand—as characteristics depreciate they are
replaced; (2) a negative replacement demand—as characteristics
depreciate they are not replaced; (3) a combinational process
whereby new characteristics are joined with characteristics that
are already joined together—a new activity in the terminology
adopted by Lancaster 14 ; and (4) the construction of entirely
new bundles of housing characteristics. The stock of housing
-------
-106-
f
these four ways is operative. A glance out one's window is a
convincing argument for the pervasiveness of the latter three ways
and thus the extent of disequilibrium in the stock of housing
characteristics. Therefore a model which intends to include all
general classes of factors influencing the inventory of housing
characteristics must have some means of explaining discrepancies
between actual and desired inventories and the manner in which
suppliers of housing characteristics respond to these discrepancies<
Such a model would be aware that changes In expected air pollution
dosages can be a cause of any discrepancy between actual and
desired inventories of housing characteristics.
A recognition that a long-run equilibrium may not persist in
markets for bundles of housing characteristics implies that the
production of these bundles is responsive to changes in air
pollution dosages. That is, in addition to the price adjustments
to changing air pollution dosages which have been explicitly
recognized throughout this study, a quantity adjustment can occur
as well. When a quantity adjustment can enter, the possibility
that the damage function relevant to increasing air pollution
dosages differs from the damage function relevant to decreasing
air pollution dosages emerges. This possibility could be of real
importance in situations where the values of fixed assets such as
bundles of housing characteristics are afflicted by air pollution
-------
-107-
Remembering that we view the householder as purchasing housing
goods to generate bundles of housing characteristics, consider the
problem the householder faces in his decision to increase, maintain,
I
or divest himself of a given b.undle. Anyone who has ever
participated in the housing market is aware that there are •
substantial expenses (closing costs, real estate agent's fees,
prepayment penalties, etc.) associated with the acts of purchasing
or selling a house. In general, at any point in time for the
individual householder these expenses cause acquisition price,
p., to be at least as great as sale price, p . Otherwise, one
A s
could always make money by reselling immediately. Thus in long-run
equilibrium it must be that p. dz p p , where p is the
A '-' ' S
dx
willingness of the householder to pay for an additional unit of the
housing characteristics bundle. A simple arithmetic example
lends insight to the difficulties this formulation can introduce.
Let us assume that the acquisition costs on a $20,000 house
are $500 and the selling costs are $1,000. Thus, assuming that .
air pollution is the sole cause of variations in p, under no !
circumstances would the householder sell the house unless his air .
pollution damages were at least $1,000. Now let us assume that
for some reason air pollution decreases and the householder must
decide whether or not to acquire the same bundle of housing
-------
-108-
damages caused by the decrease in air pollution was at least $500.
In short, the mix and magnitude of bundles the householder holds
over a given interval of air pollution dosages can differ according
to whether air pollution dosages are increasing or decreasing. At
identical levels of air pollution dosages, the same individual
householder can be employing different mixes and magnitudes of
i
housing goods and can therefore suffer different air pollution
damages. It may therefore be worthwhile in future investigations
to investigate in depth the theoretical and the empirical
implications of this point. Intuitively, the point would seem to
imply that the construction of some empirically usable measure of
the trend of the air pollution dosage history would be advisable.
Another of the issues carefully avoided in this study's
theoretical framework was that of the determinants of the
householder's sensitivity to air pollution dosages. Thus the
assertion was made that sensitivities do in fact differ among
householders and the analysis was carried through to its conclusions
on the basis of this assertion. No attention whatsoever was
devoted to the not unimportant question of why these sensitivities
differ. The lack of attention given to these determinants is
evident, for example, in the discussion of the results presented
in Table 19, where it was stated that the hypothesis of declining
-------
-109-
left unstated, the perceptive reader will have recognized that
neither are the table's results inconsistent with increasing
house age (HSAGE) or decreasing income (TCINC). Only a theoretical
argument can provide a basis for ascertaining whether individual
householder differences in sensitivity to a:Lr pollution dosages
are wholly caused by differences in the actual disutility
people attach to air pollution ("tastes"), or whether these
sensitivity differences are due in part to householder income
differences or differences in some other factor. The issue's
importance becomes apparent when one recognizes that income
determined sensitivity implies that a change in income causes a
change in the householder's willingness to pay for cleaner air
locations relative to other goods. This, in turn, can bring about
changes in urban spatial configurations since it can imply that
prices of clean air locations will, independently of changes in
pollution dosages, change relative to the prices of locations
having greater air pollution dosages.
Many implications for urban spatial configurations follow
immediately from the study's theoretical and empirical conclusion
that land values are more sensitive to variations in air pollution
dosages than are property values. For example, on the basis of
this conclusion, any increase in air pollution dosages is held to
-------
-110-
equilibrium is established in which bundles of other characteristics
are substituted for bundles of housing characteristics and overall
property values are reduced, with the price of land bundles being
affected more than the price of nonland bundles. Under a broad
range of conditions, one would expect land bundles to be substituted
for nonland bundles. The new equilibrium could thus be described
as being relatively more land intensive. Since a new equilibrium
is supposed to have been established, one might ask if this new
equilibrium is stable — particularly when the household sufferer
from air pollution dosages is treated as a more or less passive
observer of the passing air pollution scene.
As was earlier noted, a treatment of the householder as a
completely passive observer implies that the only argument in the
function which generates the sufferer's expectations about future
dosages is some history of realized dosages. In short, the new
equilibrium land use pattern resulting from a change in dosages
is based only upon a change in a dosage history resulting from
the preexisting land use pattern. But associated with each
locational equilibrium could be a unique configuration of air
pollution generating sources and dosages. For example, a less
dense population distribution over space could change the
individually perceived price of automobile relative to mass
-------
-Ill-
increased transportation costs as individually perceived would
be greater than the individually perceived benefits of relocation
is worth investigation.
Furthermore, greater population dispersal at least over some
substantial lange of an index of dispersal would seem to imply a
greater number of individual pollution sources, each of which emits
a relatively small quantity of pollutants. Thus, given the quite
reasonable assumption that the cost of achieving a given reduction in
a given quantity of total emissions varies directly with the number
of emission sources, the marginal cost of air pollution control
could conceivably increase rather than decrease with increased air
pollution dosages. That is, it might be that over some range Df
increasing land-nonland housing bundle ratios, air pollution is
increased and the marginal cost of attaining and maintaining a
given absolute pollution reduction increases. The latter increase
in cost could occur because greater numbers of pollution sources
imply reduced economies of scale in emitter control equipment and
greater outlays on control agency policing and information services.
In any case, from this and the previous two or three paragraphs, it
should be obvious that considerations of household locational
behavior with respect to air pollution can under quite reasonable
conditions influence the supply of air pollution, optimal air
pollution control strategies, and the general pattern of urban
-------
-112-
Estimation. The offer functions for bundles of housing
characteristics presented in this study are representative of all
previous attempts to estimate cross-sectional housing demand
models in which the offer price is a function of various attributes
of the house in question and the householder's income. In other
words, the present study has by no means exhausted the possibility
of improving the basic theory by experimenting with formulations
t
differing from previous formulations in terms of the explanatory
variables included, in terms of the functional form in which these
variables enter the models, and in terms of the techniques employed
for obtaining the estimates. Empirical insights acquired by
statistical means can provide direct information about functional
forms and variable weights. This information can often be used
to strengthen and to extend the insights obtainable by deductive
theoretical reasoning. One requires two legs to walk.
Most of the statistical experimentation suggested here can be
carried out with the Chicago data employed for the present study.
Thus additional checks on the declining marginal damage hypothesis
can be obtained by introducing a form for the pollution variables
giving greater weight to low dosages and lesser weight to high
dosages. Assuming no problems of nonorthogonality with other ex-
planatory variables, that set of weights which maximizes the
"t-values" of the pollution variables would, in statistical terms,
-------
-113-
Various specifications of the offer function in terms of
explanatory variables included and functional forms can be
evaluated in terms of the accuracy with which they forecast offer
price. Consider a situation in which the actual values of offer
price are denoted by COSTS, the forecasts of COSTS generated by
one specification as f,, and the forecasts of another specification
as f2- In Hoel 57 is found a "t-test" which permits the
predictive ability of f« to be tested against that of f . In
effect, the regression
COSTS - fl = a + b (f2 - fj)
is calculated. A significantly positive b implies that f2 *-s
statistically a better choice than f,. A significantly negative b
in the regression
COSTS - f2 = a1 + b1 (fl - f2)
would tend to reenforce this finding. In this manner a ranking of
specifications can be established yielding some idea of the
tradeoffs involved between forecast accuracy and the costs of
additional data collection and computation which underlie more
detailed and complex specifications.
Various manipulations of the data employed in this study gave
-------
-114-
pollution coefficients because of the improper exclusion of
explanatory variables. However, it must be admitted that these
manipulations were applied to a very small number of variables.
About 150 of the approximately 180 nonpollution variables for
which infonuation had been collected were eliminated in the study's
very earliest stages. The criterion employed for summary dismissal
was simply an inspection of simple correlation coefficients for
offer price and the variable; and the signs and levels of
statistical significance in a relatively small number of regressions
combined with some prior knowledge based on "feel", economic theory,
and previous empirical studies of the extent to which particular
variables can be expected to contribute to offer price. This
partly ad hoc procedure is unlikely to exclude explanatory variables
of any real Importance if householders do in fact always make their
evaluations in terms of these individual variables. The problems
of multicollinearity and losses in degrees of freedom which these
variables separate inclusion would entail would be very costly in
statistical terms. Nevertheless, though these variables may
individually contribute little to an explanation of variations in
offer price, certain combinations and collections of them may have
a good deal to offer. If householders make their evaluations in
terms of a scalar index measure of these combinations, then certain
-------
-115-
excluded. The pollution coefficients obtained in the present
study may therefore be biased. According to Kane 58 p. 277 ,
a factor analysis can reduce the large group of variables which
may generate this possible bias into a potentially smaller set of
reference variables or factors. If the resulting factors are
orthogonal, they can then be employed as explanatory variables in
specifications employing the standard regression procedures.
A further source of possible and as yet untested bias in the
pollution coefficients enters if one suggests that offer price
and the pollution variables are somehow jointly determined. Similar
suggestions could be advanced for the school quality and mortgage
duration variables employed in this study. For example, one could
construct an argument consistent with economic theory in which the
perceived cost to an air pollution control agency of bringing
about a given absolute reduction in the emissions from a given
set of sources varies inversely with the value of the property being
effected. People who own valuable property are presumed to be
able and willing to put more pressure on an air pollution control
agency. Though this ability and willingness is undoubtedly
usually captured by inclusion of an explanatory variable for
permanent income, it is not beyond belief that air pollution
control authorities become more upset about a given dollar
-------
-116-
25
in a low property value area. If the costs the authorities
feel are in any way related to the level of property values
independently of the residents' income levels, then the problem of
simultaneity with its accompanying biases enters. The writer is
strongly inclined to dismiss as rather fanciful the real importance
26
of this source of bias. Nevertheless, simultaneity does constitute
one basis for criticizing the results of the present study. As
Goldberger 36, pp. 329-336 shows, an estimating procedure known
as two-stage least squares provides a means of ridding the
pollution coefficients of whatever simultaneous equations bias
may exist in them.
The prime estimation difficulty associated with the present
study has been the failure to employ a way of estimating lagged
responses to air pollution dosages which had even a moderate
degree of reliability. Provision of these estimates was initially
envisioned as one of the study's central purposes. In addition
to further time-consuming and costly attempts to produce a
nonlinear distributed lag program of the genre discussed in the
previous section, other less complex means of estimating these
lags suggest themselves. For example, a straight time-series
analysis using "canned" distributed lag programs could be performed
if one was to use some measure of central tendency of the
-------
-117-
possess adequate degrees of freedom to permit this, though, of
course, the usual aggregation problems would exist. Furthermore,
different: properties would contribute to each month's average. A
central tenet of time-series analysis would therefore be violated.
Nevertheless, a time-series analysis of the above sort if
supplemented by pooled cross-sectional estimates employing simple
lag forms could produce a collection of estimates establishing with
a fair degree of confidence the upper and lower bounds of the
typical lag's magnitude. For example, the weight given past
pollution dosages in the formation of a householder's expectations
about future dosages may be made some polynomial function of the
elapsed time between the dosage and the present. Though there
would be some loss in degrees of freedom, ordinary least squares
a-fbt
procedures can readily deal with such terms as p , where p
represents the dosage, t is elapsed time, and a and b are
parameters to be estimated. Taking the logarithm of this term
yields ( a 4- bt) Inp which is identical to a Inp + bt Inp ,
an expression that is linear in the parameters. In effect, pooled
cross-sectional pollution coefficients would be expressed as
functions of time.
Alternatively, rather than continuing to attempt directly
to establish the lag terms in the offer price equation, one could
-------
-118-
past pollution dosages would be obtained. This scalar value would
then be entered directly into the offer price equation. Alternative
first-step weighting schemes would be employed until pollution
coefficients were obtained in the second-step that met "suitable"
conditions. The conditions of suitability in this utterly ad hoc
estimation procedure would presumably be some mix of intuitive
reasonableness, t-values for the pollution coefficients, and the
—2
offer price equation's R . However, it should be explicitly
recognized that it would be the form of the lag rather than the
hypothesis of adaptive expectations which would constitute the
theoretical ad hockery. That is, the existence of a lag is
readily justified in economic theory, but there is at present no
basis in that theory as it applies to air pollution damages for
a priori specification of the lag's form. Regardless of the
estimating procedures one onploys, one at present is dependent
upon the data to give insight into the lag form. The truth about
the lag form is supposed to jump from the data. If one employs
the quarterly or annual dosages found in the Chicago data, some
indication of the nature of the lag form could probably be obtained
without incurring great expense in computer time or programming.
Empirical Issues. The questions raised in the subsections
dealing with theoretical and estimation issues all have their
-------
-119-
work to be done calling for no substantive extensions in theoretical
frameworks or estimation procedures. Since many of the empirical
applications raised in the theory and estimation subsections are
immediately apparent, this subsection will address itself only to
those applications not readily apparent as well as more or less
strictly empirical questions that have not yet been given any
attention.
A fair number of studies of the covariation between air
pollution dosages and property or land values now exist. Without
exception, those studies employing the Lancaster formulation of the
damage function have found that dosages and property values are
significantly and inversely related. Nevertheless, these studies
indicate that there are some differences in sensitivities among
cities. The damage elasticities in Chicago, for example, appear to
be somewhat higher than those found for other cities. The
theoretical framework of the present paper implies that at least
a part of these differences in marginal damages and damage
elasticities is attributable to differences in air pollution
dosages. However, it could be that the factors which determine
pollution sensitivity differ among cities. For example, if
increasing air pollution dosages do in fact cause land to be
substituted for improvements in the production of bundles of
-------
-120-
nonpolluting transport alternatives can be expected to suffer the
smaller air pollution damages. One can readily conceive of property
value studies of a large number of cities where intercity comparisons
would be made of land and property damage functions and responsiveness
to uncertainty about air pollution dosages. The study's prime
objective would be to acquire insight into the causes of these
differences among cities. The term "acquire insight" rather than
"explain" is employed because it seems unlikely to the present writer
that a formal process of initially deriving propositions from
economic theory and then subjecting them to formal tests would
prove especially productive. This is simply because there are an
extremely large number of causes that are consistent with this
theory. Instead, after an initial empirical identification of those
differences that do exist, economic theory can be employed to
determine which of these existing differences can in fact explain
differences in air pollution sensitivities.
On a less ambitious scale, several other empirical studies can
be conceived. We do no more than list them here. As a check on
the conclusions that were drawn from the regressions in which land
values and property values were employed as dependent variables, the
value of improvements alone should also be employed as a dependent
variable.
All property value studies have used only suspended particulates
-------
-121-
studies should be attempted in which additional types of pollutants
are introduced. There is no necessary reason why these two types of
pollutants constitute good proxies for the many other pollutant
types.
The measures used in the present study of negative influences
upon property value other than air pollution are not the best
imaginable. If the measurement errors in such variables as NHAGE
or CRIMX are systematically correlated with the air pollution var-
iables , statistical biases can be introduced into the damage
estimates. Some thought could be given to devising better measures.
One possibility, which under certain assumptions about the data's
nature is already available in the Chicago FHA data, is the use of
fire and property damage rates as indicators of the joint effects
of neighborhood threats and fire and police protection upon a
property's value.
Summary and Conclusions on Desirable Research Extensions
A discussion of desirable research extensions implies that
the possible extensions differ in the extent of their desir-
ability. Their desirability can be ranked according to the
contributions each can make to the fundamental problems of interest
as well as the costs of carrying out these extensions. But, as
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Any ranking of possible extensions thus requires some fairly
'substantial attempt to explain and defend it. In the present
context, the returns accruing to such an effort are difficult to
identify. Accordingly, this subsection restrains itself and limits
its remarks to listing in tabular form the topics presented in the
research extensions section. Appended to each topic is a remark
indicating whether or not the empirical version of the topic can
be studied employing the data used in the present study. Since
data is costly and time-consuming to collect, any topic whose
empirical version can be studied using the existing Chicago data
has at least one positive advantage relative to alternative topics.
t... Theoretical issues
1) Weakening the conditions for the declining marginal
damage function—no additional data required.
2) Construction of supply function for bundles of housing
characteristics—most, but not all, data already
collected.
3) Damage functions for increasing and decreasing air
pollution dosages—careful inspection of Chicago air
pollution data necessary, but likely this data would
be suitable.
4) Determinants of sensitivity to air pollution dosages—
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-123-
5) Impact of air pollution dosages on urban spatial
configurations—substantial new data collection efforts
required.
B. Estimation—no new data collection efforts are required for
any topic in this subsection,.
C. Empirical issues
1) Differences in pollution sensitivities among cities—
large and expensive new data collection efforts required.
2) Value of improvements as a dependent variable—no new data
collection efforts required.
3) Improved measures of neighborhood influences upon
property values—new data collection efforts are required.
4) Additional pollutant types—new data collection efforts
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FOOTNOTES
1. It is assumed throughout this essay that the compensating
variation and air pollution damages are synonymous. The reader is
warned that willingness to pay is not necessarily identical to what
a receptor rrould have to be paid in order to be willing to accept
a little more air pollution.
2. The expression "well-behaved" is a euphimisra for some rather
strong regularity conditions. In particular, (zn) ^Zi2-* ^
z., z.o for all i and Zjo^O ^or at ^east one *•• Furthermore, as
the offer function is derived in Appendix B, must have strictly
positive first order partial derivatives and continuous second
order partial derivatives everywhere. Nevertheless, this representation
is weaker than is usual, for, as Lancaster 14, pp. 156-157 shows,
the formulation of employed here need not be convex .
3. For more on this point, see Appendices A and B.
4. Since our offer function reads c = c(z * y), this view of the
identity of offer prices for housing and consumer expenditures for
housing could mean that we have a greater number of different
characteristics than we have price observations on goods. That is,
any arbitrarily specified bundle of characteristics could be
embodied in more than one good. Therefore no unique utility
maximizing housing location could be discovered. However, as
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and convex, an n-diraensional slice of (z), where n r, will have
the same general properties as (z) defined in r-dintensions.
In any case, the problem of excessive characteristics does not
seem relevant here. Kain and Quigley 17 could enumerate no
more than twenty-one characteristics making a statistically
significant contribution to housing offer prices.
5. The developments in this and the succeeding subsection
owe much to readings of Lind 8 , Muth 27 , and Alonso 28
6. The formal reasoning underlying these statements can be
developed from Brandow 29 and Muth 30
7. This does not preclude ex post adjustments of behavior
(adaptations of expectations) to realized errors in forecasts. The
necessary conditions for the validity of certainty equivalence are
ably presented in Malinvaud 18.
8. The latter approach, termed the time-state preference
approach to uncertainty, applies a discount rate to future
contingent claims, where the rate discounts for futurity and for
probability. A detailed presentation of the approach is available
in Hirshleifer 19 .
9. The following development leans very heavily upon the
presentations in Levy 20 and Hanoch and Levy 21
10. For an excellent short review of the principal features
and implications of these alternative criteria, see Tisdell
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-126-
11. Data made available to the writer from the Chicago
offices of the FHA indicate more or less constant marginal costs
for a wide variety of structural characteristics. The sign of
3
c o would thus be positive when it is recognized that
z
attempts to .alter neighborhood characteristics involve the formation
of coalitions of households. It is generally thought that increasing
the number of coalition members implies increasing marginal costs of
coalition formation.
12. See Nerlove 10, pp. 22-23 .
13. Past and present administrators of the Chicago Air
Pollution Control District have described the District's sampling
and control program in a number of published papers and reports. A
description is available, for example, in Stanley 37 . Additional
information on the District's sampling and control program as well
as the general nature of Chicago's air pollution problem is
presented in Upham 39 , Johnson 40 , Stanley and Heller 41 ,
and Northeastern Illinois Planning Commission 42
14. The necessary meteorological data could not be obtained
from the Chicago Air Pollution Control District.
15. A more thorough development of these points is available
in Green 15, pp. 99-103 .
16. The following provides a .notion of the diversity of the
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-127-
improvement's exterior had a fiberboard finish, the inclusion of
a dishwasher in the sale, the type of water service, wife's age,
rate of commitments for felonies by neighborhood males from 1958
to 1962, the percentage of pupils in Sept. 1967 at the nearest
elementary school below national reading norms, the floor space
in the second closest shopping center, the zoning classification,
and the seat miles of mass transit service available at the nearest
rapid transit facility.
17. The economic-theoretic nature of the relation between
permanent income and offer prices is presented in Reid 45
18. This is a bit of an overstatement since Ridker and Henning
2 carry out some residualization procedures because of perceived
colline'arity between their measures of permanent income and air
pollution. Three comments are in order about their results. First,
their air pollution data was grouped in that air pollution dosages
over fairly wide intervals were assigned unique single values. This
grouping would tend to increase the correlation between the air
pollution and the income variables. Second, the air pollution
damage coefficients Ridker and Henning obtained using a
residualized permanent income measure as a regressor were within the
standard error of the pollution coefficient when the income measure
was not residualized. Third, as was noted in Anderson and Crocker
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-128-
or unresidualized, reflected the effect of mistakenly entering the
median fejnily income of a single census tract as zero.
19. - It is worth noting here that an application for the t-test
to any of the air pollution coefficients presented in this section
/\
means, given that it carries the correct sign, that b is signifi-
cantly different from zero. We specify as the null-hypothesis the
claim of some who argue that residential property values will not
register any air pollution damages whatsoever. Thus, we are test-
ing for coefficients permitting rejection of this null hypothesis.
In short, we wish to follow a testing strategy which minimizes the
chance of accepting the false hypothesis that an air pollution coef-
ficient is significantly different from zero when it actually is not,
20. One coul perhaps ease this problem by employing an
interaction term such as In (PRT66) (SUL66) in the regressions.
However, the definition of the interaction term requires the ex
ante and in this case ad hoc assignment of a weight to each
pollutant. Thus the choice was made in this study to employ
pollution measures which permit realistic interpretations in
ordinary regressions, though these measures raise doubts about the
use of analysis of covariance. The cost of this choice was the
foregoing of an arbitrary assignment of weights to each pollutant
-------
-129-
relation to any real situation could be interpreted in any manner
the reader saw fit.
21. This statement is compromised by our earlier statement
about the validity of the use of the analysis of covariance in a
context wheie the pollutants are synergic.
22. One should note that the influence of variance in air
pollution dosages upon expected utility could conceivably be
i
non-linear in the variables and in the parameters. The earlier
discussion of the cubic utility function could be made to suggest
that the impact of the second moment upon expected utility varies
with the level of air pollution dosages. Specifically, the
behavior could change from risk-aversion to risk-preference as
dosages fall, given that the marginal utility of less air pollution
is always positive.
23. This program was written especially for this project by
R. J. Anderson, Jr., formerly of Purdue University's Department of
Economics.
24. An attempt was made to avoid the problems in the
distributed lag estimating procedure by entering as separate
explanatory variables the mean annual dosages of each pollutant
for the three years immediately preceding 1967. However, the
collinearity of these measures was so great as to render the
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-130-
25. If ability and willingness to impose pressures upon the
control agency is a function of permanent income and if offer price
or property value is a function of permanent income, then the prob-
lem is one of the improper exclusion of permanent income from the
list of explanatory variables rather than the simultaneity of
property value and the air pollution measures.
26. A major argument ,for dismissal is that even if property
values do have an independent impact upon air pollution dosages,
there is likely to be a substantial lag between the control
agency's perception of cost and its completion of the action to
reduce dosages. The observed pollution in the current period would
therefore be predetermined, i.e., the simultaneity problem would
-------
-131-
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21. Hanoch, G., and H. Levy, "Efficient Portfolio Selection with
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! and Profit, Princeton, N.J.: Princeton University Press, (1968)
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'24. Wald, A., Statistical Decision Functions, New York: John Wiley
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Chicago Press, (1969).
28. Alonso, W., Location and Land Use, Cambridge: Harvard
University Press, (1964) .
29. Brandow, G.E., "Demand for Factors and Supply of Output in a
Perfectly Competitive Industry," Journal £f_ Farm Economics,
44, (August, 1962), pp. 895-899.
30. Muth, R.F., "The Derived Demand Curve for a Productive
Factor and the Industry Supply Curve," Oxford Economic Papers,
16, (July, 1964), pp. 221-234.
31. Babcock, L.R., Jr., "A Combined Pollution Index for Measurement
of Total Air Pollution," Journal ££ the Air Pollution Control
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(Washington, D.C.: U.S. Government Printing Office, 1962).
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37. Stanley, W.J., Chicago's Air Resource Planning Program,
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40. Johnson, K.L., "Citizen Complaints of Air Pollution in
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in the Chicago Metropolitan Area," Journal o£ the Air Pollution
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48. Malone, J.R., "The Capital Expenditure for Owner-Occupied
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-------
Appendix A
Property Values and the Demand For Clean Air:
Cross Section Study for St. Louis
Kenneth F. Wieand
A Paper Presented at the
Committee on Urban Economics Research Conference,
-------
A-l
Introduction
It is widely recognized that urban dwellers cannot pay for
individual quantities of clean air and that they cannot, as
individuals, charge polluters for damages caused by their effluents.
Consequently, the control of pollution has passed into the hands
of governmental agencies which are often empowered to set air
quality standards and to enforce these standards by levying fines
or instituting legal action against violators.
Officials in these agencies have discovered that the absence
of market determined prices and quantities of air quality prevents
them from determining the level of air quality where total
benefits accruing from cleaner air neither exceed nor fall short
of the required costs. Because this information is necessary to
achieve an economically efficient use of resources, economists
have attempted to measure indirectly the revealed preference for
air quality.
One strategy for determining the demand for air quality
argues that the negative effects of air pollution will be
capitalized into the site value of residential housing. It follows
that the demand for clean air can be determined by comparing
differentials in property values in areas where pollution is high
with property values where pollution levels are low. This paper
summarizes an attempt to test the hypothesis that air pollution
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A-2
equation is based upon a recent adaptation of the location model
first proposed by Thunen [1] . Because of the lack of historical
price data, the model is tested with data from a cross section of
census tracts in the St. Louis area.
Ridker [2] and Crocker and Anderson [3] found a
significant relationship between pollution and housing expenditures
using the same data source as is used in the current study. This
paper compares their studies to the one described here.
Pollution and the Price gf Land
There is reason to believe that the property value-pollution
level relationship will accurately reflect the deleterious effects
of air pollution upon persons and property. Although pollution
levels tend to be high in centers of production and population,
factors such as wind direction and industry location distribute
pollutants unevenly within surrounding housing markers. If housing
consumers in a city recognize that pollution levels vary within
the housing market, and if they prefer areas of higher air quality,
sites in neighborhoods where pollution levels are low will be
bid up relative to sites in neighborhoods where pollution
concentrations are higher.
Because the concentration of air pollution is a characteristic
of the housing unit's location, the price for clean air will be
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A-3
illustrated by considering the investor who may build a house
either in an area where pollution is high or in an area where it
is low. Presumably, nonland costs are similar at the two sites.
The investor will compare the discounted income streams of the
two sites. He must subtract the added maintenance costs (or
more rapid deterioration of the structure) from the income stream
at the polluted site. The difference in the discounted income
streams w-ill be the price differential that the investor must
pay for the site where pollution is low.
The appropriate model for testing the pollution-property
value relationship can therefore be written P. * P., (x, , ...Xj,, AP)
where P, is the per unit price of land, x^ ,...xn are determinants
of land prices, and AP is an index of air pollution.
The Price £f_ Land and the Price £f Housing
As in most urban residential areas, the number of empty
lots in the St. Louis housing market relative to all sites is
negligible. Therefore, the price of land is not observable.
Studies such as the one discussed here attempt to use the unit
price of housing as a proxy for land prices. Housing prices are
determined by the price of land and by the prices of nonland
factors. Assuming that the housing market is competitive, and that
households maximize profits at each site, the price of housing
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A-4
fact, Equation (1) relates housing expenditures to factor inputs.
(1) PhH = P! L + PnN
where Ph is the per unit price of housing, H is the quantity of
housing, P, is the price of land, L is the quantity of land, and
P and N are the per unit price and the quantity of all nonland
factors.
Assumptions of competition and profit maximization imply
that a change in housing quantity will equal the sum of changes
in land and nonland factors multiplied by their marginal
productivities. Therefore, upon differentiating Equation (1)
we derive
(2) HdPfo » LdPj^ + NdPn
Equation (2) suggests that the price of housing will vary
directly with the price of land. The price of housing is,
therefore, an appropriate proxy for the price of land.
Total Expenditures, Unit Price, and Land Use Intensity
A major difference between the present study and the work of
Ridker and of Anderson and Crocker is in the choice of die
variable representing the price of housing. The latter two studies
utilized the average rent and average market value statistics
reported in Census of Population and Housing. 1960 as their
dependent variables, while the author employed these same
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A-5
in tens i ty .
Average rents and housing prices arise from transfers of
housing services between economic units. In all transactions
involving housing services, both those involving rentals over a
period of time and those involving transfers of ownership, the
total price is a multiple of the price per unit that the services
can command, P^, times the quantity of housing services that are
involved in the transaction H.
In other words, average rents and average market values
are not measures of the unit price of housing, P, , but of total
family expenditures on housing, P. H. It can be shown that total
family expenditures may move inversely with respect to the unit
price of housing, if the quantity of housing consumed, H, changes
in response to the change in Pi.. This fact can be demonstrated by
taking the derivative of P.H with respect to P, .
n h
(3) dPhH HdPh + PhdH
or
dP H
7~- =
dph
where e = price elasticity of demand
If e is equal to -1, a change in P^ will leave total expenditures
unchanged. If e is less than -1, total expenditures will vary
inversely with changes in P, . Recent research suggests that, in
the case of individual units, e may be -1 or smaller.—
_!/ Richard F. Muth, Cities and Housing, (Chicago: University of
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A-6
Therefore, PnH is not an adequate surrogate for P. .
The use by past writers of family expenditures as a surrogate
for unit price may result from an implicit assumption that the
quantity of housing can be held constant between units by the
addition to the list of regressors of variables which measure the
quantity of housing. The quantity, H, of housing services depends
upon floor space, layout and room design, materials used in
construction of the unit, site size, and a number of other factors.
A reasonably complete list of the components of H has been compiled
by Kain and Quigley [4] . If these data were available, they
could perhaps be added to the list of regressors to hold variation
of H constant. The 1960 Census did not make available the
necessary detail, however, and H is not held constant.
Civen an additional piece of information, the problems
encountered in using household expenditures can be avoided. Muth
[5] has shown that the intensity of land use will vary directly
with the price of land, hence with the price of housing, P^. To
briefly reconstruct his proof, return to Equation (1) and divide
both sides by L.
PhH
<*>—'i *-£-'.
Taking the derivative of Equation (4) in natural logs, one can
-------
A-7
(5) dlnPhH
- = 1 + fn 6dlnPn
f., = factor share of land
f = share of nonland factors
n
= elasticity of substitution
*JL
L will vary directly with the price of land, provided that
the cost of nonland factors is constant throughout the labor
market, because 6, f , and f, are positive. If 6 is
approximately 0.75 and the share of land is about 5 percent,
relative changes in PQH will be about fifteen times the size of
relative change in P^, and about the same magnitude as changes
21
in PI»~
The primary measure of land use intensity employed in this
paper was derived by multiplying average rentals plus 0.01 of owner
estimated market values in each census tract by the number of each
type of unit in the tract. (In the real estate profession 0.01 is
the conversion rate used to appraise the rental of homes given their
market value.) This figure measures the total monthly expenditure
on housing in each census tract. The land area of each tract was
computed, and a land use map was used to net out industrial and
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A-8
commercial acreage. Total monthly expenditure on housing was
then divided by the residential land area measured in acres to
arrive at monthly rent per acre. This variable, measured in
natural logs, is namedVALAND. VALAND is similar to the variable
used by Muth in a study for south Chicago [ 6] . The lists of
regressors used in the two studies are also quite alike, except
for different measures of the age of housing and for the
addition of the pollution variables in the present study.
Predictably the two sets of results are quite similar.
A measure of average expenditures on housing (VALHOU),
similar to that used by Ridker and by Crocker and Anderson, was
also utilized as a dependent variable in an attempt to compare
the performance of the independent variables in the three studies.
Determinants of the Intensity of Land Use
The independent variables used to try to explain variance
in VALAND were the percent of standard units in a census tract
(STDPER), average age of housing in the census tract (AVGAGE),
percent of units built before 1920 in the tract (BEF20), percent
white population in the tract (WHITE), average income in the
tract (INCOME), distance in miles from the central business
district (DISCED), a dummy for proximity to major highways (HIWAY),
a dummy for tracts in East St. Louis, 111. (ESL), a dummy
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A-9
dummy for proximity to Industry (INDUS), and a dummy for proximity
to commercial areas (COMM).
The first three variables were intended to explain the
variance in VALAND resulting from changes in the unit price and
quantity of tlte nonland portion of housing services. STDPER was
included to isolate tracts where housing units have large amounts
of deferred maintenance; theory suggests that the coefficient of
this variable is positive. AVGAGE measured the change in land
use intensity over time. Decreasing transportation costs over
time should make the coefficient of AVGAGE positive, but it
could be negative if the variable picked up housing deterioration
in older units. BEF20 measured technical change in newer housing
such as expanded electrical circuitry, and gas and electric
heating systems; the coefficient of BEF20 should be negative.
The next two variables measured neighborhood effects. The
unit price of housing services was expected to rise in high income
areas because of neighborhood amenities. It has been argued both
that non-whites pay more and that they pay less than whites for
equal quantities of housing. The coefficients of WHITE and
BOUND could not be prejudged.
The final five variables defined the locational characteristics
of the housing in a tract. Increased commuting costs tend to
cause housing prices to decline as distance from the CBD increases.
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A-10
with respect to VALAND, whereas decreased commuting time near
expressways should cause the coefficient of HIWAY to be positive.
Proximity to industry may either increase or decrease VALAND:
while commuting to work is easier, adverse external effects tend to
drive down housing prices. Finally, units near commercial
centers should command a higher price.
Data on sulphur pollutants and particulates are available
on a spatial basis for a number of large cities. Ridker and
Crocker and Anderson included sulfation, measured as sulphur
trioxide, and suspended particulates, measured with hi-vol samplers,
in their models. The paper under discussion utilized this
information along with measures of dustfall and sulphur dioxide.
Like the other variables in the model, pollution levels vary
spatially. Unlike the other variables, pollution concentrations
also fluctuate over time. One can prove that the average
concentration of a pollutant for a given period of time will
accurately reflect the disutility of the pollutant's temporal
distribution only if the marginal disutility of pollution is
constant. Because the effects of pollution become more noticeable
as concentrations increase, the assumption of constant marginal
disutility does not seem warranted. Therefore, measures of the
variance of the temporal distribution were also included. As
the inclusion of these measures did not improve the performance
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A-ll
variables are not presented here.
In the following presentation of results PAR stands for
variables measuring suspended particulates, and S0~ represents
measures of sulphur trioxide. Existing data do not define either
particulates or sulphur for each census tract in the study area.
It was therefore necessary to estimate pollution levels for most
tracts. Three methods of estimation were employed. sPAR and
sSO-j are variables obtained from isopleths (lines of equal actual
value) found in t:he Interstate Air Pollution Study [7] . If the
majority of a census tract lay between two isopleths, air
pollution in .the tract was assumed to equal the level prevailing
on the boundary of the isopleth furthest from the CBD. These
variables are similar to the proxies used by Ridker and by Crocker
and Anderson.
Pollution measured in this fashion resembles a step function
decreasing with distance from the CBD. One would expect pollution
to decline continuously rather than in discrete jumps. Therefore,
variables iSO^ and iPAR were estimated by interpolating in a
straight line between isopleths. Finally, SO^ and PARm were derived
using data from isopleths, monitoring stations, and information on
wind direction. 803 and PARm are expected to be the most accurate
measures of the average levels of particulates and sulphur pollution
-------
A-12
Empirical Results and Conclusions
Table I. reports the results obtained by regressing VALAND
against regressors other than the pollution variables. All but
HIWAY have signs consistent with a priori expectation, all but
BOUND, HIWAY, and COMM are significantly related to VALAND, and
the magnitudes of the coefficients are reasonable.
Table II. lists the coefficients of the pollution variables.
INDUS, COMM, and BEF20 are correlated with the pollution variables,
For purposes of exposition, these three variables are omitted
from the estimating equation.
The coefficients of pollution are negative in most cases
but are not significantly related to VALAND. If either ESL or
STDPER is omitted from the estimating equation, the coefficients
of the pollution variables fall and become significant at the .05
level. The author doubts that multicollinearity between pollution
and ESL and STDPER is responsible for the lack of a significant
relationship between pollution and VALAND for two reasons. First,
the standard errors of the pollution variables do not fall when
ESL and STDPER are deleted from the equation. Also, a subsample
of 86 observations was selected by dropping all tracts in East
St. Louis and all tracts where the percent of standard units was
small to determine whether ESL and STDPER obscured a significant
relationship between pollution and VALAND. When the equation is
tested using the subsample, the pollution variables behave as they
-------
A-13
Table III. lists the percentage changes in VALHOU and
VALAND implied by 10 percent changes in some of the independent
variables. Examination of Table III. shows that the relationships
between VALHOU and the exogenous variables may be quite different
from the relationships between these variables and VALAND. The
coefficients of INCOME in the VALHOU regressions imply that the
average value of housing in the study area is twice the size of
the average yearly income, reflecting the fact that average
housing prices in the SMSA were about $12,000 in 1960, and that
average income was about $6,000. This relationship obviously
reflects the fact that the elasticity of demand for housing is
greater than zero. If relative changes in VALAND are fifteen times
the changes in the price of housing, the 7.5 percent change in
VALAND implies a 0.5 percent change in the price of housing.
Consider also the changes in VALHOU implied by a 10 percent
change in DISCED. Three of the VALHOU regressions state that
expenditures increase with distance when we would expect price to
decline. Positive distance coefficients are consistent with a
price elasticity of less than -1. The VALAND regression implies,
on the other hand, that the price of land declines at 12 percent
per mile and therefore, that the price of housing falls by a
little less than 1 percent per mile.
This paper concludes that, although there is reason to
-------
A-14
with levels of air pollution, average rentals, market prices, or
other measures of household expenditures are not adequate proxies
for the price of housing. The output land ratio used in the study
summarized here is a suitable proxy for the price of housing.
When the output land ratio is regressed against levels of air
pollution and other determinants of housing prices, the regression
coefficients of the pollution variables are generally negative,
but are not significantly different from zero at the .05 level.
The results of the study discussed above do not prove that
the effects of air pollution are not harmful to urban dwellers.
They do caution against using past findings to justify reductions
-------
A-15
Table I
Results of Regressing VALAND Against Variables
Other than Pollution Variables
Variable
STDPER
WHITE
AVGAGE
BEF20
INCOME
DISCED
INDUS
ESL
HIWAY
BOUND
COMM
R2
Constant
Coefficient Equation
(Standard Error) 4.2
0.59
(.20)
-0.22
(.10)
0.021
(.005)
-0.61
(.11)
0.6x10 "t
(.2xlO~ )
-0.116
(.023)
-0.24
( .064)
-0.75
(.11)
-0.10
(.064)
0.12
(.080)
0.091
(.077)
0.64
term 6.06
4.3
0.59
(.20)
-0.29
(.096)
0.021
(.005)
-0.61
(.11)
0.7xlO~
(.2x10 )
-0.122
(.023)
-0.26
(.061)
-0.74
(.11)
0.62
6.05
Degrees of
freedom
126
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A-16
Table II
Performance of Three Alternate Measures of Particulates
and of Sulfur Trioxide in Explaining VALANDa
Variable
Sulfur Trioxide
S03
iS03
sS03
Particulates
PARro
iPAR
sPAR
Coefficient
+0.0036
-0.0790
-0.0870
-0.0015
-0.0011
-0.0012
a
Th"3 specification used is as
Standard Error
0.001
0.105
0.150
0.0013
0.0017
0.0021
follows: VALAND
R2
0.45
0.45
0.45
0.45
0.45
0.45
» f (pollution
variable. DISCED, STDPER, AVGAGE, INCOME, WHITE, ESL)
Measured in milligrams/hundred cubic centimeters
£
-------
A-17
Table III
CHANCE IN VALHOU AND VALAND RESULTING FROM A TEN PERCENT CHANGE IN
SELECTED INDEPENDENT VARIABLES: COMPARISONS OF WIEAND
RIDKER, AND CROCKER - ANDERSON STUDIES
Independent Variable
Depend end en t Variable
VAI.HOIT VALAND
Wieand
owned and
rented
Crocker - Anderson
owned rented
Ridker
owned
Wieand
owned and
rented
sS03
SPAR
INCOME
DISCED
Built before 1940
Condition
Percent Standard
Percent Dilapidated
WHITE
AVGAGE
Median Rooms
Constant (log,,)
R2 6
Degrees of freedom
-1.0
26.0
2.7**
-1.0**
5.1
-2.8
7.8
0.75
139.0
-2.0
-1.7
19.0
-4.0
-0.4
16.0
-1.2
3.5
0.76
236.0
-0.2**
-1.1
14.0
1.0**
-1.0
13.2
-0.8
-1.2
0.77
174.0
-0.8
20.0
1.3
-0.1
9.0
7.3
0.94
167.0
-0.9**
-1.2
7.5
-12.0
6.6
-2.3
8.0
6.1
0.66
139.0
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A-18
REFERENCES
1. R.F. Muth, "Rural Urban Land Conversions," Econometrica,
XXIX (January, 1961), 1-23; see also R.F. Muth, "The
Spatial Structure of the Housing Market," Regional Science
Association; Papers and Proceedings, VII (1961), 207-20;
R.F. Muth, "Variation of Population Density and Its
Components in South Chicago," Regional Science Association;
Papers and Proceedings, XI (1964), 173-83; W. Alonzo, "A
Theory of the Urban Land Market," Regional Science
Association: Papers and Proceedings, VI (1960), 149-57;
L. Wingo, Transportation and Urban Land, (Washington:
Resources for the Future, Inc., 1961).
2. Ronald G. Ridker, The Economic Costs of Air Pollution:
Studies in Measurement. Praeger, 1967.
3. Thomas Crocker and Robert Anderson, "Air Pollution and Housing:
Some Findings," Institute For Research in the Behavioral,
Economic, and Management Sciences, No. 264 (January, 1970).
4. J.F. Kain and J.M. Quigley, "Measuring the Value of Housing
Quality," Journal of the American Statistical Association,
LXV, (June, 1970), 532-48.
5. R.F. Muth, Cities and Housing, (Chicago, University of
Chicago Press, 1968).
6. R.F. Muth, "The Variation of Population Density and Its
Components in South Chicago," Regional Science Association;
Papers and Proceedings. XI (1964), 173-83.
7. U.S. National Center For Air Pollution Control, Cincinnati,
"Air Quality Measurements," Interstate Air Pollution Study,
Phase II Project Report iii (Washington: Government Printing
-------
Appendix B
A COMMENT ON"PROPERTY VALUES AND AIR POLLUTION: A CROSS SECTION
ANALYSIS OF THE ST. LOUIS URBAN AREA*,' BY KENNETH WIEAND
Robert J. Anderson, Jr.
Purdue University
Thomao D. Crocker
University of California Riverside
I.
In accordance with principles of commentary reportedly
established by Mark Anthony, we come not to praise what is
praiseworthy in Wieand's paper, but rather to bury that which we
believe to be in error. Ironically, we contend that Wieand's
dismissal on logical grounds of our results and those of other
investigators Is fundamentally illogical.
In section II, Wieand's contention that we and others have used
a theoretically incorrect dependent variable in our empirical
work is evaluated. Then, in section III, some results from past
property value studies not generally available are reported. In
section IV, we present some new empirical evidence and offer some
concluding comments.
II.
It is well-known that no universally accepted concept of a
commodity exists in economics. Witness the economist's continuing
concern with aggregation problems. To modify only slightly
-------
B-2
defined In accordance with the purposes of a theory. The
fundamental difference between Wieand's work and that of previous
investigators lies in the adopted definition of commodity units.
Wieand treats "housing" as a single commodity, whereas other
investigators treat physically different properties as distinctly
different commodities.
Following Muth (1969), Wieand defines observed "property
s,
values" or rentals to be identically the product of two
unobservable magnitudes, the "price of housing services" and the
"quantity of housing services". Under general assumptions, Wieand
demonstrates that if such a definition is adopted, then it is the
case that property value is neither equal to nor does it vary
with the "price of housing services". This conclusion is
unimpeachable, as is the logic to which it gives rise in the search
for an observable proxy variable for the "price of housing services".
It does not follow, however, that property value is not a
measure of price under all definitions of commodity units and
attendant prices. Yet Wieand's criticism of our work rests, insofar
as we are able to determine, on precisely this non-sequitur. To
reject theorems based on one set of definitions and axioms because
they happen to differ from one's own theorems based on a different
set of definitions and axioms is at best unfair, and at worst bad
logic.
-------
B-3
work of previous investigators is Lancaster's (1966) formulation
of consumer behavior and Baumol and Quandt's (1966) empirical
work on the demand for abstract modes of transportation. We
shall follow Lancaster.
The point of departure of these approaches to demand theory
is that utility functions are defined not over traditionally
conceived goods but rather over characteristics embodied in goods.
The endowment of characteristics embodied in any good is presumed
to be objective in the sense that all consumers perceive identical
endowments in the same good. The allocation problem of the consumer
is to consume that basket of goods which yields a mix and magnitude
of characteristics maximizing his utility subject to his budget
constraint. Assuming that goods and characteristics are linearly
related (that the consumption technology is linear in Lancaster's
phrase), the problem of the consumer may be formulated
instructively as
Maximize: U(z)
subject to: p'x = y
z = Bx
z,x > 0
where z is an mxl vector of characteristics, p is an nxl vector of
good prices, y is a scalar representing disposable money income, and
B is an mxn matrix, the (i,j) element of which gives units of the ith
-------
B-4
Consider the first order conditions of consumer equilibrium,
(1) U1 Vt z - Xp = 0 i = 1, ..., n
y - p'x = 0
where U1 is the transpose of 3 U/ 9 z, and where V ^z = 9 z/ J)x^. In
the particular case of a linear consumption technology, V z = b^ is
the ith column of the consumption technology matrix B.
If the conditions of the implicit function theorem are
fulfilled by the implicitly defined vector function (1), there
exists a unique explicitly defined vector function
(la)/ J\ = G(x, y)
The coordinate functions of G( ) which pertain to the price vectors
of p may be interpreted as offer functions, giving prices offered
for various quantities and income. These functions may be easily
obtained directly from the first-order conditions, which by
rearrangement and substitution yield
y U1
(lb.1) Pi -5
£ U1 V,zx,
y
It is evident that the consumption technology is instrumental
in the determination of marginal rates of substitution among
commodities and hence Is instrumental in determining demands. Note
-------
B-5
the characteristics which it yields. That is, goods which yield
the same mix and magnitude of characteristics (goods for which the
V . z are identical) are perfect substitutes, on a unit for unit
basis, and therefore bear the same price.
Equation (lb.1) is the theoretical underpinning for the
statistical work with property values performed by us and others.
Treating the observed average characteristics of each census
tract as an observation on 7,z = b., and median property value as
an observation on p^, we have attempted to explain differences in
2
PI in tern's of y and b . We thus treat each census tract
observation as though it were an observation on a different
commodity, while Wieand treats his observations as though they
pertain to the same commodity.
Some results from past studies of air pollution and residential
property values are reported below in Table I. All investigators
believe they have found statistically significant negative
relationships between air pollution and property values. While
the specifications differ in some respects, the air pollution
results are remarkably uniform. That is, several replications
have yielded very similar results, even though the structure of
residential property markets among cities may differ widely. This
is cause to be cautiously confident that some misspecification
is not at base responsible for the observed negative relationship.
-------
B-6
investigators, precise comparisons are not possible. Nevertheless,
estimates of marginal property value losses vary between roughly
$250 and $1000 per residential unit for ten to fifteen percent
increments in the mean value of the various pollution measures used.
Clearly these results and the conclusions which might be drawn from
-------
Dependent
TABLE I
Some Results of Past Studies of Air Pollution and Residential Property Values
ndependent
CONSTANT
In PPT
In AMS
In ITL
In MRM
In PPU
In RMFI
In RHPM
In UKR
In JEW
In M)0
In MFI
In DIS
In OLD
In NWT
In DLP
2
R2
*•
S
F
Zerbe(1969V
In MPV
8.97
-0.1206
0 .0041
0.2570
0.1720
0.0001
-0.0001
0.0082
0.0043
0.0029
0.942
0.0846
107.83
r Zerbe(1969)^
In MPV
8.72
-0.0810
0.1260
0.00004*
0.0101
0.00004*
0.923
0.0488
72.55
Peckham(1970)
In MPV
4.7821
-0.1155
-0.0958
0.44973
0.4867
0.0575
-0.0415
-0.0054*
-0.0257
0.766
80.07
Anderson- +
Crocker(1970)
In MPV
-1.0705
-0.0627
-0.0412*
1.0996
0.7598
-0.0885*
-0.0036*
-0.0004*
-0.0267
0.877
0.0138
Anderson- +
Crocker(1970)
In MPV
-1.2325
-0.06M
-0.0649
0.8246
0.8130
0.0349*
-0.0464
-0.0133
-0.0028*
0.916
0.0114
Anderson- .
Crocker (1970)
In MPV
1.1617
-0.1698
0.0010*
0.9064
0.9970 ?
-0.0312 ^
-0.0213
0.0321
0.0113*
0.790
0.0179
*Not significantly different from zero at .05, 1 tailed test.
^Regression included only observations on tracts where at least 75% of dwelling units were single
family residential (generally suburban areas) .
it
-------
B-8
NOTES TO TABLE I
PFT annual arithmetic mean suspended participates
AMS annual arithmetic mean sulfation
ITL percentage Italian
MRM median number of rooms
PPU people per dwelling unit, average
RMFI residualized median family income
RHPM residualized housing units per mile
OKR percentage Ukranian
JEW percentage Jewish
MOO neighborhood occupational homogeneity
MFI median family income
DIS distance to central business district
OLD percentage of housing units more than 20 years old
NWT percent nonwhite
DLP percent housing units dilapidated
Regressions reported in columns of this table are based respectively
on data from Toronto (Ontario, Canada), Hamilton (Ontario, Canada),
-------
B-9
IV.
If we may take it as established that the logical problem
Wieand claims to have demonstrated in previous work is really no
problem at all, it remains to determine the source of the
difference between his results and those of other investigators.
Although it is possible to entertain a near infinitude of dark
suspicions of misspecification and other errors in giving
empirical content to both theories, we believe that the divergence
of results is a matter of chance pure and simple. This conjecture
is based primarily on some regressions we have recently run using
better data than the Census material on which all earlier work
has been based.
The results in Table 2 are based on FHA data for individual
3
property transactions in the City of Chicago. Air pollution
measures, which are interpolations from basic point measurements
made by the Chicago Air Pollution Control District, refer to the
mean annual suspended particulates and sulfur dioxide in the calendar
year immediately preceding the year of property sale. As with our
earlier work with census tract data, we have included measures of
both suspended particulates and sulfur oxides in all equations
even though the two tend to be so collinear that it is difficult
to gauge the independent effect of each. In column 1 of the
table, a specification analogous to that of Anderson and Crocker
-------
B-10
price at which the transaction occurred. Column 2 reports the
results for a regression in which the natural log of the FHA
estimated price of the site for each transaction in the sample
is used as the dependent variable. The results reported in
column 3, where the natural log of the ratio of sale price to lot
size is used as the dependent variable, were obtained using a
specification analogous toWieand's.
Under each specification, the coefficient of at least one of
the pollution measures is significantly negative and the sum of the
coefficients is negative. In forms not reported in Table 2
which employ only one pollution measure as an explanatory variable,
the coefficient of the included variable is always significantly
negative. Evaluated at the means of the relevant variables, the
marginal capitalized damages in column 1 are $474.16 for each
additional ten ug/M/day of suspended particulates plus an
additional one ppb per twenty-four hours of sulfur dioxide. In
column 2, the analogous damages are $191.06. A similar computation
for column 3 produces marginal capitalized damages of $.21 per
square foot of lot size. This yields an average marginal
capitalized damage per residential property of $869.19, a figure
among the highest estimates obtained in all previous studies.
Comparisons of Wieand's results for St. Louis with our own, and
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B-ll
TABLE 2
Some New Results for Chicago - 1967
Constant
PRT66
SUL66
TCINC
LIVAR
HSAGE
MODUR
LOTSZ
SQIDX
INC ID
DISSM
DLAKE
INC66
FRAME
DTTYP
NHAGE
CRIMX
STDPER
WHITE
INDUT
CMMRC
R2
\ 1) *
In SALEP-
4.1532
-0.3998
0.0610*
0.3305
0.2356
-0.0465
0.4063
0.0917
-0.0729
0.0361
0.0321*
-0.0202
0.1216
-0.0810
0.1004
-0.0296
0.771
(2)
In SITEP
7.0780
-0.0005
0.0001*
0.0004
0.0002
-0.0543
0.0003*
-0.0024
0.00005
-0.0027
0.0056
0.0003*
-0.0041
-0.0013*
0.567
(3)
In SALEP
LOTSZ
2.6615
-0.0053
0.0012*
-0.00005*
-0.00004*
-0.0039
0.0011
-0.0138*
-0.0028
-0.0011*
-0.1070
-0.2906
-0.0262*
0.0009*
0.0017
-0.0059
0.0049
0.315
S 0.1126 0.1866 0.2455
*Not significantly different from zero at .05, 1 tailed test.
-------
B-12
Notes to TABLE 2
PRT66 = annual arithmetic mean suspected particulates, 1966, in
ui;/M3/ day.
SUL66 = annual arithmetic mean sulfur dioxide in ppm by volume per
twenty-four hours.
TCINC = total current income of family in dollars.
LIVAR = living area of house in square feet.
HSAGE - age of house in years.
MODUR = mortgage duration in years.
LOTSZ = lot size in square feet.
SQIDX = school quality index 1 » highest, 4 = lowest.
INC ID = incidental expenses associated with house in dollars.
DISSM = distance to the intersection of State and Madison in tenths
of miles.
DLAKE = distance to lake in tenths of miles.
INC66 = median family income in community area, 1966, in dollars.
FRAME = dummy for house type.
DTTYP = dummy for detached.
CRIMX = neighborhood crime rate, an index where the base is the
arithmetic mean rate for the City of Chicago.
STDPER= percent standard.
WHITE = percent white.
INPUT = industrial land within one square mile in hundredths of
square miles.
CMMRC = commercial land within one square mile in hundredths of
square miles .
SALEP = sale price .
-------
B-13
suggest that Wieand, in general, explains a smaller proportion
of the variation in his dependent variable than we explain in the
dependent variable we adopt. That is Wieand's specification
apparently involves a substantially higher "noise-to-signal ratio"
than does that under which we proceed. Other things being
equal, one would suppose that it is harder under Wieand's
specification than it is under ours to distinguish the relatively
minor influence of air pollution on property values from other
-------
B-14
FOOTNOTES
1. We assume that the non-negative constraints are not binding.
2. Under common restrictions on U(«)» X is a function of y alone.
given p.
3. The research for these results was supported by Research
Contract CFA 22-69-52 of the National Air Pollution Central
-------
B-15
BIBLIOGRAPHY
1. Anderson, R.J., Jr., and T.C. Crocker, Air Pollution and
Housing: Some Findings. Paper No. 264, Institute for Research
In the Behavioral, Economic, and Management Sciences, (Jan. 1970).
2. Lancaster, K.J., "A New Approach to Consumer Theory," J.
of Political Economy, 74 (April 1966), 132-157.
3. Muth, R.F., Cities and Housing, Chicago: Univ. of Chicago
Press (1969).
4. Quandt, R.E., and W.J. Baumol, "The Demand for Abstract Transport
Modes: Theory and Measurement," J. of Regional Science,
6 (Winter, 1966), 432-441.
5. Peckham, B.W., Private communication dated May 13, 1970.
6. Zerbe, R.O., Jr., The Economics of Air Pollution: A Cost
Benefit Approach. Toronto: Ontario Dept. of Public Health
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