Socioeconomic Environmental Studies Series
INTRA-URBAN MORTALITY AND AIR QUALITY:
AN ECONOMIC ANALYSIS OF THE COSTS
OF POLLUTION INDUCED MORTALITY
Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Corvailis, Oregon 97330
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, US Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
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The nine series are:
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2, Environmental Protection Technology
3 Ecological Research
4 Environmental Monitoring
5 Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
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This report has been assigned to the SOCIOECONOMIC ENVIRONMENTAL
STUDIES series. This series includes research on environmental management,
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impacts of alternative poficies; analyses of environmental planning techniques
at the regional, state, and local levels; and approaches to measuring environ-
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This document is available to the public through the National Technical Informa-
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EPA-600/5-77-009
July 1977
INTRA-URBAN MORTALITY AND AIR QUALITY:
AN ECONOMIC ANALYSIS OF THE COSTS OF
POLLUTION INDUCED MORTALITY
BY
John J. Gregor
The Center for the Study of Environmental Policy
The Pennsylvania State University
University Park, Pennsylvania 16802
Grant R803609-01
Project Officer
John Jaksch
Criteria and Assessment Branch
Corvallis Environmental Research Laboratory
Corvallis, Oregon 97330
Corvallis Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
EPA - RTP LIBRARY
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DISCLAIMER
This report has been reviewed by the Corvallis Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publi-
cation. Approval does not signify that its contents necessarily reflect
the views and policies of the U.S. Environmental Protection Agency nor
does mention of trade names or commercial products constitute endorsement
or recommendation for use.
ii
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FOREWORD
Effective regulatory and enforcement actions by the Environmental Protection
Agency would be virtually impossible without sound scientific data on pollu-
tants and their impact on environmental stability and human health. Respon-
sibility for building this data base has been assigned to EPA's Office of
Research and Development and its 15 major field installations, one of these
is the Corvallis Environmental Research Laboratory (CERL).
The primary mission of the CorvalliE laboratory is research on the effects
of environmental pollutants on terrestrial, freshwater, and marine ecosystems;
the behavior, effects and control of pollutants in lake systems; and the
development of predictive models on the movement of pollutants in the bios-
phere.
This study was initiated by the Washington Environmental Research Center,
Office of Research and Development, Washington, D.C. and completed at the
CERL, Office of Research and Development, Corvallis, Oregon.
A. F. Bartsch
Director, CERL
iii
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ABSTRACT
The possibility that extrmely high levels of air pollution can shorten
lives and affect the quality of human life was painfully brought to the
attention of individuals in the United States by the 1948 episode at
Donora, Pennsylvania. Today few people would argue that the existence
of pollution concentrations of Donora's magnitude do not have significant
health effects. There is substantially less agreement, however, on the
significance of the effects of smaller levels of air pollution on health.
This report has attempted to quantify in both physical and monetary terms
the effects of existing ambient levels of air pollution on human mortality.
A model for the isolation of air pollution's influence on human mortality
was developed based on insights derived from existing experimental, episo-
dic, and epidemiological studies. This model was then estimated using
weighted linear regression analysis and data from the 1968-1972 experience
of Allegheny County, Pennsylvania. The resulting pollution-related mor-
tality functions were then monetized through the use of the most theoreti-
cally consistent economic valuation of mortality changes. Specifically,
the estimated age-sex-specific pollution-related mortality functions were
monetized by applying existing estimates of individual's willingness to pay
for mortality decreases.
The results of this study lend support to the contention that an improvement
in ambient air quality will produce social benefits in the form of decreased
probabilities of death. Specifically, the results obtained for Allegheny
County suggest that ceteris paribus efficient resource allocation would be
enhanced by devoting relatively more financial resources to the control of
particulate matter rather than sulfur dioxide. The validity of this asser-
tion is contingent upon existing technology. Specifically, the present
marginal costs of controlling sulfur dioxide exceed the morginal costs of
controlling particulate matter; and the estimated mortality benefits of
decreasing particulate matter exceed the estimated mortality benefits of
decreasing sulfur dioxide. Therefore, on both counts it would appear
that relatively more resources should be devoted to the control of parti-
culate matter rather than sulfur dioxide. It must be emphasized, however,
that this latter conclusion is based solely on the mortality component of
the social benefit function and thus excludes any non-mortality benefits of
pollution reduction.
This report was submitted in fulfillment of Grant R803609 by the Center for
the Study of Environmental Policy under the sponsorship of the U.S. Environ-
mental Protection Agency. This report covers the period January 1, 1968,
to December 31, 1972, and was completed as of July 31, 1976.
IV
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CONTENTS
Foreword •
Abstract iv
Figures vi
Tables vii
Acknowledgment .viii
I. Summary and Conclusions 1
II. Resource Allocation and Air Pollution 4
Introduction 4
Efficient Use of Resources 5
Externalities, Transaction Costs and Public Goods . 6
Statement of the Problem 8
III. Air Quality and Mortality: Development of the Model . . 9
Previous Studies, Insights and Problems 9
The Model 16
IV. Estimating the Model: Results for Allegheny
County, Pennsylvania 21
Variable Estimation, Units of Observation
and Data Sources 21
Estimation 28
Results 29
V. Cost-Benefit Analysis: Economic Guidelines for
Social Decisions 38
Cost-Benefit Analysis—The Theory 38
Cost-Benefit Analysis—The Application 48
VI. Evaluation of Mortality Benefits: Monetization of
Decreases in Mortality 51
Spurious Monetization Procedures 51
The Correct Conceptual Measure 54
Dollar Estimates of Social Benefit 57
References 68
Bibliography 77
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FIGURES
Number
1 Location of air quality monitoring stations within
Allegheny County, 1968-1972 25
2 Marshallian consumer's surplus 40
3 Hicksian consumer's surplus 42
4 Utility possibility curves before and after air quality
improvement 45
5 Marginal air pollution costs and benefits 50
6 Individual's indifference map for risk and income 55
7 Market reflection of risk-income trade-off 5R
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TABLES
Number Page
1 Summary of Lave and Seskin Inter-Urban Mortality Functions 14
2 Summary of Independent Variables Included in General Model 20
3 Underlying Causes of Death Considered to be Related to Air
Pollution 22
4 Percentage of Households with Some Form of Health Insurance
by Household Income 24
5 Means and Standard Deviations of Variables Included in
Equations 29
6 Mortality Function Estimates 30
7 Age-Sex-Cause Distribution of Allegheny County White
Deaths During 1968-1972 33
8 Elasticity Estimates 37
9 Means and Standard Deviations of the Variables Included in
Thaler and Rosen's Wage Functions 60
10 Thaler and Rosen Regression Estimates of Weekly Wage Rates
Part A. Linear 61
Part B. Semi-Log 62
11 Thaler and Rosen's Sample Occupations and Risks 63
12 Changes in Age-Sex Specific Pollution-Related Mortality Rates
Resulting from 1 Percent Decrease in S02 64
13 Average Age-Sex-Specific Marginal Annual Dollar Benefits for
Pollution-Related Mortality Changes Resulting from
1 Percent Decrease in S02 or TP 65
14 Total Age-Sex-Specific Marginal Annual Dollar Benefits for
Pollution-Related Mortality Changes Resulting from a
1 Percent Decrease in S02 or TP 66
VJ.1
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ACKNOWLEDGEMENTS
The author is indebted to numerous individuals and organizations for
providing data, technical advice, and other assistance for this study. Of
special merit were the inputs provided by Dr. Frank B. Clack and his
colleagues at the Allegheny County Health Department. At The Pennsylvania
State University, Dr. Monroe Newman (Department of Economics), Dr. Terry
Ferrar (Center for the Study of Environmental Policy), Mr. Richard Yarzap
(Computer Center) and Mr. Alan Brownstein (Center for the Study of Environ-
mental Policy) made very important contributions. Of course, the author
retains full responsibility for any inadequacies which the study may contain.
The U. S. Environmental Protection Agency and The Center for the Study
of 'Environmental Policy at The Pennsylvania State University supported this
work financially.
viii
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SECTION I
SUMMARY AND CONCLUSIONS
The motivation for this study was based on the desire to obtain alloca-
tional efficiency in the use of the scarce resource clean air. Due to the
inherent public good nature of the air resource and the resulting breakdown of
th"e exclusion principle, no market has developed in which property rights
could be exchanged. Thus, an optimum allocation of this scarce air resource
could not be attained in a private enterprise market economy. Some form of
collective or governmental action is required, therefore, to obtain a more
efficient allocation of this resource. From an efficiency viewpoint, such
governmental intervention should be guided by cost-benefit criteria. This
study was designed to facilitate this efficient allocation of clean air by
isolating air quality's aggravation effect on intra-urban mortality and then
quantifying this portion of the marginal social benefit function in a manner
consistent with the theoretical basis of cost-benefit analysis.
The results of this study are of importance to both the theoretician and
the public decision maker, since this effort provides a conceptually accurate
quantification of the costs of pollution-aggravated mortality. Moreover, the
significant policy-relevant contribution of this study is its ability to
assist government officials in establishing socially efficient standards for
ambient air quality.
While empirical estimates of certain components of the marginal social
benefit function have previously been calculated, severe difficulties are
encountered when attempting to empirically determine the optimum level of air
quality. In particular, the efforts to quantify the marginal social benefit
function are greatly complicated by problems of isolating air pollutions's
many potential effects and evaluating these effects in monetary units. In
this study, a regression equation for the isolation of air pollution's in-
fluence on human mortality was developed based on insights derived from
existing experimental, episodic, and epidemiological studies. The mortality
component of the marginal social benefit function was then estimated using
weighted linear regression analysis and data from the 1968-1972 experience of
Allegheny County, Pennsylvania. The resulting pollution-related mortality
functions were then monetized through the use of the most theoretically con-
sistent economic valuation of mortality changes for inclusion in cost-benefit
analysis. Specifically, the estimated age-sex-specific pollution-related
mortality functions were monetized by applying existing estimates that approx-
imate an individual's willingness to pay for mortality decreases. The weight
of the evidence uncovered in this study suggest the following conclusions:
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(1) Both air quality variables, total particulares and sulfur
dioxides, exhibit the expected positive relationship to
pollution-related mortality. These exacerbating effects
while small in absolute terms, are statistically significant
for total participates although statistically insignificant
for sulfur dioxide when sulfur dioxide is considered as a
separate independent variable.
(2) The absolute size of the air quality coefficients generally
increase with age indicating either that the ability of the
body to withstand the influences of total particulates and
sulfur dioxide decreases with age, or that there exists a
cumulative influence of air quality on mortality. Thus,
the distribution of benefits from pollution abatement
cannot be isolated by age.
(3) The absolute size of the air quality coefficients in the
pollution-related mortality functions are generally twice
as large for males as for females in the less than sixty-five
age groups. For the sixty-five and over age group, however,
the coefficients are approximately equal for males and females.
In essence, this result suggests the possibility of relatively
higher exposure levels at work for males compared to exposure
levels experienced by females in the residential environment.
(4) The estimated air pollution coefficients indicate that at
the mean, a 1 percent reduction in total particulates will
lead to between a 0.23 and a 0.89 percent reduction in pol-
lution-related mortality. It should be recognized that even
if the sulfur dioxide coefficients were statistically signi-
ficant, a similar 1 percent reduction in sulfur dioxide would
only result in between a 0.01 and a 0.05 percent reduction in
pollution-related mortality. In essence, this result implies
a relatively greater importance of total particulates compared
to sulfur dioxide.
(5) Utilizing existing willingness to pay estimates for mortality
reductions, it can be concluded that individuals in Allegheny
County would be willing to pay a minimum of $7 million annually
in order to maintain total particulates at a level 1 percent
below those experienced during the 1968-1972 period. However,
for the same period such individuals would be willing to pay
only $0.5 million annually for a similar percentage reduction
in sulfur dioxide if the coefficients of sulfur dioxide were
statistically significant. Thus, the marginal social benefits
accruing to the individuals in Allegheny County from a 1 per-
cent reduction in both of these pollutants exceeds $7.5
million or the value of the change in the mortality component
of the marginal social benefit function.
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The results of this study, therefore, lend support to the contention that
an improvement in ambient air quality will produce social benefits in the form
of decreased probabilities of death. Specifically, the results obtained for
Allegheny County suggest that ceteris paribus efficient resource allocation
would be enhanced by devoting relatively more financial resources to the
control of particulate matter rather than sulfur dioxide. The validity of
this assertion is contingent upon existing technology. Specifically, the
present marginal costs of controlling sulfur dioxide exceed the marginal costs
of controlling particulate matter; and the estimated mortality benefits of
decreasing sulfur dioxide. Therefore, on both counts it would appear that
relatively more resources should be devoted to the control of particulate
matter rather than sulfur dioxide. It must be emphasized, however, that this
latter conclusion is based solely on the mortality component of the marginal
social benefit function.
The expression of air pollution's aggravation effects on mortality in
dollar values consistent with the other components of cost-benefit analysis
will, however, facilitate the efficient allocation of society's scarce re-
source clean air. By monetizing the mortality component of the marginal
social benefit function, more enlightened decisions about the socially
optimum level of air quality can be formulated. In essence, these dollar
estimates will allow decision makers to more closely approximate the optimum
level of air quality by permitting the direct comparison of mortality re-
duction and other benefits of air pollution abatement with the costs associ-
ated with the various abatement policies.
Further research is, however, required to test the reliability of both
the mortality functions and willingness to pay estimates. For example, it
is not completely clear whether the relatively large influence of particulate
matter on mortality is due to the specific elements of which it is composed
in Allegheny County or the inherent characteristics of particulate matter.
Thus any extrapolation of these results to other geographic areas must be
made with extreme caution. Additional research is also needed on individuals1
willingness to pay for mortality decreases including the valuation of family,
friends and society and the other components of the marginal social benefit
function.
Changing lifestyles and increased population have forced man to recognize
that the assimilative capacity of his natural environment is indeed limited.
Hence, environmental preservation possesses a long-term problem of resource
allocation and as such the environment must be efficiently managed. Public
decision makers as well as the general public should begin taking affirmative
action to control environmental degradation. It is hoped that this study has
contributed to both an increased understanding of the impacts of air pollution
as well as stimulated the efficient use of society's scarce resource clean
air.
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SECTION II
RESOURCE ALLOCATION AND AIR POLLUTION
INTRODUCTION
Since his appearance on earth, man's pursuit of well-being, and in fact
his very existence, has been a source of pollution. Historically, nature has
been capable of absorbing man's organic and inorganic waste with little
difficulty.! Despite isolated instances, it was not until the twentieth
century that pollution was considered more than simply an annoyance.
The emerging concern about environmental degradation has been prompted
by a combination of recent developments. As world population grew larger in
size and affluence, so did society's wastes. New and exotic goods created by
technology put even more of a burden on nature's recycling capabilities since
many of the new products were not readily biodegradable.2 Moreover, increased
leisure time resulting from greater affluence enabled man to enjoy what was
left of his once pristine environment. Through experience and the mass
communication media, society became aware of incidents in which the health
and well-being of large numbers of people were affected by their increasingly
polluted environment. The 1948 episode at Donora, Pennsylvania,3 the 1962
London fog,4 and the almost daily smog surrounding Los Angeles became topics
of conversation, concern and controversy.
Man has now been forced to recognize that nature's assimilative capacity
is indeed constrained and, consequently, clean air and water are scarce
resources. The abatement of pollution requires, either explicity (in terms
of pollution control methods) or implicitly (in terms of foregone output)
the utilization of scarce resources that have alternative uses. In essence,
the decision on the degree of abatement thus becomes an economic problem of
maximizing the net gain associated with'changes in environmental quality. If
man desires to improve his well-being, he must begin applying to the use of
air and water the same efficiency criteria that economists have traditionally
applied to the allocation of other scarce goods. One point remains certain:
... we have to go on using the environment . . .(man's)
activities cannot be abolished, though they can be con-
trolled. Controlling them means finding the proper
balance between the utility of these activities to the
individual and the disutility they impose, via the
environment, on others.5
Although this report is primarily intended to make a contribution toward the
efficient allocation of the scarce resource clean air, the results will none-
theless be applicable to the allocative decisions concerning other environ-
mental goods.
4
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EFFICIENT USE OF RESOURCES
Any analysis designed to evaluate alternative allocation schemes for a
scarce resource must be an exercise in applied welfare economics. As such,
the analyst must recognize that alternative distribution schemes "differ with
respect to both efficiency and equity"^. Therefore, the alternatives must be
evaluated in terms of both efficiency and equity considerations.
Equity considerations involve normative judgments which are generally
recognized as outside the appropriate realm of the economist as an economist.
Analysis of changes in the distribution of wealth which result from changes
in allocative procedures, however, should not be ignored by the economist.
(Such distribution aspects will be discussed in Section V.7) Evaluation of
the relative efficiency of alternative allocation schemes is, however, the
forte of economists. It is traditional for economists to assess an optimal
organization of economic activity in terms of efficiency. In general, an
economy is said to be optimally organized when "it is not possible, by any
reallocation of factors, to make anyone better off without making at least one
person worse off".8 Any situation which fulfills this criteria is said to be
a "Pareto Optimum," "Pareto Efficient" or simply "Efficient" position for
society.
Before any progress can be made toward the efficient allocation of the
scarce resource clean air, one must initially consider the general efficiency
criteria and the reasons why such criteria have not traditionally been applied
to this resource in man's quest for well-being. The conditions necessary for
the attainment of a Pareto optimum can be stated in terms of either consumption,
production or more generally, as a combination of both. In the general case
the necessary condition requires that equality exist between the marginal
rates of substitution in consumption (MRS) between any two goods (e.g., a_ and
b_),9 and the marginal rates of transformation in production (MRT) between the
same two goods.10 This condition can be expressed as:
MRS = MRT , (1)
ab ab
One of the more engrossing insights gained by a closer inspection of this
marginal condition is that a society characterized by perfectly competitive
markets in which all costs and benefits are transacted will allocate its
resources in a Pareto efficient manner provided that certain technological and
motivational assumptions are fulfilled.-^ Indeed, this is the modern
reasoning behind Adam Smith's famous statement:
. . . every individual necessarily labours to render the
annual revenue of the society as great as he can. He
generally, indeed, neither intends to promote the public
interest, nor knows how much he is promoting it. By
preferring the support of domestic to that of foreign
industry, he intends only his own security; and by
directing that industry in such a manner as its produce
may be of the greatest value, he intends only his own
gain, and he is in this, as in many other cases, led by
an invisible hand to promote an end which was no part of
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his intention. Nor is it always the worse for the
society that it was no part of it. By pursuing his own
interest he frequently promotes that of the society more
effectually than when he really intends to promote it.12
The implications of this result for the problem under consideration in this
study are quite significant, especially at the theoretical level. In effect,
this result suggests that if the necessary relationships hold in all markets
except the market for clean air, then the welfare of society might be improved
to the maximization point without making any individual worse off. Unfortun-
ately, "(few) markets in our economy are perfectly competitive, because few
markets fulfill the conditions of perfect competition"^. Indeed, as will be
illustrated later, one of the primary problems associated with the allocation
of the scarce resource clean air is the absence of a market for this resource
due primarily to the high transaction costs involved in establishing such a
market.
What then is the purpose of basing policy recommendations for welfare
improvement on implications derived from the perfectly competitive model?
The primary virtue of this model is that if its assumptions are met "it
provides a standard of efficiency by which actual economic institutions and
organizations can be appraised . Thus, by basing the analysis on a compari-
son of the existing economic situation with what might be attained in the
perfectly competitive model, insight into corrective policy measures can be
formulated. This is the procedure to be followed in this study since it
enables policy makers, if they so choose, to more closely approximate the
results of an optimal (perfectly competitive) market situation and thereby,
hopefully lead to improvement in society's welfare.
EXTERNALITIES, TRANSACTION COSTS AND PUBLIC GOODS
Abstracting from the problem of obtaining the necessary conditions for
perfect competition, allocation problems can still arise due to "Pareto-
relevant" externalities which preclude the attainment of welfare maximization.
The problems which arise because of such externalities are the primary reason
why even under perfect competition, efficient utilization of such resources
will not result from the free interaction of market forces. As Pigou notes:
... we may set out first a number of instances in which
marginal private net product falls short of marginal social
net product, because incidental services are performed to
third parties from whom it is techically difficult to
extract payment ... It is true of resources devoted to
the prevention of smoke from factory chimneys: for this
smoke in large towns inflicts a heavy uncharged loss on
the community, in injury to buildings and vegetables,
expenses for washing clothes and cleaning rooms, expenses
for the provision of extra artifical light, and in many
other ways.16
Pigou's statement implies that externalities cause our marginal equality
condition for the attainment of efficient resource allocation to be violated
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and thus become an inequality. This result can be visualized by recognizing
that the MRTa^ is simply equal to the ratio of the marginal costs of a and b_.
As stated earlier, the MRTat, included both private and social costs;17
MRTab = MCa/MCb (2)
In the case of externalities in the production of _a, the marginal private costs
(MFC) no longer equal the marginal social costs (MSC):
MFC /MFC, = MSC /MSC, (3)
a b a b
In effect, this latter relationship implies, given the basis of our efficiency
criteria, either too much of some goods and services or too little of certain
other goods and services are being produced, prohibiting the attainment of
maximum social welfare. In order to alleviate this situation, some method
must be employed to equate private costs to social costs. Ideally, from an
efficiency viewpoint, these costs and benefits should be directly included in
the individual's or firm's decision-making process. In this way, all costs
and benefits (private and social) would be internalized and society could
conceivably attain a Pareto efficient position. Coase has provided one of the
earliest and most significant treatments of this internalization process. He
has demonstrated that optimum resource allocation will result if the party
imposing the externality and the party receiving the externality are able to
negotiate at zero costs.18 xhe key qualification to recognize is "at zero
costs," because:
Once the costs of carrying out market transactions are taken
into account it is clear that such a rearrangement of rights
will only be undertaken when the increase in value of pro-
duction consequent upon the rearrangement is greater than the
costs which would be involved in bringing it about.1°
Indeed, it can be argued that market failure in the case of allocation of
pollution rights and other externalities "is the particular case where trans-
actions costs are so high that the existence of the market is no longer
worthwhile".20
The primary reason for these prohibitively high transaction costs is that
no individual may be excluded from the consumption of clean air. Thus, the
exclusion principle becomes inapplicable and precludes transactions at any
cost. Hence, no individual can be relied upon to reveal his preference since
he knows that he will benefit from the corrective actions of others. There-
fore, an individual can enjoy a "free ride" at society's expense, while
incurring zero private costs. This problem while inherent to varying degrees
in all public goods, is especially relevant to air. In essence, this resource
is a classic example of a pure public good in that "each individual's consump-
tion of such a good leads to no substraction from any other individual's
consumption of that good".21 Hardin demonstrates the resulting allocation
problems of communal resources in his example of common grazing land: •
. . . the conclusion reached by each and every rational
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herdsman sharing a commons . . . [is] that the only sen-
sible course for him to pursue is to add another animal
to his herd. And another; and another .... Therein
is the tragedy. Each man is locked into a system that
compels him to increase his herd without limit—in a
world that is limited.22
Recognizing that no individual may be excluded from the consumption of
ambient air, determinization of the socially efficient level of air quality
must consider each individual's MRS. Thus, the pervasive nature of public
goods requires the modification of the simple efficiency criteria presented
earlier. Since all individuals may potentially consume equal quantities of
pure public goods, the relevant efficiency criteria must equate the summation
of their MRS with the MRT.23
STATEMENT OF THE PROBLEM
From the preceding discussion it is apparent that an optimum allocation
of the scarce resource clean air cannot be attained in a private enterprise
market economy. In other words, social welfare cannot be maximized via the
free interaction of market forces because of the prohibitively high trans-
action costs associated with overcoming the breakdown of the exclusion
principle. The only viable alternative to the free interaction of market
forces appears to be some form of collective or governmental action. Indeed,
as Buchanan notes "a basic reason for political or government action . . .
[is] reduction in transaction costs where benefits can only be secured from
large-number exchanges".^ This reduction in transaction costs can be
attributed to state intervention because the state "by its nature, . . . has a
monopoly of coercive power and coercive power can be used to economize on
transaction costs".25
Specifically, this report is designed to facilitate the efficient alloca-
tion of our scarce resource clean air by isolating air quality's aggravation
effect on intra-urban mortality and then quantifying these costs in a manner
consistent with the theoretical basis of cost-benefit analysis. The results
from this study will be of importance to both the theoretician and the public
decision-maker, since this effort provides a conceptually accurate quantifi-
cation of the costs of pollution aggravated mortality. Moreover, the
significant policy-relevant contribution of this report will be to assist
government officials in establishing socially efficient standards for ambient
air quality.
The following section will develop an econometric model designed to
isolate the aggregation effect of long-term low-level dosages of air pollution
on individuals. This model will then be used to quantify the pollution-
mortality relationship for Allegheny County, Pennsylvania in Section IV.
Section V will trace the development of criteria that can be used as a guide
for the suggested collective action in the quest for efficient allocation of
the scarce resource clean air. Section VI addresses the issue of assigning
dollar values to air pollution-induced mortality in a manner consistent with
the guidelines developed in Section V and then applies existing empirically
estimated results to the pollution-mortality results obtained earlier for
Allegheny County.
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SECTION III
AIR QUALITY AND MORTALITY: DEVELOPMENT OF THE MODEL
The objective of this section is to develop an appropriate model for
empirically estimating the aggravation effects of ambient air quality on
mortality. This model will then be used for later quantification of these
effects in both absolute and dollar units. The model developed in this
section is based on insights derived from existing experimental, episodic,
and epidemiologlcal studies.
PREVIOUS STUDIES, INSIGHTS 'AND PROBLEMS
The possibility that extremely high levels of air pollution can shorten
lives and affect the overall quality of human life was painfully brought to
public attention by the 1948 episode at Donora, Pennsylvania.2" Today few
people would argue that the existence of pollution concentrations such as were
present during the Donora episode do not have significant health effects.
There is substantially less agreement, however, on the significance of lower
levels of air pollution on health.
The existence of these potential health effects has received increased
attention in recent years. A growing number of experimental episodic, and
epidemiological studies have shown inverse relationships between air quality
and various measures of health. Although the entire spectrum of potential
health effects on humans have been studied, "mortality is currently the best
documented and defined health indicator available".^7 Therefore, this study
will use the insights derived from these earlier works in an attempt to develop
a model capable of estimating the relationship between ambient air quality and
mortality differentials.
Experimental Studies
Any attempt to isolate air quality's impact on human mortality must
initially recognize that air quality is only one of numerous factors which
influence an individual's probability of death;28 the7'efore, these other
factors must be held constant experimentally or controlled statistically.
While the list of potentially dangerous atmospheric contaminants increases
annually, the current effort concentrates on sulfur oxides and partlculate
matter since these are two of the most pervasive stationary source contaniinents
found in the atmosphere. The responses of several animal species, including
man, to sulfur oxides and particulate matter have been studied using various
experimental techniques. Although such experimental studies have shown changes
in vital functions and mortality in animals, only changes in selected functions
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(primarily pulmonary) could be studied in man due to legal and ethical
considerations.
The majority of clinical experiments on animals have demonstrated that
sulfur oxides, usually sulfur dioxide or sulfuric acid, irritate the respira-
tory system.29 jn an attempt to induce animal mortality from such contaminants,
however, these studies required concentration far in excess of those doses
likely to be found even in extremely polluted areas. As the U.S. Department
of Health, Education and Welfare (USHEW) notes:
Compared to realistic air pollutant levels, it requires
relatively high concentrations of sulfur dioxide or
sulfuric acid to produce pathological lung change or
mortality in animals.30
Particulate matter unlike sulfur dioxide or sulfuric acid, is composed
of a variety of substances, many of which are known to be toxic (e.g.,
asbestos, beryllium and lead). Since most of these contaminants are primarily
area specific, an evaluation of the effects of each of these individual sub-
stances is outside the scope of this study.31 The current effort focuses on
"general" particulate matter of the type usually monitored by high-volume
samplers. Experimental investigations have demonstrated three ways in which
particulate matter may exert toxic effects:
1. The particle may be intrinsically toxic due to its inherent chemical
and/or physical characteristics.
2. The particulate may interfere with one or more of the clearance
mechanisms in the respiratory tract.
3. The particle may act as a carrier of an absorbed toxic substance.32
Some experimental studies with animals have also demonstrated the
existence of synergistic effects of various types of particulates and sulfur
oxides. Busbtueva (1957, 1962) has shown that the exposure of guinea pigs
to a 0.5 m§/m3 sulfuric acid produced only slight lung irritation, although
when combined with 0.9 m8/m3 sulfur dioxide considerable changes in lung
pathology resulted. Other experiments (Gross, et^ al_. , 1967) have also
indicated that normally inert particles (e.g., carbon) can be made irritant
when combined with sulfur dioxide or nitrogen dioxide. Toyama (1962), for
example, has demonstrated the existence of similar synergistic effects with
sulfur dioxide and sodium chloride. Experiments involving humans, however,
are much harder to interpret due to the variability of responses between
different individuals and the same individuals at different times.33 This
fact, combined with the high levels of exposure required to induce mortality
in clinical animals, has resulted in qualitative inferences about air quality
rather than quantitative estimates concerning the effects of ambient air
quality on human mortality.
10
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Episodic Studies
Analysis of actual extreme exposure episodes provides one method of
overcoming the many technical, legal and ethical constraints associated with
experimental studies. In essence, by utilizing real-life experience,
information can be obtained on human mortality changes associated with
extremely high levels of air quality. In fact, most episodic studies (Schrenk,
et_al_. , 1949; Wilkins, 1954; Scott, 1963; Riggan, _et al. , 1976) have confirmed
the existence of a direct positive relationship between high levels of air
pollution and mortality. When the 1948 episode of Donora, Pennsylvania was
analyzed, Schrenk, _et _al. , (1949) discovered that most of the twenty indi-
viduals who died during the episode had previously existing cardiovascular
or respiratory diseases. Therefore, while quantification of air quality's
influence on mortality was not possible due to insufficient air quality data,
insights were attained concerning the illnesses likely to be exacerbated by
air pollution.
Wilkins (1954) estimated that the December 1952 London fog resulted in
approximately 3,500 to 4,000 excess deaths. The most frequent causes of death
listed during this episode were chronic bronchitis, bronchial pneumonia, and
heart disease. Similar, although not so drastic results ("only" 700 excess
deaths) were obtained by Scott (1963) for the three day 1962 London episode.
While measurements of air quality (e.g., smoke and sulfur dioxide) were
available for both of these episodes, such data were not detailed enough to
attempt quantification of a dose-response function.
The most recent air pollution episode, the 1976 Pittsburgh experience,
was analyzed by Riggan, e_t aj^. After adjusting for incomplete death records, 34
days of the week, temperature, precipitation, and season, researchers still
determined that at least fourteen excess deaths occurred during the period.
Although episodic studies have the advantage of being able to study human
mortality, such studies are limited in usefulness since they deal only with
specific episodes of abnormally high pollution. Therefore, episodic investi-
gations are not applicable to the everyday ambient levels of pollution faced
by individuals in urban areas and any extrapolation of dose-response functions
from these episodes must be considered tenuous at best. As Anderson notes:
Although the deleterious effects of acute exposures to air
pollution are well established, it is not possible to
extrapolate from these data to the low levels of air pol-
lution to which persons are exposed in a modern urban
society.35
Analyzing changing patterns of human mortality that occur during high exposure
episodes, howevers can provide insights into which illnesses are most likely
to be exacerbated by air pollution at the lower, more typical levels to which
individuals are exposed daily.
11
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Epidemiological Studies
The limitations of episodic and experimental research have resulted in
the increased use of epidemiological studies to isolate the effects of ambient
levels of pollution on mortality. Epidemiological studies analyze the effects
of pollution at typical, rather than abnormally high, levels of exposure.
Moreover, individuals are studied in their everyday environment and not in a
laboratory, thus adding to the attractiveness of employing such studies.
Indeed, as USHEW notes "other countries, notably the Netherlands and Sweden,
have based their air quality criteria solely on epidemiological studies".36
Results from most epidemiological studies have also shown an inverse
relationship between air quality and mortality. The procedure used in these
studies typically involves simply calculating different mortality rates (or
partial correlation coefficients for populations exposed to different air
quality conditions. These studies have typically controlled for socioeconomic
variables which influence an individual's probability of death by dividing the
population of the area under study into four or five socioeconomic groups.37
The difficulty with using these types of statistical control techniques is
that there exists many other factors correlated with air pollution that affect
human mortality and are not adequately controlled for by the use of partial
correlation coefficients. Freeman (1972), for example, has shown that air
quality levels of white neighborhoods are higher than those of non-white
neighborhoods. In addition, individuals with relatively high income and
education levels also tend to reside in less populated areas of relatively
better air quality, while the lower income and less educated classes tend to
be constrained to the more polluted, crowded sections of the city. Since
income, educational levels, and population density all influence mortality,
these relationships cause difficulty in isolating air quality's influence
on mortality through the use of simple correlation techniques. Indeed, as
Lave and Seskin note:
If the explanatory variables were orthogonal to each other,
the inability to get measures on all variables would not be
important. If they were dependent, one could find the
effect of any variable on the mortality rate by an univariate
regression. However, orthogonality is not a reasonable
assumption .... This collinearity among explanatory
variables means that univariate regression, or simple
cross tabulations (which constitutes the preponderance of
evidence), are not likely to produce results that one would
interpret.38
In an attempt to circumvent these limitations, Lave and Seskin estimated
their own relationships using mortality data for 117 Standard Metropolitan
Statistical Areas (SMSA's) for the period 1959-1961. Their study used
multiple regression analysis to explain the variance in thirty-four different
mortality rates (characterized by age: under twenty-eight days, under one
year, fourteen years and younger, fifteen to forty-four, forty-five to sixty-
four, and sixty-five and older; race, white, and non-white; and sex, male and
female). The independent variables specified by Lave and Seskin were minimum
sulfates, mean particulates, minimum particulates, percent poor, population
12
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per square mile, percent of population sixty-five or older, percent non-white.
It should be recognized that only some of these variables appear in any of
their specific linear regressions since only the "best" results were publically
presented. As illustrated in Table 1, the results of their linear regressions
demonstrate a predominantly direct relationship between levels of pollution
and mortality. The sole exception to the expected positive relationship was
the negative coefficients of minimum sulfates for the white population in the
fifteen to forty-four age group. This result combined with the generally
increased magnitude of the pollution coefficients with age suggests that:
(1) individuals in this age group die primarily from non-pollution related
causes; (2) the ability of the body to withstand the influence of pollution
decreases with age; or (3) there exists a cumulative effect of pollution on
human mortality.
Another interesting insight attained from a careful examination of Table
1 is that the effect of particulates is greater on white males than white
females in the less than sixty-five age groups. This result suggests the
possibility of relatively higher exposure level for white males as a result
of work-related experience.
The generally larger coefficients for the non-white population relative
to the white population may indicate actual racial differentials in response
to air pollution. Alternatively, the larger coefficient for non-whites may
result from the fact that non-whites tend to reside in more heavily polluted
areas (implying a non-linear dose-response curve), are generally less educated
and earn lower incomes than the white population. Unfortunately, it is
impossible to determine which, if any, of these relationships is appropriate
due to data limitations experienced by Lave and Seskin.
While attempts at rationalizing the racial differences in the coefficients
highlight the difficulties arising from data limitations, the restrictions
imposed on Lave and Seskin's analysis by such constraints are far more
pervasive. The most important of their data limitations was the use of only
one monitoring station's readings for an entire SMSA in order to measure
ambient air quality. As they readily acknowledge, "it is a heroic assumption
to regard these figures as representative of an entire SMSA in making compari-
sons across areas".39 it is also possible that the inaccuracy of their
mortality rate calculations compound the difficulties of interpreting their
results. As Lave and Seskin recognize:
These age specific death rates were derived by dividing the
number of people who died by the total population. If the
age distribution of people differs across cities, these
approximate death rates will not even be proportional to the
true rates.^
Errors in the measurement of these dependent variables could also be a reason
for the relatively low coefficients of determination for their disaggregated
(age-sex-specific) mortality rates.41
In an attempt to determine if their results had isolated a true relation-
ship between ambient air pollution and mortality and not a relationship caused
13
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TABLE 1. SUMMARY OF LAVE AND SESKIN INTER-URBAN MORTALITY FUNCTIONS*»'('
15-44 45-64 65 and Over
Male Female Male Female Male Female
PART A. WHITE OVERALL MORTALITY
R2 .236 .164 .336 .395 .385 .295
Constant 52.921 28.626 45.138 131.695 698.367 470.984
Mean particulates .036 .026 .127 .086
Minimum Sulfates -.021 -.005 .069 .185 .637 .806
Population per
square mile .000 .001 .006 .003
Percent of population
non-white -.023 -.013 .107 -.028
Percent of population
over 65 -.062 -.025 .202 .065
Percentage of poor .069 .023 .154 -.009
PART B. NON-WHITE OVERALL MORTALITY
R2 .321 .345 .311 .477 .051 .108
Constant 49.719 30.009 237.856 141.855 679.310 499.750
Mean particulates .150 .111 .252 .373
Minimum sulfates .028 .068 .099 .980 .927 .904
Population per
square mile .003 .00.1 .006 -.004
Percentages of population
non-white .140 .104 .326 .472 -.066 -.066
Percentage of population
over 65 .033 .054 .406 -.109
Percentage of poor .180 .110 .667 .333
'''Source: Lave and Seskin (1970b).
tAll mortality rates (dependent variables) are in deaths per 10,000.
14
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by meteorological differentials or personal pollution from home heating
sources, Lave and Seskin (1972) added various climatic and home heating
variables (e.g., humidity, temperature, and various types of home heating
equipment) to their model. This analysis while also based on 117 SMSA's was
not age-sex-specific since only total and infant mortality functions were
estimated.^ The inclusion of these additional variables did not alter the
positive nature of the association between air pollution and mortality nor
the stability of the air quality coefficients.
In general neither climate nor home heating variables
cause the air pollution variables to lose significance.
While there are individual pollution coefficients which
do lose significance, the coefficients are quite stable.
An exception occurs when home heating fuels are added.
These variables are associated closely with measured air
pollution and both pollution and heating fuel variables
tend to become insignificant. . . . Apparently, the type
of fuel used for home heating is a major contributor to
the air pollution level in the city. Note that this
interpretation does not mean that the previous
association between air pollution and mortality is
disproved, but rather it is made more specific by
directing the association to home heating fuels, rather
than at all sources of air pollution.^3
The use of simple total mortality figures instead of an age-standardized
total mortality ratio could introduce some biases (e.g., higher or lower
estimates of the effects of air quality) into the analysis,^ especially if
the age distribution of the SMSA's varies with their air quality.^^
Even with these limitations, Lave and Seskin have significantly advanced
our insights into the epidemiological association between ambient air
quality and mortality. Specifically, their studies have demonstrated that,
after controlling for other factors which may affect mortality, air quality
does exhibit a significant relationship with mortality. Experimentation with
alternative specifications (i.e., functional forms) have given results not
significantly different from the general linear model depicted in Table 1.
The first of these involved a comparison of the linear
model with a log-linear specification. It was found
that the elasticities associated with the pollution
variables . . . [in the linear model] were quite similar
to the coefficients of the pollution variables in the
log-linear formulation. When a quadratic model was
fit . . . (squared values of the pollution variables
as well as an interaction term), the results of an F-test
indicated that the gain in explanatory power was
insignificant.46
Whether these associations are causal is still an unsettled issue. However,
the experimental and episodic works previously discussed strengthen
arguments for at least the existence of an aggravation effect.
15
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Recognizing the probable existence of this aggravation effect, the next
section will detail a generalized model developed from the insights of
earlier studies, which is capable of isolating such effects. Specific
attention will be given to demographic considerations, initial variable
selection and overcoming the technical, legal, ethical and data problems
associated with previous attempts at isolating the relationship between air
quality and mortality.
THE MODEL
This section describes a general model that isolates the effects of
various factors affecting mortality differentials and explains the candidate
variables. The model is designed for application to a specific urban area,
and thus avoids many of the difficulties encountered by other investigators
(primarily Lave and Seskin) who analyzed inter-urban mortality differentials.
Although specifically designed for intra-urban analysis, the model is also
applicable to analyzing inter-urban mortality differentials.
Dependent Variables
Any attempt to provide a reliable estimate of the effects of air quality
on mortality via intra-urban mortality analysis must recognize that other
factors, many of which are collinear to air quality, influence the risks of
death. Therefore, in order to isolate the affect of ambient air quality on
mortality, it is necessary that these other factors be controlled. The first
of these factors to be controlled for will be the demographic influences.
Such components are most readily controlled through the use of age-sex-race-
specific mortality rates.
In general, children are not subject to the same hazards as adults.
This observation, coupled with a decreasing ability of the body to protect
itself after a certain age, leads to the expectation of mortality
differentials with respect to age. In fact, there exists an inverse
relationship between age and mortality after early infancy.
Differentials in risk of death can also be expected on the basis of
sex. Whether or not these differentials are biological or social is still an
unsettled question, although females dc. enjoy more favorable mortality rates.
Differential mortality is also exhibited by different races within any
sex-age group. With the exception of those causes of death related to
inherent genetic deficiencies such as sickle cell anemia, this may result
from social class differences. Despite lack of clear understanding of the
real causal factors, the significance of racial differences in mortality is
sufficient reason to control, at least initially, for race when analyzing
the effect of air quality differentials on mortality.
Finally, it must be recognized that air quality can be expected to
accentuate the risks of death from certain causes (e.g., bronchitis,
emphysema, asthma, etc.). Therefore, deaths should be separated into
various causes to enable the isolation of those types which are most likely
to be influenced by various levels of air quality. Thus, by controlling for
16
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age, sex and race as well as examining cause-specific mortality rates, it is
possible to partially isolate the effects of air quality on mortality from
those other influences. Toward this objective, age-sex-race-cause-specific
mortality rates will be used as the dependent variables in the multiple
regression analysis. Another advantage of using these specific mortality
rates (particularly age and sex) as dependent variables is that such
variables provide valuable indicators of the primary etiological effects of
air pollution. Specifically, isolating preschool and school-aged children
and, to a lesser extent housewives, avoids the complications of exposure to
pollutants at work.^'
Independent Variables
The existence of important factors in addition to age, sex, race and air
quality that may be collinear to other independent variables and also
influence an individual's risk of death justifies the use of multiple
regression analysis. These factors include income, education, social class,
occupation, place of residence, housing, climate, availability and access to
quality medical care, quantity and quality of food consumed, tobacco
consumption, sanitation and marital status (Kosa, et. al., 1969, Shryock and
Siegel, 1971). Unfortunately, measurement or observation of many of these
factors is extremely difficult, if not totally impossible. Certain proxies
and estimates, however, can be used in the absence of direct measurement.
The following independent variables will be considered in the initial model:
Income (Y)
In general, individuals with higher incomes tend to consume higher
quality goods which should favorably affect their health. A negative
association between income or some other proxy for social class has been
demonstrated by many investigators researching class differentials in
mortality (Chapin, 1924; Mayer and Hauser, 1950; Yeracarls, 1955: Ellis, 1957,
Kitagana and Hauser, 1968; Roberts, et^ al., 1970). Fuchs (1965, 1973) and
others (e.g., Auster, et al., 1969), however, have shown that after control-
ling for other factors (e.g., education), income does not indicate a
significant negative relationship and may even exhibit a positive relation-
ship. In this analysis, therefore, income will be used primarily as a proxy
for unmeasured socioeconomic variables.
Education (E)
"Higher levels of education may be associated with relatively more
medical care at preventive stages".^8 Moreover, education levels may also be
associated with the possession of better knowledge of preventive care and
willingness to seek and follow a doctor's advice. Negative associations
between education and mortality have been found by Kitagawa and Hauser
(1968), Fuchs (1965, 1973) and Auster, et. _al. , (1969).
Cigarette Consumption (C)
The deleterious effects of cigarette consumption have been brought to
the public's attention primarily by the U.S. Government (U.S. Department of
Health, Education and Welfare, 1964, 1969c). Positive associations between
cigarette consumption and mortality have been demonstrated by Auster, et
al., (1969) and Fuchs (1968). —
17
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Health Insurance (I)
It is generally believed that the possession of health insurance may
have a significant effect on an individual's decision to seek medical care.
Feldstein (1971, 1973) and Rosett and Huang (1973) have empirically
demonstrated this possibility. Therefore, differences in the incidence of
health insurance will account for a portion of the variance in mortality
rates.
Population Density (PD)
Proximity to other individuals can influence one's exposure to various
diseases. Lave and Seskin (L970a, 1970b, 1972 and 1973) have been shown a
significantly positive relationship between population per square mile and
inter-SMSA differentials in mortality.
Total Particulates (TP), Dustfall (D) , Sulfur Dioxide(SC>2), and Suspended
Sulfates (SS)
These proxies are the most commonly used air quality measures and
should be considered as the air quality variables. Total particulates and/or
dustfall should be considered because of the belief that they are "the most
important constituent11^ Of aj_r quality's influence on health due to their
almost universal presence and relative magnitude. Sulfur dioxide should be
considered due to its use in the laboratory studies mentioned earlier
(Bustueva, 1957, 1962; Gross, ej^ al_. , 1967 and Toyama, 1962) and also to test
for possible synergistic effects with total particulates and/or dustfall.
Suspended sulfates should also be examined for their possible long-run
effects since recent Community Health and Environmental Surveillance System
(CHESS)50 studies indicate that health effects of short-term exposures to air
pollution "should be attributed to suspended sulfate levels rather than to
observed concentration of those [sulfur dioxide or total particulates]
pollutants".51
Average Annual Temperature (TEMP), Average Annual Daily Maximum
Temperature (DMAX), Average Annual Daily Minimum Temperature (DMIN), Number
of Degree Days (DDAYS), Total Amount Precipitation (TPRE), Number of Days
with Maximum Temperature 90° or Greater (#90+), Number of Days with Maximum
Temperature 32° or Less (#32-), the Number of Days with 0.1 Inches or More
Precipitation (//P. 1+) and Relative Humidity (RHUM)
These are the most readily available climatological variables. Although
climate has been recognized as an important factor in mortality (Hirsch,
1941; Peterson, 1947; Berke and Wilson, 1951), the literature on the cause-
effect mechanism has not been developed to the stage where it can determine
which climatological variables are of major importance. This reason,
together with data availability, is responsible for the selection of these
plausible explanatory climatological variables. It should also be noted
that these nine variables were among the fourteen originally considered by
Lave and Seskin (1972).
General Model
Initially considering all variables discussed earlier and recalling
Lave and Seskin's (1973) findings that the relationship appears to be linear,
the following general mortality function is proposed:
18
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M
a
+
+
4- '
=b^ + b. Y . + b0
,s,r,c,i 0 1 r,i 2
b5 PD. = b6 TP. + b? D. + I
b DMAX.. + b12 DMIN.. + br
b.£ (ER90+). + b.7 (0T32-),
ID i i /
E + b D . + b, I .
r,i c a,s,r,i 4 r,i
'8 S°2i + b9 SSi + b!0 TEMPi
, DDAYS. + b.. TPRE. + b (#P.1+).
3 i!4 iij i
L + b!8 mm±
(4)
where:
M = the mortality rate for cause c_, age group a_, sex £, race _r
a,s,r,c, i
in area i- A11 independent variables are those previously discussed.
Table 2 summarizes the variables included in this general model. 52
Indicated in this table are the acronyms used to designate the variables and,
where jj priori sign estimates can be made, the expected relationship of
each independent variable to the dependent variable. A detailed description
of each variable's derivation and their respective units of measurements is
contained in the following section.
19
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TABLE 2. SUMMARY OF INDEPENDENT VARIABLES INCLUDED IN GENERAL MODEL
Variable
Name
Variable
Description
A Priori Relationship
to Dependent Variable:
Direct (+) Inverse (-)
or Uncertain (?)
Y Per capita income
E Percent; of adult population with
high school education
C Per capita tobacco consumption
I Percent of population with health
insurance
PD Population density
TP Average annual concentration of total
particulates
D Average annual concentrations of
dustfall
SO Average annual concentrations of
sulfur dioxide
SS Average annual concentration of
suspended sulfates
TEMP Average annual temperature
DMAX Average daily maximum temperature
DMIN Average daily minimum temperature
DDAYS Average annual number of degree days
TPRE Average annual precipitation
//P. 01+ Average annual number of days with
.01 inches or more precipitation
//T90+ Average annual number of da'ys with
maximum temperature 90° or greater
//T32- Average annual number of days with
maximum temperature 32° or less
RHUM Average annual relative humidity
+
-t-
20
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SECTION IV
ESTIMATING THE MODEL: RESULTS FOR ALLEGHENY COUNTY, PENNSYLVANIA
The preceding section demonstrated that the epidemiological approach was
likely to be fruitful in the attempt to isolate ambient air quality's
aggravation effect on human mortality. In addition, it was also suggested
that regression analysis provided a useful technique to statistically control
the numerous factors influencing mortality.
The objective of this section is the estimation of the general model.
Using cross-sectional data from Allegheny County, Pennsylvania, these
various mortality functions are estimated. Specifically, weighted linear
regression analysis is used to estimate age-sex-race-cause-specific
mortality functions. The results of this application are then discussed in
terms of the physical social benefits (decreases in probability of death)
to be expected from improvements in ambient air quality.
VARIABLE ESTIMATION, UNITS OF OBSERVATION AND DATA SOURCES
The procedures used to estimate the variables initially considered in
the model and their data sources are presented below. All variables were
obtained either directly at the census tract level or were estimated for
the individual census tracts.
Census tracts were used as the primary unit of measurement because such
divisions provide a more accurate assessment of the individual socio-
economic factors believed to influence mortality.53 The use of census tract
data, however, limits the ability to control for individual's migration
patterns. Thus, this approach implicitly assumes that if individuals moved
during the period under study (1968-1972), the migration patterns were
between areas of relatively equivalent air quality.^
MR
a,s,r,c,i
All age-sex-race-cause-specific mortality rates were based on deaths
occurring in Allegheny County, Pennsylvania during the five-year period
1968-1972. Separate mortality rates were estimated for overall, population-
related and non-pollution-related causes of death. The causes of death
considered pollution-related are presented in Table 3.
The required information was obtained from individual death
certificates supplied by the Allegheny County Department of Public Health.
These mortality rates were calculated using the following standard
demographic procedures :^5
21
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1. a. List total deaths for all individuals of age group _a,
sex _s_, race r who resided in census tract i at: the
time of their death during the period 1968-1.97?
(deaths);56
b. List deaths from cause c in census tract i for this
age, sex, race group during these years (cause); and
c. Multiply five times the. 1970 population of age _a; sex j=,
race r in census tract i_ (population) . The reason for
this step is that the procedure involves a five year
average mortality rate and 1970 is the raid-year of this
period. It is assumed that the changes in the
population during this period occurred at a constant
linear rate.
2. Add one-half of item l.a (deaths) to the figure in item 1.c
(population). This calculation provides an estimate of the
population at risk at the beginning of the period and is
based on the assumption that half the deaths precede the
mid-point.
3. Divide the figure in item l.b (cause) by the results of step
2_ in order to obtain the desired mortality rate. Algebraically,
this calculation may be written as:
J4 _ Cause [l.b]
Deaths [l.a]
Population [l.c] +~ ,,.%
TABLE 3. UNDERLYING CAUSES OF DEATH CONSIDERED TO BE
RELATED TO AIR POLLUTION
Underlying Cause of Death T.C.D.A. Codes*
Tuberculosis of the respiratory system 010-012
Malignant neoplasms of buccal cavity and pharynx 140-159
Malignant neoplasms of respiratory system 160-163
Major cardiovascular diseases 390-448
Acute bronchitis and bronchiolitis 446
Chronic and unqualified bronchitis 490-491
Emphysema 492
Asthma 493
* Based on Eighth Revision of the International Classification of
Diseases, Adapted 1965.
22
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It should be recognized that the rationale for using a five year
average mortality rate is that it will help reduce the variance in these
rates caused by small and differing sample sizes (population of the census
tracts). This is an important consideration since the stability of these
mortality rates rather than their absolute size is essential. Illustrative
of this concern is a census tract with twenty individuals one of whom dies
during our five-year study. In this case the five year average mortality
rate will be 1/100 although the yearly rates will be highly unstable ranging
from 1/20 to zero (undefined).
These age-sex-race-cause-specific mortality rates were calculated for
three age groups (less than 45, 45-64 and 65 and older) although only for
white males and females. The reason for excluding non-whites was the small
sample size in the population of Allegheny County.^7
In
The 1969 per capita income for race _r in census tract _i was calculated
from data contained on the 1970 Census of Population and Housing Summary
Tapes - First Count (Census Tapes).
The percentage of the population of race r_, 25 years old and over, in
census tract i_ with at least high school education was calculated from data
contained on the Census Tapes.
a.s,r,i
The estimated tobacco consumption per capita for age group _a, race _r in
census tract i^ was estimated from data in the 1963-1972 Panel Studies of
Income Dynamics. The estimates used were the national average expenditure on
tobacco by individuals of age £, sex s^t race r_, with an income equivalent
(to the nearest $1,000) to Yr-f This estimation procedure assumes that
Allegheny County is typical of the nation as a whole.
The estimated percentage of the population of race jr in census tract jL
with some type of health insurance. This variable was estimated using the
1969 family income of the individual families of race r_ in census tract ±_ and
the data in Table 4 which is based on national averages. It was assumed
that the same percentage holds for all individuals of race _r in census tract
jL. These estimates were then summed for all Allegheny County census tracts
and the total number of individuals with some form of hospitalization
estimated using this procedure was verified with a control total supplied by
Blue Cross of Western Pennsylvania.-^ This comparison revealed only a slight
differential (6 percent).
23
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TABLE 4. PERCENTAGE OF HOUSEHOLDS WITH SOME FORM OF
HEALTH INSURANCE BY HOUSEHOLD INCOME*
Household Income
Percent of Households With
Some Health Insurance
L.E. $ 1,500
G.T. $ 1,500 - L.E. $ 2,500
G.T. $ 2,500 - L.E. $ 3,500
G.T. $ 3,500 - L.E. $ 4,500
G.T. $ 4,500 - L.E. $ 5,500
G.T. $ 5,500 - L.E. $ 6,500
G.T. $ 6,500 - L.E. $ 7,500
G.T. $ 7,500 - L.E. $ 8,500
G.T. $ 8,500 - L.E. $ 9,500
G.T. $ 9,500 - L.E. $10,500
G.T. $10,500 - L.E. $11,500
G.T. $11,500 -
37.3
48.8
62.5
73.1
79.8
83.0
84.5
85.5
87.3
88.9
87.8
88.2
* This table was derived from data presented by Rosett and Huang (1973).
PD,
Three alternative measures of population density (crowding) were
utilized. The first of these variables was population per square mile in
census tract _i (P/mii2).60 This figure was calculated by dividing the total
1970 population of census tract _i by the area of tract ji in square miles. 61
The second proxy for a crowding variable, population per room (P/R^ r) in
census tract _i of race jr, was calculated by dividing the population 'of race
_r in census tract jL by the total number of rooms occupied by the individuals
of race £ in census tract i_. The third crowding variable proxy, population
per residential area (P/RA^) in census tract i_, was calculated by dividing
the 1970 census population of census tract JL by the total residential area
(square miles) in census tract JL.
TP
The five year arithmetic mean of annual averages of total particulates
in ug/m3, for the calendar years 1968-1972 was calculated for each census
tract using the procedure described below.
1. Calculate the five-year average of annual arithmetic means
by monitoring station. (Use the average values for a
24
-------
.1. Location of air quality monitoring stations
within Allegheny County, 1968-1972.
25
-------
specific individual station to estimate missing values
for the station.)
2. Locate the individual monitoring stations on a map
according to USGS coordinates. (See Figure 1)
3. Estimate values for the remaining points in Allegheny
County using the SYMAP computerized mapping program.
The interpolation procedure used by this program involves
calculating the weighted averages of slopes from values of
nearby data points developed by a gravity-type model and
modified to consider distance and direction."2
4. Plot these interpolated values on a map of Allegheny County
in order to facilitate the estimation of aw-np.o values for
each census tract.
5. Calculate the average value of the r.r ; al p-ic1 I relates by
super-imposing a clear overlay on the computer-generated map.
Sum the values of individual point estimates and divide by
the number of points.
The original data on total participates was coi lectO'.1 at i:he indiv; dua.l air
monitoring stations operated by the Allegheny County Bureau of Air Pollution
Control. The number of monitoring stations employod rnnger' from four in
1968 to fourteen in 19~'2. Measurements were in micrograms per cubic meter
and based on hi-volume sampler readings. In order to determine if the
original data points were sufficiently dispersed for meaningful cartographic
data portrayal, SYMAP provided an estimate of a "point distribution
coefficient". Essentially, a point distribution coefficient of 0.0 indicates
a complete cluster (all observations located at one point) while a value of
2.2 indicates a square lattice (distributed regularly in a hexagonal pattern).
The value of tliis coefficient tor the data points used to extrapolate the
census tract estimates ---f the various air quality variables was 0.75. This
estimate indicates that while the data points used for extrapolation were
slightly clustered, their spatial distribution was approaching a random
distribution. Thus, although not ideally dispersed, the monitoring stations
are sufficiently dispersed to assure relatively accurate extrapolations.^3
It should be noted that the use of air quality measurements coincident
with the potential mortality effects under study implicitly assumes that
either average air quality has been relatively constant over the preceding
years or that the preponderance of air quality's influence on mortality is
experienced almost immediately. The latter possibility has received support
from the investigation conducted by Brown, _et_ _al_. (1975) concerning the
mortality effects resulting from the 1974 fuel crisis. Specifically, the
authors tested whether decreases in vehicular exhaust fumes would have
beneficial short-term health effects. Their analysis uncovered decreases in
first quarter 1975 mortality rates for Alameda County, California, ranging
from 11.2 percent for cardiovascular diseases to 38 percent for chronic lung
disease.
26
-------
The five year arithmetic mean of annual averages of dustfall (soluble
and insoluble) in tons/square mile/month for the calendar years 1968-1972 was
calculated for each census tract using the procedures outlined above for
total particulates. Data was collected at the individual air monitoring
stations operated by the Allegheny County Bureau of Air Pollution Control.
The number of monitoring stations ranged from forty-nine in 1968 to five in
1972. Measurements were in tons per square mile and calculated by weighing
monthly samples of particulate matter collected in dustfall jars.
The five year (1968-1972) arithmetic mean of annual averages of sulfur
dioxide in PPT/24 hours for the calendar years 1968-1972 was calculated for
each census tract using the same procedures applied to total particulates.
Data was collected at the individual air monitoring stations operated by
the Allegheny County Bureau of Air Pollution Control. The number of
monitoring stations ranged from forty-two in 1968 to forty-seven in 1972.
Measurements were based on the sulfation rates of lead peroxide candles and
converted to PPT S02/24 hours by application of the Foran and Gibbon
conversion factors for the years 1968-1971 and from Huey Plates in 1972.
cc
_i
No estimate of suspended sulfates was available; therefore, this variable
could not be included.
Climatological Variables
The five year (1968-1972) arithmetic mean of all climatological
variables were calculated for each census tract using the same procedure
applied to total particulates. The original data was collected at five
monitoring stations (three in Allegheny County and two in neighboring
counties) operated by the U.S. Department of Commerce. The following list
represents the climatological variables used in thn's study:
TEMP - average annual temperature
DMAX - average daily maximum temperature
DMIN - average daily minimum temperature
DDAYS - average annual number of degree days
TPRE - average annual precipitation
#P. 1-f ~ average annual number of days with 0. ! inches or more
precipitation
//T90+ - average annual number of days with maximum temperature
90° or greater
-------
/'T32 - average annual number of days with minimum temperature
32° or less
RHUM - average annual relative humidity.
ESTIMATION
The general model developed in Section III was estimated using the
variables described in the preceding section. Specifically, eighteen age-
sex-race-cause-specific linear mortality functions were estimated using
weighted regression analysis. 64 xhe rationale for using weighted regression
analysis v>as to correct the problems of non-constant variance of the error
rr.nn (heteroscedasticity). The existence of heteroscedasticity violates the
c<5 sumptions of ordinary least-squares regression analysis thereby introducing
biyrer into the estimated results. 65 Smith has demonstrated how this problem
eiders into cross-sectional analysis as well as the appropriate procedure
-for eliminating heteroscedasticity. 66
Since the death rate is a proportion (or a
proportion times a constant) , the variance of the
observed death rate would be a^/N where a^ is the
variance of a proportion and N is the sample size.
Assuming that a is appropriately the same for all
samples for a given age group, then the variance of
the observed death rate is inversely proportional to
the sample size. In the regression, instead of
minimizing the sum of squares of errors, EE-^ where
Ei is the difference between observed death rate and
9
estimated death rate, one wishes to minimize ££•;/
(a^/Ni), which, assuming a is constant, will be
minimized when EEj^N^ is minimized or when I(E^N^4)^
is minimized. This means the errors should be
weighted by a factor equal to the square root of the
sample size.67
Following Smith's example, each of the observations were weighted by
the square root of the sample size since this linear weighted regression
analysis resulted in the "best" estimate.68 for example, all the independent
variables associated with while male mortality in the over sixty-five age
group in each observation were multiplied by the square root of the white
male population over sixty-five in the corresponding census tract.
In the regressions which follow, several candidate variables were
excluded from the equations. Three alternative crowding variables
(P/Mi2, P/R, P/RA) and two measures of the dirtiness of air pollution (D,TP)
were initially considered. Final selection of variables P/RA and TP was
based on statistical significance requirements. Similar reasoning was also
applied to the selection of the climatic variables //P.1+, and //T32- from
among the nine originally considered (TEMP, DMAX, DMIN, DDAYS, TPRE, //P.1+,
//T90+, //T32-, and RHUM), since there was no a priori preference. In the
cases of Y and I, the decision not to include these variables was based on
the desire to avoid the effects of multicollinearity. 69 Specifically, both
28
-------
of these variables were highly correlated with E (e.g., the simple correlation
coefficient between E and Y was .8 while that between E and I was .4). Since
no observations were available on SS, this variable could not be estimated.
The estimates for C were extremely unreliable; and, therefore, when it was
determined to be statistically insignificant, the variable was deleted. To
facilitate the discussion which follows, the means and standard deviation of
the variables included in the various mortality functions are presented in
Table 5.
TABLE 5. MEANS AND STANDARD DEVIATIONS OF VARIABLES
INCLUDED IN EQUATIONS
Variable Mean Standard Deviation
Percent of adult white
population with high
school education 52.063 16.122
Total -particulates
(ug.irT) 122.571 15.381
Sulfur dioxide
(PPT/24 hrs.) 37.860 8.933
Number of days
precipitation > 0.1" 83.117 2.542
Number of days
maximum temperature < 32° 34.709 2.759
Population per .01 sq. mi.
(residential) 212.895 189.530
RESULTS
The results of the weighted linear regression analysis using the final
set of independent variables (E, S02, TP, #P.01+, #T32-, and P/RA) regressed
on the various age-sex-cause-specific white mortality rates are presented in
Table 6. The figures in parenthesis represent the student t-values associated
p
with each coefficient and R is the (corrected) coefficient of determination.
The statistical significance of each variable's coefficient is indicated by
the use of asterisks. The inclusion of additional candidate independent
variables for each mortality function did not significantly increase the
equation's overall explanatory power (R^). The percent of the variance in
the dependent variables explained by the individual regressions presented in
Table 6 range from 1.2 percent for white female non-pollution-related causes
of death in the less than forty-five age group to over 51 percent for white
male overall mortality in the sixty-five and over age group. The reason for
the separation of overall mortality rates into pollution and non-pollution-
related causes is, as stated earlier, that a priori air quality can only be
29
-------
TABLE f.. ".ORTAUTY FfNCTtOM ESTIMATES*
(1968-1972 ALLEGHENY COUNTY, PE'WFVLVANIA)
Variable
Percent of Adult popula-
tion with high school
education
S02 (PPT/26 hrs.)
Total p.irticulates
(ur,/n3)
Number of days
precipitation > . 1"
Number of days maximum
temperature < 32°
Population per .01
sq. mi. (residential)
Constant
K2
Less than 45
Vale Fertile
PAP.T A. MIIIF: n'T. '•:
-3.907 -1.693
(6.994)* (3.828)*
-1.206 0.056
(1.294)**(0.083)
0.766 0.267
(1.500}**(0.726)
0.649 2.076
(0.218) (0.968)
-1.521 -0.405
(0.678) (0.245)
0.218 0.158
(3.490) (3.300)*
371.653 13.340
(1.360)**(0.067)
.179 .024
PART B. MUTE POLLUTION-RELATE!'
Percent of adult white
population with high
school education
S02 (PPM/24 hrs.)
Total participates
tug/in1)
Nurber of dnyfl
precipitation > .1"
Number of days maxlnun
tenperature < 32°
Population per .11
sq. ml. (residential)
Constant
K2
PART C. WHITE
Percent of adult white
population with high
school education
S02 (Pi'T/24 hrs.)
Total participates
(UR/IT.3)
Number of days
precipitation > . 1"
Number of days maximum
ccuper.iture < 32°
Population per .01
sq. ml. (residential)
Constant
Tfl
-1.348 -0.569
(4.604)* (2.706)*
0.043 0.031
(0.087) (0.097)
0.500 0.349
(1.867)* (1.995)*
-0.506 1.736
(0.325) (1.7P2)-
1.104 -0.286
(0.938) (0.364)
0.037 0.050
(1.116) (2.194)*
105.106 -111.460
(0.734) (1.178)
.161 .013
45-6'
f'alf
'.L!. "ORTALnV I
-17.003
(8.16(i)'
1.747
(0.474)
5.632
(2.712)*
25.344
(2.099)*
-3.174
(1.319)
1.056
(4.426)*
-332.125
(0.298)
.338
CAUSE-SPECIFIC
-11.565
(7.392)*
1.632
(0.617)
4.014
(2.693)*
20.723
(2.392)*
-3.873
(0.542)
0.609
(3.556)*
-510.918
(0.677)
.278
Finale
["ICTTONS
-P.850
(6.472)'
0.408
(0.245)
3.373
(3.469)*
10.218
(1.814)*
2.334
(0.493)
0.334
(3.173)*
246.402
(0.470)
.370
XOSTALITY
-5.021
(7.558)*
0.265
(0.253)
1.570
(2.572)*
3.970
(1.123)
1.595
(0.536)
0.209
(3.163)*
42.982
(0.130)
.330
f>5 anc Over
>'ale Female
-45.141 -17.348
(6.995)* (3.217)*
-0.466 -1.056
(0.041) (0.116)
14.244 13.276
(2.036)* (2.281)*
107.875 34.947
(2.661)* (1.017)
-62.560 -42.924
(1.87<>)* (1.565)**
0.711 -0.158 .
(1.134) (0.319)
1247.897 3168.511
(0.335) (1.003)
.514 .453
FUNCTIONS'!-
-31.158 -13.181
(6.223)* (3.209)*
1.014 2.683
(0.116) (0.386)
10.291 9.514
(1.897)* (2.146)*
54.390 26.136
(2.063)* (i.OO)
-41.826 -30.642
(1.619)** (1.467)**
0.332 -0.162
(0.6C2) (0.429)
1708.121 2124.704
(0.500) (0.883)
.183 .425
NON-POLLUTION RELATED CAUSE-SPECIFIC MORTALITY FrtJCTTONS-1-1-
-2.560 -1.124
(5.993)* (3.102)*
-1.249 0.025
(1.752)* (0.045)
0.267 -0.082
(0.683) (0.272)
1.156 0.340
(0.503) (0.194)
-2.625 -0.119
(].530)**(O.OB8)
0.182 0.108
(3.800)* (2.755)*
266.546 124.797
(1.276) (0.756)
.100 .021
-6.238
(6.754)*
0.115
(0.074)
1.619"
(1.841)*
4.622
(0.904)
0.700
(0.1661
0.447
(4.424)'
208.791
(0.442)
.280
-1.S29
(3.092)*
0.143
(0.154)
1.S03
(3.317)*
6.248
(1.984)*
0.740
(0.279)
0.125
(2.125)*
289.384
(0.987)
.307
-13.982 -4.167
(6.076)* (2.188)*
-1.480 -3.739
(0.368) (1.162)
3.953 3.762
(1.585)** (1.830)*
42.985 8.811
(2.974)* (0.726)
•20.734 -12.282
(1.747)* (1.268)
0.379 0.004
(1.696)* (0.022)
-460.228 1043.817
(0.34«) (0.935)
.377 .340
* All mortality rates (dependent v.irlables) are in deatlio per 100,010.
** Significant at. 0.05 probability level (two-tailed test).
*** Significant at 0.10 probability level (two-tailed test).
t These mortality rates are based on total deaths frorc tuberculosis of the respiratory system,
malignant neoplasms of burc.Vi. cavity, pharynx and rerpirnrory system, major cardiovascular
disease, acute and chronic bronchitis and brrjnct'i'.v itis, eirphascr.a and asthma.
+t These mortality rates are based on tntnl deaths from all causes other rhan tubcrrulosls of
the respiratory system, rval l£r,->:H neophascts of the bucr.fl cavity, pharynx and rcsplr.itcry
system, major cardiovascular disease, acute and rhronlc- bronchitis and bronchfolitis,
eoiphasema and asthenia.
30
-------
expected to influence the probability of death from certain causes (e.g.,
respiratory diseases) while supposedly having no discernable effect on
others (e.g., motor vehicle accidents).
Part A of Table 6 presents the results of applying the general model to
overall white mortality and is analogous to the Lave and Seskin results pre-
sented earlier.™ The signs of the coefficient for all variables are as
expected with the exception of S02 for males less than forty-five, SC>2 for
males and females sixty-five and over, and P/RA for females sixty-five and
over. In general the absolute value of most coefficients increases with age
as does the R£. The increase in R^ is probably the result of both the inverse
relationship between accidental deaths and age and the direct relationship
between sample size (number of deaths) and age. The unexpected negative sign
of 502 f°r males less than forty-five could be due to the fact that younger
people dies primarily from non-pollution-related causes.
In order to test this hypothesis, separate mortality functions were
estimated for pollution related (Table 6, Part 8) and non-pollution-related
(Table 6, Part C) causes of death using the same model as for overall mor-
tality.^ This procedure allows the testing of this hypothesis since the
coefficients of the variables in the overall mortally function are simply
the sum of the coefficients form the pollution-related and non-pollution-
related mortality functions.
For the pollution-related causes of death all air pollution variables
have the expected sign, thus indicating that air quality exacerbates these
types of illnesses regardless of age. It is also noteworthy that generally
the coefficients increase with age indicating that possibly the absolute
effect of air pollution is greater on the elderly or that there exists a
cumulative effect of exposure to air pollution. Part C of Table 6 confirms
the assertion that the coefficients obtained for overall mortality variables
are simply the sum of pollution-related and non-pollution-related causes of
death. The signs of the air pollution variables' coefficients in Part C are
of little other concern SI'SK:.-: these causes were not expected to be affected
by air quality.
To achieve a clearer interpretation of the results attained from applying
the general air pollution-mortality model to Allegheny County and thereby
addressing many of the salient issues regarding the air pollution-mortality
question, each independent variable must be examined. Specifically, the
remainder of this section analyzes the estimated coefficients for the various
independent variables in order to derive a better understanding of the
theoretical and policy implications associated with responses in human mor-
tality resulting from differences in air quality.
E.
The percentage of the adult white population with a high school education
is inversely related to all mortality rates. Using the pollution-related
mortality function for white males sixty-five and over as an example, an
increase of 1 percent of the adult white population with a high school
31
-------
education will lead to a decrease of approximately thirty-one pollution-
related deaths per annum for every 100,000 males in this age-race group.
The coefficients of E are highly significant (as indicated by the t -r,
statistics in parenthesis below the coefficient) in all mortality functions."
It may thus be concluded that the effect of education is significantly
different from zero and inversely related to mortality; thereby suggesting
that more education results in increased quantity and/or quality of medical
care at the preventive stages of an illness. The high correlation of education
with income also suggests the possibility that higher quality goods which favor-
ably affect mortality are consumed by the higher educated groups. In essence.
these results confirm those obtained by Kitagawa and Houser (1968), Fuchs
(1965, 1973) and Auster, et al . (1969).
It should be recognized that while the absolute magnitude of the
coefficient of E for the overall mortality functions are the largest of tiie
three mortality functions, such a result is to be expected. It is also
interesting to note that the absolute size of E's coefficient is larger
('indicating a lower probability of death, ce ten's pan' bus) for pollution-
related causes than for non-pollution-related causes regardless of sex after
age forty-five. This result may be attributable to favorable occupational
and/or residential exposure to air pollution on the part of more educated
individuals. The probability of occupational differentials is reinforced by
analysis of the sex differentials in the absolute size of E. Specifically.
the male coefficients are absolutely larger than the female coefficient
indicating that males with more education may enjoy significantly less
hazardous occupations.
The coefficients of sulfur dioxide (S02) are not significant for any of
the pollution-related mortality functions. Thus, it may not be concluded that
the effect of $02 is significantly different from zero or that S02 is pos-
itively related to mortality. This result does not imply that S02 has no
impact on mortality. In fact, this result may indicate that S02 requires a
carrier (e.g., particulate matter) in order to enter the body and exhibit its
deleterious effects or that concentrations found in Allegheny County during
the 1968-1972 period were not intense enough to induce a statistically sig-
nificant effect. It should be noted that when a multiplicative interaction
term between S02 and TP was used in the regression analysis, the coefficient.
of this synergistic variable was predominately positive and significant at
the 0.15 probability level (two-tailes test). The overall equation using this
multiplicative variable, however, was not as statistically reliable as when
separate air quality terms were used. 73
Even though the estimated 50^ coefficients are statistically insignifi-
cant, they warrant further discussion since SOg has been widely considered a
major contributor to air pollution's adverse health effects. S02 exhibits
the expected positive relationship to pollution-related mortality although
SO;? is often inversely related to non-pollution-related mortality (three of
the six coefficients have negative signs). No a £ri_qri_ rationalization for n
3?
-------
positive relationship between S02 and non-pollution-related causes of death
exists. Consequently, the predominance of negative signs is not unexpected.
The negative coefficient obtained for males less than forty-five and both
males and females sixty-five and over in the over-all mortality functions,
however, is to be expected since this coefficient is the sum of the
coefficients from both the pollution-related and non-pollution-related mor-
tality functions. Indeed, it is because of this intrinsic summation process
and the fact that most deaths in the less than forty-five age group are from
non-pollution-related causes (see Table 7) that similar negative coefficients
were obtained by Lave and Seskin (1970b) for minimum sulfates in the fifteen
to forty-four age group.7^ Using the pollution-related mortality function
for white males sixty-five and over as an example, an increase of average
annual S02 concentrations by one PPT/24 hours will result in an increase of
approximately one pollution-related death per annum for every 100,000 males
in this age group.
TABLE 7. AGE-SEX-CAUSE DISTRIBUTION OF ALLEGHENY COUNTY
WHITE DEATHS DURING 1968-1972*
Deaths
Less than 45
Male Female
45-64
Male Female
65 and Over
Male Female
Overall
Pollution-related
Non-pollution
related
3,555
(100)
757
(21)
2,798
(79)
2,203
(100)
440
(20)
1,763
(80)
13,647
(100)
8,976
(66)
4,671
(34)
7,636
(100)
3,752
(50)
3,884
(50)
25,604
(100)
18,261
(71)
7,343
(29)
25,596
(100)
18,463
(72)
7,133
(28)
*Figures in parentheses are percentage of column total.
It should also be recognized that the size of the SOg coefficients gen-
erally increase with age for all pollution-related mortality functions, and
that these S02 coefficients are constantly larger for pollution-related mor-
tality functions than for the non-pollution-related mortality functions. As
Table 7 indicates, the increase in the size of the coefficients with age is
to be expected since the number of individuals dying from pollution-related
causes increases with age. The probable explanations for these results are
that: (1) the ability of the body to withstand the influence of SOg decreases
with age, or (2) there exists a cumulative influence of SC>2 on mortality.75
33
-------
TP
Total particulate predominately exhibits the expected positive relation-
ship to all mortality rates although TP is inversely related to non-
pollution-related mortality for females in the less than forty-five age group.
Since no a priori rationalization for a positive relationship between TP and
non-pollution-related causes of death exists, the presence of the negative
sign for females less than forty-five is not unexpected. Using the
pollution-related mortality function for elderly white males as an example.
an increase of average annual TP concentrations by one u/nr will result in an
increase of approximately ten pollution-related deaths per annum for every
100,000 males in the sixty-five and over age group.
It should also be recognized that the size of the TP coefficients is gen-
erally larger for the pollution-related mortality functions than for the non-
pollution-related mortality functions. The coefficients of TP increase v/ii:
age for all mortality functions and not just pollution-related as is UK- .••:•.-:<:•
with S02's coefficients. As Table 7 indicated, this result is to be expected
since the number of individuals dying from all causes, especially pollution-
related, increases with age. The probable explanation of this result is that:
(1) the ability of the body to withstand the influences of TP decreases with
age, or (2) there exists a cumulative influence of TP on mortality,
The observed sex-differential in the size of the TP coefficient sugyesis
the possibility of relatively higher exposure levels at work for males com-
pared to exposure levels experienced by females in the residential environ-
ment.7° In essence, this result suggests that if potential sexual differences
in response to air pollution are ignored, the "true" effect of TP on mortality
(estimated at the place of residence) is that level represented by the female
coefficient. Since it is impossible, however, to discount the potential
sexual differences in response, the estimated male and female coefficients
should be considered valid.
The coefficients of TP are generally statistically significant for mo;;t
of the mortality functions. The exceptions occur in the less than forty-five
age group where the female overall and non-pollution-related coefficients and
the male non-pollution-related coefficients are not significantly different
from zero at the 0.20 probability level (two-tailed test). The relative
insignificance of this variable for this group can be attributed to the com-
paratively small sample on which the mortality rates are based. Therefore,
it can be concluded that (in general) the effect of TP is significantly
different from zero and positively related to mortality, especially pollution-
related mortality.
The number of days with precipitation greater than 0.1 inch is directly
related to all mortality rates except that of the male less than forty-five
age group for non-pollution-related mortality. Again using the pollution-
related mortality function for elderly white males as an example, an ?;m:ial
increase of one day with precipitation greater than 0.1 inch will result in
an increase of almost sixty-five pollution-related deaths among white riales
sixty-five and older per annum for every 100,000 males in this age group.
34
-------
The coefficients of #P.1+ are significant in eight of the sixteen mor-
tality functions. In these cases, the coefficients of #P.1 + are significant.
at the 0.50 probability level. Therefore, it cannot be generally concluded
that the effect of rainfall is significantly different from zero and
directly related to mortality.
It should also be noted that the absolute size of the coefficients
increase with age and are consistently larger for males in each age-cause
mortality function. These results indicate that the elderly and males are
more severely impacted by rainfall. The probable explanations of these
results are that: (1) the ability of the body to withstand the influence of
damp weather decreases with age; and (2) males, due to their working environ-
ment, tend to be exposed more often to damp weather.
#T32-
The number of days that maximum temperature is 32° or less is negatively
related to mortality in thirteen of the eighteen mortality functions
estimated and positively related in the remainder of the mortality functions.
It appears that these results, together with the fact that #32- is only sig-
nificantly different from zero in less than 50 percent of the cases examined,
can only be explained by asserting that cold weather influences various age-
sex groups differently. Again using the sixty-five and older, pollution-
related white male mortality estimates as an example, an increase of one day
per year with a maximum temperature equal to or less than 32° will result in
a decrease of forty-two pollution-related deaths per annum for every 100,000
males in this age group, a result that would not generally have been expected.
P/RA
Population per 0.01 square miles of residential land area predominantly
exhibits a positive relationship to mortality although P/RA is inversely
related to female over sixty-five mortality from pollution-related and over-
all causes. Since the a priori expectation was for a positive relationship
between population densTty and mortality, these negative coefficients were
unexpected. However, none of the negative coefficients are significantly
different from zero at the 0.20 probability level. All P/RA coefficients
in the forty-five to sixty-four age group are positive and significantly
different from zero at the 0.05 probability level. Thus, it can be concluded
that population density generally increases the probability of death for the
more mobile age groups (less than sixty-five), probably caused by increasing
exposure to a variety of diseases.
Elasticities
Another interesting way of viewing the regression results presented in
Table 6 is in terms of the elasticities of the independent variables.
Specifically, elasticity estimates facilitate the comparison of effects from
a single explanatory variable on a variety of dependent variables (mortality
rates). Table 8 presents the elasticities (calculated at the mean) of each
explanatory variable in the various age-sex-cause-specific white mortality
functions. Using the standard example, the earlier results may be
35
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reinterpreted as estimating that a 10 percent increase in each of the
independent variables will produce the following percentage changes in
annual elderly white male population-related mortality rates:
F.(-3.0), S02 (+0.1), TP (+2.3), #P.H(+10.0), #32-(-2.7), and P/RA(+0.1).
It can also be seen from Table 8 that the effects of TP on the various
pollution-related mortality rates is generally greater than TP's effect on
non-pollution-related mortality rates. From the estimates in Table 8, it can
also be concluded that TP have a larger relative effect on all pollution-
related mortality rates than S02 even if the estimated SO? coefficients were
statistically significant. Possible explanations for this result is that
some of the particulate matter located in Allegheny County may be independently
and inherently harmful (e.g., asbestos) or that the particulate matter acts
as a carrier of other hazardous elements.
Finally, the weight of the evidence from Allegheny County suggests that
long-term low-level dosages of air pollution, measured as TP and S02, do in
fact have exacerbating effects on certain (pollution-related) causes of
death. These effects, while small in absolute terms, are statistically sig-
nificant for TP although statistically insignificant for S02 when SC^ is con-
sidered as a separate independent variable.
Therefore, based on the results obtained for Allegheny County, it may
be expected that an improvement in ambient air quality will produce social
benefits in the form of decreased probabilities of death. These potential
mortality reductions, in addition to the numerous other potential costs and
benefits, must be further evaluated in order to determine the socially
optimum level of air quality. Whiel detailed analysis of these other costs
and benefits is beyond the scope of this study, the current effort will con-
centrate on the development and application of criteria to facilitate the
efficient use of society's scarce air resource.
36
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TABLE 8. ELASTICITY ESTIMATES
Less than 45
Male Female
Part A. Independent Variables from
Percent of Adult
White Population
with High School
Education
Sulfur Dioxide
Total Particulates
Number of Days
Precipitation
> .1 Inch
Number of Days
Maximum Temp.
< 32°
Population per
.01 sq. ml.
(Residential)
Part B.
Percent of Adult
White Population
with High School
Education
Sulfur Dioxide
Total Particulates
Number of Days
Precipitation
> .1 tnch
Number of Days
Maximum Temp.
< 32°
Population per
.01 sq. mi.
(Residential)
Part C.
Percent of Adult
White Population
with High School
Education
Sulfur Dioxide
Total Particulates
Number of Days
Precipitation
> .1 inch
Number of Days
Maximum Temp.
< 32°
Population per
.01 sq. mi.
(Residential)
-0.77
-0.02
0.36
0.20
-0.20
0.18
-0.58
0.01
0.22
1.13
-0.09
0.2?
Independent Variables
-0.69
0.02
0.59
-0.41
0.38
0.08
Cause-Specific
-0.6?
0.02
O.R9
3.01
-0.21
0.22
43-64
Male Female
l«hite Overall Mortality
-0.54
0.04
0.40
1.23
-0.06
0.13
from White
Mortal ity
-0.53
n.os
0.44
1.53
-0.12
0.11
-0.43
0.02
0.50
1.03
0.10
0.09
Pollution-Pe
Functions
-0.63
0.02
0.46
0.80
0.13
0.11
65 and
Male
Functions
-0.31
-0.002
0.23
1.18
-0.29
0.02
Uteri
-0.30
0.01
0.23
1.00
-0.27
0.01
Over
Female
-0.
-0.
0.
0.
-0.
-0.
-0.
0.
0.
n.
-0.
-0.
17
01
31
55
28
01
13
03
31
57
28
01
Independent Variables from White Non-Pollution-Related
-0.82
-0.29
0.20
0.59
-0.56
0.24
Cause-Specific
-0.56
0.01
-0.10
0.?7
-0.04
0.22
Mortality
-0.60
0.01
0.35
0.67
0.0*
0.17
Funct Ions
-0.23
0.01
0.53
1.26
O.OP
0.06
-0.3?
-0.02
0.21
1.56
-0.31
0.04
-0.
-0.
15
10
0.32
0.
-0.
0.
ro
29
00
37
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COST-BENEFIT ANALYSIS: ECONOMIC GUJ.DEl.lNKf> F0f; f.OCT.AL DECISIONS
Preceding sections have provided insight.-, or bo;.h t.he economic nature1 •->;
the air pollution problem and air pollution'r. Imp.-irt on human mortality. It
was also demonstrated that some form of collective action was needed in order
to achieve efficient resource allocation and thus facilitate an increase in
social welfare. Specifically, the second section concluded that because of
the inherent "public good" characteristic of the scarce resource clsan air,
no private market allocative mechanism has developed, primarily due to the
high costs involved in negotiating property rights when the exclusion
principle is not applicable. A response to this situation may take the form
of either a collection of tax-subsidy schemes or direct regulatory
policies.'7 Therefore, the primary concern of this section is to identify
specific criteria that should be used to guide the suggested governmental
intervention. This section analyzes the theoretical foundations of cost-
benefit analysis in order to provide a basis for later monetization of the
estimated changes in human mortality resulting from changes in ambient air
quality.
COST-BENEFIT ANALYSIS—THE THEORY
Econonv'cs provides certain analytical techniques that can be employed
to assist governmental decision makers concerned with th? problem of
allocating scarce resources such as clean air. Collectively, these.
techniques are known as cost-benefit analysis. The objective of these
procedures is to maximize social welfare or "to maximize the present value
of all benefits less that of all costs, subject to specific constraints".^
Specifically, the question is one of assessing whether social welfare would
be enhanced with the anticipated governmental action rather than in the
absence of such market intervention.79 Since -changes in welfare are
contingent upon changes in utility, "the problem therefore becomes one of
assessing the impact of policy changes on individuals' utility levels as well
as that of determining the net change in welfare from a set of changes in
utility levels".SO xhe primary economic concept traditionally employed to
assess perturbations in utility is consumer's surplus. Consumer's surplus,
together with the various compensation principles developed by economists,
form the theoretical bases for current cost-benefit analysis. Each of these
principles will '.;•• disc.ufssed in tho following sections in order to demonstrate
that cost-benefit analysis is based on a consistent conceptual framework
rather than simply being a set of arbitrary rules and procedures. It is only
by definitively examining Uie thecit-t:i.rnl rr».^srrtone-? of cost-benefit
analysis that the .existing literature conca.c.u .ig ; ue dollar costs of
pollution-induced mortality can be evaluated and the frontiers of knowledge
38
-------
expanded. The theoretically correct quantification of these costs is an
essential prerequisite in guiding government allocation of the scarce
resource clean air and as such is a major contribution of the current
research.
Consumer's Surplus
The idea of expressing a gain (loss) in terms of money income that
accrues to the consumer as a result of a fall (rise) in the price of a
particular good originated with Dupuit in 1844. It was Marshall, however,
who popularized and refined the concept commonly known as consumer's surplus.
The essential elements of Marshall's presentation may best be illustrated
using Figure 2. Employing classical utility theory and the assumptions of
diminishing marginal utility and constant amounts of all other goods consumed,
the curve MM' represents the marginal utility derived from the consumption of
good X. If it is further assumed that the marginal utility of money is
constant, the individual will maximize his utility at any price of X by
purchasing all units for which the marginal utility exceeds price
multiplied by the marginal utility of money. Given the constant marginal
utility of money,°2 the vertical axis can be expressed in terms of money
thereby transforming MM' into the demand curve for X. If the individual were
originally in equilibrium at point A and the price of X were decreased from
PI to ?2, the surplus that would be received from the last (X£ - X^) units of
X purchased would be equal to his total change in utility (Xi ABX2) minus the
cost incurred (Xi CBX2) or ABC. In addition to this surplus, the individual
also benefits by an amount equal to P2P}AC due to the decrease in price on
the first Xj units of X. This results in a total consumer's surplus of
P2PiAB. Using similar analysis, it can be demonstrated that the consumer's
surplus for the first Xj units of X is equal to PjMA, the area under the
demand curve above the price line.
The unrealistically strict assumption associated with Marshall's
methodology fostered much dissatisfaction. Specifically, since the analysis
assumes constant marginal utility of money and ignores the effects of changes
in real income resulting from price changes, the approach represented an
undesirable method of assigning a dollar value to changes in utility and
hence welfare. Alternative and more theoretically acceptable measurement
techniques have since been developed, primarily by Hicks (1944 and 1956).
The methods developed by Hicks for expressing consumer's surplus can
most easily be expressed with the aid of the individual's indifference map
shown in Figure 3. In this figure, the numeraire (or money) is measured on
the vertical axis and X, the commodity in question, on the horizontal axis.
Assuming that the individual received an income of OM and that the price of
X is originally P^ or OM/OX^, equilibrium is achieved at point A on
indifference curve I where the individual's MRS is equal to the MRT or the
slope of his budget constraint (MX3). If the price of X decreases from P^
to P2 or Om/OX^, maintaining constant money income (OM), the individual will
increase his consumption from Xi to X2 and attain an equilibrium position at
point B on indifference curve II where his MRS is equal to his nev; budget
constraint (MX^). This increase in utility (i.e., movement from
39
-------
CO
)-<
CO
rH
r-1
O
o
Quantity of X
Figure 2. Marshallian consumer's surplus,
40
-------
indifference curve I to indifference curve II) represents his change in
consumer's surplus. The problem associated with this method of assessing
consumer's surplus is in the conversion of the changes in utility to
monetary units. In order to determine the dollar value of this increase in
utility Hicks developed four different measures of consumer's surplus.
The first method is termed the price-compensating variation (PCV) which
measures "the amount of (money) income he would have to lose in order to
offset the gain due to the fall in price".°^ jn order to assess this quantity
a line is constructed 171 th the slope of the new budget constraint, MXz,. tan-
gent to indifference curve I at point C. If the individual's income is re-
duced by the amount B B^ while maintaining the new price ?2, he will be
attaining the same level of satisfaction (represented by indifference
curve I) at C as he war, ;;t A. The amount B B^ is therefore a monetary
measure of the amount of income required to just offset the gain due to the
fall in price. In essence, this amount is the Hicksian PCV measure of
consumer's surplus resulting from the decrease in the price of X.
The price-equivalent variation (PEV) is the second measure of consumer's
surplus developed by Hicks. PEV measures "the gain in income which, if
experienced without the price falling, would make the consumer as much better
off as he is made by the fall in price without a change in money income". 4
In order to determine this quantity a line is constructed with the slope of
the original budget line, MX3, tangent to indifference curve TT nt point D.
If the individual's income is increased by the amount A A| while maintaining
the original price PI, he will be attaining the same level of satisfaction
(represented by indifference curve II) at D as he was at B. The amount A A]
is therefore the monetary measure of the amount of income he would have to
acquire in the absence of a price decrease to be equally satisfied. This
amount is thus the Hicksian PEV measure of consumer's surplus resulting from
the decrease in the price of X. It should be noted that the FCV for a given
price decrease is exactly equal to the PEV for the alternate price increase
and vice versa.
Recognizing that the PCV measures the change in income required to off-
set the change in price and not the change in income required to offset the
change in quantity resulting from a price change, Ilir.ks developed a quantity-
compensating variation (QCV). This concept may also be demonstrated with the
aid of Figure 3. After the price decrease, consumption of X increases from
X^ to X£. If the individual's income were now reduced by an amount B B2, he
would still be able to purchase X2 while maintaining the .level of satisfaction
associated with the original indifference curve I. The amount of B B2 is
therefore the monetary measure of the QCV.
The fourth and final measure of consumer surplus developed by Hicks is
the quantity-equivalent variation (QEV). Analogous to the QO7, this method
is concerned with income changes required to offset quantity chingps.
Specifically, QEV measures the income change required to attain a new level
of satisfaction while maintaining the original quantity consumed. Given the
original budget constraint MXo, the individual maximizes his utility at
point A consuming Xj units of X. If his income were now Increased by an
-------
X
Quantity of X
Figure 3. Hicksian consumer's surplus.
42
-------
amount A A2, he would still be able to purchase Xi while attaining the level
of satisfaction associated with the new indifference curve II. The amount
A A-2 is therefore a monetary measure of QEV. It should be recognized that if
the price changes ave relatively small or the good in question composes a re-
latively small portion of the individual's budget, t h:he ifi::i:£iY;3. L social costs oi
a and b, this relationship may be. ex^rt's^d as:
MRS , ••= MSC /MSC, (G)
ab a b
Winch (1971, p, 143) notes that the 'MRS between :; eommoolty and money for
an individual corresponds to his c-hange in roiTnii^v1 --. srrpl.v:-. (ACS) since h:U;
ACS represents the suvpl.uK (>f whr;«. lit- ' = v; n. u[, >.••• $:;•./ ov •• , hat which he
actua'Lly must pay. This relationship, combine'! viiV; t\:? •.-'ii!-< *-.rsion of v',o;;J
b to money (allowing b_ to ; 01 respond to alj gi-oti except a).- pf:riuji.s the re-
writing of the efficiency crft-eHa for -A -:-od ns:
ACS =•- MSC (7:
P i-
When ;.'uL)j ic goods are involved i.e.g,, cleau -':i /}, hov/>. ...; , this criteriua
is not di:e.ctiy applicable due to the ^.y.cJ.asion pi j'acijjle; cheroiore as
Samuelson (1969) notes, the relevant efficiency crUier:*os; becomes the equality
of tli« sum of individual MRS and the MRT. Kec:o£ui:zLng this relationship, the
-------
efficiency criteria applicable to public good a_ must be written as:
EACS = MSC
a a
The possibility of applying this efficiency criterion to the analysis of
non-Paretian changes (i.e., some individuals are made absolutely worse off
while others are made absolutely better off) in public goods by summing
individual's changes in consumer surplus' has received considerable
attention. This concern arises because non-Paretian changes generate
positive as well as negative changes in consumer's surplus. This summing
estimates of consumer surplus appears to imply some type of interpersonal or
normative comparison of utility since all individual changes in consumer's
surplus are weighted equally in the summation procedure. The implied
normative judgment that all individuals are to be treated equally is generally
avoided by positive economists who contend that implied value judgments are
outside the realm of economists. Since any new allocation scheme for the
scarce resource clean air will be non-Paretian change, this concern is of
central importance to the current effort of valuing the benefits of changes
in human mortality resulting from improvements in ambient air quality.
Essentially the problem of summing changes in consumer's surplus is analogous
to comparing alternative welfare distributions since both involve evaluating
changes in the relative positions of individuals. Economists have tradition-
ally analyzed alternative welfare distributions in terms of the ability of
the individuals who gain satisfaction to compensate those who lose satis-
faction. The development of these compensation principles is the topic of
concern in the following section.
Compensation Principles
Barone in 1908 was the first economist to suggest that changes in an
individual's welfare could be quantified in terms of the equivalent amount of
income he would be willing to accept or pay in order to allow a return to his
original welfare position. An expansion of this idea to the whole community
forms the basic underlying structure of the Hicks-Kaldor compensation
principle (H-K). Specifically, the H-K principle states that if a policy
change results in some individuals being made better off while others are
made worse off, welfare would be increased if the gainers could somehow com-
pensate the loser so as to have them, both better off. In the case of improve-
ments in ambient air quality, this criterion may be restated in terms of con-
sumer's surplus. If the sum of the positive changes in consumer's surplus
resulting from a proposed policy change (i.e., an improvement in ambient air
quality) exceeds the sum of any resulting negative changes in consumer's
surplus, then social welfare could be improved by implementing the new policy.
While neither Hicks (1939) nor Kaldor (1939) suggest that the actual com-
pensation be paid, this issue as well as the possibility of paradoxial results
have led to much debate and refinement concerning the compensation principle. ^
Utility possibility curves for a community of two individuals, A and B,
before and after a proposed policy change intended to improve air quality are
depicted in Figure 4.90 These utility possibility curves will be used to
demonstrate the application and development of the compensation principle.
The Qi points on the Q\ Cj curves in each panel represent the utility
44
-------
<
o
Utility of B
Case a
Utility of B
Case b
<
o
•H
4J
Utility of B
Case c
Utility of B
Case d
Figure 4. Utility possibility curves before and after
air quality improvement.
45
-------
levels attained by individuals A and B associated with the existing levels of
air quality. All other points on these curves represent alternative
possibilities which could be attained through alternative compensation schemes
given existing policies (i.e., C.). The C^ points on the Q2 £-2 curves re-
present the utility levels attained by individuals A and B associated with air
quality levels resulting from the proposed policy change. The other points
on the Q2 C2 curves represent alternatives attainable through different
compensation schemes given the new policy (i.e., €2). In examples a_ through
jl, individual B benefits from the policy change since he moves to a higher
indifference curve (i.e., B is the recipient of a positive change in his
consumer's surplus), while individual A loses from the policy change since he
moves to a lower indifference curve (i.e., A is the recipient of a negative
change in his consumer's surplus).
Cases b_ and d_, however, demonstrate instances where the H-K criterion is
not fulfilled. Specifically, in neither of these cases may individual B
sufficiently compensate individual A for his loss in a manner that will leave
A minimally as well off as before the policy change. Therefore, regardless
of whether compensation is actually paid, the proposed policy change in cases
b_ and d_ may not unequivocally result in an improvement in social welfare. In
fact, if the policy change in case b_ were implemented, the H-K criterion yould
be satisfied by reversing the policy alteration. Specifically, a policy
change resulting in a movement from Q2 to Q]^ would unequivocally increase
social welfare after allowing individual A (recipient of the positive chance
in consumer's surplus) to compensate individual B (recipient of the negati' e
change in consumer's surplus) in a manner capable of moving to a point on the
Qj_ GI curve to the northeast of Q2 (e.g., point C^).
Cases a_ and _c_ demonstrate instances where redistribution from Q2 to C2
would represent sufficient compensation by the gainer (individual B) to the
loser (individual A) so as to leave both parties better off after the policy
change.
Upon further examination, however, case c_ leads to a rather interesting
result. If Q£ was the original position and Q^ the new position, a movement
from QI to C\ would result in sufficient compensation to allow both parties
to be better off. Thus, in case c_ using the H-K criterion, although a policy
change resulting in a movement from Qj; to Q2 increases social welfare after
allowing for compensation; a movement from Q2 to 0^ will also lead to an
increase in overall welfare after allowing for compensation. This paradox
was first noted by Scitovsky (1941) leading him to advocate a double test
criterion for welfare improvement. Scitovsky contends that potential
increases in welfare resulting from policy changes can unequivocally be
claimed as an actual welfare improvement only if the H-K test before the
policy change show no points superior to those after the change. That is,
unequivocal statements concerning social welfare improvements may only be
asserted in the absence of reversal patterns similar to case c_.
Little accepts similar compensation criteria but also poses an additional
criterion that potential redistribution is not a sufficient basis for making
unequivocal statements on welfare improvement. Specifically, Little asserts
that "an economic change is desirable (and increases welfare) if it causes a
46
-------
good redistribution of wealth, and if the potential losers could not profit-
ably bribe potential gainers to oppose it". 91 Thus, in order to fulfill this
criterion the resulting position after implementing the policy change must
actually be socially preferred to the position before the policy change.
Without any a priori information on social preferences, the only way policy
changes can unequivocally result in welfare improvements is if the redistri-
bution results in the attainment of a position to the northeast of the
original utility possibility point. Thus, the evaluation of any policy change
must be made on the basis of both its efficiency aspects (i.e., the Scitovsky
modified H-K criterion) and its equity or distributional aspects. While these
criterion may appear restrictive, it must be recognized that most individual
policies only minutely modify the existing income distribution. As Krutilla
suggests:
The relative magnitude of the redistribution associated
with . . . decisions for which benefit-cost expenditure
criteria have been traditionally employed will be of the
second order of smalls in terms of its implications for
measuring the change and, for practical purposes, can bj;
ignored. (1964, p. 228)52
Hence, as Mishan notes:
The possibility of such a reversal [the Scitovsky paradox]
actually occurring in the real world, where there are a
large number of goods and people, is much smaller, how-
ever, than the impression conveyed by a two good two-
person diagram. (1973, p. 321)93
Therefore, as long as the redistributional aspects of a policy change are
this small, cost-benefit analysis may concentrate on the estimation of changes
in society's welfare without regard to modifications in the distribution of
welfare among individuals.
It has now been demonstrated that cost-benefit analysis has its funda-
mental roots in theoretical economics. Whether this link is "the basis of
. . . all economics" as stated by Haveman and Weisbrod or a "dilluted
version of ... allocation theory"^ is not of major importance. What is of
paramount concern is the existence of a consistent conceptual framework
composed of the concept of consumer's surplus and the compensation principle
within which cost-benefit analysis must be performed. In essence, the basic
objective of cost-benefit analysis may be summarized as the maximization of
the present value of net social benefits. Benefits can now be defined as
those results of a policy change that generate positive changes in consumer
surplus or cost savings (increases in welfare) while costs include those
results which generate negative changes in consumer surplus or increased
costs (decreases in welfare). The objective of the following section is to
examine the application of cost-benefit analysis in determining the optimum
level of air quality.
47
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COST-BENEFIT ANALYSIS—THE APPLICATION
While traditional applications of cost-benefit analysis have involved
public investment projects, the term "project" can be applied more generally
to include proposed changes in laws, regulations, and various tax-subsidy
schemes.96 For present purposes, the "project" is the attainment of an
optimal use of the scarce air resource. That is, given the alternative uses
of the air (e.g., waste-assimilation, life-support), what level of air
quality represents an optimal allocation of clean air between these uses?
The following statement by Krutilla synthesizes the arguments developed
earlier for the use of cost-benefit analysis in the treatment of this problem:
Essentially, a private cost-gains calculus is employed in
deciding private firms' policies; externalities and other
divergences between private and social product are
neglected. Benefit-cost analysis, on the other hand,
seeks to take account of such divergences as a basis for
guiding public action either when market prices do not
actually reflect social value or when, by virtue of the
individual's nature of collective goods, no market exists
from which to observe directly objective evidence of the
community's valuation of the social marginal product."'
In examining the theoretical foundations underlying the application of cost-
benefit analysis, it was demonstrated that the efficiency criterion could be
stated in terms of dollar values.°° Specifically, the optimum level of air
quality was attained when the sum of the changes in individual's consumer
surplus resulting from increases in ambient air quality equaled the marginal
social costs (MSC) of attaining that level of air quality. By grouping all
benefits and costs, this criteria may be restated as: 9'
MSC = MSB
where MSB is equal to marginal social benefits.
Attempts at single, all encompassing, estimates of air pollution costs
to society (i.e., the benefits of pollution abatement) have been conducted
primarily through the analysis of property value differentials.^^ The
advocates of this approach contend that:
If the land market were to work perfectly, the price of a
plot of land would equal the sum of the present discounted
streams of benefits and costs derivable from it. If some
of its costs rise (e.g., if additional maintenance and
cleaning costs are required), the property will be
discounted in the market to reflect people's evaluation of
these changes. Since air pollution is specific to
locations and the supply of locations is fixed, there is
less likelihood that the negative effects of pollution
can be significantly shifted onto other markets. We should
therefore expect to find the majority of effects reflected
in this market, and can measure them by observing associated
changes in property values.101
48
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Although property markets do not function perfectly, property value differen-
tials may reflect many of the social costs resulting from air pollution. It
is unrealistic, however, to expect consumers to completely discount such costs
if their existence is not generally recognized (e.g., health costs).
In an attempt to partially account for these costs, estimates have been
made of the effects of air pollution on human health,1^2 materials,103
vegetation,104 and other aspects.105 Using effect-specific dose-response
estimates (the effects of alternative levels of pollution) , it is also possible
to calculate the MSB of pollution abatement. This approach requires a careful
summation of the various effect-specific benefit functions (e.g., human
health, vegetation) to determine society's overall marginal benefit function
for air quality improvements. Equating this inclusive MSB function with the
inclusive MSC for improving air quality will result in the attainment of the
socially optimum level of air quality. This approach is illustrated using
the hypothetical marginal social benefit curves depicted in Figure 5.
Specifically, MSB , MSB , MSB , and MSB represent the hypothetical MSB curves
for health, materials, vegetation, and all other dose-response relationships,
respectively. The summation of these individual MSB is represented by the
curve labeled MSB. The optimum level of air quality is where the MSB curve
intersects the hypothetical MSC curve or X . At any point to the left of X ,
the social gains from a marginal increase In air quality exceed their costs,"
indicating that society can experience a net increase in welfare by attaining
the next higher level of air quality. For points to the right of X , the
social costs of an additional unit of air purity exceed the value or the
changes in social benefits; therefore, no further increase in air quality is
socially desirable. Any increases in air purity beyond X would in fact
decrease social welfare.
While empirical estimates of the hypothetical MSB curves depicted in
Figure 5 have been calculated, severe difficulties are encountered when
attempting to empirically determine the optimum level of air quality. In
particular, the efforts to quantify the MSB are greatly complicated by
problems of isolation and valuation in monetary units of air pollution's many
potential effects. The MSC, while not simple to calculate, are substantially
less difficult to estimate since measurements primarily involve direct dollar
costs rather than estimates of consumer surplus. Therefore, economists have
concentrated on estimating the benefits of pollution abatement. Following
this precedent, the remainder of this present effort will focus solely on
properly monetarizing the social costs of pollution-induced mortality estimated
in Section IV. The reasons for this concentration are threefold. First,
Section 109 of the Air Quality Act of 1967 requires the establishment of
primary air quality standards "to protect the public health." Second, there
exists substantial debate on the issue of ambient air quality's aggravation
effect on mortality, particularly at daily exposure levels. Finally, prior
quantification of these costs has been consistent with the underlying
assumptions of cost-benefit analysis. 106
49
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0)
(j
rt
O
O
MSC
Air Quality
Figure 5. Marginal air pollution costs and benefits.
50
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SECTION VI
EVALUATION OF MORTALITY BENEFITS: MONETIZATION OF
DECREASES IN MORTALITY
Section IV has provided estimates of physical social benefits, measured
as potential decreases in mortality, that can be expected from improvements
in air quality. The present section will review and evaluate methods for
quantifying these benefits in dollar terms. Specifically, the various pro-
cedures for monetizing changes in probabilities of death will be reviewed for
consistency with the Paretian basis of cost-benefit analysis as outlined in
the preceding section. Finally, the most theoretically precise empirical
estimates currently available will be applied to the mortality functions
estimated in Section IV in order to monetize the mortality component of the
total marginal social benefit function.
SPURIOUS MONETIZATION PROCEDURES
Thus far, most attempts at monetizing changes in life expectancy
(mortality) have been inconsistent with the Paretian basis of cost-benefit
analysis. In general, these approaches have focused on either the incorrect
measure (e.g., lives rather than probability of death) or valuation of life
or both. Some economic studies have even attempted to boldly ansxcer the
philosophical question — What is the value of life?
Four broad classifications of such spurious monetization procedures can
be identified; (1) present value of future earnings; (2) net present value of
future earnings; (3) the insurance principle; and (4) governmental decisions. 107
Each of these procedures will be evaluated for consistency with the theoreti-
cal basis of cost-benefit analysis. The reason for this type of comparative
evaluation is that when properly utilized, cost-benefit analysis can provide
an efficient means of collectively allocating scarce resources. Specifically,
this section will demonstrate why each of these four monetization procedures
is incorrect for assessing what individuals are willing to pay for welfare
improvements or decreases in mortality.
Present Value of Future Income
One of the iaof;t r^Tunonly used methods of estimating the value of mortality
changes is based on the present value of future income (PVY).IOS When applied
to mortality rate changes, this approach involves a two-step procedure. First,
calculate the PVY for an average expected stream of future income using the
following formula:
51
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D -
-------
Net Present Value of Future Earnings
Another spurious method for evaluating mortality reductions is the PVY
net of the individual's own consumption (NPVY).m This approach was
originally designed by Dublin and Lotka (1946) to determine how much insurance
an individual should maintain in order to avoid undue economic hardship on his
family in the event of an untimely death. Most of the criticisms of this
approach are identical to those of PVY. In addition, however, this technique
also may lead to the conclusion that individuals with small or negative NPVY
(e.g., individuals on welfare, retired persons and housewives) have little or
no economic value to society. Carried to an extreme, this approach may even
result in an "economic" justification for genocide.
Insurance Principle
Another monetizing technique is based on the life insurance premium an
individual pays and the probability of dying. If, for example, an individual
pays $100 annually for life insurance and his probability of death is 0.001,
then the individual values his life at $100,000. This estimate is invalid on
several grounds. First, the $100 is only a minimum estimate, since an
individual may be willing to pay in excess of the $100 premium. Second, an
individual is not securing any change in his probability of death (increases
in welfare), only purchasing insurance for family security. While a single
individual may not purchase life insurance, he probably is willing to pay for
a decrease in his probability of death and certainly should be compensated for
increased risks of death imposed on him. This measure reflects neither of
these likelihoods, and, therefore, the insurance principle cannot be used as a
surrogate for willingness to pay for increases in life expectancy.
Governmental Decisions
The final spurious monetizing technique is based on analysis of govern-
mental decisions. The advocates of this approach contend that society
evaluates mortality changes daily in the form of governmental decisions on
safety. If such decisions were drastically at odds with the evaluation of
their constituency, then gove...,-.;ient decision makers would not be reelected.
While this approach may appear to reflect social willingness to pay for mor-
tality reductions, this conclusion is not valid since:
[1] decisions to invest in certain projects are not
determined by popular vote; . . .
[2] investment decisions are not motivated primarily
by the desire to advance the general welfare; . . .
[3] an implicit value attributable to loss of life by
a particular public programme will differ widely
from an implicit value derived from another public
programme.
53
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Moreover, Usher has demonstrated that using this approach governmental safety
decisions are inconsistent when extrapolated from the base level risk (e.g.,
one in a million reduction in probability of death) to "certain death."113
Specifically, Usher has shown the existence of wide ranging estimates from
the $37,000 recommended by the National Safety Council for use in cost-benefit
analysis to $4,500,000 extrapolated from the decision to produce a special
ejector seat in a jet plane. The examination of these governmental decisions,
therefore, cannot be expected to reveal society's willingness to pay for de-
creases in mortality.
THE CORRECT CONCEPTUAL MEASURE
The theoretical inconsistencies between the four previous monetizing
techniques and the theoretical basis of cost-benefit analysis have been
recognized by Schelling (1968), Usher (1973), Mishan (1973) and others (e.g.,
Hirshleifer, et al. , 1974 and Zeckhauser, 1975). As stated earlier, con-
sistency with the foundations of cost-benefit analysis requires that changes
in welfare be expressed as either the compensation required to return an
individual to his original utility level (or bundle of goods) after a decrease
in welfare or as willingness to pay in order to maintain an increase in
welfare. Specifically, if an improvement in air quality reduces mortality,
the correct social valuation of this benefit is the summation of the resulting
positive changes in consumer surplus or the summation of what individuals
would be willing to pay rather than forego this increase in welfare. Alter-
natively, if a reduction in ambient air quality leads to increases in an
individual's probability of death, then the correct social valuation of these
costs is the summation of the resulting negative changes in consumer surplus
or the summation of what individuals would require in compensation to regain
their original level of welfare.
This type of approach to the evaluation of changes in mortality for an
individual consumer can simplistically be depicted with the aid of the in-
difference map in Figure 6. In this figure, income (or all other goods) is
represented on the vertical axis while the individual's probability of life
(one minus the mortality rate) is depicted on the horizontal axis. If an
individual is originally receiving income Yo and experiencing a probability
of life of XQ) his welfare position is expressed by indifference curve I. If
ambient air quality improves such that his probability of life increases from
Xo to Xj_, this change in welfare is expressed- by the movement from indiffer-
ence curve I to indifference curve II. The relevant dollar valuation now
becomes the amount of income the individual would be willing to give up in
order to maintain this new higher probability of life (X^) or the amount of
money he would have to lose in order to offset the gain in his utility due
to the decrease in his mortality rate. This amount is equal to BC since the
individual would be just as well off ( indifference curve I) at the new
lower mortality rate as before.^^
The summing of BC, or its equivalent, for all members of society should
then provide an estimate of the total benefit received by all individuals from
a reduction in their own mortality rates resulting from an improvement in
ambient air quality. This amount, however, is not the total social benefit
resulting from the air quality improvement. In addition to benefits in the
areas of public health, material preservation and vegetation growth there also
54
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0
Probability of Life
Figure 6. Individual's indifference map for risk and income.
55
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exists benefits to friends, family and society from decreases in the individ-
ual's probability of death. Specifically, friends and family gain by enjoying
the individual's comradeship longer and also there is the potential gain to
society in the form of extra output generated from a reduction of any indi-
vidual's probability of death.115 Thus, the relevant social benefit from a
reduction in any individual's probability of death is the sum of what he, his
friends and relatives, and society are willing to pay rather than forego the
reduction. Summing these valuations for all individuals in society, the total
social benefit for any change in mortality can be estimated.
Now that the concept of consumer's surplus (willingness to pay) has been
theoretically applied to the valuation of changes in mortality, the relevant
question becomes whether reliable empirical estimates of this theoretical
construct can be obtained. The possibility of simply asking individuals what
they are willing to pay for changes in their probability of death or that of
friends and relatives is the logical starting point. There are, however,
serious problems inherent with this approach. First, individuals may not
'express their true willingness to pay because of the free rider problem
evolving from the inapplicability of the exclusion principle to the public
good air. Second even if individuals would express their valuation, most
of the probabilities usually discussed are relatively small (e.g., one in a
million), and it has been argued that individuals cannot adequately assess
such minute probabilities.i1^ In an attempt to circumvent these problems,
economists have focused on the market system to explore the possibility that
individuals reveal monetary valuations of changes in their own probability of
death by actually trading such probabilities for changes in money income. If
such activity does occur, then it should be possible to ascertain the values
revealed. Fortunately, such a market reflection does exist in the form of
explicit or implicit premiums paid to various occupations for assuming extra
risk. These risk premiums may be in the form of direct income or indirect
compensation (e.g., pension benefits). There are, however, difficulties in-
volved with the use of these premiums, most of which have been well stated by
Zeckhauser:
The logical problem is that the people who are assuming the
risks are those who value them the least in relation to the
benefits they get for risking them. They may be the poor,
they may be the people whose probability assessments are
most in error, they may be the people who legitimately have
the lowest probability of being injured, they may be the
people who will die soon anyway, or they may be the people
who value their own lives the least highly.i1?
In addition to these considerations is the belief that individuals will seldom
accept any monetary payment in exchange for the certainty of death. There-
fore, complete extrapolation from observed values to "the value of a life" is
impossible.ll
In light of these criticisms, market reflections of compensation required
to induce an individual to accept additional risk must always be qualified.
Specifically, since such estimates only approximate one of the components of
society's total valuation, any extrapolation of these results to the
56
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monetization of the benefits of decreases in mortaility resulting from
improvements in ambient air quality must be interpreted as an extreme lower-
bound estimate. Following Mishan, however, it may be argued that "there is
more to be said for rough estimates of precise concepts than precise estimates
of economically irrelevant concepts".H9 Applying Mishan's reasoning to
obtaining estimates of willingness to pay for decreases in the probabilities
of death, the labor market may be viewed as a reflection, however imprecise,
of the economically precise concept.
Figure 7 graphically depicts how the labor market reflects individual's
monetary valuation of risk changes. Specifically, this figure shows how an
individual can increase his welfare by rationally choosing between changes in
risk and corresponding changes in compensation or payment. For example,
assume, an individual at point A has the opportunity to gain income by in-
creasing his risk. If his trade possibilities are summarized by MM', the
market equilibrating trade-off curve between risk and income, he will maximize
his welfare by trading income for security and move from A to B. The monetary
value of this change in his welfare is BC, the Hicksian QCV. What is observed
in the labor market, however, is the income differential Y0Y^ which is larger
than BC since the marginal utility of money is not constant. Using the trade
possibility curve MM', the marginal value of this market reflection of the
compensation required to induce the individual to assume the small increase
in his probability of death may be expressed as -dy/dx or YQY^/X X^. Extra-
polating this marginal valuation to the individual's valuation of life (e.g.,
OM) may not be valid if the individual has a high probability of death (low
probability of life) beyond which he will not make income-risk trade-offs.
This possibility is demonstrated in Figure 7 by the vertical line extending
from the low probability of life X. As Hirshleifer notes: "Willingness to
make small or 'marginal' adjustments at this rate of exchange does not by any
means imply willingness to make large adjustments at the same terms."120
Recalling that air pollution-induced mortality changes are small (at
least for the ambient concentrations typically found in Allgeheny County),^21
marginal approximations of the Hicksian QCV will therefore suffice for esti-
mating the dollar amount that individuals would be willing to pay for decreases
in their mortality rates (the Hicksian QEV) resulting from increases in
ambient air quality. Indeed, it should be recalled that the Hicksian QCV of a
price rise (increase in risk) is the mirror image of the Hicksian QEV of a
price fall (decrease in risk). Thus, the assignment of these dollar values
to changes in the mortality rates associated with improvements in ambient air
quality can be made, provided that dollar estimates consistent with this
theoretical interpretation can be found.
DOLLAR ESTIMATES OF SOCIAL BENEFIT
The gap between an acceptable theoretical determination of the willingness
of individuals to pay for decreases in mortality and quantification of the
abstract model is quite large. Fortunately, recent work by Thaler and Rosen
(1973) has managed to obtain valid empirical estimates of the marginal
valuation curve (MM1 in Figure 7).
57
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X 1
o
Probability of Life
Figure 7. Market reflection of risk-income trade-off.
58
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By matching risk data which detailed the number of excess deaths by
industry and occupation from the 1967 Occupation Study of the Society of
Actuaries with the 1967 Survey of Economic Opportunity data on personal and
industrial characteristics of individuals, Thaler and Rosen were able to
construct a data base consisting of 907 adult male heads of household. The
means and standard deviations of their variables are. presented in Table 9.
Using this data, the authors statistically controlled for "other" factors in
addition to risk which influence wage rates. Specifically, regional, demo-
graphic, social and job characteristic differentials were controlled for by
fitting various hedonic demand curves to this data through the use of multiple
regression analysis. Utilizing this technique, Thaler and Rosen were able to
estimate a set of implicit marginal prices for risk acceptance. The results
of their regression analysis, both linear (part A) and semi-log (part B) are
presented in Table 10. The reason for the presentation of two functional
forms is that their data did not "provide enough resolution on functional form
to make a choice".122
The coefficients presented in Table 10 (parts A and B) are estimates of
the wage equation assuming that "all the non-risk variables . . . simply shift
the wage-risk relationship leaving its slope intact".123 Recalling from
Table 9 that the risk variable has been scaled by a factor of 10^, the
estimated risk coefficient 0.0352 in equation one part A indicates that indi-
viduals will accept an increased probability of death equal to 0-001 for an
extra $3.52 per week.124 Assuming a fifty-week working year, this estimate
translates to an annual risk premium of $176 for an increase of 0.001 in an
individual's probability of death.
Equation two in part A replaces the occupational dummy variable with
social economic status (SES) dummy variables. In this equation, the estimated
coefficient 0.0520 indicates that individuals will accept a 0.001 increase in
their probability of death for an extra $5.20 per week of $260 per year.
Corresponding estimates for equations one and two of Table 10 part B (semi-log)
estimated at the mean are somewhat smaller than those of part A (linear).
Equation one of the semi-log form implies an annual risk premium of $136 for
the 0.001 increase in probability of death while equation two implies an
annual premium of $189. Extrapolating these marginal values to the point of
a "statistical death" their estimates "lie in a reasonably narrow range of
about $200,000 + 60,000".125
Before proceeding to use these results to quantify in dollar terms the
benefits of air quality-related mortality reductions, it should be noted that
these risk premiums contain an inherent bias. Specifically, as demonstrated
in Table 11, Thaler and Rosen's sample was composed of relatively risky
occupations. Therefore, the individuals included in the sample were relatively
less risk averse than the general population. This downward bias coupled
with the fact that these risk premiums only approximate the individual's own
willingness to pay for risk reductions and not those of family, friends and
society insure that any benefit estimates based on the Thaler and Rosen
results will unequivocally represent a lower bound estimate.
59
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TABLE 9. MEANS AND STANDARD DEVIATIONS OF THE VARIABLES
INCLUDED IN THALER AND ROSEN'1 S WAGE FUNCTIONS*
Variable Mean Standard Deviation
Dummy Variables**
Urban .69 .46
Northeast .28 .45
South .29 .45
West .17 .38
Family size exceeds two .76 .42
Manufacturing industry .24 .42
Service industry .58 .49
Worker is white .90 .30
Worker employed full-time .98 .10
Worker belongs to union .45 .49
Worker is married .92 .26
Occupation is operative .27 .44
Occupation is service .45 .49
Occupation is labor .22 .42
Continuous Variables
Age (years) 41.8 11.3
Education (years) 10.11 2.73
Weeks worked in 1966 49.4 5.4
Hours worked last week 44.9 11.6
Risk (probability x 105) 109.8 67.6
Weekly wage (week prior
to survey) $132.65 50.80
*Source: Thaler and Rosen (1973).
**The mean of the dummy variables is proportion in sample with the
designated characteristic.
60
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TABLE 10. THALER AND ROSEN REGRESSION ESTIMATES OF WEEKLY WAGE RATES*
Part A. Linear
Independent
Variables
Risk
Urban
Northeast
South
West
Age
(Age)2
Education
2
(Education)
White
Union
Full-rime
Hours Worked
Occ 1 Operative
Occ 2 Service Worker
Occ 3 Laborer
SES 1
SES 2
SES 3
R2
Equation
(1)
.0352
(.0210)**
13.80
(4.2)
-3.71
(3.65)
-8.86
(3.70)
9.13
(4.13)
3.89
(0.80)
-.0479
(.0092)
3.40
(0.55)
_
22.92
(4.53)
25.5
(3.25)
-1.63
(12.9)
1.50
(.12)
-18.7
(9.2)
-24.6
(9.5)
-25.6
(13.*)
-
_
_
.41
Equation
(2)
.0520
(.0219)
15.71
(2.95)
-4.29
(3.67)
-8.90
(3.74)
10.50
(4.18)
3.81
(0.83)
-.0468
(.0097)
3.27
(2.40)
-.021
(.128)
22.93
(4.50)
27.16
(3.25)
-.86
(12.6)
1.41
(.12)
-
-
-
4.68
(5.17)
-17.17
(3.34)
-20.69
(5.53)
.41
*Source: Thaler and Rosen (1973).
**Standard errors are in parentheses.
61
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TABLE 10. THALER AND ROSEN REGRESSION ESTIMATES OF WEEKLY WAGE RATES* f
Pare B. Semi-Log
Independent
Variables
Risk
Urban
Northeast
South
West
Age
(Age)2
Education
(Education)
White
Family Size > 2
Union
Full-Time
Hours Worked
Occ 1 Operative
Occ 2 Service Worker
Occ 3 Laborer
SES 1
SES 2
SES 3
R2
Equation
(1)
.000206
(.000167)**
.114
(.033)
-.00357
(.0029)
-.0623
(.0295)
.0857
(.0327)
.0381
(.0063)
-.000469
(.000073)
.0332
(.0044)
.228
(.036)
-
.203
(.026)
.275
(.103)
.0113
(.00096)
-.0885
(.0728)
-.126
(.075)
-.218
(.106)
-
-
.47
Equation
(2)
.000286
(.000174)
.132
(.024)
-.00573
(.0291)
-.0568
(.0298)
.0974
(.0332)
.0385
(.0065)
-.000475
(.000077)
.0531
(.0190)
-.00129
(.00101)
.228
(.036)
-.00204
(.027'.)
.214
(.025)
.303
(.101)
.0105
(.00095)
-
-
-
.0152
(.0411)
-.128
(.026)
-.194
(.042)
.46
*Source: Thaler and Rosen (1973, p. 35).
**Standard errors are In parentheses.
hDependent variable Is the log of the weekly wage rate.
62
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TABLE 11. THALER AND ROSEN'S SAMPLE OCCUPATIONS AND RISKS*
Occupation
Risk** Occupation
Risk**
Fishermen
Foresters
Teamsters
Lumbermen
Mine operators
Metal filers, grinders
and polishers
Boilermakers
Cranemen and derrickmen
Factory painters
Other painters
Electricians
Railroad brakemen
Structural iron workers
Locomotive firemen
Power plant operatives
Sailors and deckhands
Sawyers
19
22
114
256
176
41
230
147
81
46
93
88
204
186
06
163
133
Switchmen
Taxicab drivers
Truck drivers
Bartenders
Cooks
Firemen
Guards, watchmen and
doorkeepers
Marshals, constables,
sheriffs and bailiffs
Police and detectives
Longshoremen and stevedores
Actors
Railroad conductors
Ships' officers
Hucksters and peddlers
Linemen and servicemen
Road machine operators
Elevator operators
Laundry operatives
Waiters
152
182
98
176
132
44
267
181
78
101
73
203
156
76
02
103
188
126
134
*Source: Thaler and Rosen (1973, p. 30).
**Units of measure are extra deaths per 100,000 policy years.
By selectively combining the average marginal compensation for risk-
estimates (0.001 = $200) derived from the Thaler and Rosen analysis with the
various age-sex-specific pollution-related mortality functions estimated in
Section IV, it is now possible to monetize the pollution-aggravated mortality
component of the marginal social benefit function. The resulting dollar
estimates, unlike those traditionally employed in cost-benefit analysis of
mortality reductions, will be consistent with the Paretian basis of cost-
benefit analysis because such estimates will be based on changes in consumer's
surplus. Specifically, the marginal compensation premiums estimated by Thaler
and Rosen may be interpreted as estimates of the compensation required to
offset a negative change in an individual's consumer surplus (e.g., acceptance
of increased risk) which is equal to the amount he would be willing to pay
rather than forego an equivalent positive change in his consumer's surplus
(e.g., a reduction in risk). This equivalency was discussed in Section V
63
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along with the development of the Hicksian concepts of consumer's surplus.
The procedure used to combine the risk and mortality estimates involves the
following four steps:
(1) Estimate changes in the various pollution-related mortality
rates for a 1 percent improvement in each of the air quality
variables. This task was undertaken by using percentage
changes around the mean values of S02 and TP while holding
all other independent variables constant at their mean
values. The results of these estimates for Allegheny County
are presented in Table 12.
TABLE 12. CHANGES IN AGE-SEX SPECIFIC POLLUTION-RELATED MORTALITY
RATES RESULTING FROM 1 PERCENT DECREASE IN S00 OR TP*+
Sex Age S02 TP
Male Less than 45 0.016 0.613
45 - 64 0.618 4.924
65 and over 0.384 12.614
Female Less than 45 0.012 0.428
45 - 64 0.100 1.924
65 and over 1.016 11.661
*A11 mortality rate changes are per 100,000.
+A11 other variables held constant on their mean value.
(2) Multiply these changes in mortality rates per thousand
individuals by the Thaler and Rosen marginal compensation
estimate of $200. This results in an average marginal
social benefit estimate for the various age-sex specific
pollution-related mortality rate changes which is
consistent with the Paretian basis of cost-benefit
analysis. The results of these procedures are presented
in Table 13.
64
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TABLE 13. AVERAGE AGE-SEX-SPECIFIC MARGINAL ANNUAL DOLLAR BENEFITS
FOR POLLUTION-RELATED MORTALITY CHANGES RESULTING FROM
1 PERCENT DECREASE IN S02 OR TP*
Sex Age S02 TP
Male Less than 45 0.032 1.226
45 - 64 1.236 9.848
65 and over 0.768 25.228
Female Less than 45 0.024 0.856
45 - 64 0.200 3.848
65 ana over 2.032 23.322
*A11 figures are in 1970 dollars.
(3) Multiply these average marginal social benefit estimates by the
population at risk. This step involves multiplying the various
age-sex values in Table 13 by the corresponding 1970 white pop-
ulation of Allegheny County in order to obtain estimates of the
total age-sex-specific mortality benefits of pollution abate-
ment. The results of these multiplications are presented in
Table 14.
65
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TABLE 14. TOTAL AGE-SEX-SPECIFIC MARGINAL ANNUAL DOLLAR BENEFITS
FOR POLLUTION-RELATED MORTALITY CHANGES RESULTING
FROM A 1 PERCENT DECREASE IN S02 OR TP*
Sex
Age
SO,
TP
Male
Less
45 -
than 45
64
65 and over
Total Male
15
205
50
270
557
1,636
1,652
3,845
Female
Total Female
Less than 45
45 - 64
65 and over
11
38
189
238
408
638
2,167
3,213
Total Male and Female
508
7,058
*A11 figures are in thousands of 1970 dollars ($1,000).
(4) Sum the age-sex-specific total benefit estimates in Table 14
to obtain an estimate of the total benefits accruing to the
residents of Allegheny County from decreases in mortality
resulting from improvements in ambient air quality. The
results of these summations are also presented in Table 14.
From the results presented in Table 14 it can be concluded that the
benefits of reduced mortality derived from an abatement or particular matter
are substantially higher than for sulfur dioxide abatement. That is, indi-
viduals in Allegheny County are willing to pay at least approximately $7
million annually in order to maintain TP at a level 1 percent below those
experienced during the 1968-1972 period but only $.5 million annually for a
similar percentage reduction in S0£. These relative dollar differentials
were to be expected on the basis of the results from the mortality model
estimated in Section IV, especially, the elasticity estimates of Table 8,
Part B.
It must be emphasized, however, that the relationships estimated in this
chapter are designed as inputs in an overall cost-benefit analysis of air
quality, and only relative conclusions concerning air quality's effects on
mortality can be drawn from these estimates. The expression of air pollution
66
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aggravation effects on mortality in dollar values consistent with the other
components of cost-benefit analysis, however, facilitates the efficient allo-
cation of society's scarce resource clean air. By monetizing the mortality
component of the marginal social benefit function, more enlightened decisions
about the socially optimum level of air quality can be made. Specifically,
these dollar estimates will permit decision makers to more closely approximate
the optimum level of air quality by permitting the direct comparison of mortal-
ity reductions as well as other benefits of air pollution abatement with the
costs associated with such abatement policies.
67
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SECTION VII
REFERENCES
1. There are, however, incidents where nature has required assistance.
Because the sewage generated by a city of one million people made the
water unpotable, the first aqueducts were constructed by the Romans.
2. For a good discussion of this issue, see: Barry Commoner, Michael
Coor, and Paul Stampler, "The Causes of Pollution," Environment 13
(April 1971): 2-19.
3. For a good discussion of this episode, see: H. H. Schrenk et al.,
Air Pollution in Donora, Pennsylvania (Washington, D.C.: U.S.
Government Printing Office, 1949).
4. For a good discussion of this episode, see: J. A. Scott, "The London
Fog of December 1962," Medical Officer 109 (1963): 250-252.
5. Robert Dorfman and Nancy Dorfman, eds., Economics of the Environment
(New York: W. W. Norton, 1972), p. XIX.
6. Tiber Scitovsky. Welfare and Competition. Revised ed. (Homewood,
Illinois: Richard D. Irwin, 1971), p. 65.
7. See Section V, pp. 44-47.
8. E. J. Mishan. "A Survey of Welfare Economics, 1939-59," The Economic
Journal 70 (June 1960): 206.
9. The marginal rate of substitution in consumption of a_ for b_ measures
the number of units of b_ that an individual is willing to sacrifice
per unit of a_ attained so as to maintain a constant level of satis-
faction.
10. The marginal rate of transformation in production is the number of units
by which the production of b_ must be decreased in order to expand the
output of a^ by one unit. This ratio is simply equal to the (minus)
ratio of the marginal costs of a_ and b_ where these costs include both
private and social costs.
11. See, for example: James M. Henderson and Richard E. Quandt, Micro-
economic Theory; A Mathematical Approach (New York: McGraw Hill 1958),
pp. 202-208.
68
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12. Adam Smith. The Wealth of Nations. The Modern Library Edition.
(New York: Random House, 1965), p. 423.
13. Scitovsky, Welfare and Competition, p. 18.
14. Ibid.
15. An externality is defined to be Pareto-relevant when the extent of the
activity may be modified in such a way that the externally affected
party can be made better off without the acting party being made worse
off. See: Buchanan and Stubblebine, "Externality". In A.E.A. Readings
in Welfare Economics, pp. 199-212. Edited by Kenneth J. Arrow and Tibor
Scitovsky. (Homewood, Illinois: Richard D. Irwin, 1969).
16. A. C. Pigou. The Economics of Welfare. 4th ed. (London: Macmillan
and Co., 1952), pp. 183-184.
17. See footnote 10.
18. For an excellent discussion of this process, see: Ronald Coase, "The
Problem of Social Costs." In Economics of the Environment, pp. 100-129.
Edited by Robert Dorftnan and Nancy S. Dorfman. (New York: W. W.
Norton, 1972).
19. Ibid., p. 111.
20. Kenneth J. Arrow. "The Organization of Economic Activity: Issues
Pertinent to the Choice of Market Versus Nonmarket Allocation." In
Public Expenditure and Policy, pp. 59-73. Edited by Robert H. Haveman
and Julius Margolis. (Chicago: Markham, 1970), p. 68.
21. Paul A. Samuelson. "The Pure Theory of Public Expenditure." In
A.E.A. Readings in Welfare Economics, pp. 179-182. Edited by Kenneth
J. Arrow and Tibor Scitovsky. (Homewood, Illinois: Richard D. Irwin,
1969), p. 179.
22. Garrett Hardin. "The Tragedy of the Commons." In The Environmental
Handbook, pp. 31-50. Edited by Garrett DeBell. (New York: Ballentine
Books, 1970), p. 37.
23. For a detailed development of this modification, see: Samuelson,
"The Pure Theory of Public Expenditure."
24. James M. Buchanan. The Bases for Collective Action (New York: General
Learning Press, 1971) , p. b.
25. Arrow, "The Organization of Market Activity," p. 69.
26. For a good discussion of this episode, see: Schrenk et al., Air
Pollution in Donora.
69
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27. W. Riggan et al. "Mortality Models: A Policy Tool." In Proceedings
of the Conference on Environmental Modeling and Simulation, pp. 196-
198. Edited by Wayne R. Ott. (Springfield, Virginia: National
Technical Information Service, 1976), p. 196.
28. For an excellent discussion of the various factors which influence
an individual's probability of death, consult Harry S. Shryock and
Jacob S. Siegel, The Methods and Materials of Demography, 2 Volumes
(Washington, B.C.: U.S. Government Printing Office, 1971).
29. See, for example, U.S. Department of Health Education and Welfare,
Air Quality Criteria for Sulfur Oxides (Washington, B.C.: U.S.
Government Printing Office, 1969).
30. Ibid., p. 84.
31. For discussion of specific pollutants, consult the various Litton
Systems, Inc. reports referenced in the bibliography.
32. U.S. Department of Health, Education and Welfare. Air Quality Criteria
for Particulate Matter. (Washington, D.C.: U.S. Government Printing
Office, 1969), p. 141.
33. N. R. Frank, M. 0. Amdur, and J. L. Wittenberger. "A Comparison of
Acute Effects of S02 Administered Alone or in Combination with Nad
Particles on the Respiratory Mechanics of Health Adults," International
Journal of Air and Water Pollution 8 (February 1964): 125-133.
34. The adjustments to these mortality rates have been correctly criticized
by Carol K. Redmond, "Review of the Riggan et al.: Mortality Models:
A Policy Tool," (Pittsburgh: Mimeographed, 1976).
35. Donald 0. Anderson. "The Effects of Air Contamination on Health:
A Review, Part II," Canadian Medical Association Journal 97 (September
9, 1967), p. 585.
36. U.S. Department of Health, Education and Welfare, Particulate Matter,
p. 148.
37. See, for example: Warren Winkelstein et al., "The Relationship of Air
Pollution and Economic Status to Total Mortality and Selected
Respiratory System Mortality in Men. I. Suspended Particulates,"
Archives of Environmental Health 14 (January 1967): 162-171.
38. Lester B. Lave and Eugene P. Seskin. "Does Air Pollution Shorten
Lives?," Proceedings of the Second Research Conference of Inter-
University Committee on Urban Economics (Chicago, 1970), p. 295.
39. Lester B. Lave and Eugene P. Seskin. "An Analysis of the Association
Between U.S. Mortality and Air Pollution," Journal of the American
Statistical Association 68 (June 1973), p. 286.
70
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40. Lave and Seskin, "Does Air Pollution Shorten Lives?," p. 148.
41. The inaccuracy of these mortality rates is important to recogniEe
when comparing results.
42. The desirability of using age-sex-race-specific mortality rates is
developed in detail on pages 16 and 17.
43. Lester B. Lave and Eugene P. Seskin. "Air Pollution, Climate and Home
Heating: Their Effects on U.S. Mortality Rates, "American Journal of
Public Health 62 (July 1972), p. 910.
44. For an excellent discussion of the limitations involved with using
observed total mortality rates for comparisons between populations and
the desirability of using standardized rates, see: Shyrock and Siegel,
Methods volume 2, pp. 418-424.
45. The difference in age distributions between SMSA's is quite apparent
when comparing the Boston SMSA, (population is relatively young) to the
Scranton SMSA (population is relatively old).
46. Lave and Seskin, "An Analysis of the Association Between U.S. Mortality
and Air Pollution," p. 288.
47. Donald 0. Anderson. "The Effects of Air Contamination on Health:
Part III," Canadian Medical Association Journal 97 (September 23, 1967),
p. 806.
48. Richard Auster, Irving Leveson, and Deborah Sarachek. "The Production
of Health, An Exploratory Study," Journal of Human Resources 4 (Fall
1969), p. 415.
49. Anderson, "Part III," p. 805.
50. Recent criticism of these studies has cast sufficient doubt upon their
veracity to compel EPA to contract with the National Academy of Science
for a reevaluation of the methodology and the conclusions reached by
CHESS.
51. U.S. Environmental Protection Agency. Health Consequences of Sulfur
Oxides: A Report from CHESS, 1970-1971 (Washington, D.C.: U.S.
Government Printing Office, 1974), pp. 7-20.
52. It is not expected that all of these independent variables (especially
all climatological variables) will be present in the final results.
53. Residence was coded on the death certificates in terms of 1960 census
tracts and socioeconomic data was obtained from 1970 census tracts;
therefore the census tracts were grouped in order to insure that
comparable areas were covered. The resulting groupings were then
further aggregated in order to achieve a minimum of 300 deaths per
area for the period 1968-1972.
71
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54. Attempts to control for migration with the inclusion of an additional
independent variable (i.e., percentage of the population who always
lived at present residence) did not improve the overall explanatory
power of the model. In fact this variable was seldom significantly
different from zero.
55. See, for example, Shryock and Siegel, Methods volume 2, p. 417.
56. The residence on the death certificates was coded on the basis of 1960
census tracts while most other information was coded on the basis
of 1970 census tracts. Therefore, groupings of census tracts were
formed to make the boundaries consistent.
57. Only 9 percent of the 1970 population of Allegheny County was Negro.
58. While attempts at estimating tobacco expenditures were made using
regression analysis, these results were too poor to use for predictive
purposes.
59. The Blue Cross estimates were received from personal correspondence
with Mr. Dale Colby.
60. This formulation is identical to the crowding variable used by Lave
and Seskin, "Air Pollution and Human Health," Science 169 (August 1970)
723-732.
61. The figures for total and residential areas of the individual census
tracts were derived from data received from the Southwestern
Pennsylvania Regional Planning Commission.
62. For a more detailed description of the interpolation procedures see:
Donald S. Shepard, SYMAP Interpolation Characteristics (Cambridge:
Graduate School of Design, Harvard University, April 1970).
63. For a more detailed description of the point distribution coefficient
see: Laboratory for Computer Graphics and Spatial Analysis, SYMAP
(Cambridge: Graduate School of Design, Harvard University, July 1975).
64. Alternative functional forms including various air quality interaction
terms were tried, although the "best" results were obtained using the
weighted linear form. This conclusion is essentially the same reached
by Lave and Seskin, "Association Between U.S. Mortality and Air
Pollution," p. 288.
65. The main effect of heteroscedasticity, as noted by Teh-wei Hu,
Econometrics; An Introductory Analysis (Baltimore: University Park
Press, 1973), p. 82, is not the biasness of the estimated regression
coefficient but on the efficiency — the variance of the estimated
regression coefficient.
72
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66. Also see: N. Draper and H. Smith, Applied Regression Analysis (New
York: John Wiley and Sons, 1966), pp. 77-80.
67. Wayne E. Smith. "Factors Associated with Age-Specific Death Rates,
California Counties, 1965," American Journal of Public Health 58
(October 1968), pp. 1943-1944.
68. The choice of the statistically "best" equations were based on the
following three criteria: (1) the highest "R^ found to be significant
by the corresponding F statistics; (2) regression coefficients that were
statistically significant (t test); and (3) a residual pattern which
best supported the assumptions that the error terras are independent,
have zero mean, and constant variance.
69. As noted by Hu, Econometrics, p. 74, the common case of multi-
collinearity will cause the standard error of the coefficient to be
larger than it is in the case of no collinearity.
70. See Section III, pp. 12-14.
71. See Table III, p. 22 for a listing of which causes of death are being
considered pollution related.
72. Two-tailed tests of significance were used for all variables even when
a priori sign expectations were met. The reason for this was
consistency with those variables for which no a_ priori sign
expectations could be made. One-tailed tests for those variables whose
JL priori sign expectations were met did not alter the instances in
which the variable was not significant.
73. See footnote number 68 above.
74. See Table 1, p. 14.
75. This possibility was investigated by introducing the percent of
individuals residing in the tract since I960 as an independent variable.
However, the test proved inconclusive.
76. This statement implies only that labor force participation rates are
less for female, rather than indicating a zero female participation
rate. The 1970 Allegheny County labor force participation rate of
females sixteen and over was 35 percent compared with 75 percent for
males.
77. Another policy option is the maintenance of the status quo.
78. A. R. Prest and R. Turvey. "Cost-Benefit Analysis: A Survey," The
Economic Journal 75 (December, 1965), p. 686.
79. For a more detailed discussion of the theoretical foundations of cost-
benefit analysis, see: D. M. Winch, Analytical Welfare Economics
(Baltimore: Penquin, 1971).
73
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80. Winch, Analytical Welfare Economics, p. 135.
81. This definition of consumer's surplus is suggested by J. R. Hicks,
Value and Capital, 2nd ed. (London: Oxford University Press, 1968),
p. 40.
82. As noted by Winch, Analytical Welfare Economics, p. 139, unless, the
elasticity of demand is unitary there will be some transference of
expenditures to or from other goods, but with a constant marginal
utility of money this is of no consequence.
83. J. R. Hicks. "The Four Consumer's Surpluses," Review of Economic
Studies 11 (January 1944), p. 34.
84. Ibid., pp. 34-35.
85. This result can be verified by reviewing Hicks original algebraic
formulations, Ibid., p. 37.
86. For a proof of this statement see Winch, Analytical Welfare Economics,
p. 142.
87. The arguments are essentially the same as those developed by Winch,
Ibid.
88. See, for example, Ibid.
89. For an excellent discussion of the issues surrounding the compensation
principle, see Mishan, "A Survey of Welfare Economics."
90. Although these curves resemble production-possibility curves, in this
figure the axis measures a specific individual's welfare, ordinal
utility.
91. I. M. D. Little. A Critique of Welfare Economics. 2nd ed. (London:
Oxford University Press, 1957), p. 109.
92. John V. Krutilla. "Welfare Aspects of Benefit-Cost Analysis," Journal
of Political Economy (June 1964). Quoted in Robert Spore, "Property
Value Differentials as a Measure of the Economic Costs of Air Pollution,"
p. 16. Ph.D. dissertation, The Pennsylvania State University, 1972.
Emphasis added by author.
93. E. J. Mishan. Cost-Benefit Analysis (New York: Praeger, 1973), p. 321.
Emphasis added by author.
94. R. H. Haveman and B. A. Weisbrod. "The Concept of Benefits in Cost-
Benefit Analysis: With Emphasis on Water Pollution Control Activities."
In Cost-Benefit Analysis and Water Pollution Policy, pp. 37-66.
Edited by Henry M. Peskin and Eugene P. Seskin. (Washington, D.C.:
The Urban Institute, 1973"), p. 49.
74
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95. Mishan, Cost-Benefit Analysis, p. 316.
96. Prest and Turvey, "Cost-Benefit Analysis," p. 685-686.
97. Krutilla, "Welfare Aspects of Benefit-Cost Analysis," p. 226.
98. See, pp. 39-44.
99. This formulation is identical to ZACSa = MSCa since EACSa represents
a net figure containing both positive and negative consumer surplus'.
100. See, for example, Ronald G. Ridker and J. Henning, The Determinants of
Residential Property Values with Special Reference to Air Pollution,"
Review of Economics and Statistics 49 (May 1967): 246-257.
101. Ronald G. Ridker. Economic Costs of Air Pollution: Studies in
Measurement (New York: Praeger, 1967), p. 25.
102. See, for example, Lave and Seskin "Air Pollution and Human Health."
103. See, for example, R. C. Fink, F. H. Buttner, and W. K. Boyd.
Technical Economic Evaluation of Air Pollution Corrosion Costs in
Metals in the United States (Columbus: Battelle-Columbus Laboratories,
1971).
104. See, for example, H. Benedict, C. Miller, and R. Olson. Economic
Impact of Air Pollution on Plants in the United States (New York:
Coordinating Research Council, 1971).
105. For an excellent discussion of various studies, see* Thomas E.
Wadell, The Economic Damages of Air Pollution, U.S. Environmental
Protection Agencies Socioeconomic Environmental Studies Series
(Washington, D. C.: U. S. Government Printing Office, 1974).
106. This statement is verified in detail later in Section VI, pp. 51-54.
107. This type of classification is suggested by Mishan, Cost-Benefit
Analysis, pp. 153-155.
108. This method was used by Lave and Seskin, "Air Pollution and Human
Health."
109. This estimate was "refined" to include the market value of housewives'
services by Burton A. Weisbrod, Economics of Public Health (Philadelphia:
University of Pennsylvania Press, 1961).
110. T. C. Schelling. "The Life You Save May Be Your Own." In Problems in
Public Expenditure Analysis, pp. 127-176. Edited by Samuel B. Chase.
(Washington B.C.: The Brookings Institution, 1968), pp. 149-150.
Emphasis added by author.
75
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111. This method was originally formulated to determine the amount of life
insurance an individual should purchase. See: Louis I. Dublin and
Alfred J. Lotka, The Money Value of a Man (New York: Ronald Press,
1946).
112. E. J. Mishan. "Evaluation of Life and Limb: A Theoretical Approach,"
Journal of Political Economy 79 (July/August 1971), p. 157.
113. Dan Usher. "An Imputation to the Measure of Economic Growth for
Changes in Life Expectancy." In The Measurement of Economic and Social
Performance, pp. 193-232. Edited~~by~Milton Moss (New York: National
Bureau of Economic Research, 1973), p. 210.
114. For a rigorous mathematical treatment of this derivation, see: Michael
Jones-Lee, "The Value of Changes in the Probability of Death or
Injury," Journal of Political Economy 82 (July/August, 1974): 549-552.
115. This is not to imply that this value is large relative to the others
considered. It may in fact be negative for a. perpetual criminal.
116. Richard Zeckhauser. "Procedure for Valuing Lives," Public Policy 23
(Fall, 1975), p. 444.
117. Ibid., p. 436.
118. It is for this reason that Schelling, "The Life You Save," makes the
distinction between a "statistical" death and an "individual" death.
The current analysis is concerned only with the "statistical" death
(i.e., the death of an unknown individual).
119. Mishan, "Evaluation of Life and Limb," p. 174.
120. J. Hirshleifer, T. Bergstron, and E. Rapport. Applying Cost-Benefit
Concepts to Projects which Alter Human Mortality (Los Angeles: School
of Engineering and Applied Science, U.C.L.A., 1974), p. 23.
121. See Table 6, p. 30.
122. Richard Thaler and Sherwin Rosen. "The Value of Saving a Life:
Evidence from the Labor Market." Paper Presented at the National Bureau
of Economic Research Conference on Income and Wealth, Household Pro-
duction and Consumption, Washington, D. C., November 30, 1973, p. 32.
123. Ibid.
124. All dollar values are in 1967 dollars.
125. Thaler and Rosen, "The Value of Saving a Life," p. 36.
76
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SECTION VIII
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Bushtueva, K. A. "Toxicity of H2S04 Aerosol," in U.S.S.R. Literature on Air
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Haveman, R. H., and Margolis, L. , eds. Public Expenditures and Policy
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Hirsh, Joseph. "Comfort and Disease in Relation to Climate." In Climate and
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. "Does Air Pollution Shorten Lives?," Proceedings of the Second
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/5-77-009
3. RECIPIENT'S ACCESSION"NO.
4. TITLE AND SUBTITLE
Intra-Urban Mortality and Air Quality: An Economic
Analysis of the Costs of Pollution Induced Mortality
5. REPORT DATE
July 1977
6. PERFORMING ORGANIZATION CODE
'. AUTHOR(S)
John J. Gregor
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING ORGANIZATION NAME AND ADDRESS
The Center for the Study of Environmental Policy
The Pennsylvania State University
University Park, PA 16802
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
EPA Grant R803609
12. SPONSORING AGENCY NAME AND ADDRESS
Office of Research & Development
Environmental Protection Agency
Corvallis Environmental Research Laboratory
Corvallis, OR 97330
13. TYPE OF REPORT AND PERIOD COVERED
Final. 1968-1972
14. SPONSORING AGENCY CODE
EPA/600/02
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This report has attempted to quantify in both physical and monetary terms the effects
of existing ambient levels of air pollution on human mortality. A model for the iso-
lation of air pollution's influence on human mortality was developed based on insights
derived from existing experimental, episodic, and epidemiological studies. This
model was then estimated using weighted linear regression analysis and data from the
1968-1972 experience of Allegheny County, Pennsylvania. The resulting pollution-
related mortality functions were then monetized through the use of the most theoreti-
cally consistent economic valuation of mortality changes. Specifically, the estimatec
age-sex-specific pollution-related mortality functions were monetized by applying
existing estimates of individual's willingness to pay for mortality decreases. The
results of this study lend support to the contention that an improvement in ambient
air quality will produce social benefits in the form of decreased probabilities of
death.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Air Pollution
Economic Analysis
Benefit/Cost Analysis, Air Pollution
Economic Effects, Air Pollution
Economic Effects, Health
Air Pollution Economics
Economic Impact
Air Pollution Effects
(Health)
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
92
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
85
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