vvEPA
Umt<
Envn
Ecol cts
! DC 20460
EPA-600/5- 79-001 a
'.579
pment
Methods Development
for Assessing Air
Pollution Control
Benefits
Volume I,
Experiments in the
Economics of Air
Pollution Epidemiology
-------
OTHER VOLUMES OF THIS STUDY
Volume II, Experiments in Valuing Non-Market Goods: A Case Study of
Alternative Benefit Measures of Air Pollution Control in the South
Coast Air Basin of Southern California, EPA-600/5-79-001b.
This volume includes the empirical results obtained from two experiments
to measure the health and aesthetic benefits of air pollution control in the
South Coast Air Basin of Southern California.
Volume III, A Preliminary Assessment of Air Pollution Damages for
Selected Crops within Southern California, EPA-600/5-79-001c.
This volume investigates the economic benefits that would accrue from
reductions in oxidant/ozone air pollution-induced damages to 14 annual
vegetable and field crops in southern California.
Volume IV, Studies on Partial Equilibrium Approaches to Valuation of
Environmental Amenities, EPA-600/5-79-001d.
The research detailed in this volume explores various facets of the two
central project objectives that have not been given adequate attention in the
previous volumes.
Volume V, Executive Summary, EPA-600/5-79-001e.
This volume provides a 23 page summary of the findings of the first four
volumes of the study.
This document is available to the public through the National Technical
Information Service, Springfield, Virginia 22161.
-------
EPA-600/5-79-001a
February 1979
METHODS DEVELOPMENT FOR ASSESSING
AIR POLLUTION CONTROL BENEFITS
Volume I
Experiments in the Economics of Air Pollution Epidemiology
by
Thomas D. Crocker and William Schulze
University of Wyoming
Laramie, Wyoming 82071
Shaul Ben-David
University of New Mexico
Albuquerque, New Mexico 87131
Allen V. Kneese
Resources for the Future
1755 Massachusetts Avenue, N.W.
.Washington, D.C. 20036
s
USEPA Grant #R805059010
Project Officer
Dr. Alan Carlin
Office of Health and Ecological Effects
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
OFFICE OF HEALTH AND ECOLOGICAL EFFECTS
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
-------
DISCLAIMER
This report has been reviewed by the Office of Health and Ecological
Effects, Office of Research and Development, U.S. Environmental Protection
Agency, and approved for publication. Approval does not signify that the
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
-------
ERRATA
Please make the change shown below In
METHODS DEVELOPMENT FOR ASSESSING AIR POLLUTION CONTROL BENEFITS,
Volume I, EPA-600/5-79-001a, February 1979, p. 154
Volume V, EPA-600/5-79-001e, February 1979, p. 8
Change $0.071 to 0.071 cents in the first arithmetic equation
on these two pages.
-------
PREFACE
The motivation for this volume originated in the authors* mutual and
reinforcing convictions that economic analysis and its techniques of empir-
ical application could contribute to the resolution of certain puzzles in
studies of the incidence and severity of diseases in human populations,
particulary the epidemiology of air pollution. The prior works of Lester
Lave, Eugene Seskin, and V. Kerry Smith have provided an excellent base from
which to initiate our efforts. These researchers, in addition to Dennis
Aigner, Shelby Gerking, Leon Hurwitz, and Roland Phillips have also provided
many worthwhile comments and criticisms. None of these individuals are
responsible, however, for the results we have obtained.
iii
-------
ABSTRACT
This study employs the analytical and empirical methods of economics
to develop hypotheses on disease etiologies and to value labor productivity
and consumer losses due to air pollution-induced mortality and morbidity.
Since the major focus is on methodological development and experimentation,
all the -reported empirical results are to be regarded as tentative and on-
going rather than definitive and final.
Two experiements have been conducted. First, using aggregate data from
sixty U.S. cities, 1970 city-wide mortality rates for major disease cate-
gories have been statistically associated with aggregate population charac-
teristics such as physicians per capita, per capita cigarette consumption,
dietary habits, air pollution and other factors. Dietary variables, smoking,
and physicians per capita are highly significant statistically. However, the
estimated contribution the latter variable makes to reducing mortality rates
becomes evident only after we recognize that human beings attempt to adjust
to disease by seeking out more medical care. The estimated effect of air
pollution on mortality rates is about an order of magnitude lower than some
other estimates. Nevertheless, rather small but important associations are
found between pneumonia and bronchitis and particulates in air and between
early infant disease and sulfur dioxide air pollution.
The second experiment, which focused on morbidity, employed data on the
generalized health states and the time and budget allocations of a nationwide
sample of individual heads of household. For the bulk of the dose-response
expressions estimated, air pollution appears to be significantly associated
with increased time being spent acutely or chronically ill. Air pollution,
in addition, appears to influence labor productivity, where the reduction
in productivity is measured by the earnings lost due to reductions in work-
time. The reduction in productivity and to air pollution-induced chronic
illness seems to be much larger than any reductions due to air pollution-
induced acute illness.
IV
-------
CONTENTS
Chapter I:
Introduction, to Volume I 1
Chapter II: Some Issues 3
2.1 Epidemiology and Economics 3
2.2 When Microeconomics Doesn't Matter 5
2.3 When Microeconomics Does Matter 9
2.4 The Costs of Pollution-Induced Disease 12
Chapter III: Sources of Error 15
3.1 Problems in Statistical Analysis 15
3.2 Heteroskedasticity 15
3.3 Multicollinearity . 16
3.4 Causality and Hypothesis Testing 17
3.5 Aggregation 19
Chapter IV: The Sixty-City Experiment 24
4.1 Objectives of the Experiment 24
4.2 Value of Life Vs. Value of Safety 27
4.3 A Methodological Basis: Does Economics
Matter? 32
4.4 The Sixty-City Data Set: Selection of
Variables • • 35
4.5 Empirical Analysis 53
4.6 A Tentative Estimate of the Value of
Safety from Air Pollution Control 70
Chapter V: The Michigan Survey Experiment 72
5.1 Objectives of the Experiment 72
5.2 The Sample and the Variables 72
5.3 Estimates of Dose-Response Rates for Acute
and Chronic Illness 96
5.4 Recursive Estimates of the Effect of Air
Pollution Upon Health, Labor Earnings,
and Hours of Work 119
5.5 A Model of the Effect of Air Pollution
on the Demand for Health 137
5.6 Some Empirical Results: The Demand for
Freedom from Air Pollution-Induced
Acute and Chronic Illness " 142
5.7 Overview of Empirical Results 148
-------
CONTENTS
(continued)
Chapter VI: An Estimate of National Losses in Labor
Productivity Due to Air Pollution-
Induced Morbidity 153
6.1 Introduction 153
6.2 The Assumptions . 154
vi
-------
FIGURES
Number Page
2.1 Alternative Measures of Disease Incidence 7
3.1 Marginal Purchase Price and Marginal Willingness-to-Pay ... 22
4.1 Hypothetical Hunan Dose-Response Function 26
6.1 A Representation of the Effect of Air Pollution Upon Labor
Productivity 153
vii
-------
TABLES
Number Page
4.1 Objectives and limitations, 28
4.2 Mortality Variables 36
4.3 Dietary Variables 37
4.4 Social, Economic, Geographic, and Smoking Variables 38
4.5 Air Pollution Variables 39
4.6 Sources of Data 41
4.7 Simple Correlation Matrix for 1965 Diet Variables 43
4.8 Simple Correlation Matrix for Air Quality Variables 45
4.9 Simple Correlation Matrix for Included Variables 46
4.10 Complete Listing of Data Used 47
4.11 Summary of Two-Stage Linear Estimates of Factors in Human
Mortality Hypotheses not Rejected at the 97.5% Confidence Level
(One-tailed t-test, t >_ 2.0) 54
4.12 Reduced Form Equation 56
4.13 Total Mortality . 57
4.. 14 Vascular Disease 58
4.15 Heart Disease 59
4.16 Pneumonia and Influenze 60
4.17 Emphysema and Bronchitis 61
4.18 Cirrhoris 62
4.19 Kidney Disease 63
4.20 Congenital Birth Defects . . . 64
viii
-------
TABLES
(continued)
Number Page
4.21 Early Infant Diseases 65
4.22 Cancer 66
4.23 Methodology for Health Benefits Assessment . 69
4.24 Urban Benefits from Reduced Mortality: Value of Safety for
60% Air Pollution Control 71
5.1 Complete Variable Definitions . . . 74
5.2a Representative Means and Standard Deviations of Health and
Air Pollution Variables for Samples Involving Family Heads
Currently Employed or Actively Looking for Work*"...... 78
5.2b Representative Means and Standard Deviations of All Other
Variables3 79
5.3 Expected Signs for Explanatory Variables in Estimated Dose-
Response Functions t . 88
5.4 Proportions of Entire Survey Research Center Sample
Processing a Particular Characteristic During'1971 ..... 93
5.5 Matrix of Simple Correlation Coefficients for a 1971
Representative Dose-Response Function Sample . . 99
5.6a Dose-Response Rates for ACUT: Unpartitioned Samples .... 100
5.6b Dose-Response Rates for ACUT: Partitioned Samples 104
5.7a Dose-Response Rates for LDSA: Unpartitioned Samples .... 105
5.7b Dose-Response Rates for LDSA: Partitioned Samples 109
5.8 Lagged Effects of Total Suspended Particulates Upon Duration
of Chronic Illnesses (LDSA) of Respondents Who, as of 1975,
Had Always Lived in the Same State 117
5.9 Simple Correlation Coefficients Between Labor Supply and
Certain Other Variables for a 1970 Sample 120
5.10a Empirical Results for a 1971 Sample Recursive Labor Supply 124
5.10b Empirical Results for a 1970 Sample Recursive Labor Supply . 126
5.10c Empirical Results for a 1971 Sample Recursive Labor Supply . 127
ix
-------
TABLES
(continued)
Number Page
5.10d Empirical Results for a 1969 Sample Recursive Labor Supply . 128
S.lla Labor Supply Effects of Air Pollution-Induced Chronic and/or
Acute Illnesses 129
5.lib Value of Labor Supply Effects of Air Pollution-Induced
Chronic and/or Acute Illnesses for Pollution Concentrations
TWo Standard Deviations Removed from the Mean Concentration . 131
5.12 Willingness to Pay to Avoid Acute Illness 145
5.13a Two-Stage Least Squares Estimates of WAGE Expressions for
Chronic Illness 146
5.13b Two-Stage Least Squares Estimates of Chronic Illness
Expressions (LDSA) '. 147
6.1 Major Assumptions Limiting Generality of Results 155
6.2 Distinguishing Features that Enhance the Generality of Results 157
6.3 Estimated Expressions to be Used to Calculate the Effect of
Air Pollution-Induced Illness on Labor Productivity . '•. . . 158
6.4 Estimated Per Capita Aggregate Gains in 1970 U.S. Labor
Productivity Due to a 60 Percent Reduction in Air Pollution . 161
-------
CHAPTER I
INTRODUCTION TO VOLUME I
Volume I focuses on developing methodology for valuing the benefits
to human health associated with air pollution control. Air pollution may
affect human health in three ways: (1) by increasing mortality rates,
(2) by increasing the incidence and the severity of chronic illness
(morbidity), and (3) by increasing the incidence and the severity of
acute illness (morbidity).
A number of approaches for determining health effects and valuing
them in economic terms are developed within the study. First, if' a dose-
response relationship is known between mortality rates and air pollution
or between days lost from work due to illness (productivity loss) and air
pollution, economic losses can be approximated. In the former case, one
must know how consumers value increased safety. Thus, if air pollution
control reduces risk of death from air pollution related disease, studies
of the value consumers place on safety in other situations — on the job,
in transportation, etc. — can be applied to measuring the benefits of
pollution control programs. Note, however, that valuing safety for small
changes in risk is very different from the alternative of valuing human
life through lost earnings — an approach rejected here. Rather, the
focus is on examining the value of safety to individuals; that is, how much
consumers are willing to pay for safety obtained through pollution control.
For morbidity losses, lost time from work and lost productivity during
hours of work can be relatively easily valued using observed wage rates.
A second approach for valuing the effects of air pollution on human
health is to attempt to observe the effect of air pollution directly on
economic factors, thus avoiding the necessity of developing dose-response
relationships. If one can develop relationships employing data on wages,
wealth, socioeconomic and health status characteristics as well as air
pollution concentrations, consumer willingness to pay to avoid illness can
be derived. We term this second methodology the willingness to pay approach.
It is based on traditional microeconomic theory.
Volume I contains two experiments. First, a data set on sixty U.S.
cities is explored to determine if some of the problems of aggregate
epidemiology — epidemiology using aggregate data on groups of individuals
as opposed to data on individuals — can be overcome. The study attempts to
estimate a human dose-response function wherein city-wide mortality rates for
major disease categories in 1970 are statistically related to population
characteristics such as doctors per capita, cigarettes per capita,
-------
information on dietary patterns, race, age and air pollution. The study is
unusual in two respects. First, it is the first such aggregate epidemiological
study of the effect of air pollution on mortality to include dietary variables,
which, along with smoking and medical care, prove to be highly significant.
Second, it may be the first study using aggregate data to account for the
fact that human beings will attempt to adjust to disease by seeking out
more medical care. Thus, cities with high mortality rates are likely to
have more doctors per capita. This adjustment process has in the past
prevented an estimate of the direct effect of doctors on the prevention of
disease. An estimation technique for handling this bias problem is employed,
which identifies the contribution medical care makes in reducing mortality
rates. The impact of including these new variables in the analysis is sub-
stantial.
The second experiment focuses on morbidity rather than mortality. It
employs data on the health and the time and budget allocations of a random
sampling of the civilian population nationwide. The sample, which was
collected by the Survey Research Center of the University of Michigan,
consisted of approximately 5,000 heads of households for nine years from
1967 through 1975. Generalized measures of acute illness, stated in
terms of annual work-days ill, and of chronic illness, stated in terms
of years ill, are available.
The procedures used to estimate dose-response expressions have two
somewhat unusual features: (1) care has been taken to employ as explana-
tory variables only those factors not influenced by the individual's current
decisions or health status; and (2) by randomly drawing different samples
of individuals, substantial effort was devoted to replicating results.
This volume begins in Chapter II by discussing the role of economic
analysis in epidemiology. We then introduce in Chapter III the formidable
list of statistical problems faced by epidemiological analysis of air
pollution. Finally, Chapters IV and .V present the Sixty-City and Michigan
Survey Experiments, respectively. Chapter VI presents additional economic
results on the valuation of air pollution-induced morbidity.
-------
Chapter II
SOME ISSUES
2.1 Epidemiology and Economics
The motivation for this volume originated in the authors' mutual
and reinforcing convictions that economic analysis and its techniques of
empirical application could contribute to the resolution of certain puzzles
in studies of the incidence and severity of diseases in human populations,
particularly the epidemiology of air pollution. The results of our initial
efforts to provide empirical support for this perspective are presented
in succeeding chapters. Before proceeding to these chapters, however,
it is necessary, in order to display the basic rationale for our empirical
efforts, to explain our position that economics has some worthwhile things
to offer epidemiology.
Many reviews of the epidemiological literature dealing with pollution
have remarked upon the relative lack of consistent findings across studies
for the effects thought to be caused by any one pollutant. Various reasons
are typically advanced for these inconsistencies: inadequate characteriza-
tion of the pollutants; the use of noncomparable, and sometimes questionable,
estimating techniques; failure to account for other environmental influences
and self-induced health stresses such as ambient temperature and cigarette
smoking; failure to distinguish between pollution levels at work and at
home; insufficient attention to differences in genetic endowments, and
other factors. The list is sufficiently long and repetitive to be re-
miniscent of the beat of a somber military cortege. This march has two
elements: measurement error and specification error.
The first error element refers to the fact that some variables included
in epidemiological studies are inaccurately measured. Sources of error of
this sort, however, are hardly unique to epidemiology. They are at least
equally common in empirical applications of economic analysis and will
therefore be accorded our scrutiny when we discuss our empirical efforts.
For the moment, we wish to consider those possible sources of specification
error in epidemiological studies that have a basis in the microeconomic
theory of the behavior of the individual human being. Our fundamental point
is that human beings, the objects of epidemiological attention, make
purposive choices with respect to health states and phenomena that influnce
health states. To the extent that health states are a result of the
individual's purposive acts, one must explain these acts in order to
comprehend the determinants of the health state. "Microeconomics provides
a means for grasping the determinants of the individuals's purposive acts.
-------
Acceptance of this perspective adds another dimension (in addition to the
social provision of preventive and ameliorative medical inputs) by which
social policy can influence the health states of the population, i.e., those
factors that influence choices of acts affecting health states can serve as
policy instruments.
Specification error occurs in epidemiology (and in economics) when
some varibles relevant to the explanation of variations in the health
state of interest are improperly introduced or are altogether excluded from
the analysis. The biased and incosistent estimates that are the result
of excluding nomorthogonal explanatory variables from an expression to be
estimated are well-known and intuitively obvious in any case. One can
hardly, for example, expect to obtain an accurate estimate of the impact of
cigarette smoking on circulatory diseases if the ages of the sample
individuals are not controlled. Less obvious, however, are the reasons
why common economic variables such as prices often are relevant to
epidemiological analyses and why certain variables, both biologic and economic,
are sometimes improperly Introduced to these analyses.
Some of the most widely known findings in the epidemiology literature
concern the respiratory effects (cancer, acute bronchitis, emphysema, the
common cold, and pneumonia) of air pollution. View the absence of these
respiratory effects as an output that can be reduced by various combinations
of clean air and ameliorative medical care, where the latter are considered
to be Inputs. The literature suggests that there are significant differences
in the input-input ratios and in the input-output ratios among various
locales, where these locales frequently differ in population size. Suppose
it has been observed that:
1. Per capita absence of respiratory diseases is inversely associated
with city size.
2. Per capita availability of ameliorative medical care is directly
associated with city size.
3. Per capita absence of respiratory disease is directly associated
with per capita availability of clean air and ameliorative medical
care.
A. Per capita clean air is inversely associated with city size.
5. Respiratory disease absence per unit of clean air and ameliorative
medical care is directly associated with city size.
Do the five observations have sufficient informational content to justify a
judgment that the dirty air often found in large population concentrations
is associated with greater incidence of respiratory diseases and is therefore
a plausible cause of these diseases? It would not be surprising if different
epidemiological investigators drew a variety of largely contradictory conclus-
ions about the relationships between respiratory diseases, clean air, and
ameliorative medical care from these five observations. Contradictions are
perhaps inevitable because the ratios expressed in the observations will
often be inappropriate means by which to attempt to make judgments about
4
-------
the relative susceptibilities of human beings to respiratory diseases.
\
An intuitive notion of the incidence of a disease refers to the fre-
quency of occurrence, given particular levels of instigating factors. In-
tuition is sometimes misleading. Observation (1) suggests that small cities
have less incidence because they have less respiratory disease. Observation
(5) leads to the opposite conclusion since large cities have fewer respiratory
diseases relative to their clean air. But observation (4) makes small cities
look favorable because of their greater provision of clean air. Or do large
cities subject their populations to greater incidence of respiratory effects
by having fewer units of ameliorative medical care available? Observation
(3) again favors small cities because of the greater per capita availability
of ameliorative medical care.
-One might suspect from (5), (4), and (2) that larger cities have more
ameliorative medical care relative to clean air than do smaller cities. The
former have dirtier air and thus try to compensate by providing additional
ameliorative medical care. It is thus not surprising that the ratio of
of absence of disease per unit of available medical care favors the larger
cities. An alternative interpretation of (3) is that disease frequency
increases with city size not only because of dirtier air but also because
the price to the consumer of medical care is greater than in smaller cities.
Greater prices of these services for the consumer can imply greater returns
for the profession that provides these services. Greater returns attract
these professionals, resulting in greater availability of their services.
However, these same higher prices also mean that sufferers from a respiratory
disease of given severity will seek out less ameliorative medical care.
Are then these prices, the dirty air, or the consumption of medical care the
causes of the incidence of the respiratory disease? Recognition that they
are intertwined is a significant but insufficient step. The nature of the
intertwining remains to be explained.
2.2 When Microeconomics Doesn't Matter
Microeconomic analysis specifies the conditions under which decision-
makers (human beings) are expected to have identical ratios of inputs and
outputs. Basically, these identical ratios would occur if: (1) all
decisionmakers had identical biological endowments and transformed inputs
into health states in precisely the same fashion; (2) all decisionmakers
faced the same prices in (implicit and explicit) input and health state
markets; (3) all decisionmakers had the same real income; and (4) all
decisionmakers had identical preference orderings. If all these conditions
were fulfilled with respect to a particular pollutant, only one point could
be observed on the epidemiologist's dose-response curve: there would be no
variation whatsoever in the observable behavior of individuals.
We nevertheless observe decisionmakers in the real world with similar
states-of-health who have different biological endowments and varying ways
of transforming inputs into these health states. One can, of course, pass
muster in explaining the real world by assuming that decisionmakers (?) behave
randomly or that all health states, whether present or future, are determined
by physical or biological factors beyond the decisionmaker*s present control.
-------
This is no different than assuming that the decisionmaker is abysmally
ignorant of cause-and-effect with respect to health states or that he just
does not care about his health state. If any of the conditions in this
paragraph are in fact true, then current epidemic logical procedures, which
tend to give short shift to economic variables and which implicitly treat
the individual as being completely unable to exercise influence over events
that affect his choices, are entirely satisfactory. This abrupt statement
requires clarification.
Panels I through VI of Figure 2.1 represent two unit isoquants (loci of
points showing all combination of two inputs that will yield equal health
states) for inputs X., and X. (e.g., medical care and clean air), with the
current positions of decisionmakers R (a rural person) and C (a city person)
indicated. Each isoquant represents the same state-of-health as the other
isoquant. Note that the effectiveness of each input in providing the unit
health state for each individual is assumed to decline progressively as more
of one input is substituted for the other. Thus additional medical care
becomes progressively less effective as the air becomes dirtier. Similarly,
cleaner air. becomes an increasingly poor substitute for medical care as
less and less medical care becomes available.
All panels are drawn so that on the basis of his state-of-health per
unit of clean air, decisionmaker C is in better shape than decisionmaker R.
Conversely, decisionmaker R does better than C in terms of his health state
per unit of medical care. In each panel, therefore, C uses relatively less
clean air and R uses relatively less medical care to attain the unit health
state. This situation is consistent with the previous five observations on
the associations between city size, clean air, and ameliorative medical care.
Panels I and II refer to the case where the question of whether
economic variables should be included in dose-response function analysis,
and, if included, how to include them, need never arise. The clean air
and medical care each individual requires to attain the unit health state
are determined by physical and biological (technical) considerations alone.
Purely economic considerations play no part. Nevertheless, the two panels
do provide insights about cautions to exercise when attempting to establish
dose-response functions by studying several individuals at one instant in
calendar time. In Panel I, in the absence of knowledge about the isoquants •
of R and C, any attempt to establish the population dose-response function
by averaging over the current positions of R and C is doomed to be a
misrepresentation. The unit isoquants of Panel I belong to dose-response
functions that differ not only by a constant term but which also embody
entirely different responses of health states to particular cominations of
medical care and clean air. The "average" or population dose-response
function or isoquant established by pooling a single medical care-clean air
combination from each isoquant will differ according to where each individual
happens to be on his isoquant when he is ob.served. For example, the average
of R and C* differs substantially from the average of R* and C. If and only
if several medical care-clean air combinations for each individual were
observed could a representative dose-response function be obtained. This
would generally require that several observations over time be made of each
individual.
-------
Figure 2.1
Alternative Measures of Disease Incidence
II
c1
III
X
X
IV
X.
-------
In Panel II, several observations of each individual over time are not
required because the isoquants belong to dose-response functions differing
only by a constant term. This term could represent differences in biological
endowments, childhood environment, previous lifestyles, and other factors with
which epidemiologists traditionally deal. These same factors, however,
could also explain the nonconstant difference between the isoquants of Panel
I. Clearly, the current situation favors individual C in Panels I and II
since he is able to attain the unit health state with smaller quantities
of both medical care and clean air.
Panel III introduces the economic information of relative prices and
the income that each individual has already decided to devote to health
maintenance. Assume, for the moment, that each individual has decided to
devote the same income and faces exactly the same prices for medical care
and clean air. The result is that individual R is unable to attain or main-
tain the unit health state, although individual C, given his income and the
relative prices, is fully able to do so. Individual R, due to his economic
circumstances and his dose-response function, must settle for something less
than the unit health state. Both biological and economic factors inhibit him
from reaching the unit health state. Insofar as health states do not affect
incomes and relative prices, this panel would appear to justify the common
epidemiological practice of introducing incomes into a dose-response expres-
sion that is to be estimated. Panel IV, which has the incomes of the two
individuals differing but presumes they continue to face identical relative
prices, also seems to justify this practice. The justification is a mirage.
If the objective of epidemiological investigation is to ascertain
the extent to which various physical and biological factors contribute to
differences in the R and C-isoquants, then the introduction of income into
a dose-response expression must reduce the estimated impact of inputs such
as the medical care and clean air of Panel IV. The introduction of income
is redundant. Income, along with relative prices and the form of the isoquants,
determines the quantities of medical care and clean air each individual
consumes. As the panels indicate, for given relative prices, the greater
the individuals*s income, the more health care and clean air he will consume,
assuming he has not yet reached the unit health state. The quantities of
medical care and clean air that enter the dose-response function estimate
are thus partially determined by each individual's income. Thus the latter
is a measure of the former and must capture part of the influence that
would and should otherwise be attributed to clean air and medical care.
Bluntly, epidemiological studies that include income reduce the odds that
clean air will be seen as contributing "to good health. The degree to which
this reduction in odds is worthy of concern is dependent upon the extent
to which income determines the consumption of clean air. The little evidence
that is available indicates that at least within individual cities the
association between income levels and cleaner air tends to be quite high.
Panel V depicts a situation where individuals R and C have nothing in
common: they have different unit health isoquants, devote different income
levels to health maintenance, and face different relative prices for medical
care and clean air. Both individuals consume similar quantities of medical
care but radically different quantities of clean air. Again, however, the
8
-------
epidemiologist interested solely in dose-response functions can safely neglect
giving any attention to incomes and relative prices, for these serve only to
determine the quantities of medical care and clean air consumed that directly
determine health states. Nevertheless, this conclusion does not justify
appealing to observations similar to those mentioned in the previous section
as grounds for judging that clean air improves health states.
There are several alternative explanations for the ratios expressed in
these observations. Different individuals may have different dose-response
functions. Sometimes these differences.may be captured by a constant term;
at other times, the slopes of the functions may be dissimilar, invalidating
attempts to ascertain population dose-response functions solely by observing
each sample individual only once. Moreover, variations in individual incomes
and in the relative prices of health inputs may be the cause of the observed
ratios. This implies that the policymaker can influence the quantities of
these health inputs consumed by doing nothing more than manipulating a limited
set of purely economic variables. Under the conditions specified in this
section, however, these variables have no bearing on estimating, via standard
epidemiological procedures, the responses of the human organism to variations
in the quantity of clean air.
2.3 When Microeconomics Does Matter
The preceding section employed stated, but not very visible, assumptions
to arrive at the conclusion that epidemiological studies err when they devote
attention to economic variables in attempting to establish dose-response
functions. In particular, it was assumed that the individual had already
decided the resources he would dedicate to health maintenance and that this
decision did not influence any other decisions he might make. If either or
both of these assumptions are inaccurate descriptions of reality, then
microeconomics does matter in the determination of dose-response functions.
The assumptions had the effect of removing the purposive nature of the
human being from consideration: all the individual's choices were presumed
to have already been made.
In implicit form, a good approximation of the expressions that epidemio-
logists frequently use to estimate the response of a particular mortality or
morbidity effect to a particular environmental exposure is:
TT± - f^X.Y.Z.E.e), (2.1)
where IT is the probability of the ith individual dying or becoming ill from
the exposure; X is a vector of available ameliorative medical care inputs;
Y is a vector indicating the individuals's socioeconomic class, medical history,
ethnic group, etc.; Z is a vector of the individual's activities representing
lifestyle habits such as diet and exercise regimens; E is a vector of en-
vironmental exposures that, a_ priori, are thought to be physical or biological
instigators of the health effect; and e is a stochastic error.
The form of f CO is typically unknown and must therefore be approximated,
perhaps by a linear expression. The coefficient attached to the exposure
of interest would, given an acceptable level of statistical significance, then
-------
be interpreted as the increase in the health effect incidence caused by a
one-unit change in* the exposure. Would it then be reasonable to infer a
dose-response association from the coefficient of the exposure variable?
The aforementioned inference would be correct if and only if it is
possible to alter the environmental exposure without altering the value of
any other explanatory variables in the expression. It is easy to show that
this cannot be done when the structure is presumed to consist of no more
than one relationship. The reason is that (2.1) contains at least two
variables, the current and future levels of which are subject to at least
some control by the individual; that is, during the period in which it is
thought the health effect can occur, the individual can influence by his
voluntary choices the magnitude of explanatory variables supposed to
determine the health effect. For example, the probability of the individual
suffering the health effect, IT, is dependent upon the extent to which he
chooses to use the available medical care and the mix and magnitude of
activities he chooses to undertake. In order to explain the health effect
outcome, one must also explain the structure underlying these choices. The
following simple example shows one way in which ir and Y, interpreted as
income, might be jointly determined.
If both the ir and T functions can be linearly approximated, they can
be written as:
iri = «± + «2E + «3X + «4Y + «5Z + e^ (2.2)
(2.3)
Expression (2.2) states that the question of whether or not the individual
is suffering from chronic bronchitis is related respectively to the non-cig-
arette bronchitis-causing agents (e.g., air pollution) to which he is exposed,
the ameliorative medical care he consumes, his income, and the number of
cigarettes he smokes. In turn, (2.3) states that the individual's income
is determined respectively by whether or not he has bronchitis, his absenteeism
rate, his schooling, and the length of time he has been on the job.
Solving (2.2) and (2.3) for TT alone, we have:
+ X + ,
Consider the coefficient attached to E in (2.4). If E is air pollution,
(2.4) shows that an estimate of (2.2) will not yield the response of bron-
chitis incidence to dosages of air pollution, even though, in the language
of epidemiologists, the dose-response is "adjusted" for medical care, life-
style, and socioeconomic class. Instead, the coefficient for E in (2.2)
will be a mix of effects due to air pollution, income, and the effect of
10
-------
bronchitis on income. The product of the coefficients for the latter two
effects would have to approach zero in order for the response of bronchitis
to air pollution alone to be obtained. For this to occur, chronic bron-
chitis could have no effect on the individual's income and this income could
have no effect on his chronic bronchitis. Both assertions, particularly the
first, are quite implausible. In fact, in the absence of further informa-
tion, the sign that would be obtained for the coefficient of E in (2.2) is
ambiguous since « > 0, «=.. < 0, and 3- > 0. It is entirely conceivable, if
i — H "~* i ~~
one were to estimate (2.2) alone, that one would find air pollution reduc-
ing chronic bronchitis! In any case, because the product of «. and B2 is
negative in sign, the effect of air pollution on health will be underesti-
mated. One could readily obtain a similar result for Z, cigarette smoking.
It might be reasoned that the difficulty with the preceding example
could be removed if income were excised as an explanatory variable from
(2.2). The expression would not then have any pecuniary variables in it
and would therefore seem amenable to the customary epidemiological minis-
trations. These customary ministrations would, however, continue to be
incorrect, for the individual is able to influence the quantity of cigar-
ettes, Z, that he smokes during the current period. If air pollution
exposures change, the individual is likely to change the quantity of cigar-
ettes that he smokes. Thus, even after excising the income variable from
(2.2), possibilities for biasing the air pollution coefficient remain. To
see this, write:
1± = ^ + «2E + «3X + «AZ + e^ (2.5)
Z = Bj_ + »21± + &-3Pz + 34Pk + 35Y + er (2.6)
The variables in expression (2.5) are defined as in (2.2). Expression (2.6)
states that the quantity of cigarettes the individual currently smokes is a
linear function respectively of whether or not he has chronic bronchitis,
the price of cigarettes, the prices of goods that are complements and/or
substitutes for cigarettes, and his income.
Upon solving (2.5) and (2.6) for H , the coefficient attached to air
pollution, E, proves to be « 11 - aA32]» which represents a mix of effects
due to air pollution, cigarette smoking, and the effect of bronchitis on
cigarette smoking. Again, the product of the coefficients for the latter
two effects would have to approach zero for the response of bronchitis to
air pollution alone to be obtained. In addition, the sign of the E-coeffi-
cient would again be ambiguous since &2 | 0. If &2 > 0, the effect of air
pollution would be overestimated, and if 8 < 0, the effect would be under-
estimated .
To attempt to account for the additional factors thought to influence
a morbidity or mortality rate by simply stringing out variables in a single
expression must clearly often be incorrect. During the period in which the
health effect is supposed to occur, humans acting in their individual cap-
acities can choose to influence the magnitudes assumed by certain of these
11
-------
variables. Each variable susceptible to this influence must be explained by
an expression of its own. Economic analysis is necessary to impart an
interpretable form to these expressions. Physical and biological constructs
will therefore often be insufficient tools with which to provide epidemio-
logical explanations of disease incidences.
The previous two examples are about problems of joint determination
which involve economic variables. Nevertheless, the problem of joint
determination does not require the presence of economic variables. For
example, epidemiological studies frequently group disease incidences by
individual city and employ measures of central tendency of incidence and
other variables as single units of .observation. Thus one might try to
explain the frequency of deaths from cancer in a sample of U.S. cities by
relating it to the dietary habits, air pollution exposures, and median age
of the population in each city. Among the dietary variables, one might
include saturated fats and cholesterol, dietary components frequently said
to be positively related to cardiovascular disease. Inclusion of these two
variables in an expression intended to estimate the factors that contribute
to cancer incidence would probably result in negative signs being attached•
to their coefficients, implying that saturated fats and cholesterol prevent
cancer. This may, in fact, be true, but only indirectly. Specifically,
median age in each city will tend to vary inversely with the incidence of
cardiovascular mortality; in other words, earlier death reduces median age.
Thus, since cancer incidence is positively influenced by median age, one
might expect cancer to exhibit negative associations with saturated fats
and cholesterol even if they have no direct causal relationship with cancer
incidence. The apparent effects of these two dietary variables upon cancer
incidence would actually represent a confounding of: (1) the effect of the
two variables upon cardiovascular disease; (2) the relation between cardio-
vascular disease and median age; and (3) finally, but only via (1) and (2),
the effect of the two variables upon cancer incidence. In short, at least
one other expression explaining median age is required.
2.4 The Costs of Pollution-Induced Disease
The preceding sections have discussed the circumstances under which
microeconomics and:its methods of empirical application can contribute to
the epidemiology of pollution. It was observed that in trying to establish
dose-response functions for particular pollutants, it is necessary to be
extremely sensitive to the presence of jointly determined variables.
Failure to account properly for these variables in;the structure to be
estimated can result in badly distorted depictions of the effect of a
health input such as pollution upon the output, the state-of-health or the
incidence of a particular disease. One could, of course,, consider all
variables to be endogenously determined in some ultimate sense. The key
to stopping short of including the entire universe in the structure to be
estimated is the formation of intelligent judgments about those variables
important to the question of interest over which the individual or system
(e.g., urban areas) can immediately exercise no more than trivial control.
The number of expressions must equal the number of variables it is posited
that the' individual or system can control if a determinant solution is to
emerge. Most importantly for our purposes, since many of the jointly
determined variables in a dose-response structure will be economic requiring
12
-------
the application of microeconomic analysis in order to specify how they are
to be introduced to the structure, the actual design of epidemiological
studies rnqst often include microeconomic considerations.
The potential application of microeconomic analysis to epidemiological
concerns extends beyond the estimation of dose-response functions. The
analysis can be used to establish pecuniary values for pollution-induced
health effects. These values, which are consistent with the axiomatic
structure of benefit-cost analysis, can contribute to evaluations of the
economic efficacy of existing and proposed pollution control programs.
Attempts to establish these values can adopt two polar views of the
individual's degree of comprehension of the relation between pollution and
his state-of-health.
The first of these views presumes that the individual fails to com-
prehend any connection between pollution and his health state, even though
pollution does influence this state. To obtain the total loss due to a
pollution-induced health effect, this view justifies the estimation of a
dose-response function and the multiplication of the loss in health
attributed to pollution by a pecuniary value for the health loss. The
information and criteria used to set the pecuniary value, and thus the
total pecuniary loss, come from outside the system being studied. The
basic presumption is that the individual is unaware of the health effects
of pollution and therefore does not make any voluntary adjustments in
response to its presence.
In addition to being a relatively easy and therefore desirable way to
establish pecuniary values for health losses, this first view has the
further advantage of reducing the force of the joint determination problem.
It thus removes problems similar to the cigarette example of the previous
section, where, in response to the presence of increased air pollution,
the individual chose to reduce his cigarette consumption. However, the
view would affect neither the income nor the dietary examples, for the
ill-health caused by pollution can affect the individual's earnings cap-
acity and his dietary habits. These earnings and habits would therefore
change as pollution changes, even though the individual is utterly unaware
of the cause and, consequently, fails to. make any behavioral adjustments
in response to pollution.
The polar opposite of the above view is that the individual is fully
cognizant of the health effects of pollution' and continually adjusts his
voluntary behavior accordingly; that is, given the opportunities he has
available and the relative prices he faces, he alters his behavior so. as
to minimize the value of the pollution-induced health losses he suffers.
These voluntary adjustments will involve shifts in his time and budget
allocations such as reductions in the time and intensity of outdoor
activities, pursuit of a less toxic diet, and more visits to the family
physician. A view of the individual that presumes he is unaware of the
health effects of pollution does not account for these adjustments. In
effect, it assumes that, whatever the variations in pollution, the indivi-
dual's time and budget allocations have always accorded with the allocations
occurring at the time of observation. Since, according to the second view
of the individual's response to pollution variations, these observed
13
-------
allocations are the result of attempts to mitigate the health effects of
pollution, the first view of the individual results in underestimates of
pollution health effects. Furthermore, if individuals do reallocate their
time and their budgets in response to pollution variations, then measures
can be obtained of the income the individual would have to receive or would
be willing to pay to leave himself as well off as he was before a change in
pollution. These measures correspond to the ideal measures of economic
loss established in the microeconomic theory of consumer behavior.
14
-------
Chapter III
SOURCES OF ERROR
3.1 Problems in Statistical Analysis
The previous chapter introduced the problem of joint determination of
many variables - especially those which involve choice by individuals - in
epidemiological relationships. This problem, if not explicitly accounted
for, can introduce simultaneous equation bias. Estimated effects will not
approximate actual (population) values. In other words, even for large
samples (those approaching infinity) estimated coefficients are no longer
consistent; they do not approach their true population values. A number of
techniques are available for providing consistent estimates in simultaneous
equations. One of these is described in 4.3 below and the technique is
applied both in the Sixty-City experiment, Section 4.5, and in the Michigan
Survey experiment, Section 5.6. This chapter thus addresses a number of
remaining statistical obstacles to obtaining unbiased estimates and signi-
ficances of the effects of air quality on human health.
3.2 Heteroskedasticity
Any empirical exercise involves error. To act otherwise is to fool
one's self, if not the reader. The error can be due to an inability to
capture all the a priori factors that influence the phenomenon of interest,
it can be caused by failures in measuring the magnitudes of the variables
one has a priori grounds for introducing, or it may be a consequence of a
misunderstanding of the structure of the phenomenon. In addition to alter-
ing the estimated values of coefficients and/or confidence intervals,
errors are registered in the constant terms and the residuals of estimated
expressions. The so-called statistical "classical linear model," which is
employed to establish all the relations of this volume, presumes that the
mean of the error variance (a measure of the dispersion of the observations
of the magnitudes of a variable around its average magnitude) is equal to
zero. This implies that the errors are constant for observations on all
basic units of analysis.
In" our mortality study, if the unexplained portion of the incidence of
cancer-induced death tends to increase with the size of city, then the error
will not be constant from one observation to another. Similarly, in our
morbidity study, if the unexplained portion of the duration of chronic
illness increases with the value of some variable, then we have again
violated a basic premise of the classical linear model. Thus, for example,
one might reasonably expect that in locations where air pollution is low
15
-------
and that the variation around this average level would not be very great.
Low concentrations of air pollution are unlikely to generate severe chronic
illnesses of long duration. However, where air pollution concentrations
are high, both the average level of air pollution-induced chronic illness
and the variations around this average are likely to be substantial. In
low pollution locations, even those with a biological propensity to be
harmed from pollution do not suffer any ill effects. However, those with
this propensity might be struck down if they are moved to a high pollution
location, whereas those who have great resistance will suffer little, if
at all. The variation in the duration of chronic illness is therefore much
higher where pollution is suffocating because the magnitude of the greatest
suffering has greatly expanded, while the magnitude of the least suffering
continues to be zero.
Nonconstantcy of the variances of the errors (residuals) in an estimated
expression is termed "heteroskedasticity," a term the linguistic roots of
which we don't know. Because it means that variation in the errors of an
expression varies systematically over observations, it implies that the
confidence intervals for estimated coefficients will also vary systematically.
The result is that the same basis will not be used to calculate the confi-
dence intervals among observations. Thus, although the estimated
coefficients are not affected, the standard errors of these coefficients will
be biased. As a consequence, the customary tests of significance have no
meaning. Nevertheless, if one knows the direction of the bias, one can
sometimes ascertain whether these customary tests of significance accord
excessive or too little precision to the estimated coefficients. For
example, Kmenta (1971, pj 256) provides a formula that under limited cir-
cumstances, permits the calculation of this magnitude and the sign of this
bias in standard errors. He also outlines ways in which the raw data can
be corrected to negate heteroskedasticity.
3.3 Multicollinearity
Multicollinearity occurs when two or more explanatory variables are so
highly correlated among themselves that it becomes difficult to separate or'
determine the independent effect of each variable. In the extreme case
where two variables are perfectly collinear, they are effectively identical.
However, if a priori information exists on the effect of the collinear
variables, then that information can be used. For example, if in attempting
to explain stomach cancer mortality rates using cross-sectional data, two
explanatory variables, sulfur oxides in air and per capita consumption of
Polish sausage, are perfectly collinear, one might employ data from animal
experiments or epidemiological studies on select human populations (e.g.,
Polish populations and industrial workers exposed to S02 in high concen-
trations) to determine the relative incidence of stomach cancer from each
factor. By including only one of the variables in the regression, the total
effect of both explanatory variables will be captured by the estimated
coefficient on that one variable. Thus, if consumption of Polish sausage
and sulfur oxide exposures are perfectly collinear and only consumption of
Polish sausage i-s included in the estimated equation, the estimated coef-
ficient on consumption of Polish sausage will capture the effect of both
variables. How that effect is to be allocated between the two variables
depends on the availability of external information. For example, if animal
16
-------
experiments do not show a link between sulfur oxide exposures and stomach
cancer, but do show a link between consumption of cur.ed meats (including
Polish sausage) and cancer, one might allocate the entire coefficient to
consumption of Polish sausage. Of course, if this were the case, and the
investigator did not know that consumption of Polish sausage and sulfur
oxide exposures was perfectly collinear and no dietary data was available
for inclusion, then a false link between sulfur oxides and stomach cancer
might be shown using the cross-sectional data alone.
The same arguments apply to cases of near perfect multicollinearity
wherein explanatory variables are highly, as opposed to perfectly, corre-
lated. This is, of course, the most likely case. However, the outcome of
including two or more collinear explanatory variables is an increase in
the standard error of the estimated coefficients for the collinear variables.
The standard error is, of course, a measure of the accuracy with which a
coefficient is estimated — large standard errors imply that the actual
coefficient could be much larger or smaller than the estimated coefficient.
Thus, when collinear variables are included, the inability to separate
influences is reflected in the measure of uncertainty over the magnitude of
the estimated coefficients on those variables.
The approach taken here to deal with multicollinearity — and the 60-
city experiment described below has a severe problem among the dietary
variables — is to a^ priori exclude variables which are highly collinear
with respect to a representative included variable. An alternative approach
to multicollinearity is the use of a technique known as ridge regression
[see Schwing, et. al. (1974)] which, however, makes interpretation of the
resultant estimated coefficients unclear.
While multicollinearity within an available data set makes estimation
and interpretation more difficult, at least the problem can sometimes be
recognized and false conclusions thereby avoided. However, where unknown
collinearity occurs, for example when an included explanatory variable is
highly collinear with a variable which is not.available to the investigator,
the false conclusion can be reached that the included variable is solely
responsible for the estimated effect. The investigator may not recognize
that the estimated effect includes the effect of one or several other
excluded but collinear variables. We discuss this possibility below.
3.4 Causality and Hypothesis Testing
Aside from the problem of multicollinearity, the traditional problems
of causality underlying epidemiological studies still apply. For example,
if heart attacks are actually related to cigarette consumption, but smoking
is correlated with coffee consumption for behavioral reasons, a spurious
positive correlation might be shown between heart attacks and coffee con-
sumption, especially if cigarette consumption is excluded from an estimated
statistical relationship. In other words, correlation does not prove
causation, and statistical hypothesis testing can never confirm, but only
reject, a maintained hypothesis. Turning to another example, if most
nitrite (used to cure meats) ingestion is through consumption of pork
products (70 % of pork is cured), one might suspect, given the hypothesis
17
-------
of in vivo nitrosaroine Ca carcinogen) formation from nitrite, that cancer
mortality and pork consumption would be correlated. If such a correlation
can be shown Cas it has been; see Kneese and Schulze (1977) and NAS 1978)
then the only valid conclusion is that we do not reject the hypothesis that
pork consumption (and perhaps, in turn, nitrite ingest ion) is related to
human cancer. If, alternatively, one accepts the maintained hypothesis on
a priori grounds, and no bias exists in the estimation procedure, regression
analysis can give a best linear estimate of the actual relationship in the
sample population between, for example, cancer mortality and a dietary
factor such as nitrite ingestion. However, regression analysis cannot
prove causality; causality must be assumed in this procedure. This is why
it is so important to have hypotheses concerning causality before a regres-
sion equation is specified.
A set of hypotheses concerning human health, including the effect of
air pollution, forms a model of human health. The concept of a complete
model of human health as the basis for hypothesis testing is an important
one for several reasons. First, a modeling framework immediately suggests
that behavioral elements such as voluntary medical care may be important
and as pointed out above,, a simultaneous equation structure may be necessary
to test hypotheses properly. Second, the modeling framework focuses
attention on a complete specification of the determinants of human health.
A "better" model will exclude fewer relevant variables and be both a more
accurate predictor of human health and more accurately identify the effect
of each explanatory variable. The modeling approach then helps avoid the
problem of unknown collinearity by focusing on a specification which pro-
vides imformation about the effects of all relevant variables.
An alternative viewpoint has been expressed by Lave and Seskin (1977).
Their argument rests on the assumption that excluded variables (medical
care, diet, and smoking are excluded from their study of air pollution and
human health) will not bias estimated effects of included variables if the
excluded variables are orthogonal (perfectly non-collinear) with respect
to the included variables. Thus, if one assumes orthogonality with respect
to excluded variables, following Lave and Seskin (1977), one can justify
estimation of incompletely specified equations. We take a different
approach principally because we reject orthogonality as a reasonable
assumption. .If, as ecologists are fond of saying, "everything depends on
everything else," then simultaneity and collinearity are likely to be
pervasive in the "real world." In fact, we argue below based on our own
epidemiological and economic data that this is just the case.
Finally, to test specific hypotheses, we will use the standard sig-
nificance test; we will test the hypothesis that each explanatory variable
has no effect (has a coefficient of zero) by using the appropriate t-
statistic which, in this case, is approximately equal to the estimated
coefficient divided by its own standard error. For example, for large
samples, if for a specific coefficient t ^ 2.0 (if the coefficient is
greater than or equal to twice its own standard error), then, where the
hypothesis tested includes an assumed sign for the coefficient, a 97.5%
level of significance is achieved. This implies that, in random sampling
of a population, one would draw a sample which accidentally confirmed the
18
-------
hypothesis (.effect non-zero) only 2.5% of the time.
It is important to note, that as the significance level is implicitly
lowered from t « 2.Q toward t = 1.0, even In large samples, spurious rela-
tionships Begin not to Be rejected. Practical experience and econometric
tradition suggest that a 95% to 97.5% significance level is appropriate.
The desired confidence level should Be chosen a priori to avoid the temp-
tation to "prove" desired relationships By ex post lowering of the level of
significance for rejecting or failing to reject hypotheses. Similarly,
statements that an explanatory variaBle is "nearly significant" should Be
interpreted with great caution. Where costly environmental programs are to
be justified By epidemiological analysis, rigorous tests of significance
should Be employed.
3.5 Aggregation
In one or another of his many Books, Herbert Simon has used the term
"Bounded rationality" with reference to limited human aBilities to arrange,
comprehend, and manipulate large volumes of information. More succinctly,
Simon is referring to the need to simplify in order to understand. Even the
pure theorist, in Both his analysis and exposition, must partition the
universe into two parts: that with which he will and won't deal. Moreover,
he must employ a limited and often quite small number of concepts to deal
with the part he has chosen. He who would measure as well as theorize must
simplify Beyond this, for he must Be economic with his data manipulations.
Both isomorphism with his theoretical variables and his less than fully
robust empirical tools require this. Simplification is synonymous with
throwing away information, But that which is thrown away is often Beyond our
powers of use. As Stigler (1967) has remarked, "... information costs are
the costs of transportation from ignorance to omniscience and seldom can a
trader afford to take the entire trip."
In the material to follow, we have played the role of the aforementioned
trader in two ways. First, in the mortality study, we have employed grouped
data for estimation; that is, we have employed a single measure of central
tendency (usually "the arithmetic mean) of the distribution of some attribute
across a group of people or locations (a city) as the sole representation of
the group's diversity. We have melted entire cities into one pot. Here we
wish to discuss the issues this poses for estimation.
A second aggregation thing we have done is to embrace the notorious
representative individual when discussing the pecuniary benefits or costs of
a given health effect. Too fond an emBrace of this representative can lead
to gross errors if his responses are incautiously applied to flesh and blood
individuals. We wish to explain why. Initially, however, we will discuss
the estimation issue.
- In the mortality study, the unit of analysis is a city or some larger
jurisdictional unit and the values attached to a particular variable repre-
sent the per capita magnitudes of the variaBle in the cities. To form these
per capita magnitudes, someone had to collect observations on the values of
the variables for the distinct individuals in each city. By using the per
capita rather than variation of the individual observations within each city
19
-------
and thereby reducing the efficiency of our estimators. Simultaneously, we
are lessening the degrees of freedom and, thus, the variety of statistical
tests we can potentially/ employ. Our real gain from this, is: a drastic
shrinking of the size of the' data Base we must manage. A vacuous gain also
exists.
Ry using the per capita magnitudes for the values of our variables, we
have not changed the underlying sample of individual observations, but have
reduced the variability of the sample we are using for estimation. We have
stripped the outlying individual observations of influence. The result is
that the per capita magnitudes will be less dispersed around any expression
we estimate, allowing us to appear to explain a larger proportion of the
variation in the sample; that is, the magnitude of the coefficient of deter-
mination (R2) is enhanced. This enhancement, however, is misleading since
it is entirely due to our prior exercise of collapsing all the variations of
individuals' observations in a city to a single sealer measure. Similarly,
nonvacuously, and therefore much more importantly, by reducing the variation
in the sample, we are reducing the standard errors of each estimated (and
still unbiased) explanatory variable coefficient. As a consequence, we may
be overstating the level of significance to be attached to these coefficients.
Yet another nonvacuous and altogether serious way exists for the
estimates obtained from per capita data to be seriously misleading. The
measurement unit one is using for any particular variable may differ from
city to city. Thus, for example, one might be measuring cigarette con-
sumption per capita in the equivalent of packs in one city, and pounds in
another. Consider the following simple algebraic argument.
Assume that a disaggregated dose-response expression for respiratory
disease is to be estimated. Let this expression be given by:
n L r
where i refers to a particular pollutant, j to a particular individual, a
and b are coefficients to be estimated, and e is an error term having the
customary properties. Per capita responses and doses are clearly:
With aggregation, the intercept and error terms are:
S. a,
(3-2)
(3*3)
(3.4)
E - £i eij (3.5)
.' . '.. n
The aggregate relation is therefore:
Cj = a + bP + E., (3.6)
20
-------
where b, the coefficient of P., is apparently
O.7)
In other words, the per capita response depends on the exposures suffered by
the n individuals. This perhaps seems reasonable, since (3.6) continues to
be linear and includes an error term the expected value of which is zero for
Disregarding a and E., note, however, that both b and P. are aggregated.
Thus:
bP = (£i bi) (Pi)-- Vbi-Pjj , (3.8)
J n n n
and therefore „ v
. 'iVl] . (3.9)
"' *i
Nothing goes awry if the dose-response functions are identical among sufferers.
However, if they do differ, it is apparent from (3.8) that the value of the
pollution exposure parameter, b, will be a weighted mean of the same parameter
for the individual suffers. In particular, those sufferers having high
responses will have a disproportionately strong influence upon a group's
(e.g., a city) contribution to the value of the exposure parameter in (3.8).
Similarly, those groups having low responses will have a disproportionately .
weak influence. The conclusion is the rather dismaying one that the measure
of responses, employing some group or aggregation of individuals as the
fundamental unit of observation, can differ from one group to another. There
eould conceivably be as many unique measures employed as there are groups.
The preceding remarks refer to the prior aggregation of individual
observations and the subsequent use of the aggregates for estimation purposes.
Suppose we employ individual observations for estimation purposes, establish
responses for the representative individual among these observations, and
then use the presumedly representative responses of this representative
individual to obtain an aggregate measure of total response; that is, we
aggregate -after rather than before estimation. The study of the morbidity
effects of air pollution that follows readily lends itself to this treatment.
Because it does so, we feel it worthwhile to caution the reader about the
dangers this form of aggregation poses. We state the discussion in terms of
demand functions although dose-response functions would serve equally well.
Only because it is perhaps the most widely cited study to aggregate indivi-
dual observations of air pollution damages, we employ Waddell (1974) as a
basis for discussion.
Waddell (1974) first reviewed a collection of studies that had estimated
marginal purchase price functions with respect to sulfur oxides and/or
suspended particulates for eight different cities. Interpreting the values
of the air quality parameters in these several studies as measures for the
average household in each study of equilibrium marginal willingness to pay
at given air quality states and with given demand functions for air quality,
he selected a value within the range of these estimated values. By selecting
this value within the range of values, he assumed that what was interpreted
21
-------
as the. equilibrium jmarginal willingness to pay was the same for all household
in all cities.
Then, using the further assumption that this assumed equilibrium marginal
willingness to pay was in fact the actual marginal willingness to pay for all
air quality states, he multiplied the constant marginal willingness to pay by
the number of households and the number of air quality states to obtain an
estimate of aggregate national air pollution damages. That is, if b is the
marginal willingness to pay and Q is an air quality state, Waddell (1974)
calculated aggregate national air pollution damages, D, as
n
D - bZAQi (3.10)
i=l
where the i's index households.
In effect, Waddell (1974) assumed that the decision problem of each and
every household in each urban area of the country could be represented as
depicted in Figure 3.1. In Figure 3.1, 8P/8Q is the marginal purchase price
function and 3D/3Q is the function representing marginal willingness to pay
3D
for improvements in air quality. Since ~ « b is invariant with respect to
oQ
changes in air quality, calculation of that willingness to pay for the
household of Figure 3.1 involves only the multiplication of b by whatever
change in air quality is postulated. Thus, the value to the depicted house-
hold of an improvement in air quality (Q** - Q*) is simply b(Q** - Q*).
Given then that b is the same and invariant for all households, the sole
distinction one need make among households in order to calculate aggregate
national damages is to account for the location of each household on the Q
axis.
Figure 3.1
Marginal Purchase Price and
Marginal Willingness-to-Pay
3D/3Q
i
i
i
Q**
22
-------
Among the more significant i.e., stronger assumptions in the afore-
mentioned calculation procedure are the following. First, it is assumed
in the procedure that the b's are invariant across households. By dropping
this assumption, the immediately preceding expression becomes:
D - b± I A Q.^ (3.11)
This would mean that differences in willingness to pay for Improvements in
air quality due to differences among households in such personal attributes
as income, age, and degree of risk aversion to health effects would now be
taken into account. Aggregation would then not entirely destroy knowledge
about relative sufferer valuations of alternatives.
A further weakening of assumptions would occur if the marginal willing-
ness to pay function is permitted to be nonconstant and even nonlinear. In
this case, the above expression for D would be:
(3.12)
Clearly, this would be a very complex expression with which to calculate
aggregate national air pollution damages. Not only are the marginal
valuations of given air quality states permitted to vary among households
but the responses of different households to similar variations in air
quality are also permitted to differ. The sensitivity of the aggregation
procedure to. differences in the economic, and air pollution circumstances of
households would be greatly enhanced. Freeman (1974, pp. 81-82) lists
several frameworks for constructing algorithms that might approximate this
last expression for D.
The above discussion has been devoted to a single aggregation over
individual households. It has been implicitly presumed that only a single
class of air pollutants is relevant. Typically, however, estimates of
national air pollution control benefits involve aggregation over multiple
classes of pollutants as well as over households. On occasion, aggregation
may, in addition, take place over time. Sealer estimates of the national
benefits of air pollution control may thus involve two or three distinct
types of aggregation, each of which embodies unique assumptions about the
similarities among the units undergoing aggregation.
An additional decision problem, over and above the problem involving
the manner in which the units in each type of aggregation are to be treated
as similar, is thus introduced: one must choose thich type of aggregation
is to be performed first in arriving at a sealer representing air pollution
control benefits for households, for pollutants, and for time intervals.
Moreover, in deciding how to perform the first aggregation, one must take
into account how the aggregation for the second and third steps will be
carried out. The order in which the aggregation is performed can make a
difference in the estimate one obtains of aggregate national benefits.
23
-------
Chapter IV
THE SIXTY-CITY EXPERIMENT
4.1 Objectives of the Experiment
Identification of substances in the environment which effect human
health and accurate quantifications of their effects, is extremely dif-
ficult. Often there are multiple substances involved, there may be long
latency periods before effects are seen, and the amount and time of expo-
sureis often unknown. There are three general approaches to identifying
such substances and quantifying their impact — all more-or-less imperfect.
In the first, laboratory animals are exposed to large doses of the suspect
substance and, if effects appear, an effort is made to extrapolate them to
the human population. The correct manner in which to execute the second
step is not well extablished. The second approach is to develop aggregate
cross-sectional data., usually for cities or standard metropolitan areas,
on a number of variables which might be associated with mortality rates or
illness rates and then to use regression analysis in order to discover
statistically significant associations. A third approach is to gather very
detailed data on individuals and to again use statistical analysis to de-
termine the effect of various factors including environmental exposures on
individualized measures of health status.
The purpose of the research reported in this chapter is to explore
both the possibilities and limitations of the second approach mentioned
above —aggregate epidemiology — in the estimation of human dose-response
functions which include exposure to air pollution. The principal advantage
of the use of aggregated data on cities or metropolitan areas is quite
simply the widespread availability and low cost of such data as opposed to
data generated from animal experiments or collected on individual human
beings through specialized surveys. However, the use of aggregated data
creates a number of special problems.
First, one ideally wishes to estimate a dose-response relationship or
function as shown in Figure 4.1. Based on a priori considerations one
would suppose that for human populations, risk of death for an individual
would be a function of medical care, age of the individual, the genetic
endowment of the individual, the behavior of the individual—does he or
she exercise, smoke, etc.—the diet of the individual, and exposures to
possibly harmful substances or circumstances. However, aggregate epidemi-
ology provides no data on individual risks or characteristics but only data
for population characteristics as a whole. Thus, aggregate mortality rates
in, for example a city are used as a proxy for risk of death in the
24
-------
estimation of an individual dose-response function where it is implicitly
assumed that individuals can be represented by the average individual in
each city. Thus, in using the data set developed below for sixty U.S.
cities to estimate a dose-response function of the form shown in Figure
4.1, it is implicitly assumed that each city represents one average individ-
ual. However, the list of assumptions required to allow such aggregation
(all relationships must be perfectly linear, etc.) are not likely to be met
in practice. Thus, one must recognize that estimated results are biased
to an unknown extent by the very use of aggregated data.
A second problem arises from the fact that aggregate epidemiology
must rely on secondary data. Since the investigator must depend on data
already collected, he cannot add a question to a survey nor can he vary
the design of an animal experiment to test the importance of a new variable.
In the past this problem has led to the exclusion of data on important
variables such as smoking, diet and exercise from aggregate epidemiological
studies [see, for example, Lave and Seskin (1977) and Schwing, et. al.
(1974)] We have been able to gather some data — not necessarily good
data — on both smoking and diet and as we show below, these are important
omissions from previous studies. The current study still excludes any
measure of exercise.
Finally, aggregate epidemiological studies are lik'ely to suffer from
a number of simultaneous equation biases. One of the most obvious con-
cerns the effect of medical care. The existing epidemiological literature
has failed to show any significant effect of medical care on human mortality
rates. This counterintuitive result is easily explained. For example, in
our sixty city sample, no effect of per capita doctors in each city can be
shown on aggregate mortality rates for each city when simple regression
techniques such as ordinary least squares are used. The explanation is
that, although doctors most likely do reduce mortality rates (as shown
below), people in cities with higher mortality rates have in turn more ill-
ness per capita and seek out more medical care, increasing the observed
number of doctors in such communities. In other words, higher mortality
rates create a greater demand for doctors. Thus, we have two offsetting
effects—doctors reduce mortality, while mortality increases the demand for
doctors—and simple regression analyses cannot untangle them. Several
statistical techniques are available for coping with simultaneous equation
problems.We use a very simple approach, two-stage least squares, a tech-
nique described in a little detail below.
A second simultaneous equation problem may arise because of multiple
causes of death. Cities with high coronary death rates may likely have
lower cancer death rates because people die of heart attacks before they
have a chance to die of cancer. In this situation, factors which, for
example, show up positively correlated with coronary disease may show up
with a spurious negative correlation with cancer rates. This simultaneous
equation problem is likely to work "through" the age variable in that
median age is determined in part by mortality rates of individual diseases,
while, in turn, age is used to explain mortality rates. We therefore have
also employed two-stage least squares on the age variable, but with no
impact on the estimated equations so these results are not reported here.
25
-------
Figure 4.1
Hypothetical Human Dose-Response Function
O\
MORTALITY' RATE - F(MEDICAL CARE, AGE, GENETIC FACTORS, BEHAVIOR & HABITS, DIET, EXPOSURES)
HEART DISEASE
CANCER
VASCULAR
DISEASE
PNEUMONIA &
INFLUENZA
CIRRHOSIS
EMPHYSEMA &
BRONCHITIS
KIDNEY
DISEASE
CONGENITAL
ANOMALIES
DISEASESOF
EARLY INFANCY
DOCTORS/
CAPITA
HOSPITAL
s/C,
EDS/CAPITA
MEDIAN AGE
RACE
EXERCISE
SMOKING
ROOM DENSITY
RACE
RADIATION
AIR POLLUTION
COLD
VITAMINS
SATURATED
FAT
CHOLESTEROL
PROTEIN
ADDITIVES
ALCOHOL
COFFEE
-------
An alternative approach to the problem which we do not employ, is use of
specific mortality rates.
A third possible source of simultaneous equation bias occurs because
people make voluntary choices over location. Migration in and out of our
sixty city sample is effectively disregarded. People may, for example,
contract an air pollution related disease and, on a physician's advice,
move from a highly polluted area to an unpolluted area, .only then to die.
A false negative association between air pollution and pollution-related
mortality might then be shown. Although in the past we have included a
net migration variable [see Kneese and Schulze (1977)] which was statis-
tically significant, we have excluded such a variable in this analysis
because it defies interpretation in a dose-response function context.
Table 4.1 summarizes the objectives and limitations of the current
study and to some extent those of aggregate epidemiology in general. We
now turn to development of methodology for estimating the value of reducing
health risks and for the effect of medical care on human health. This
latter section focuses on the role of exonomics in aggregate epidemiology.
4.2 Value of Life Vs. Value of Safety
The direct costing approach employed by economists for evaluating the
mortality costs of diseases which result from environmental exposures is
straightforward but difficult to quantify fully [see, for example, Kneese
and Schulze, 1977], First, the population at risk must be known. Second,
the increased risk of mortality associated with environmental exposures
must be quantified either through epidemiology or through extrapolation
from animal experiments. Third, the amount of money or the value that
individuals place on safety (avoiding risk of death) must be known. Multi-
plying these three values together then gives an approximation of the incre-
mental benefits of reducing such exposures. This cost or benefit is not in
any way related to a "value of life" which is most likely unmeasureable,
but rather focuses on a concept of the value of safety (alternatively "cost
of risk") to individuals where risks are statistically small.
27
-------
Table 4.1
Objectives and limitations
Purposes of Study Are:
(1) To explore methodology for isolating an aggregate human dose-
response function.
(2) to add medical inputs.
(3) to add diet.
(4) to add smoking.
(5) to account for simultaneous equation bias where possible
including:
(a) demand for doctors.
(b) multiple possible causes of death.
The Study Fails to Account for:
(1) simultaneous equation problems caused by migration.
(2) exercise.
(3) radiation.
(4) Biases introduced by estimating an aggregate as opposed to
individual dose-response function.
28
-------
Economists in the past have attempted to value human life as the sum
df the present value of future earnings over an individual's lifetime [see
Lave and Seskin, 1970 and 1977]. This approach, however, is no longer
viewed as acceptable. In the first place, it assumes that the value of
life can, in fact, be measured — a point certainly open to debate. Sec-
ond, it implies that the lives of children, housewives, retired and other
unemployed individuals are worth less than the lives of employed heads of
households.
Two measures can be used to value safety or risk to life which are
based on ".the economic concepts of equivalent variation (EV) and compensating
variation (CV). An EV measure of the value of life is the amount of money
an individual would pay to escape from or prevent certain death; in theory,
a rational individual would part with all his available wealth to save his
life. CV, in contrast, measures the compensation required to induce an
individual to accept voluntarily a situation where the probability of
death is increased. As the probability of death approaches unity, the CV
measure can be taken as an estimate of the value the individual places on
his life. Logically, though, the value of life measured this way must be
infinite, because as the probability of death approaches certainty, the
probability of enjoying any compensation offered (and thus the value of the
compensation) approaches zero. Thus, neither EV (which requires coercion)
nor CV (which makes the value of life immeasurable) provides a wholly
satisfactory way of extimating the dollar costs of mortality in realy
world situations that involve risk. An eleboration of the CV concept,
however, can provide a useful measure of the compensation necessary to
induce an individual to accept a slight increase in the probability of
death.
Mishan (1971) was the first to distinguish between the concept of cost
of risk, which is ethically appealing, and earlier efforts to value human
life based on lost earnings, which as a methodology, has strange and intu-
itively objectionable features. The latter measure of the "value" of human
life has now been rejected by economists both on theoretical and, to some
extent, on ethical grounds. Thaler and Rosen (1975), using wage differ-
entials between jobs varying in the level of job-associated risk of death,
were the first to estimate explicitly the value of safety. In other words,
workers in high risk jobs receive higher wages and a value of safety can
be inputed by examining risk-related wage differentials. Unfortunately,
however, their study dealt with a high risk class of individuals. The
Thaler and Rosen (1975) estimate suggests that in current dollars a small
reduction in risk over a large number of individuals which saves one life
is worth about $340,000. Another study [Blumquist (1977)],which examines
seat belt use, suggests that the figure might be $260,000. This study
first estimates how people value their own time and then imputes a value
of safety from the amount of time a sample of individuals spent in buckling
up seat belts. These results may be biased downward because individuals
seem to perceive risks differently when an element of personal control
such as driving an automobile is involved. Finally, Smith (1975) in a study
similar to Thaler and Rosen (1975) has suggested that, for a more typical
population and for job-related risks, the figure may exceed $1,000,000.
Clearly, the cost of risk is not precisely known, and perhaps will never
be, since attitudes — risk preferences — presumably can change over time,
between groups, and can even vary in different situations. But, we at
29
-------
least have a range of values with which to make order-of magnitude estimates
of the costs of environmental risks. This range of values does not, however,
overlap the value-of-life estimates based on lost earnings. For example,
Lave and Seskin (1977) use a value in the thirty to forty thousand dollar
range for a life lost. The Thaler and Rosen (1977) value of safety is,
for example, about an order of magnitude larger than the Lave and Seskin
(1977) lost earnings number.
The theoretical basis of a value of safety or cost of risk concept can
be shown briefly as follows: Assume that an individual has a utility
function, U(W), where utility is an increasing function of wealth, W. If
risk or death is II, expected utility is (l-II)U(W). If we hold expected
utility constant, we have (l-H)U(W) - constant, and the total differential
of this equation is:
-u(w)dn + (i-n) u'(w)dw = o (4.1)
where the prime denotes differentiation. Holding utility constant then
implies that the increase in wealth (or income) necessary to offset an
increase in risk is:
dW/dH = U/[lT (1-n)]. (4.2)
This is the compensating variation measure of the cose to an individual
attributable to an increased risk of death. Analysis of the last expres-
sion can be simplified if we assume a constant elasticity of utility with
respect to wealth, nf such that U(W) = n and consequently TI = -7:7 —. Then
(4.2) can be rewritten as:
dw/dn = w/h (i-n)]. (4.3)
The right hand side of (4.3) suggests several interesting points about the
value of safety or cost of risk. First, if we assume that the elasticity
of utility is less than one, people are risk averse. This in turn implies
that since the risk of death is positive (II>0) that (dW/dII)>W. In other
words, if an individual is risk averse, his life, in terms of the risk
premium necessary to get him to accept risk, is worth more to him than his
wealth. Second, from (4.3), as wealth increases, the risk premium required
to accept an increase in risk voluntarily, dW/dll must increase with age,
ceteris paribus. Thus, one would expect older people to act in a more risk
averse manner than younger individuals (require greater compensation to
voluntarily take a risky action), both because of increased income and
because of increased initial age-related risk of death.
This model contrasts for a number of reasons'with the value of lost
earnings approach previously used in economic analysis. First, if lost
income itself is the measure, the "value of life" measured through lost
earnings obviously cannot exceed wealth [see Conley, 1977]. Second, in-
creased wealth will increase the lost earnings measure as well as the cost
of risk measure. However, the cost of risk measure may not increase pro-
portionately if a different utility function is used. Third, the lost
earnings measure must decrease with age at some point as individuals get
30
-------
older because the expected remaining earnings must decrease, while the cost
of risk, as we argued above, will likely increase. Finally, it is clear
from (4.3) that as II approaches unity, dW/dll approaches infinity. In other
words, the compensation required to induce an individual to accept a cer-
tainty of death voluntarily is infinite. The lost income measure has no
slmiliar property. Nevertheless, the implication is that small increases
in risk may be valued in terms of compensation required to induce individ-
uals to accept such risks voluntarily. Individuals, of course, rationally
accept small risks on a daily basis, presumably on the basis of some
monetary or psychic return.
Given the analysis above, the current methodology of multiplying value
of safety numbers times experimentally or epidemiologically determined
enviromental risks can then be justified as follows: assuming a utility
function U(W) where W is wealth, if risk of death is n, the marginal cost
of risk, as derived earlier, is (dW/dlDfjs* U/U'(1-H), where U is a constant
utility level. If risk, U, is a function of pollution, X, where utility
functions are identical for N individuals, one would wish to maximize
expected utility,
N[l-It(X)]U(W), (4.4)
subject to a constraint on total wealth, W, or income of society
W - NW - C(X°-X) = 0 (4-5>
which is allocated to individual wealth, assumed identical for purposes of
exposition, (NW), and costs of controlling environmental pollution from the
initial level X°, [C(X -X)]. Noting that H > 0, and C' > 0, the first
order conditions are (where X is the multiplier on (4.5) and L denotes the
Lagrangian):
3L/3W = N(l-n)U' - NX = 0
3L/3X - -NIL.U - AC* - 0
J\.
These imply:
N- [U/U' (l-II)]nx = C* (4.6)
or that the number of individuals, N, times the marginal cost of risk,
[U/U"(1-II)], times the marginal effect of pollution on risk, H , equals the
marginal cost of control, C". Clearly, this model abstracts from many
welfare threoretic problems but it does imply that estimation of the left
hand side of (4.6) as suggested at the beginning of this section is a
legitimate approximation of the incremental benefits of environmental con-
trol.
In summary, the direct costing of mortality has the advantage of
focusing attention on one positive output of environmental agencies which
has clear economic value — safety. It is important, however, to distin-
guish between the value of safety to consumers which does have measurable
economic value — environmental agencies may be viewed as selling safety
31
-------
to the public — as opposed to techniques which claim to measure the value
of human life. Benefit-cost arguments for environmental programs should
and can rest on demonstrable increases in public safety delivered at
costs comparable to what the public is willing to pay for safety, not on
claims as to the value of human life. However, the assessment of the risk
of mortality associated with environmental exposures such as air pollution—
whether based on animal experiments or epidemiological studies — remains
difficult and uncertain and is central to the direct costing methodology.
Surprisingly, perhaps, the authors feel there is likely to be less profes-
sional debate as to the economic measure of the dollar value of safety than
as to the quantification of environmental health effects. We now turn to
the possible role of economic analysis in the epidemiology of air pollution.
4.3 A Methodological Basis; Does Economics Matter?
The question posed above could be rephrased "does rational human
behavior matter in the estimation of dose-response functions?" Economists
would certainly answer in the affirmative; individuals are likely to re-
spond to illness with numerous ameliorative measures. Clearly, such mea-
sures, must be accounted its a properly specified dose-response function
is to be estimated. What follows is a simplified economic model of human
behavior in response to health risks which in turn allows specification of
appropriate statistical techniques for estimating a human dose-response
relationship.
Let II denote risk of death for an individual where that risk can be
reduced by medical care which we denote D, synonymous with our empirical
measure, doctors per capita. Thus, risk can be written as a function, II(D),
where dll/dD = H* < 0. If the price of medical care is p and income is
denoted Y, then utility, U, can be written U(Y - pD), a function of income
net of expenditures on medical care, pD. In an uncertain world, economic
analysis assumes that an individual will choose to maximize expected util-
ity — the odds of remaining alive (1-H) times the utility level U — or
[1 - H(D)] U(Y - pD), (4.7)
so the first order condition for the quantity of medical care chosen when
rearranged is:
P = JL (L K\
(l-H)U' -IT ^'o;
The term on the left-hand side of (4.8) is easily recongizable from section
4.2 above as the marginal value of safety (or compensation required to
voluntarily accept a small increase in risk), while the term on the right
is the marginal cost of increased safety through medical care. Thus, this
model of human behavior implies that an individual will choose a level of
medical care which equates his or her marginal value of safety to the
marginal cost of reducing risk through medical care. Of course, an individ-
ual's perception of risk and of the ability of medical care to reduce risk
of death may be imperfect. However, from (4.8) it is easy to show that
individuals who are more risk averse, i.e., those with a large marginal
32
-------
value of safety, will seek more medical care than those who are less risk
averse.
An explicit set of functional forms will simplify interpretation. Let
us again (as in Section 4.2) assume a constant elasticity of utility with
respect to income, n» so U = (Y - pD). Also assume a linear (approximate)
dose-response relationship, II = II + H'D, where H* < 0 is now a fixed
coefficient and II is a positive constant. Equation (4.8) can then be
written as:
D = (^r) - (jjT)n + (|)Y (4.9)
which is a demand equation for medical care. If we take the supply price
of medical care to be fixed P =P* (infinitely elastic supply of medical
care), the individual demand for medical care, doctors per capita for
example, is then a linear increasing function of total risk n, since
(:=nr) > 0, and of income Y, since -=j- > 0. Of course, we wish, as our prin-
cipal objective for policy purposes, to estimate the dose-response function:
n = n + n'D; (4.io)
o
in particular, we wish to obtain an unbiased estimate of n1, the effect of
medical care on mortality and of the effect of other variables such as air
pollution. However, any attempt to directly estimate (4,10) is doomed to
failure. This occurs because the equation specified for statistical
estimation (equivalent to 4.10 where a and a are parameters for esti-
mation)
n = a + a-D + un (4.11)
o 1 11
has a disturbance term y which is not independent of D. In other words,
y is correlated with D. This is easy to show if we specify the demand
equation for doctors (equivalent to 4.9 above with parameters 3 , B, and
B ) as stochastic:
D - 3 + 8,n + B,Y + y_ (4.12)
O 1 e. D
as well, with a disturbance term y . Now suppose some factor (random)
embodied in y causes n to rise in (4.11). But if n rises, by (4.12), D
must increase since, from (4.9), R > 0 and D, through ^, depends on n.
Thus, D depends on y through (4.12) and D and y are correlated. Now, if
in estimating (4.11) this correlation is not accounted for, not only will
estimates of a1 and a_ be biased, but if we had included other factors which
affect morality such ac diet or pollution in ('.-.11), coefficients on these
variables would be biased c.s veil. It is also true that if simultaneous
equation biased is
33
-------
present and not accounted for, it becomes possible that the estimated
effect of medical care, a-, will appear not significantly different from
zero or even of the wrong sign (note we assume that a_ < 0; that doctors
reduce mortality).
We can break the dependence of D on y^ by first substituting (4.10)
into (4.9), or (4.11) into (4.12), to obtain a reduced form equation for
medical care,
D + 2^-2F+2f*Y°rD = Yo + YlY + \ (A-13)
where y is the disturbance term in the reduced form. This equation can be
legitimately estimated since the income variable is exogenous, determined
outside the relevant system of equations, and the endogenous variables D
and n, those determined within the system, do not appear on the right-hand
side of (4.13). Now, if we estimate (4.13) and obtain unbiased estimates
of the two coefficients Y = OorfT - "orf^ and Y, = COD*) we can use these
along with data on income, Y, to generate a new variable, estimated medical
care, D, where
D = Y + Y,Y. (4.14)
o 1
Note that this new variable, D, generated from data on Y does not depend
on u_ and can be used instead of actual data on D to estimate a dose-
response function:
a + a,D + u ~ (4.15)
o 1 ll
This estimated equation gives a consistent estimate of o or II1. In fact,
if the hypothesis that doctors are both important and effective in reducing
mortality rates is correct, a should show up negative and significantly
different from zero as estimated in (4.15). Note, however, that if indi-
viduals perceive that doctors are effective, they will have a strong
incentive to seek medical help when ill, thus making a direct least squares
estimate of the effect of medical care as specified in (4.11) impossible.
The procedure we have outlined above, two-stage least squares, has been
used successfully in many instances to resolve simultaneous equation pro-
blems and has the advantage of requiring minimal additional data. In gen-
eral, if an unbiased estimate of a structural equation (one equation is a
simultaneous system) is desired, one need only use ordinary least squares
to estimate each of the endogenous variables as a function of all of the
exogenous variables in the model (estimate a set of reduced form equations) .
Then, using the data on the exogenous variables, an estimated data set for
each of the endogenous variables is created. Consistent structural equa-
tions can then be obtained by replacing each endogenous variable
34
-------
on the right hand side of a structural equation by its estimated equivalent
using ordinary least squares.
4.4 The Sixty-City Data Set! Selection of Variables
In this section, we describe the data set itself and also examine some
properties of the data with special emphasis on collinearity and consequent
implications on the variety and kinds of hypotheses which can be approp-
riately tested.
Tables 4.2-4.5 present a listing of the variables available for
analysis along with the year of the variable, units, mean, standard dev-
iation (S.D), and sources for the data by number, where the number
refers to the listing of sources in Table 4.6. Table 4.2 includes total
mortality rate calculated from 1970 data on mortality by city divided by
1970 census population. Disaggregated mortality data by disease category —
heart, vascular, pneumonia and influenze, emphysema and bronchitus, cir-
rhosis, nephritis and nephosis, congenital anomalies, early infant diseases,
and cancer — were also collected for 1970, and divided by 1970 census
population to develop mortality rates; exceptions are the congential
anomolies and early infant disease categories which were divided by the
number of births in each city for 1970 in order to define an appropriate
mortality rate. Mortality data for 1970 were chosen because reliable city
population estimates are available for that year as opposed to more recent
data requiring use of non-census year city population estimates in place of
actual data. The disaggregation of total mortality by disease may not be
appropriate. However, only data on city mortality was available, as
indicated in Table 4.2.
Table 4.3 describes per capita dietary data by city for the years 1955
and 1965. The procedure used to construct the dietary data sets was some-
what involved. Food consumption estimates were first constructed for each
of the 60 cities, using data on a sample of about 3,000 urban households,
distributed among eight income brackets, for four regions of the United
States, collected by the Department of Agriculture for 1955 and 1965. The
results are regionally-specific weighted averages of consumption of various
foods by families in each income bracket, multiplied by the fraction of
each city's population in each income bracket. Data for specific dietary
factors were then generated by multiplying the consumption rates of 49
foods by their respective concentrations of a given substance. A number
of additional variables are available from the Department of Agriculture
for 1965 as opposed to 1955. These include total protein, total fats, and
total carbohydrates. As such, these variables provide a better indication
of broad dietary patterns as opposed to the 1955 data set.
Table 4.4 describes our data on socioeconomic, geographic, and smoking
variables. The socioeconomic and geographic variables were chosen for
their consistency for estimating the aggregate dose-response function
hypothesized in previous sections. Both the income and education variables
are hypothesized to enter the demand equation for medical care, not the
dose-response function. We must therefore employ the two-stage least
squares estimation technique outlined above. Doctors per capita was chosen
as the best available indication of available medical care, b oth in terms of
35
-------
Table 4.2
Mortality Variables
Variable Year Units
Mean
S.D.
Sources
Mortality Variables
M070
HA70
VA70
PN70
EM70
CI70
NE70
C/B%
I/B%
CA70
Total Mortality 1970 deaths/1000 pop.
Heart Disease 1970 "
Vascular Disease 1970 "
Pneumonia & Influenza 1970 "
Emphysema & Bronchitis 1970 "
Cirrhosis 1970 "
Nephritis & Nephrosis 1970 "
Congenital Anom/Births 1970 %
Early Infancy /Births 1970 %
Cancer Mortality 1970 deaths/1000 pop.
11.283
4.216
1.566
0.375
0.178
0.238
0.058
0.473
1.294
1.958
2.161
1.078
0.395
0.114
0.059
0.106
0.027
0.105
0.333
0.402
(18) (6)
(18) (6)
(18) (6)
(18) (6)
(18) (6)
(18) (6)
(18) (6)
(18) (6)
(18) (6)
(18) (6)
-------
Table 4.3
Dietary variables
Variable
Year
Units
Mean
S.D.
Source
Dietary Variables
NTRI
NTRA
SFAT
FROT
CHOL
CVIT
CALO
COFF
ALCO
XPRO
XFAT
XCAR
XASA
6NTI
6NTA
6SFT
6PRO
6CHL
6CAL
6CVT
6COF
6ALC
Nitrites in Food
Nitrates in Food
Saturated Fatty Acids*
Protein*
Cholesterol*
Vitamin C**
Calories.
Coffee
Alcohol (S value)
Total Protein
Total Fats
Carbohydrates
Ascorbic Acid
Nitrites in Food
Nitrates in Food
Saturated Fatty Acids*
Protein*
Cholesterol*
Calories
Vitamin C**
Coffee
Alcohol ($ value)
1955
1955
1955
1955
1955
1955
1955
1955
1955
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
g/yr/cap
g/yr/cap
g/yr/cap
g/yr/cap
g/yr/cap
g/yr/cap
kcal/yr/cap
kg/yr/cap
$/yr/cap
g/yr/cap
g/yr/cap
g/yr/cap
mg/yr/cap
g/yr/cap
g/yr/cap
g/yr/cap
g/yr/cap
g/yr/cap
kcal/yr/cap
g/yr/cap
kg/yr/cap
$/yr/cap
1.
69.
16220.
26557.
234.
16.
1149.
5.
17.
39845.
57512.
123490.
42281.
1.
52.
16315.
28128.
219.
1171.
18.
5.
25.
27
86
00
00
81
96
7
83
30
14
87
9
1
65
40
97
0.
9.
874.
1314.
6.
1.
56.
.
6.
706.
1795.
3623.
2364.
.
2.
976.
1603.
5.
27.
1.
.
6.
14
05
65
00
98
46
27
70
06
46
7
0
2
16
47
3
4
80
63
3
18
45
(2) (4) (27)
(2)
(2')
(2)
(2)
(4) (27)
(3) (4)
(3) (4)
(3) (4)
(2) (3) (4)
(2)
(2)
(3) (4)
(3) (4)
(2) (3) (4)
(4)
(4)
(3)
(3)
(3)
(3)
(3)
(3)
(28)
(28)
(28)
(28)
(28) (27)
(28) (27)
(4) (28)
(4) (28)
(4) (28)
(4) (28)
(4) (28)
(4) (28)
* Includes only animal products.
** Includes only vitamin C content for fruits and vegetables eaten fresh.
37
-------
Table 4.*
Social, Economic, Geographic, and Smoking Variables
Variable
Year
Units
Mean
S.D.
Sources
Social, Economic, Geographic
MDOC
IN69
EDUC
DENS
COLD
NONW
MAGE
Medical Doctors
Median Income
Education
Crowding in Homes
Cold Temperatures
Nonwhite Population
Median Age of Popu-
lation
1970
1969
1969
1969
1972
1969
1969
M.D. 's/100,000
$/yr /Household
%>25 yrs w/H.S.
diploma
Z>1.5 persons/
room
(days temp < 0
oec.
Fraction
Years
162.
10763.
55.
0.
86.
0.
28.
8
3
022
9
226
82
54
1060
7
0
47
0
2
.2
.
.4
.013
.7
.154
.74
(19)
(6)
(6)
(8)
(9)
(6)
(6)
Snoking Variables
C156
CI68
Cigarettes
Cigarettes
1956
1968
packs/yr/capt
packs /yr/captt
183.
165.
52
80
26
23
.66
.25
(22) (4)
(7X1)
t Data for states, 1960 census population used.
ft Data for states, 1970 census population used.
38
-------
Table 4.5
Air Pollution Variables
Variable
Year
Units
Mean
S
.D.
Sources
Air
SU66
AM66
NI66
PA66
N069
PA70
5070
NI70
HI90
SU70
SU90
LEAD
C074
BETA
Pollution
Sulfate
Ammonium
Nitrates
Suspended Particulates
Nitrogen Dioxide
Suspended Particulates
Sulfur Dioxide
Nitrate, annual mean
Nitrate, 90th %-tile con.
Sulfate, 'annual mean
Sulfate, 90th %-tile con.
Lead
Carbon Monoxide
Beta Radioactivity
1966
1966
1966
1966
1969
1970
1970
1971-73
1971-73
1971-73
1971-73
1970
1974
1966
yg/m
yg/m
3
yg/m
o
yg/m
ppm
pg/m3
yg/m
yg/m
yg/m
3
yg/m
yg/m
3
yg/m
mg/m
PC±/m3
10.
1.
1.
114.
0.
102.
26.
3.
5.
10.
17.
1.
11.
0.
67
15
96
83
076
30
92
13
21
65
69
33
86
261
5
1
0
33
0
30
22
0
1
4
7
0
3
0
.44
.42
.68
.97
.034
.11
.20
.92
.80
.01
.62
.54
.50
.091
(20)
(20)
(20)
(20)
(11)
(13)
(13)
(14)
(14)
(14)
(14)
(16)
(15) !
(20)
32
-------
preventative and ameliorative care. Alternative variables such as hospital
beds per capita were judged inferior, in that underutilization of hospital
facilities is a common problem and adjustments for utilization factors
would prove troublesome. Also, if one assumes a less than perfectly elastic
supply of medical care, the doctors per capita variable is an appropriate
supply side variable in that it reflects patient loads for doctors in a
particular city. The possible importance of age and cold temperatures in a
dose-response relationship are clear. However, the nonwhite and crowding
variables may be more difficult to interpret. The nonwhite variable would
ideally control to some extent for genetic variations in the population.
Obviously, however, this variable may well proxy for education, poverty,
habits, etc. Similarly, crowding would ideally be an indication of pos-
sible contagion but may really proxy for poverty, old age, or even race.
Thus, the role of these variables should be interpreted xvrith great care.
Cigarette consumption was estimated from cigarette tax revenues for
each state in which a sample city was located; the result is thus a state-
wide average that includes rural populations. Per capita cigarette consump-
tion was estimated using the total state population over 16 years of age
both for 1956 and 1968. It should be noted that both our dietary and our
smoking variables are quite crude, reflecting problems in utilizing second-
ary data. However, the possible importance of their effects on human health
may justify use of even these measures. We also attempted to develop a
measure of total exposure to radiation, collecting data on beta radioactiv-
ity in air, terrestrial gamma radiation, and cosmic ray exposures, but have
to this point been able to account for only about half of the average indi-
vidual annual dose associated with medical exposures. As a result, no
suitable-total exposure variable, is available at this time.
Table 4.5 presents the air pollution variables available for testing.
All data are annual geometric means for each city unless otherwise specified.
Dnf prtunately,' hydrocarbon data was only available for about ten of our
sample cities and are excluded for this reason. Finally, as noted above,
Table 4.6 presents our data sources.
In summary, data available for testing include: (1) 1970 mortality
rates for total mortality and for major disease categories; (2) data on
dietary patterns for 1955 and 1965; (3) data on medical doctors and socio-
economic factors for 1970 or a nearby year; (4) data on smoking patterns for
1956 and 1968; and (5) data on air quality for each city for 1970 or a
nearby year.
Since only 60 observations are available, we must obviously select a
subsample of the available explanatory variables for hypothesis testing.
To allow straightforward statistical tests of the significance of estimated
coefficients, it is necessary to make the selection of included variables
a_ priori rather than testing each of the variables in various combinations
for significance and excluding some on the basis of relative significances.
Techniques do exist for testing significance where pre-testing has been
employed but the standard t-statistic is no longer applicable.
The first problem in specifying the final data set is a decision on
including lagged variables. Given a highly mobile U.S. population, the
40
-------
Table 4.6
Sources of Data
(1) Advisory Commission on Intergovernmental Relations, State and Local
Finances; Significant Features arid Suggested Legislation, 1972, Table
120, 1970.
(2) U.S. Department of Agriculture, Household Food Consumption Survey, 1955,.
Reports No. 2-5.
(3) , Composition of Foods; Raw, Processed and Prepared, Watt,
Bernice K., and Merrill, Annabell L., "Agricultural Handbook No. 8, 1968.
(4) U.S. Department of Commerce, Bureau of the Census, U.S. Census of the
Population: 1960.
(5) , Cross Migration by County; 1965-1970, Current Population
Reports Series P-25, No. 701, issued May 1977.
(6) , U.S. Census of Population; 1970, Vol. 1-50.
(7) , State Tax Collections; 1968, Series GF 68 No. 1, Tables 7, 9.
(8) , 1970 Census of Housing by State.
(9) ____, National Oceanic and Atmospheric Administration, Environmental
Data Service, Climatological Data, National Summary; Annual 1972, Vol.
23, No. 13, Asheville, North Carolina.
(10) U.S. Environmental Protection Agency, Natural Radiation Exposure in the
United States: 1972. Report No. ORP/SID 72-1, Table A-l, 1974 Reprint.
(11) ' ' ' Air Quality Criteria for Nitrogen Dioxide. No. AP-84, Tables
6-10, January 1971.
(12) -, Chemical Analysis of Interstate Carrier Water Supply System,
PB-257600/7BE April, 1975.
(13) , Air Quality Data - 1970 Annual Statistics, EPA-450/2-76-019,
October 1976.
(14) , Air Quality for Nonmetallic Inorganic Ions. 1971 through 1974;
From the National Air Surveillance Networks. EPA-600/4-77-003, January,
1977.
(15) , Air Quality Data - 1974 Annual Statistics. EPA 450/2-76-011,
August, 1976.
(16) U.S. Environmental Protection Agency, Air Quality Data for Metals 1970
through 1974; From the National Air Surveillance Networks, EPA-600/4-
76-041.
41
-------
Table 4.6
(continued)
(17) Department of Health, Education and Welfare, Public Health Service,
National Center for Health Statistics, Vital Statistics of the United
States; 1960.
(18) , Vital Statistics of the United States; 1970.
(19) , Health Manpower — A County and Metropolitan Area Data Book.
(20) , National Air Pollution Control Administration, Air Quality
Data from the National Surveillance Network and Contributing State and
Local Networks, 1966 Edition.
(21) , Vital Statistics of the United States; 1972.
(22) Tobacco Tax Council, Cigarette Taxes in the United States. 1956.
Table 15.
(23) Directory of Medical Specialists. 1960-71, Marquis - Who's Who, Inc.,
Chicago, Illinois.
(24) Adams, John A., et. al., eds., The Natural Radiation Environment II.
Proceedings of the Second International Symposium on the Natural
Radiation Environment, Houston, Texas, August 7-11, 1972.
(25) Hickey, John, et. al., The Development of an Engineering Control
Research and Development Plan for Carcinogenic Materials. U.S. Govern-
ment Printing Office, Washington, D.C. (1977 in press).
(26) Pazand, Reza, Environmental Carcinogenesis — An Economic Analysis of
Risk. PhD. Dissertation, The University of New Mexico, July 1976.
(27) White, Jonathan W., Jr., "Relative Significance of Dietary Sources of
Nitrate and Nitrite," Journal of Agricultural and Food Chemistry,
Vol. 23, No. 5 (1975), Table VI, p. 890.
(28) U.S. Department of Agriculture, Household Food Consumption Survey. 1965-
66, Reports No. 7-10 and Reports No. 13-16.
42
-------
Table 4.7
Simple Correlation Matrix for 1965 Diet Variables
XPRO XFAt XCAR XASA 6NTI 6NTA 6SFT 6PRO 6CHL 6CVT 6COF 6ALC
XPRO 1.00 0.46-0.01 0.53-0.64 0,43 0.16 0.29 0.67 0.88-0.14 0.70
XFAT 0.46 1.00 0.85-0.17 0.34 0.74-0.62-0.41 0.50 0.12-0.09-0.28
XCAR -0.01 0.85 1.00-0.33 0.66 0.58-0.66-0.46 0.33-0.31-0.22-0.71
XASA 0.53-0.17-0.33 1.00-0.69-0.16 0.86 0*93 0.58 0.79-0.59 0.58
6NTI -0.64 0.34 0.66-0.69 1.00 0.20-0.66-0.67-0.36-0.77 0.25-0.93
6NTA 0.43 0.74 0.58-0.16 0.20 1.00-0.47-0.31 0.46 0.20 0.16-0.13
6SFT 0.16-0.62-0.66 0.86-0.66-0.47 1.00 0.96 0.26 0.55-0.39 0.54
6PRO 0.29-0.41-0.46 0.93-0*67-0.31 0.96 1.00 0.51 0,63-0*53 0.50
6CHL 0.67 0.50 0.33 0.58-0.36 0.46 0.26 0.51 1.00 0.64-0.48 0.21
6CVT 0.88 0.12-0.31 0.79-0.77 0.20 0.55 0.63 0.64 1.00-0.16 0.81
ACOF -0.14-0.09-0.22-0.59 0.25 0.16-0.39-0.53-0.48-0.16 1.00 0.03
6ALC 0.70-0.28-0*71 0*58-0.93-0.13 0.54 0.50 0,21 0.81 0*03 1.00
-------
question becomes, "do people now living in a city represent the same sample
as individuals who lived in cities 14-15 years before (the lags on smoking
and diet, respectively)?" If the answer is no, and if people carry their
dietary and smoking characteristics with them as they move, the most recent
available data is likely to better represent long-term dietary and smoking
patterns of individuals in a particular city. For these reasons, in this
study, we use the available data closest to 1970 throughout. However, it
may well be, for diseases with long lags such as cancer, that lagged varir
ahles are superior in any case. The real answer is, of course, to account
properly for mobility — a near impossibility when using aggregate data.
The second consideration in specifying variables for inclusion is multi-
collinearity. Typicall, multicollinearity problems can be avoided if the
simple correlations between explanatory variables are less than 0.4 to 0.6.
Tables 4.7 and 4.8 present simple correlation matrices for 1965 diet and air
quality variables, respectively.
Table 4.7 shows that a very high level of collinearity is probably
present among dietary variables. It appears so high, in fact, that the
problem becomes one of finding a set of dietary variables which is suf-
ficiently non-collinear to allow reasonable estimation of individual coef-
ficients. Perhaps the broadest indicators of dietary patterns are the
total protein (XPRO), total fat (XFAT) and total carbohydrate (XCAR)
variables. Protein and fat will tend to indicate high consumption of meat
and nuts, while high carbohydrate consumption will indicate consumption of
grains, fruits, vegetables, and refined sugars. However, total carbohydrate
and-total fat have a correlation coefficient of 0.85; too high to allow
inclusion of both variables in an estimated equation. However, if we
replace total fats (XFAT) with animal fat (6SFT), a good proxy for con-
sumption of saturated fats, the correlation between fat (now animal fat)
and carbohydrates drops to 0.66, which although still high, will likely
cause less difficulty. Thus, we include these three diet variables as
broad indicators of dietary patterns where, however, it must be clearly
recognized that the estimated coefficients on these variables may well
include the effect partially or totally of a number of other highly col-
linear dietary variables. For example, total protein (XPRO) has a cor-
relation with cirrhosis, one might justifiably doubt that a causal relation-
ship exists between protein and cirrhosis as opposed to one between slcohol
and cirrhosis.
Table 4.8 suggests that multicollinearity may well be a problem within
the air quality data set as well. Given previous research (see, for example,
Lave and Seskin, 1977), the air quality measures of most concerti are those
for NO., SO., sulfate, and participates, so we focus on these variables
here, However, our measures of SO and sulfate for 1970, the year of the
mortality data, are highly collinear — S070 and SU70 have a simple correl-
ation of 0.74 — so any separation of their relative importance is likely
impossible. As a result, we use SO- (S070) as a proxy variable for both
pollutants. Note also that among the included air pollution variables,
NO, (N060), particulates (PA70), and S02 CS070), collinearity problems may
exist with respect to ammonium, carbon monoxide and lead (some correlations
greater than or equal to 0.4). Since we exclude these variables here (as
44
-------
Table 4.8
Simple Correlation Matrix for Air Quality Variables
AM66
NI66
SU66
N069
PA66
PA 70
SO 70
NJ70
NI90
LEAD
CO 74
SU70
SU90
AM66
1.00-
-0,16
0,78
0.28
0.51
0.32
0.52
-0,15
-0,08
0 , 04
0.14
0.66
0,64-
NI66
-0.16
1.00
0.07
0.36
0.24
0.08
0.04
0.48
0,44
0.51
0,19
0,07
-0,01
SU66
0,78
0,07
1,00
0,34
0,68
0.43
0.72
0.08
0.11
0.07
0.28
0.86
0.73
N069
0*28
0*36
0,34
1.00
0 » 30
0.09
0,35
0.31
''0.33
0.40
0,21
0.37
0.21
PA66
0.51
0,24
0,68
0 . 30
1.00
0,69
0,50
0*11
0.12-
PA70
0,32
0,08
0,43
0.09
0.69
1.00
0,25
0.17
0.11
0,19-0,00
0,36
0,53
0,53
0.36
0.37
0.31
S070
0,52-
0,04
0,72
0,35
0,50
0.25
1.00
0 , 20
0,28
0,10
0.80
0,74
0 , 56
NI70
-0.15-
0.48
0.08
0,31
0,11
0.17
0,20
1.00
0,92
0,18
0,24-
0.19
0.04
NI90
•0.08
0.44
0.11
0,33
0,12
0,11-
0.28
0,92
1.00
0,20
0,24
0,22
0.14-
LEAD
0.04
0*51
0 * 07
0.40
0.19
•0.00
0.10
0.18
0.20
1.00
0 * 20
0*00
-0.08
C074
0.14
0.19
0 . 28
0.21
0.36
0.36
0.50
0.24
0 . 24
0.20
1.00
0,34
0.25
SIJ70 SU90
0.66 0.64
0.07-0.01
0*86 0*73
0*37 0.21
0,53 0,53
0,37 0.31
0,74 0,56
0.19 0.04
0.22 0.14
0.00-0.08
0.34 0.25
1.00 0.85
0.85 1.00
-------
Table 4.9
Simple Correlation Matrix for Included Variables
CTi
NONW MAGE IN69 EDUC DENS COLD CI68 XPRO XCAR 6SFT
NONU
MAGE
IN69
EDUC
DENS
COLD
CI68
XPRO
XCAR
6SFT
N069
S070
PA70
1
0
-0
-0
0
-0
0
0
0
0
0
0
0
.00 0,02-0.26-0.22 0.40-O.04 0.02 0.
.02 1.00 0.08-0.14-0.30 0.01-0,03 0.
.26 0.08 1,00 0.49-0.32 0.02 0.05 0.
.22-0.14 0,49 1*00-0.22 0*04-0*28 0.
,40-0.30-0,32-0.22 1,00-0,38-0.08 0.
,04 0,01 0.02 0.04-0.38 1 .-00 0.33-0,
,02-0,05 0,05-0*28-0,08 0*33 1.00-0.
,02 0.22 0.20 0.26 0.03-0.60-0.24 1.
.23-0.24-0.23-0.35 0.39-0.38-0.01-0.
,02 0. 32-0,05-0, 13-0, 26 0.34 0.09 0.
.22 0,21 0,12-0.16 0,08-0.03 0.17 0*
.29-0.25-0.12-0.34-0.03 0.35 0,23-0.
.03 0.13-0.25-0.24-0*07 0.34-0,08-0.
02 0
22-0
20-0
26-0
03 0
60-0
24-0
00-0
01 1
16-0
11-0
08-0
31-0
«
*
*
*
.
*
.
.
.
»
«
*
,
23 0
24 0
23-0
35-0
39-0
38 0
01 0
01 0
00-0
66 1
18 0
33 0
03 0
.
.
»
.
.
.
.
.
*
,
,
,
«
02
32
05
13-
26
34-
09
16
66-
00
16
59
12
N069 S070 PA70
0
0
0
-0
0
-0
0
0
-0
0
1
0
0
.22 0
,21 0
.12-0
,16-0
.08-0
.03 0
.17 0
.11-0
.18-0
,16 0
.00 0
.35 1
.09 0
.29 0
.25 0
.12-0
.34-0
.03-0
.35 0
.23-0
,08-0
.33-0
.59 0
*3S 0
.00 0
.25 1
.03
.13
.25
.24
.07
.34
.08
»31
.03
.12
.09
.25
,00
-------
Table 4.10
Listing of Data Used
1 BIRMG AL
2 MONTG AL
3 PHQEN AZ
4 TUCSM AZ
5 LROCK AK
6 LONGB CA
7 OAKLD CA
8 SAHDI CA
9 SFRAN CA
10 HARTF CT
11 NEUHA Cl
12 WATER CT
13 WASHG DC
14 ATLArt GA
15 CHICA IL
16 ECHIG IN
17 IMDIA IN
18 SBEND IN
19 DESMO 10
20 DUBUQ 10
21 TOPEK KA
22 Ml CHI KA
23 LEXNG KY
24 LOUIS KY
25 NEUOR LA
26 BALTI MD
27 J1ETRO MI
28 GDRAP HI
29 MINNE UN
30 KCITY MO
31 STLOU MO
32 OMAHA NB
33 CAMDN NJ
34. JCITY NJ
35 HEURK NJ
36 ALBUCt NM
37 NYORK NY
38 AKRON OH
39 CINNC OH
40 COLUtt OH
41 DAYTN OH
42 TOLEH OH
43 YTOWN OH
44 TULSA OK
45 PLAND OR
46 PHILA PN
47 PITTS PN
48 REDDG PN
49 PROVI RI
50 CHATT TN
51 MEMPH TN
52 HALLS TX
53 HOUST TX
54 PASSA TX
55 SANAN TX
56 SALTC UT
57 NFOLK VA
58 RICHM VA
59 SEATT UA
60 CHARL UV
M070
11.283
2.161
14.008
10.136
8.598
10.151
11.480
12.074
11.792
7.6S8
13.112
11.246
11.111
11.219
11.700
11.809
12.317
12.239
8.171
10.814
11.117
10.945
9.247
8.393
9.377
13.539
12.408
12.614
12.184
11.986
12.A61
11.513
15.602
9.513
12.696
12.946
11.616
8.230
11.526
10.609
1 3 . 385
9.489
11.925
11.141
13.063
8.561
13.517
12.553
14.062
IS. 198
13.727
15.141
9.358
8.423
7.803
5.018
8.131
11.246
8.008
12.503
12.047
14.321
VA70
1.566
o.39t>
2.758
1.619
1.O40
1.327
1.927
1.782
1.628
1.214
1.808
1.329
1.314
1.814
1 . 24V
1.636
1.363
1.894
1.280
1.847
1,685
1.685
1.528
1.276
1.443
2.150
1.523
1.242
1.375
1.771
2.125
1.668
2.134
1.4J.7
1.307
1.305
1.043
O.VV3
1.148
1.503
1.636
1.416
1.646
1.701
1.953
1.345
2.287
1.376
1.873
2.407
1.663
2.242
1.536
1.108
1.001
0.526
1.217
1.478
1.085
1.899
1.850
1.510
HA70
4.216
1.078
3.925
2.954
2.884
3.347
4.155
5.1O6
4.500
2.728
4.618
4.025
4.597
4.897
3.845
3.596
5.555
4.3OO
2.889
3.735
4.517
4.718
3.720
3.052
3.588
5. OS/
4.829
4.921
4.615
4.604
4.784
3.431
6.130
3.501
5.383
5.703
4.712
2.162
4.710
3.8C5
5.299
3.378
4.423
4.343
4.92V
2. 943
4.843
4.486
6.127
6.412
5.731
5.895 .
3.222
2.834
2.614
1.613
2.6O6
3.684
2.939
4.627
4 . 372
6.028
PN/0
0.37li
0. 114
0.34V
0.19S
0.359
0.373
O.271
0.332
0.281
0.165
0.440
0.405
Oi392
0.324
0.590
0.515
0.411
0.447
0.247
0.334
0.314
O.a58
0.264
0.253
0.342
0.387
0.361
0.350
O.436
0.385
0.414
0.333
0.546
0.328
0.439
0.526
0.382
0.308
i O.514
0.240
0.522
0.302
0.427
0 . 380
0.486
O.244
0.384
0.405
0.498
0,2V/,
0.3/V
O.b54
0.269
0-.261
0.266
0.202
0.266
0.273
0.260
0.501
0.377
0.727
KM70
0.1/8
o.ot/y
0.216
O.127
0.279
0.422
0.098
0.212
0.195
0.148
0.187
0.171
0,116
0.176
0.132
0.157
0.117
0.128
0.117
0.127
0.23?
0.128
0.168
0,199
0.065
0.293
0.158
0.152
0.197
0.182
0.193
0.199
0.222
0.204
0.224
0.196
0.133
0.205
0.119
0.200
0.214
0.187
0.250
0.221
0.186
0.148
0.243
0.148
0.115
0.169
0.156
0.202
0.159
0.159
0.119
0.112
0.125
0.262
0.094
0.140
0.213
0.280
47
-------
Table 4.1Q
(continued)
1 BIRMG AL
2 MONTG AL
3 PHOEN AZ
4 TUCSN AZ
5 LROCK AK
6 LONGB CA
7 OAKLD CA
8 SANDI CA
9 SFRAN CA
10 HARTF CT
11 NEUHA CT
12 MATER CT
13 UASHG DC
14 ATLAN GA
15 CHICA IL
16 ECHIG IN
17 INDIA IN
18 SBEND IN
19 DESMO 10
20 nunuo 10
21 TOPEK KAi
22 UICHI KA
23 LEXNG KY:
24 LOUIS KY
25 NEUOR LA
26 BALTI MD
27 DETRO MI
28 GDRAP MI
29 HINNE HN
30 KCITY MO
31 STUOU MO
32 OMAHA NB
33 CAhON NJ
34 JCITY NJ
35 NEURK NJ.,
36 ALHUO MM
37 NYORK NY
38 AKRON OH
39 CINNC OH
40 COLUM OH
41 DAYTN OH
42 TOLED OH
43 YTOUN OH
44 TULSA OK
45 PLAND OR
46 PHI LA PN
47 PITTS PN
48 REDDG PN
49 PROVI RI
50 CHATT TN
51 MEMPH TN
52 DALLS TX
53 HOUST TX
54 PASSA TX
55 SANAN TX
56 SALTC UT
57 NKOLK VA
58 RICHM VA
59 SEAIT UA
60 CHARL UW
CI70
0.238
O.106
0.116
0.112
0.205
0.198
0.188
0.290
0.358
0.191
O.646
0.329
0.211
0.333
0.489
0.213
0.289
0.298
0.140
0.159
0.130
0.096
0.104
0.116
0.176
0.288
0.189
0.394
0.413
0.187
0.214
0.187
0,268
0.184
0.419
0.426
0.290
0.254
0.352
0.16O
0.190
0.143"
0.177
0.190
0.243
0.130
0.314
0.219
0.277
0.251
0.262
0.218
0.154
0.165
0.166
0.101
0.194
0.222
0.146
0.248
0.266
0.392
NE70 I
0.058
0.027
0.116
0.112
0.029
0.027
0.045
0.028
0.047
0.030
O.O49
0.032
0.022
0.037
0.031
0.131
0.062
0.106
O.O58
O.O80
0.020
0.064
0.024
0.036
0.037
0 .055
0.091
0.063
0.067
0.035
0.028
0.049
0.090
0.043
0.068
0.111
0.092
0.025
0.055
O.051
0.053
O.041
O.O78
0.044
0.086
0.036
0.044
0.066
0.071
0.023
0.084
O.O76 :
O.O56
O.034
O.O39
O.O11
0.064
0.080
0.052
0.072
O.053
0.098
c\»x
0.473
0.105
0.465
0.243
0.246
0.688
0.478
0.4B2
0.401
0.167
O.36B
0.506
O.513
0.396
0.401
0.355
0.430
0.561
0.441
0.549
0.619.
0.413
0.392
0.-506
0.359
0.436
O.609
0.456
0.470
0.579
0.544
0.384
0.475
0.486
0.319
0.412
0.489
0.518
0.424
0.430
0.474
0.456
0.506
0.506
0.865
0.491
0.588
0.535
0.490
0.676
0.600
6.556
0.572
O.512
0.436
0.526
0.377
0.296
0.411
0.377
0.416
0.421
I\BX
1 .294
0 . 333
1..J27
1.333
0.975
0 . 995
1.299
1.045
1.250
1.O5U
0.934
1.519
1.758
1.18V
1.937
1.539
1.612
1.794*
1.25V
1.450
1.381
1.570
O.940
1.465
0.934
1.237
1.497
1.417
1,320
1.183
1.258 .
1.318
1.449
1.362
1.716
1.687
1.997
1.132
1.245
1.291
1.O40
O.946
1.224
0.127
1.259
1.188
0.874
1.713
1.510
1.149
1.327
2.1O5
1.143
1.297
1.264
0.789
1.182
0.765
1.447
1.684
1.075
O.843
CA70
1.958
0.402
2.343
1.732
1.499
1.719
1.942
2.049
2.090
1.316
2.493
1.987
2.004
1-4 999
2.000
1.789
2.038
2.O22
1.573
2.142
1.919
1 .894
1.568
1.4S4
1.517
2.304
2.158
2.228
2.126
2.155
2.281
1.871
2.562
1.776
2.048
2.241
1.663
1.276
2.1S1
1.968
2.510
1.740
2.048
1.964
2.389
1.586
2.425
2.170
2.426
2.618
2.69O
2.469
1.644
1.397
1.311
0.941
1.373
1.558
1.322
1.959
2.174
2.671
48
-------
Table
4.10
(continued)
1 BIRMG AL
2 MONTG AL
3 PHOEN AZ
4 TUCSN AZ
5 LROCK AK
6 LONGB CA
7 OAKLD CA
8 SANDI CA
V SFRAN CA
10 HARTF CT
11 NEUHA CT
12 WATER CT
13 UASHG DC
14 ATLAN GA
15 CHICA IL
16 ECHIG IN
17 INDIA IN
18 SBCND IN
19 DESMO 10
20 nUDUQ 10
21 TOPEK KA
22 UICHI KA
23 LEXNG KY
24 LOUIS KY
25 NEUOR LA
26 BALTI MD
27 BETRO MI
28 GORAF HI
29 MINNE MN
30 KCITY MO
31 STLOU MO
32. OMAHA NB
33 CAMDN NJ
34 JCITY NJ
35 NEURK NJ
36 ALBUQ NM
37 NYORK NY
38 AKRON OH
39 CINNC OH
-10 COLUM OH
41 DAYTN OH
42 TOLED OH
43 YTOUN OH
44 TULSA OK
45 PLANB OR
46 PHILA PN
47 PITTS PN
48 REDDG PN
49 PROVI RI
50 CHATT TN
51 MEMPH TN
52 BALLS TX
53 HOUST TX
54 PASSA TX
55 SANAN TX
56 SALTC UT
57 NFOLK VA
ViH RICHM VA
•~,<> si ATI UA
60 UHAKL WV
MAGE
28.820
2.737
29.700
27 . 700
27.500
26.800
29.600
32.700
31.400
2S.800
34.200
27.800
27.800
31.300
28.400
27.200
29.600
27.700
27.100
29.600
28.600
25.000
28.000
27.000
24.600
30.10O
27.900
28.700
29.300
27.100
29.100
29.500
31.400
26 . 700
27.500
30.700
25.900
25.100
32.400
28.500
28.800
25.400
27.800
28 . 700
31.600
28.700
32.600
30.900
33.400
36.9OO
32.100
31.100
26.100
27.200
26.000
24,400
24 . 8OO
27.700
24.OOO
29. MO
31 .v»0
34.600
IU&U
165.798
23.247
136.604
136.604
128.693
128.693
150.591
157.477
157.477
157.477
157.477
201.869
201.869
201.869
137.765
159.601
189.522
191.140
191.140
191.140
158. 9O7
158.907
146.046
146.046
203.395
203 . 395
182.361
166.384
202.620
202.620
166.797
166.797
164.695
Iti2.560
148.636
148.636
148.636
157.395
152.273
183.177
183.177
183.177
183.177
183.177
183.177
111.392
170.820
147.692
147.692
147.692
191.745
160.097
160.097
171.593
171.593
171.593
171.593
100.734
172.618
172.618
. 143.V3V
181.301
MUUC
162.807
54.226
142.000
80.400
148.500
166.6OO
229.800
186.800.
239.600
149.400
239.600
195*100
327.300
377.300
203.400
159.500
161.400
68.700
141.400
120.300
175.500
105.300
,127.300
111.500
98.9OO
159.500
2O9.100
2O0.400
152.700
125.900
156.800
156.600
144.800
160.100
158.200
101.900
195.400
188.100
250.200
143.400
157.000
186.300
113.500
128.600
128.600
143.400
11)6.200
207. OOO
144.300
112.400
157. OOO
120.700
167.900
154.800
144.500
144.500
119.600
193.600
93.600
, 231.100
185.30O
89.700
-------
Table 4.10
(continued)
1 BIRMG AL
2 HONTG AL
3 PHOEN AZ
4 TUCSN AZ
5 LROCK AK
6 LONGB CA
7 OAKLO CA
8 SANDZ CA
9 SFRAN CA
10 HARTF CT
11 NEUHA CT
12 WATER CT
13 UASHQ DC
14 ATLAN GA
15 CHICA IL
16 ECHI6 IN
17 INDIA IN
18 SBEND IN
1? DESMO 10
20 BUBUQ 10
21 TOPEK KA
22 MICH I KA
23 LEXNG KY
24 LOUIS KY
25 NEUOR LA
26 SALT I MD
27 DETRO MI
28 6DRAP MI
29 MINNE HN
30 KCITY MO
31 STLOU MO
32 OMAHA NB
33 CAMON NJ
34 JCITY NJ
35 WEURK NJ
36 ALfcUQ NM
37 NYORK NY
38 AKRON OH
39 CINNC OH
40 COLUM OH
41 DAYTN OH
42 TOLED OH
43 YTOUN OH
44 TULSA OK
45 PLAND OR
46 PHILA PN
47 PITTS PN
48 REDDG PN
49 PROVI RI
50 CHATT TN
51 HEMPH TN
32 BALLS TX
53 HOUST TX
S4 PASSA TX
SS SANAN TX
56 SALTC UT
57 NFOLK VA
t*H RICHH VA
59 SFATT UA
60 CHARL UV
K NS
O.OZ2
0.013
0.037
0.037
0.027
0.032
0.017
0.013
0.023
0.019
0.027
0.02?
0.015
0.015
O.048
0.034
O.026
0.047
O.017
0.010
0.010
0.018
0.011
6.013
0.026
0.019
0.055
0.017
0.016
0.007
0.010
O.017
0.044
O.013
0.018
0.026
O.640
O.022
0.02V
O.007
O.028
0.010
0.015
0.001
6.011
O.010
0.008
0.013
O.013
0.006
6.010
0.026
0,049
O.028
0.032
O.018
O.062
0.015
0.021
0.018
6.01O
O.012
NONU
0.226
0.154
0.422
0.336
0.067
O.052
0.231
O.O82
0.407
0.111
0.286
0.292
0.274
0.105
0.723
0.516
0.344
0.284
0.184
0.147
0.062
0.003
0.096
0.107
0.174
0.241
0.045
0.470
0.443
0.120
0.064
O.228
0.413
0.106
0.402
0.222
0.560
0.043
0.234
0.178
0.281
0.190
0.309
0.143
0.2S8
0.13V
0.078
. 0.344
0.207 .
O.O68
0.100
0.360
0.392
0.2S8
0.266
0.005
0.086
0.032.
0.302
0.424
0.12A
0.108
1N61-
10762.895
1059.562
8692.000
9933.000
11329.000
9922.000
10438.000
11804.000
11279.000
11664.000
12507.000
10011.000
10444.000
11500.000
12189.000
106SA.OOO
13527.000
10068.000
12260.000
11431.000
11350.000
11274.000
10830.000
10940.000
10033.000
9980.000
10246. OOO
10035.000
11015.000
11242.000
11127.000
11306.000
9268.000
11605.000
8627.000
10285. OOO
8637.000
10926. OOO
11632.898
11152.000
10435.000
10848.000
10329.000
11590.000
9928.000
11642.000
11377.000
10431.000
10536.000
9695 . 000
10208. OOO
8336.000
10104.000
12474.000
11737.000
11822.000
9027.000
10812.000
9236. OOO
1O62O.OOO
12557.000
1O865.000
ELiUC
55.298
7.43V
45.400
51 .600
60.100
63.100
56.500
62.000
66.100
65.300
66.100
59.100
56.80O
49.900
68.500
53.400
53.900
53.600
56.000
S4.2OO
68.000
54.600
64.800
63.200
60.100
46.900
45.800
44.600
52.100T
54 . 000
66.100
6O.100
48.000
62.700
50.600
36.300
55.1OO
66.200
51.800
55.600
48.400
60 « 700
56.200
51 . 700
52.100
58.200
62.90O
50.600
53.4OO
43.300
45.9OO
47.600
49.200
54.800
51.70O
51.700
46.800
68.50O
48.300
47.100
67. BOO
52.800
COLD
86.900
47.654
48.OOO
29.OOO
13.000
22.000
51.000
1.000
7.000
0.0
11.000
147.000
102.OOO
102.000
114.000
45.000
132.OOO
132.000
122.OOO
131.000
151.000
152.000
122.000
122.000
94.000
91.000
13.OOO
90.000
126.000
157.000
167.000
106.000
118.000
144.OOO
89.000
79.000
84.000
122.000
79.000
133.000
100.OOO
114.000
125.000
157.000
150.OOO
82.000
42.OOO
89.000
124.OOO
89.000
128.000
70.000
61.000
34.000
21.000
21.000
23.000
110.OOO
31.006
68.00O
32.OOO
95.OOO
5Q
-------
Table 4J.O
(continue!)
6SFT
16314. OM
V75./4J
1 BIRMG At. 15077.500
2 HONTG AL 15030.398
3 PHOEN AZ 16116.699
4 TUCSH AZ 16054.102
5 LROCK AK 15186.500
& LONGB CA 16079.1 O2
7 OAKLD CA 16030.898
8 SANDI CA 16090.398
9 SFRAN CA 16030.898
10 HARTF CT 18240.500
11 NEUHA CT 18118.801
12 WATER CT 18255.801
13 UASHG DC 16219.500
14 ATLAN GA 15737.398
IS CHICA IL 16404.699
16 ECHIG IN 16295.000
17 INDIA IN 16261.102
18 SPEND IN 16198.398
19 DESMO 10 16244.699
20 DUBUQ 10 16153.102
21 TOPEK KA 16070.801
22 UICHI KA 16040.102
23 LEXNfi KY 15555.602
24 LOUIS. KY 15563.398
25 NEUOR LA 15119.199
26 BALTI HB 15724.500
27 DETRO MI 16419.898
28 GllRAP HI 16266.801
29 HINNE MN 16431.801
30 KCITY HO 16217.199
31 STLOU HO 16175.398
32 OMAHA NB 16177.398
33 CAHDN NJ 17976.199
34 JCITY NJ 18157.500
35 NEWRK NJ 18148.801
36 ALBUQ NH 16052.102
37 NYORK NY 18028.102
38 AKRON OH 16307.500
39 CINNC OH 16160.301
40 COLUM OH 16194.898
41 DAYTN OH 16349.199
42 TOLED OH 16273.801
43 YTOUN OH 16232.6O2
44 TULSA OK 15467.898
45 PL AND OR 16006.199
46 PHILA PN 18187.398
47 PITTS PN 18287.898
48 REDDG PN 18399.699
49 PROVI RI 18237.699
50 CHATT TN 15181.398
51 MEHPH TN 15129.301
52 DALLS TX 15717.000
S3 HOUST TX 15626. SOO
54 PASSA TX 15947.398
55 SANAN TX 15080.699
56 SALTC UT 16013. SOO
57 MFOLK VA 15177. OOO
'^0 klCIIM VA 1U640.6V
5V SEATT UA 1604O.I99
60 CHARL UV 15233.301
XUAK-
123491.313
3618.011
129119.000
128765.000
120959.000
120957.000
129263.000
120519.000
120345.000
120865.000
120345.000
121166.000
120707.000
120882.000
126710.000
128113.000
121525.000
121512.000
121447.000
121453.000
121511.000
121495.000
121291.000
121060.000
128726.000
128982.000
128678.000
128374.000
121501.000
121560.000
121751.000
121345.000
121333.000
121345.000
119345.000
120490.000
121000.000
120684.000
120486.000
121535.000
121335.000
121321.000
121493.000
121546.000
121441.000
129016.000
121115.000
120737.000
12O748.0OO
121050.000
12O54O.OOO
129239.000
128846.000
128359.000
128489.000
128755.000
129045.000
121539.000
128966.000
128727.000
120738.000
127243.000
*»>RO
39844.547
/04.747
39517.699
39264.801
40696.199
40393.500
39630.301
41050.398
41306.898
40788. 8O1
41306.898
40740.000
40348.500
40413.301
40232.000
40143.199
39337.301
39144.000
39100.199
39005.500
39096.000
38978.102
38877.500
38827.102
39981.301
40212.000
39532.602
40248.398
39346. SOO
37075.500
3932?. 000
39047.199
.39030.199
38977.801
39174. SOO
39716.699
406O2.398
40456.801
40287.301
,39152.102
39006.602
39035.602
39215.697
39135.378
39032.500
39758.602
40881.301
40271.677
37778.602
40027.677
37969. OOO
39708.500
39S51.301
40155.177
40134.500
40775.177
37443.677
40771.102
39734.602
40184.697
41333.677
37718.378
51
-------
Table
4.10
(continued.)
1 BIRHG AL
2 MONTG AL
3 PHOEN AZ
A TUCSN AZ
5 LROCK AK
& LONGB CA
7 OAKLD CA
8 SAND I CA
V SFRAN CA
10 HARTF CT
11 NEUHA CT
12 WATER CT
13 UASHG DC
14 ATI. AN 6A
15 CHICA IL
16 ECHIG IN
17 INDIA IN
18 SBEND IN
19 DESHO 10
20 DUBUQ 10
21 TOPEK KA
22 UICHI KA
23 LEXNG KY
24 LOUIS KY
25 NEWOR LA
26 HALT I MD
27 DETRO HI
28 GDRAP HI
29 MINNE MN
30 KCITY HO
31 STLOU HO
32 OHAHA NB
33 CAMDN NJ
34 JCITY NJ
35 NEURK NJ
36 ALBUQ NH
37 NYORK NY
38 AKRON OH
39 CINNC OH
40 COLUM OH
41 DAYTN OH
42 TOLED OH
43 Y TOWN OH
44 TULSA OK
45 PLAND OR
46 PHILA PN
47 PITTS PN
48 REDDG PN
49 PROVI RI
50 CHATT TN
51 HEHPH TN
52 HALLS TX
53 HOUST TX
54 PASSA TX
55 SANAN TX
56 SALTC UT
57 NFOLK VA
SO RICHH VA
59 SEATT UA
60 CHARL HV
NU6V
O.076
O.OH4
Ot 093
0.016
0.08?
0.028
0.012
0.182
O.O53
O.106
O.095
0.077
0.072
0.037
0.069
0.096
0.160
0.086
0.079
O.031
0.033
0.072
O.023
0.064
0.062
0.096
0.061
0.099
0.116
0.090
0.076
0.045
0.135
0.075
0.128
O.065
0.092
O.048
,0.142
0.038
O.O99
0.087
0.057
O.096
0.083
0.033
0.058
O.024
0.113
0.081
0.087
0.042
0.078
O.074
O.105
0.050
0.065
0.060
0.077
o.oaa
0.095
O.O92
Pft70
102.300
30.107
138.000
91,000
117.000
104.000
71.000
102.000
69.OOO
88.000
52.000
67,000
100.000
95.000
99 .000
88.000
58.000
189.000
96.000
99.000
134.000
194.000
.97.000
95.000
71.000
117.000
79.000
136.000
128.000
77.000
88.000
84.000
120.000
132.000
114.000
108.000
111.000
102.000
109.000
68 .,000
95.000
97.OOO
102.000
111.000
134.000
110.000
60.000
144.000
137.000
121.000
93.000
127.OOO
86.000
105.000
90.000
80.000
58.000
88.000
83.000
UV.OOO
58.000
183.OOO
SO70
26.917
22.197
10.000
7.000
9.000
7.000
8.000
35.000
10.000
10.000
9.000
57,000
40.OOO
17.OOO
28.OOO
20.OOO
73.OOO
87.000
Sl.OOO
1O.OOO
11.000
16.OOO
8.000
6.OOO
12.0OO
23.000
7.000
54.OOO
38.000
13.000
38.0OO
6.OOO
42.000
12.000
69.OOO
75.000
37.00O
6.000
45.0OO
70.000
18.000
22.0OO
25.000
13.OOO.
30.0OO
8.000
14.0OO
78.000
57.0OO
30.0OO
67.000
is.ooo
17.0OO
7.OOO
10.OOO
9.0OO
8.000
. 9.0OO
26.00O
24.00O
22.0OO
27.0OO
52
-------
have most previous investigators) some unknown contribution from these pol-
lutants may be included in estimated coefficients on N0?, S0_, and partic-
"ulates. i
A complete correlation matrix for our choice of included variables is
presented in Table 4.9 with the exception of the doctors per capita variable
-for which we use two-stage least squares. Several interesting collinearity
issues are apparent here as well, not necessarily as a multicollinearity
problem since the highest simple correlation is 0.66 within the data set,
but rather as an indication of problems of exclusion of variables in previous
studies. For example, S02 (S070) shows a correlation of 0.59 with animal
fat consumption (6SFT) and a correlation of 0.23 with cigarette consumption.
In other words, air pollution as measured by S0? might not be orthogonal
with respect to diet and smoking. The implication is that diet and smoking
probably must be included to obtain unbiased estimates of the effect of S0«
on human health.
The final data set used in the analysis is presented is its entirely in
Table 4.10. [Qualified investigators wishing to know about the additional
data collected may obtain a complete listing by contacting the authors].
4.5 Empirical Analysis
The first step in estimating the model of human health we have specified
is to attempt to account for human adjustments to disease in the form of
medical care (doctors per capita). Thus, we first estimate a reduced form
equation which has as the dependent variable doctors per capita and as
independent, exogenous explanatory variables: median age, % non-white,
density, cold, per capita consumption of cigarettes, protein, carbohydrates,
and animal fat (all exogenous variables from the dose response function);
as well as per capita income and education level (exogenous variables in
the determination of the demand for doctors). This estimated equation is
shown in Table 4.12 below.
Note that we have chosen Iinear4 specifications throughout the analysis.
The linear form has several advantages. First, the entire modeling frame-
work can be interpreted as providing a set of first-order approximations
of the slopes (the effects) of the variables in the model. As a linear
approximate system, the estimated effects, if unbiased, only hold true for
the neighborhood of the estimate — that is for values of the variables
near the means of our sample. Since we do not know the precise form (pre-
sumably nonlinear) which our functions take, we are at least not implying
more about our knowledge of effects than the data can support. However, if
significant nonlinearities do exist over the range of the data in our sample
(and some of the estimated effects seem to imply this), then we have intro-
duced a specification error by choosing linear estimates.
The second step in our analysis, then, is to generate, from the estimated
reduced form equation and from data on exogenous variables in the model,
an estimated doctors per capita variable (DOCK) to replace actual data on
doctors per capita(MDOC) in the estimation of specific dose-response
functions. Table 4.11 summarizes our results, while Tables 4.13-4.22 give
53
-------
Table 4JL1
Summary of TVo-Stage Linear Estimates of Factors in Human Mortality
Hypotheses not Rejected at the 97.5% Confidence Level
(One-tailed t-test, t >. 2.0)
Variable
(Sign of Hypothetical
Effect)
Doctors/Capita* (-)
Median Age (+)
2 Nonwhite (•*•)
Cigarettes (+)
Room Density (+)
Cold (+)
Animal Fat (+)
Protein (+)
Carbohydrates (?)
Particulates (+)
R2
Total
Mortality
Rate
_
+
4
+
•f
+
+
.82
Vascular
Disease
_
+
+
.60
Heart
Disease
_ *
•f
+
•f
+
.77
Pneumonia
and
Influenza
4-
+
+
+
.54
Emphysema
and
Jronchitis
_
•f
^
.39
Cirrhosis
+
+
+
.64
*
Kidney
Disease
_
+
+
+
.54
Congenital
Birth
Defects
.22
Early
Infant
Diseases
+
+ .
.55
Cancer
.
+
+
+
+
+
.86
* Two-stage estimator employed.
-------
individual linear estimated dose-response functions where the first equation
reported excludes the air quality variables and the second (for comparison)
includes these variables. Note that the basic model actually excludes air
quality. This reflects the approach taken; to first develop a model of
human health based on variables which are hypothesized to have large effects
— age, medical care, smoking, diet, etc. Once a basic model of satisfac-
tory explanatory power is specified, it then may be appropriate to test
for variables such as air pollution which are hypothesized to have small
effects.
We choose a 97.5% confidence level (t > 2.0) for the entire analysis.
It should be noted that if actual doctors per capita are employed, the
variable is highly nonsignificant both when used in total mortality or
when used in any of the component diseases. However, as indicated in our
summary of results shown in Table 4.11 the estimated two-stage doctors per
capita variable is highly significant and has a uniform negative effect on
mortality rates in total mortality, vascular disease, heart disease,
emphysema and bronchitis, kidney disease, and cancer. We conclude, then,
from a properly structured hypothesis test, that we cannot reject the
hypothesis that medical care has a. highly important effect on human mortal-
ity.
Both the median age and % nonwhite variables are widely significant
across the estimated equations and show up with uniformly positive effects
on mortality rates.
Cigarette consumption shows significant positive partial correlations
with total mortality, vascular disease, heart disease and cancer, while
room density and cold both show significant positive partial correlations
with total mortality and pneumonia and influenza. Room density also shows
significant positive correlations for cirrhosis and kidney disease.
The dietary variables show significance in total mortality, heart
disease, and cancer — correlations between heart disease and saturated fats
and between cancer and meat consumption (note the positive association for
protein) have long been recognized — as well as in emphysema and bron-
chitis.
Again, however, it must be stressed, especially for the dietary variables,
that collinearity abounds and the estimated effect may really not be re-
lated to the specified variable but to a highly collinear one. Similarly,
an estimated effect may include the sum of the effects of several collinear
variables. In other words, causality is not established by correlation.
However, we cannot reject the hypotheses that doctors, cigarettes, and diet
are all highly important in determining human mortality rates. Unfor-
tunately, these variables have typically been excluded from previous aggre-
gate epidemiological studies [Schwing, et. al. (1974) do, however, include
a smoking variable].
Turning to the air quality variables, only two significant partial cor-
relations appear — between particulates and the pneumonia and influenza
variable, and between SO and the early infant disease variable. The lat-
ter of these effects is consistent with the work of Lave and Seskin (1977).
55
-------
Table 4.12
Reduced Form •Equation
MDOC 55 -- 10 11 13 14 21 24 54 25 27 41
VAR
X10-NONW
Xll-MAGE
X13-IN69
X14-EDUC
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
B
50.447
1.3513
0.61649D-02
1.9399
161.53
-0.12806
0.45771
0.22302D-01
0.22804D-02
0.24002D-01
-1691.3
1*1020
0.50439
0*86708
1*3418
0*26107
-0.53850
1*4919
1*4136
0*72804
1.9402
-2*7124
R-SQUARE= 0.3877
SSR= 0.1062D+06
DF= 49
56
-------
Table 4.13
Total Mortality
M070
1 — 61 10 11 21 24 54 25 27 41
VAR
X61-DQCH
X10-NONU
Xll-MAGE
X21-BENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SQUARE= 0,8195
SSR= 49,74
B
-0.53Q31D-01
5,6092
0.66172
31,910
0,14370D-01
0.21896D-01
0.19325D-02
-0.82907D-04
0»36251D-03
-78,675
DF= 50
-4*7501
5,0448
12.360
2,4494
3,1093
3,0758
3,7525
-1,5347
1.5938
-3,7169
M070
1 -- 61 10 11 21 24 54 25 27 41 31 57 60
VAR
X61-DOCH
X10-NONU
Xll-MAGE
X21-BENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-S070
X60-PA70
CONSTANT
R-SQUARE= 0.8205
SSR= 49.48
B
-0.52797D-01
5,6276
0,65893
31.772
0.14436D-01
0.21968D-01
0.19196D-02
-0,7943111-04
0.39783D-03
1.6457
-0.31302D-02
0.10744D-02
-79,296
DF= 47
-4,3493
4.5620
11.540
2.3469
2.9089
2.8120
3.5522
-1.3612
1,4508
0,35799
-0.34850
0,20059
-3,5115
57
-------
Table 4.14
Vascular Disease
VA70 2 -- 61 10 11 21 24 54 25 27 41
VAR 6
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SGUARE*
SSR=
0*5657
3.998
-0.70223D-02
0*37954
0.10936
1*7016
0.17695D-02
0*30001D-02
0.18542D-03
-0.13460D-04
-0.84316D-04
-5»5672
DF= 50
-2.2186
1.2040
7.2050
0.46071
1.3504
1.4865
1*2699
-0.87885
-1.3075
-0.92769
VA70
61 10 11 21 24 54 25 27 41 31 57 60
MAR
X61-DOCH
X10-NQNW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-S070
X60-PA70
CONSTANT
R-SOUARE= 0.6022
SSR— 3.663
B
-0.88088D-02
0*63816
0*11671
2.7540
0.20961D-02
0.42167D-02
0.23976D-03
-0.17117D-04
-0*18874D-04
-0,86198
-0*38911D-02
-0.63071D-03
-8*3456
-2.6671
1.9014
7.5127
0*74768
1.5524
1.9838
1.6306
-1*0781
-0.25297
-0*68915
-1.5922
-0,43278
' -1.3583
DF= 47
58
-------
Table 4.15
Heart Disease
HA70
3 — 61 10 11 21 24 54 25 27 41
VAR
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SQUARE= 0.7517
SSR= 17.03
B
-0.22340D-01
1.7509
0.29627
9*3338
0.43566D-02
0.13129D-01
O.66878D-03
-0.17969D-04
0.42380D-03
-35.183
DF= 50
-3.4204
2.6917
9.4592
1.2247
1.6113
3.1525
2.2197
-0.56857
3.1849
-2.8412
HA70 3—61 10 11 21 24 54 25 27 41 31 57 60
VAR B T
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-S070
X60-PA70
CONSTANT
R-SQUARE=
SSR=
0.7737
15.51
-0.19800D-01
1.3603
0.28122
7.4177
0.43300D-02
0.10868D-01
0.57165D-03
-0.22071D-05
0.39645D-03
4*8498
0.82843D-03
0.14052D-02
-32.823
DF= 47
-2.9132
1.9694
8*7965
0*97861
1.5583
2.4847
1.8893
-0.67551D-01
2,5822
1.8842
0.16473
0.46855
-2.5960
59
-------
Table 4.16
Pneumonia and Influenza
PN70 4—61 10 11 21 24 54 25 27 41
VAR B
X61-DOCH
X10-NONU
Xll-hAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SQUARE*
SSR=
0*4108
0*4556
-0.129250-02
0,18381
0.199200-01
2*9692
0,130300-02
0*615240-03
0.706540-04
-0*113290-05
0.380100-05
-3*0478
DF= 50
-1*2098
1*7274
3*8880
2*3816
2*9460
0*90310
1*4336
-0*21914
0*17462
-1*5046
PN70 4 — 61 10 11 21 24 54 25 27 41 31 57 60
VAR B T
X61-DOCH
X10-NONU
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
^(57-3070
X60-PA70
CONSTANT
R-SQUARE*
SSR=
0.5409
0*3550
-0.381150-03
0*13820
0.16194D-01
2.6677
0*104280-02
0.618160-03
0.460480-04
•0*1I0027D-05
•0.492610-05
0.55215
'0*477190-03
0*142720-02
-2.1183
DF= 47
-0.37068
1*3226
3*3484
2*3264
2*4807
0*93415
1*0060
-0*20286
-0.21208
1.4180
-X). 62722
3.1456
-1.1075
60
-------
Table .4.17
Emphyseaa•and Bronchitis
EM70 5 ~ 61 10 11 21 24 54 25 27 41
VAR B
X61-DOCH
X10-NONU
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SQUARE= 0*3559
SSR= 0*1331
-0.13851D-02
0.225330-01
0.494510-02
0.921060-01
0.189960-03
0.53419D-04
0.652610-04
-0«95199D-05
-0»17700D-04
-0*90721
-2*3989
0.39184
1*7859
0.13670
0.79468
0.14509
2*4502
-3*4072
-1.5046
-0.82870
50
EM70 5— 61 10 11 21 24 54 25 27 41 31 57 60
VAR B T
X61-DOCH
X10-NONW
XI1-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-S070
X60-PA70
CONSTANT
R-SQUARE:
SSR=
0.3876
0*1265
-0.13761D-02
0*46333D-01
0.51065D-02
0*17013
0.14392D-03
0.24382D-03
0*666870-04
-0*10427D-04
-0*138680-04
-0.11515
-0.473200-03
0.291150-03
-0.96354
DF= 47
-2.2419
0.74278
1.7687
0.24853
0.57352
0.61719
2.4404
-3.5335
-1.0001
-0.49533
-1.0419
1.0750
-0.84382
61
-------
Table 4.18
Cirrhosis
CI70 6 — 61 10 11 21 24 54 25 27 41
MAR B
X61-DOCH
X10-NONU
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SQUARE=
0*6258
0*2479
0.51923D-04
0*22721
0.17323D-01
2*1612
0*52436D-03
0.61784D-03
0.73982D-04
-0.77437D-05
-0*11197D-04
-2*3252
DF= 50
0*65875D-01
2*8943
4*5831
2*3497
1*6070
1,2293
2.0347
-2*0303
-0.69726
-1,5559
CI70 6 — 61 10 11 21 24 54 25 27 41 31 57 60
VAR B T
X61-DOCH
X10-NONU
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-S070
X60-PA70
CONSTANT
R-SQUARE= 0.6399
SSR= 0.2387
0.31818D-03
0*18469
0.16077D-01
1.9819
0.49340D-03
0»39600D-03
0.65122D-04
-0.67906D-05
-0»19734D-04
0.24209
0.51883D-03
0.69311D-04
-1.9446
DF= 47
0.37741
2*1558
4.0543
2.1080
1*4315
0.72987
1.7351
-1.6755
-1.0362
Ot75825
0.83173
0*18632
-1*2399
62
-------
Table 4.19
Kidney Disease
NE70
7 — 61 10 11 21 24 54 25 27 41
VAR
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
B
-0*673020-03
0*906610-01
0*341100-02
0.75879
0*732890-04
0,101320-03
0*157230-04
0*473490-07
0*637240-05
-0*72766
R-SQUARE= 0*5419
SSR= 0.20310-01
-2*9834
4*0353
3*1531
2*8825
0.78479
0*70439
1*5110
0*433760-01
1 * 3866
-1*7013
DF= 50
NE70 7 — 61 10 11 21 24 54 25 27 41 31 57 60
VAR B T
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-S070
X60-PA70
CONSTANT
-0,55265D-03
0.798290-01
0*308510-02
0.71889
0.290750-04
0*802860-04
0,129950-04
-0.207210-06
0.121120-05
-0*666090-01
0.269560-03
0*976470-04
-0*51502
-2.3310
3.3i34
2.7665
2.7189
0.29997
0,52619
1.2312
-0.18181
0.22615
-0.7418&
1*5366
0.93342
-1*1677
R-SQUARE= 0*5743
SSR= 0*18870-01
DF= 47
63
-------
Table 4.20
Congenital Birth Defects
C\B%
8— 61 10-11 21 24 54 25 27 41
VAR
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLO
X54-rCI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SQUARE= 0.1867
SSR= 0.5277
B
-0.110090-02
-0*10484
0*902120-02
0*51667
0*413580-03
0.11415D-02
0*32274D-04
-0*15016D-06
0«15405D-04
-1*3390
DF= 50
-0*95740
-0.91545
1.6360
0*38505
0.86881
1.5569
0.60844
-0.26987D-01
0.65758
-0.61416
C\BX 8 ~ 61 10 11 21 24 54 25 27 41 31 57 60
VAR B T
X61-DOCH
X10-NONU
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-S070
X60-PA70
CONSTANT
R-SQUARE;
0*2205
0.5058
-0.10806D-02
-0.62417D-01
0.96362D-02
0*68174
0^299080-03
0.150990-02
0.361360-04
-0.252840-05
0.168330-04
-0.47663
-0*449660-03
0*468200-03
-1*3072
DF= 47
-0.88051
-0.50047
1*6693
0*49810
0,59609
1*9116
0*66141
-0,42856
0*60717
-1.0255
-0.49518
0.86461
-0.57256
64
-------
Table 4.21
Early Infant Diseases
I\B% 9 — 61 10 11 21 24 54 25 27 41
VAR B
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SQUARE= 0.4741
SSR= 3.439
0.39159D-03
0.89283
-0.44748D-02
5.8110
0.35758D-03
-0.13312D-02
-0.10427D-03
0.17641D-04
0.15367D-03
0.68864
DF= 50
0.13339
3.0537
-0.31786
1.6964
0.29424
-0.71117
-0.76995
1.2419
2.5695
0.12373
I-NBX
9 — 61 10 11 21 24 54 25 27 41 31 57 60
VAR
X61-DOCH
X10-N8NW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-S070
X60-PA70
CONSTANT
R-SQUARE= 0.5484
SSR= 2.954
B
0.21825D-02
0.77575
-0.79126D-02
5.4464
-0.47371D-03
-0.12146D-02
-0.13747D-03
0.98932D-05
0.67486D-04
-2.0458
0.43841D-02
0.17731D-02
4.1264
DF= 47
0.73588
2.5739
-0.56722
1.6467
-0.39069
-0.63634
-1.0412
0.69390
1.0073
-1.8215
1.9978
1.3549
0.74792
65
-------
Table 4.22
Cancel
CA70 53 — 61 10 11 21 24 54 25 27 41
VAR
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
CONSTANT
R-SQUARE- 0.8556
SSR= 1.378
B
-0.71271D-02
0*63382
0*13235
3.9772
0.17859D-02
0.50032D-02
0.210380-03
-0.13166D-04
0.51683D-04
-9.5112
DF= 50
-3.8356
3.4249
14.854
1.8342
2*3216
4.2228
2.4545
-1.4643
1.3652
-2.6997
CA70 53 —61 10 11 21 24 54 25 27 41 31 57 60
VAR B T
X61-DOCH
X10-NONW
Xll-MAGE
X21-DENS
X24-COLD
X54-CI68
X25-XPRO
X27-XCAR
X41-6SFT
X31-N069
X57-SO70
X60-PA70
CONSTANT
R-SQUARE^
SSR=
0.8560
1.374
-0.70763D-02
0.64712
0.13242
4.0247
0.17298D-02
0.51394D-02
0.21071D-03
-0.14074D-04
0.51447D-04
•0.16472
-0.16143D-03
0.23494D-03
-9.4472
DF= 47
-3.4976
3.1475
13.915
1.7837
2.0913
3.9471
2*3394
-1.4471
1.1257
-0.21498
-0.10784
0.26317
-2.5101
66
-------
However, differences between our estimated air pollution effects as opposed
to the Lave and Seskin (1977) work are profound. Lave and Seskin (1977)
did not find a significant association between particulates and pneumonia.
More importantly, Lave and Seskin 0-977) found positive associations
between air quality (specifically sulfate) and a cardiovascular disease
mortality variable and between air quality and cancer mortality. Whether
we use SO. or 'the highly collinear sulfate measure, we cannot accept the
hypotheses that air pollution has any association with heart and vascular
disease or with cancer mortality. Further, our estimated total effects of
air pollution on human mortality are about one order of magnitude smaller
than those shown by Lave and Seskin (1977).
We can summarize the results of our analysis as follows. When we
increase each of thfe following significant variables by one percent over
their mean values in our sample, from the estimated total mortality equation
the following percentage change in mean total mortality rate results: (1)
for doctors per capita a 0.76 percent decline in mortality rate; (2) for
per capita cigarette consumption a 0.32 percent Increase in mortality rate;
and (3) for per capita protein consumption a 6.7 percent increase in mor-
tality rate. These results suggest several observations. First, medical
care, smoking, and diet appear to be enormously important factors in human
health. Second, if one looks to a 100% decrease from mean levels for these
variables, i.e., the impact on average total mortality of setting these
variables to zero, one obtains a 76% increase in mortality for a zero level
of doctors per capita, a 32% decrease in mortality for no smoking and a
670% decrease in mortality for no protein in diet. Obviously, the last of
these effects is impossible and suggests that we may only have linear
approximations of highly non-linear effects. Further, some protein is
required to sustain life. Thus, the estimates of mortality effects are
likely to be valid only for relatively small changes in explanatory variables.
Finally, the air pollution variables are insignificant in the total mor-
tality equation — as one might suspect if air pollution has only a small
effect on mortality rates. This is verified by the fact that the signi-
ficant estimated effects of particulates on pneumonia and influenze, and of
S0_ on infant diseases are very small in terms of total mortality as com-
pared to the effects of doctors, smoking, and diet.
Given'these results, it is important to test the sensitivity of the
model to changes in specification of included variables and structure. Two
alternative formulations have been specified and_tested. First, a version
of the model which: (1) uses lagged diet (1955 dietary variable) as op-
posed to 1965 diet); (2) employs a two-stage doctors per capita variable
which includes air pollution in the reduced form equation; and (3) adds
lead and sulfate to the air pollution variables, produces essentially iden-
tical results both for the impact of medical care and air pollution on
mortality. Sulfate air pollution is statistically insignificant across all
diseases. The second alternative formulation is identical to the one
presented in detail above but the air pollution variables are again included
in the reduced form equation for doctors per capita. The results are con-
sistent for the effect of medical care and for the positive associations
between sulfur oxides and infant diseases and for particulates and pneumonia.
More interesting, however, is a significant negative association which
67
-------
appears between doctors per capita and air pollution.in the reduced form
equation. It appears that doctors may choose riot to live in polluted
cities (perhaps for aesthetic reasons). If this is the case, one can easily
explain false positive associations Between air pollution and mortality
where medical care is excluded as an explanatory variable. If doctors
avoid polluted cities, and if doctors do reduce mortality rates, then
pollution could well be associated with higher mortality rates; but not
because of any direct health effect of air pollution on mortality. Rather,
failure to account for the locational decisions of doctors (supply and de-
mand for medical care) may well bias estimated epidemiological relationships.
In fact, the negative association between doctors per-capita and pollution
is so strong, that when pollution is included in the reduced form equation
for doctors, the estimated doctors variable used in the two-stage procedure
becomes collinear with the pollution variables. This collinearity in some
cases produced negative coefficients on the pollution variables in estimated
dose-response relationships for some disease categories where pollution is
used in the reduced form equation for docotrs per capita. Thus, it is
important that, in spite of this collinearity, stable positive associations
are retained between pneumonia and influenza and particulates and between
infant diseases and sulfur oxides. The inclusion or exclusion of air quality
from the reduced form equation has little impact on the conclusions of this
study. In part, this occurs because air pollution is collinear with diet.
In fact, saturated fats and sulfur oxides are reasonable proxy variables for
each other. It has been shown by McCarthy (1971) that the exogenous
variables which are collinear with included exogenous variables may be
excluded from estimated reduced forms with little loss in consistency in a
two-stage least squares procedure.
Another important question for analysis is the possibility that hetero-
skedasticity is present. At this point, we have only examined one disease
category — cancer mortality — for this problem. An examination of the
residuals plotted against several important explanatory variables (age, for
example) showed no evidence of heteroskedasticity.
Finally, in interpreting the results, it should be observed that the
associations we have found between mortality and air pollution are princi-
pally for diesases of the very young and very old — particularly susceptible
.groups within the population. Further, these effects are those which one
would perhaps associate with short-term as opposed to long-term air pol-
lution exposures. It may well be that aggregate epidemiology may be in-
capable of revealing the long-term consequences of air pollution exposures.
Two problems are particularly significant here. First, lagged data or
data on air pollution histories is not available for such studies. Second,
it is nearly impossible to control for population mobility in such studies.
Thus, even if one accepts the hypothesis that air pollution levels show
enough persistence over time to reveal long-term effects, population mobil-
ity will still distort and confound attempts at estimating such effects.
A partial remedy for these problems is, of course, to use data on individ-
uals as opposed to aggregate data. The next chapter provides a preliminary
exploration of just such a data set.
We now turn to an economic evaluation of the value of air pollution
control in reducing mortality based on the value of safety approach described
68
-------
Table 4.23
Methodology for Health Benefits Assessment
Benefits = (Population at Risk) x (Value of Safety) x
(Reduction in Health Risk)
Value of Safety Based on Consumer's Willingness to Pay
Low estimate: $340,000
Source: Thaler & Rosen (1975)
High Estimate: $1,000,000
Source: Robert Smith (1974)
69
-------
above.
4.6 A Tentative Estimate of The Value of Safety from Alt Pollution Control
Given all of the caveats discussed above concerning the validity of
the estimated effects of air pollution on mortality, it is possible to con-
struct benefit measures using the methodology outlined in Section 4.2
above. The methodology is briefly summarized in Table 4.23.
First, to obtain national estimates, we must know the population at
risk. Since our sixty-city sample is entirely urban, and since air pol-
lution is principally an urban problem we will use a population risk for
1970 of 150 million urban dwellers. As a range for the value of safety,
we will employ Thaler and Rosen's (1975) estimate of $340,000 (in 1978
dollars) as a lower bound and Smith's (1974) estimate of $1,000,000 (in
1978 dollars) as an upper bound. Finally, to provide an estimate of re-
duced risk from air pollution control, we will assume an average 60% reduc-
tion in ambient urban concentrations both for SO. and participates. Then,
using the mean concentration of these pollutants in our sixty-city sample
as a basis for calculation, we can derive the average reduction in risk of
pneumonia mortality for a 60% reduction in participates and the average
reduction in risk of infant diseases for a 60% reduction in SO- from our
estimated dose response functions for these diseases.
Multiplying the population at risk by the assumed value of safety, and
then by the average reduction in risk, gives a crude approximation of the
benefits for a 60% reduction in national urban ambient concentrations of
particulates and SO., respectively. National urban totals and the value of
the average individual risk reduction are shown in Table 4.24.
The value estimates as shown in Table 4.24 agree surprisingly well with
those developed by Lave and Seskin (1977) for national air pollution damages.
However, the dollar value is similar only because we use a range for the
value of safety (derived from observed market behavior of consumers) which
is about an order of magnitude larger than the "value of life" figure based
on lost earnings which is employed by Lave and Seskin (1977). We, of course,
reject the value of life notion, instead focusing on the measurable concept
of value of safety. Since there is no evidence to suggest that society
puts less value on safety for children, the aged or women than on employed
heads of households, we feel that the best measures available now for the
value of safety should be employed for all individuals. Eventually, more
refined measures of the value that different individuals place on safety
may become available. However, for the time being, these are the best
valuations of the social worth of safety we can employ.
70
-------
Table 4.24
Urban Benefits from Reduced Mortality: Value
of Safety for 60% Air Pollution Control
Disease
Pneumonia
Early Infant
Disease
Total
Pollutant
Particulates
Average Individual
Safety Benefit
(1978 Dollars/Year)
29 - 92
5-14
34 - 106
National
Urban Benefits
(1978 Billion Dollars/Year)
4.4 - 13.7
.7 - 2.2
5.1 - 15.9
71
-------
CHAPTER V
THE MICHIGAN SURVEY EXPERIMENT
5.1 Objectives of the Experiment
The data set employed in, this-chapter refers to the health status and
the tine and budget allocations of each of several thousand household heads
over a nine-year period. Its highly disaggregated form therefore avoids
many of the estimation problems associated with the aggregate data used in
Chapter IV. This avoidance is not our only purpose, however. The richness
of detail in the data set allows us to extend the range of phenomena that
we study. Most important, we are able to investigate the morbidity effects
of air pollution, considering acute effects and chronic effects separately.
The detail of the data set allows us to identify much more readily those
variables that are not current determinants of health status, thus providing
a means of avoiding the simultaneity problems that plagued the aggregate
dose-response functions 6f the previous chapter. It is important to note
that the results reported here reflect a preliminary attempt to evaluate the
usefulness of Michigan Survey Data in estimating morbidity (sickness) effects
of air pollution and consequent economic losses. As a result of the
preliminary nature of the research, many highly desirable transformations of
the variables as defined in the Michigan Survey Data set have not yet been
made. However, in spite of the preliminary nature of the results they
do represent the first attempt to qualify the economic losses due to morbidit
as opposed to mortality resulting from air pollution.
With the richness of the data available to us, we need not terminate
our efforts after having estimated a set of dose-response expressions for
the morbidity effects of air- pollution. We are able to ascertain the labor
productivity effects and the impact on willingness to pay to avoid chronic
and/or acute illness as well. Both of these additional efforts are under-
taken in this chapter.
5.2 The Sample and the Variables
Cur analysis is based on yearly interviews conducted by the University
of Michigan's Survey Research Center with a nationwide random sample of
4,802 to 5,862 families from 1968 through 1976. No families with living
members were ever intentionally deleted from the sample, and, as families
broke apart, the adult components were added to the sample as distinct
families. The cumulative interview response rate over the nine-year period
declined from 76 percent in the 1968 and first interview year to 55 percent
72
-------
in the 19.76 interview year, implying an average yearly reinterview response
rate of nearly 95 percent. From 1970 through. 1976, this yearly response
rate averaged 97 percent. Of special interest to us is that, in addition
to substantial detail on household head time and budget allocations, the
sample contains generalized measures of the head's health states as well
as information, on lifestyle and biological and social endowment variables
that might plausibly contribute to the health states.
Information from the interview has been combined with data on a limited
set of environmental variables, particularly information on air pollution
concentrations, to establish imperfect measures of the environment in which
each family head has lived during the nine-year period. To the best of our
knowledge, the Survey Research Center data set is the only one currently
available that combines, for the same set of individuals over a substantial
number of years, information on places of residence, states-of-health, and
time and budget allocations. The sample thus raises the prospect of our
being able to value, through empirical applications of the economic theory
of consumer behavior, the contributions of environmental pollution exposures
to states-of-health.
The major characteristics of our sample and the variables we employ in
our empirical efforts are presented in Tables 5.1 and 5.2. All variables
refer to household heads. Table 5.1 gives complete definitions of variables,
their scalings, and their assigned acronyms; Table 5.2 provides representa-
tive arithmetic means and standard deviations of variables used. Because
we employ various partitions of the sample throughout the chapter, we do not
use the Survey Research Center sample weights. Our samples are therefore
not entirely representative of the national population.
In Table 5.2a, so as not to make worse the already considerable and
cumbersome length of the listing, only the two health variables, LDSA and
ACUT, are listed as dependent variables. The geometric means of the air
pollution variables have their means- and standard deviations entered for
the various sample partitionings indicated at the bottom of the table.
The means and standard deviations for the other variables are listed in
Table 5.2b. This latter table refers only to the samples used for the
chronic illness expressions, while the former refers to the acute illness
expressions. Whether reference is to the partitioned or unpartitioned
samples, the means and standard deviations represent only those samples
used to estimate dose-response functions involving geometric mean measures
of the air pollution variables. All estimates employing different combina-
tions of variables, whatever the combination might be, were established
using a random drawing from the entire Survey Research Center population
sample for a particular year. Therefore, the means and standard deviations
listed in Table 5.2, although extremely representative, are not the exact
values for each of the samples used in the estimation effort.
The definition and measurement of most of the variables listed in
Tables 5.1 and 5.2 is standard, and we shall comment here only on those that
pose definitional and measurement problems for the major focus of this
"report. This criterion immediately directs attention to the air pollution
variables.
73
-------
Table 5.1
Complete Variable Definitions
Health State Variables
Acute illness (ACUT) — workdays ill times 16 for the first 8 weeks
and times 12 thereafter. Only individuals who are currently
employed or unemployed and looking for work could have positive
values for this variable.
Degree of disability (DSAB) — complete limitation on work = 1;
severe limitation on work = 2; some limitation on work = 3;
otherwise =0.
Length of disability (LDSA) — <^ 2 years = 1; 2-4 years = 2;
5-7 years = 3; ^ 8 years = 4; otherwise = 0. This is a
follow-up question to inquiries about whether the respondent
has any physical or nervous condition that limits the amount
or kind of work or housework he can do.
Biological and Social Endowment Variables
Age of family head in years CAGEH)
Grew up in city CCITY) = 1; otherwise = 0. This variable, as
transformed, is binary.
Education attainment (EDUC) — 6-8 grades =2; 9-11 grades =3;
12 grades = 4; 12 grades plus non-academic training - 5; college,
no degree - 6; college degree = 7; advanced or professional
degree = 8; otherwise =1.
Father's educational attainment (FEDU) — same scaling as for EDUC.
Family size in number of persons in housing unit (FMSZ).
Length of present employment (LOCC) — <_ 1 year = 1; 12 - 19 months
= 2; 1-1/2 - 3-1/2 years = 3; 3-1/2 - 9-1/2 years = 4;
9-1/2 - 19-1/2 years = 5; >^19-1/2 years « 6; otherwise = 0.
Marital status (MARR) — married • 1; otherwise = 0. This variable, as
transformed, is binary.
Income level of parents (POOR) — poor = 1; otherwise = 0. This
question asked whether the respondent's parents were "... poor
when you were growing up, pretty well off, or what?" The
variable, as transformed, is binary.
Race of family head (RACE) — white » 1; otherwise - Q. This variable,
as transformed, is binary.
Sex of family head CSEXH) — male - 1; otherwise - 0. This variable,
as transformed, is binary.
Member of a labor union (UION) — Yes = 1; otherwise » 0. This
variable, as transformed, is binary.
Life Style Variables
Practices absenteeism from work (ABSN) — absent once or more a week
from work = 1; otherwise = 0. This refers to a question in which
the respondent is asked if there are times when he doesn't go
to work at all, even if he isn't sick. The variable, as
transformed, is binary.
74
-------
Table 5.1
(continued)
Frequency of church attendance (CHCH) — once a week or more = 1;
otherwise = 0. This variable, as transformed, is binary.
Annual family expenditures on cigarettes in dollars (CIGE) — this
variable is not indexed for differences in prices among locales.
Participates in energetic activities (EXER) — first mention = 1;
otherwise = 0. This question asks the family head what he
usually does in his spare time. Energetic activities include
fishing, bowling, tennis, camping, travel, hunting, dancing,
motorcycling, etc.
Family food consumption relative to food needs standard in percent
CFOOD) — family food consumption refers to food expenditures in
dollars and includes amounts spent in the home, school, work,
and restaurants, as well as the amount saved in dollars by
eating at work or school, raising, canning or freezing food,
using food stamps, and receiving free food. The food needs
standard is in dollars and is based on USDA Low Cost Plan
estimates of weekly food costs as published in the March 1967
issue of the Family Economics Review. The standard itself is
calculated by multiplying the aforementioned weekly food needs
by 52 and making a series of adjustments according to the size
of the family.
Is often late to work (LTWK) — late once or more a week to work = 1;
otherwise = 0. This question asks the respondent if there are
times when he is late getting to work. The variable, as
transformed, is binary.
Daily number of cigarettes smoked per adult family member (NCIG) —
£3 = 1; 3-17-2; 18 - 22 = 3; 23 - 35 = 4; 2-3 packs = 5;
>_ 4 packs = 6; otherwise = 0.
Fundamentalist religious preference (RELG) — Mormon, United Church
of Christ, Disciples of Christ, Quaker, etc. = 1; otherwise = 0.
This variable, as transformed, is binary.
Degree of risk aversion (RISK) — a weighted index devised by the
survey team in which the individual's degree of risk aversion
increases if he drives the newest car in good condition, does
not own a car, has all cars insured, uses seat belts, has
medical insurance, smokes less than a pack a day, has some liquid
savings, and has more than two month's income saved. Nine is the
greatest degree of risk aversion that can be exhibited.
Head's annual hours working for money (WORK).
Precuniary Variables
Cost-of-living in 1970 country of residence (BDALO) — an index of
comparative costs for a four-person family living in various
areas as published by the U.S. Bureau of Labor Statistics in the
Spring 1967 issue of Three Standards of Living for an Urban
Family of Four Persons. The lowest living standard was employed.
This index is published for the thirty-nine largest SMSA's and by
region for the nonmetropolitan areas. For the remaining SMSA's,
the regional average of the metropolitan indices was used.
75
-------
Table 5.1
(continued)
Has hospital or medical insurance (INSR) — Yes = 1; otherwise * 0.
This variable, as transformed, is binary.
Family income in dollars not due to current work effort (ICTR) — this
variable includes assorted welfare payments, pensions, and
annuities, as well as earnings from assets.
Family net real income in dollars (RING) — this variable is the sum of
money income plus value of goods and services received at less
than market prices less the cost of earning income.
Savings in dollars equal or greater than two month's income (SVGS) —
Yes = 1; otherwise =0. :
Head's marginal hourly earnings rate in cents (WAGE) — in circumstances
where the head neither has a second job nor commands overtime pay,
this variable is simply total annual earnings from labor divided
by annual hours worked for money. Where he has two or more jobs,
it is his hourly earnings in the last job he names. If he has
only one job, can and does work overtime if he wishes, and
receives overtime pay,: the variable is his average overtime
hourly earnings.
Environmental Variables
Works in chemicals or metals manufacturing industries (CHEM) — yes =
1; otherwise = 0. The chemicals industry includes chemicals
and allied products, petroleum and coal products, and rubber and
miscellaneous plastic products. The metals industry includes
steel, aluminum, foundaries, etc.
Number of days in 1972 when temperatures were below freezing at some
time during the day (COLD). This data was obtained from USNOAA,
Climatological Data, National Summary 1972.
Number of persons per room in family dwelling (DENS).
Distance from nearest city of 50,000 or more people (MILE) — £ 5 miles
or outside continental United States =1; 5-15 miles = 2;
15 - 30 miles = 3; 30 - 50 miles = 4; >^ 50 miles = 5.
Nitrogen dioxide: annual 24-hour geometric mean (M), ninetieth
percentile (N), and 30th percentile CO in micrograms per
cubic meter as measured by the Gas Bubbler TGS Method-Frit
before 1974 and the Saltzman method for 1974 and after (NOX).
This data was obtained from the annual USEPA publication,
Air Quality Data — Annual Statistics.
Sulfur dioxide: annual 24-hour geometric mean (M), 20th. pejecentile
(N), and 30th percentile (T) in micrograms per cubic meter as
measured by the Gas Bubbler Pararosaniline-Sulfanic Acid Method
CSUL). This data was obtained from the annual USEPA publication,
Air Quality Data - Annual Statistics.
Total suspended particulates: annual 24-hour geometric mean (Ml,
90th percentile (N), and 30th. percentile (Tl, in micrograms per
cubic meter as measured by the Et-Vol Gravimetric method (TSP),
This data was obtained from the annual USEPA publication,
Air Quality Data — Annual Statistics.
76
-------
Table 5.1
(continued)
Ultraviolet radiation in microwatts per square centimeter (ULTV).
This data was taken from Pazand, R., Environmental Carcinogenesis
— An Economic Analysis of Risk, unpublished Ph.D. dissertation.
University of New Mexico (June 1976).
Explanation of Table
Unless otherwise stated, all data is taken from tapes described in
Survey Research Center, A Panel Study of Income Dynamics, Ann Arbor:
Institute for Social Research, University of Michigan (1972, 1973, 1974
1975i 1976).
All variables referring to an individual person refer only to the
family head.
On occasion, definitions for the samd phenomenon will differ from
year to year. If this occurs, a single integer indicating the year to
which reference is made is attached to the end of the variable acronym.
Thus 1967 = 7; 1968 =8; . . .; 1976 = 6.
77
-------
Table 5.2a
Representative Means and Standard Deviations of Health and Air Pollution
Variables for Samples Involving Family Heads Currently Employed or
Actively Looking for Work*
Variable
Acronym
Year
1967 1968 1969 1970 1971 1972 1973 1974b
Health States
ACUT 100.414 120.486 133.657 113.750 113.323 149.845 112.530
(183.594) (214.759) (332.171)-(277.022) (266.274) (427.983) (259.120)
0.953 0.645 0.337 0.363 0.268 0.290 0.260 0.348
(1.720) (1.326) (0.979) (0.971) (0.888) (0.921) (0.874) (0.952)
oo Environmental
NOXM 157.043 118.045
'(51.070) (72.230)
SULM 24.475 25.113 27.220 16.286 17.657 2.051 7.435
(19.098) (18.714) (25.013) (12.150) ( 9.449) (4.188) (11.728)
TSPM 100.403 99.917 98.713 95.534 87.213 99.157 35.310 71.108
(35.469) (30.628) (29.609) (18.943) (27.920) (30.941) (42.183) (36.085)
a Except for 1970, all samples refer to family heads who have never lived in more than
than one state. In 1971, the reference is to family heads who currently live within
walking distance of relatives.
Includes housewives, retirees, and students.
*Standard deviations are enclosed in parentheses.
-------
Table 5.2b
Representative Means and Standard Deviations of All Other Variables
vO
Variable
Acronym
Health State
DSAB
Biological and
AGEH
CITY
EDUC
FEDU
FMSZ
LOCC
MARK
POOR
(continued)
1967 1968
0.493
(1.291)
Social Endowment
43.558
(12.337)
0.646
(0.481)
3.680
(1.696)
2.391
(2.254)
3.812
(2.401)
2.257
(2.234)
0.617
(0.489)
0.578
(0.496)
1969
0.111
(0.315)
40.323
(11.841)
0.451
(0.498)
3.683
(1.747)
2.300
(2.036)
4.586
(2.542)
3.271
(1.869)
0.617
(0.487)
0.543
(0.499)
1970
0.426
(1.634)
43.745
(13.451)
0.678
(0.468)
3.878
(1.862)
2.313
(1.442)
3.993
(2.376)
-
-
-
1971
0.488
(1.011)
44.218
(13.649)
0.678
(0.468)
3.923
(1.866)
2.360
(1.473)
3.930
(2.412)
-
-
0.520
0.500
1972
0.470
(0.949)
44.305
(15.276)
0.632
(0.459)
7.705
(1.851)
2.458
(1.609)
3.508
(2.202)
2.283
(2.168)
-
0.490
(0.501)
1973
0.304
(0.754)
45.155
(16.158)
0.655
(0.476)
3.720
(1.844)
2.395
(1.451)
3.233
(2.126)
2.168
(2.188)
0.525
(0.500)
0.520
(0.500)
1974
0.800
(2.159)
37.322
(15.421)
-
3.912
(1.672)
-
-
-
0.468
(0.500)
0.551
(0.499)
1975
0.624
(1.854)
37.925
14.749
-
3.659
(1.685)
-
-
-
0.540
(0.500)
0.615
(0.488)
-------
00
o
Table 5.2b
(continued)
Variable
Acronym
RACE Q
(D
SEXH 0
CO
UION
Lifestyle
ABSN
CHCH
CIGE
EXER 0
CO
FOOD 505
(380
LTWK
1967
.469
.501)
.629
.468)
-
-.
-
-
.144
.352)
.830
.977)
-
1968 1969
0.917
CO. 276)
0.677
CO. 49 6).
0.354
CO. 479)
-
0.440
(0.448)
93.146
(124.022)
0.189
(0.392)
757.669
(372.594)
-
1970
0.410
CO. 099)
0.635
CO. 482)
0.233
(.0.423)
-
-
-
0.225
CO. 418)
822.500
(716.450)
0.070
(0.255)
1971 1972
0.500 0.443
CO. 501) CO. 497)
0.635 0.573
CO. 482) CO. 495)
0.198
CO. 399)
0.108
CO. 310)
-
- -
0.198
CO. 399)
840.990
(716.100)
0.209
(0.407)
1973 1974 1975
0.475 - 0.346
CO. 500) - CO. 477)
0.603 0.640 0.631
(0.490) (.0. 382) CO. 417)
0.198
CO. 399)
_ -
_
-
_
1030.976 1145.150
(574.163) C707.099)
-
-------
Table 5.2b
(continued)
Variable
Acronym
NCIG
RELG
RISK
WORK
00
M
Pecuniary
BDALO
INSR
ICTR
RING
1967
1.851
(1.912)
0.018
(0.136)
4.489
(1.605)
1245.875
(1059.780)
99.638
(4.720)
0.889
(0.316)
1096.22
C1314,401)
9148.605
6511.900
1968 1969
-
-
4.503
(1.452)
1989.649
(674.723)
99.220
(4.297)
0.794
(0.404)
508.249
(1124.259)
8902.377
C6100.167)
1970
-
-
4.658
(1.545)
1560.895
(1001.253)
100.413
(4.625)
0.708
(0.455)
1238.392
(1198.698)
10852.230
(7833.473)
1971
-
-
4.673
(1.540)
1527.732
(982.381)
100.266
(4.788)
0.695
(0.461)
1013.846
(.1721.377)
10875.650
C7439.632)
1972
-
-
-
1333.540
(1030.346)
100.618
(4.925)
-
1342.585
(1874.235)
9556.803
(7274.871)
1973 1974 1975
_
0.054 0.062
(0.226) (0.242)
- -
1354.137
(1056.153)
100.736
(4.819)
- -
1366.702
(1993.720)
11077.950
(8337.711)
(continued)
-------
Table 5.2b
(continued)
Variable
Acronym
SVGS
WAGE
1967 1968
0.342
(0.475)
292.119
(405.985)
1969 1970
0.289 0.333
(0.454) (0.472)
314.440 322.500
(221.346) (316.450)
1971 1972
0.371
(0.484)
358.258 298.230
(331.738) (319.890)
1973
-
336.525
(337.425)
1974
-
-
1975
-
-
Environmental
CHEM
oo COLD
DENS
NOXN
NOXT
SULN
0.022
(0.147)
81.502
(52.684)
-
-
-
107.687
(134.484)
0.008
(0.086)
-
3.420
(1.797)
_ _
— —
74.663
66.016
-
-
0.870
(1.198)
246.573
79.826
132.045
(37.087)
61.768
(38.495)
0.003
(0.050)
-
0.725
(0.414)
104.860
(75.994)
31.536
(23.964)
42.625
(31.115)
0.049
(0.216)
-
-
97.429
(44.564)
32.931
(31.761)
34.566
(42.841)
0.045
(0.206)
-
-
90.717
(22.716)
48.597
(13.911)
25.650
(41.603)
(continued)
-------
Table 5.2b
(continued)
Variable
Acronym
SULT
TSPN
TSPT
ULTV
3
1967 1968
26.041
(37.369)
176.986
(78.097)
77.605
(23.661)
1494.75
(634.638)
1969 1970
10.798
(10.663)
248.965
(339.668)
74.837
(43.932)
-
1971
11.190
(5.875)
156.185
(63.787)
74.088
(20.772)
-
1972 1973
9.551
(9.305)
170.768 147.960
(58.121) (39.684)
82.995 56.232
(26.627) (9.650)
— ••
1974
5.006
(9.955)
126.702
(43.086)
67.122
(22.200)
-
1975
7.836
8.233
120.580
(56.438)
62.779
(27.046)
-
All samples Include housewives, retirees, and students,
^Standard deviations are in parentheses,
-------
If one has detailed and real-time information on changes in health
states, ideally one would like to have real-time records of all air
pollution exposures. The coarse yearly indicators of acute and chronic
illness in the Survey Research Center (SRC henceforth) data could not
support such detail. We therefore chose to collect outdoor air pollution
data averaged over a time period corresponding to the time interval
employed in the SRC data. In addition, we wished to ascertain whether
representations of moments of the outdoor air pollution frequency
distribution other than measures of central tendency might contribute to
ill-health. The result of these deliberations was a decision to acquire
data on the geometric mean (because outdoor air pollution tends to be
log-normally distributed over time), 30th percentile, and 90th percentile
of the annual concentrations of five pollutants: nitrogen dioxide; ozone;
total oxidants; total suspended particulates; and sulfur dioxide.
Although the ozone and total oxidant data has been combined with the SRC
data, the number of monitoring locations and the monitoring time intervals
were inadequate to allow other than minor variations in the exposures of
the sample individuals. Thus the empirical results to be reported
neglect these two possibly important pollutants.
Matching the thousands of outdoor air pollution monitoring stations
in the United States to the hundreds of counties where the SRC sample
families resided could be a complex combinatorial problem. The matching
was achieved for each of the nine years at the cost of not having outdoor
air pollution information for some SRC sample families during some years
and of assigning somewhat inappropriate air pollution exposures to some
sample individuals. The full extent of this information loss is presently
unknown.
The matching process started by listing all the counties in the
United States where one or more SRC sample families had resided during the
nine year interval. Separately for each of the five previously mentioned
air pollutants, a yearly listing of the counties having outdoor air
pollution data for one or more of the three frequency distribution
measures being considered was constructed. Of the 301 counties in 56
states where sample families resided during the nine year interval,
outdoor air pollution monitoring data for one or more of the measures of
one or more of the five air pollutants existed at least for one year in
118 of the counties in 50 states. No attempts were made to extrapolate air
pollution data from one county to another, nor were any switches between
monitoring stations in a single county ever made. In counties where
multiple outdoor monitoring stations were present, the data from the single
station that had operated for the greatest portion of the nine years was
used. If two or more stations in a county had operated for equal
portions of the nine years, the station having the most complete (in
terms of numbers of pollutants and pollutant measures) was employed.
When air pollution data were available in a family's residence county for
a particular year, these criteria served to assign outdoor air pollution
exposures to all sample families. For most years, somewhat more than
3,000 families had some sort of outdoor air pollution data assigned them.
Because of our reluctance to adopt a new monitoring station location in a
county whenever the activities of a station we had previously used were
terminated, we undoubtedly missed a few opportunities to assign air
84
-------
pollution data to a few sample families. This issue pales, however,
beside the issue of the extent to which the assigned data represent
actual outdoor air pollution exposures.
The SRC family data sample provides only the family's county and
state of residence: it does not give the home town or city. Thus, for
large urban counties such as Cook County, Illinois, or Los Angeles County,
California, or occasional rural counties such as; San Bernardino County,
California, where there exist major locational differences in potential
air pollution exposures within the county, substantial error could exist
in the air pollution assignations. This important source of measurement
error could perhaps be substantially reduced if all counties having this
property were identified and if all families residing in the identified
counties were excised from the sample. We have made no attempt to perform
this excision.—
This criteria employed to select pollution monitoring stations probably
result in the assignment of downtown urban locations, where pollution
concentrations have historically tended to be greatest and where the most
extensive monitoring has heen done. Since relatively few of the SRC
sample families actually live in downtown areas, the constructed data
set generally exaggerates family outdoor air pollution exposures, implying
that the health effects, if any, of air pollution will tend to be under-
estimated.—'
Outdoor air pollution at the place of residence is not the only
plausible environmental source of deleterious health effects. Indoor
air pollution at home and in the work place, outdoor air pollution at
other locations, contaminants in diet, and water pollution are additional
widely acknowledged possible sources. We introduce measures (albeit
imperfect) of some of these plausible alternative sources in our empirical
efforts and fail to give any attention to others such as water pollution.
If these excluded types of pollution have health effects of their own, and
if their extent tends to be positively correlated with the extent of
outdoor air pollution, then the included air pollution variables will
cap.ture some of their contributions to ill-health, causing the measured
contribution of the outdoor air pollution variables to be exaggerated.
The extent of this upward bias will vary directly with the degree of
correlation between the included and the excluded variables and the extent
to which the excluded variable actually contributes to the effect of
interest. For this study, of the previously mentioned alternative
environmental pollution sources of health effects, the utter exclusion of
any measures of water pollution is perhaps the most serious* At various
points in the empirical effort, rather crude measures of indoor home air
pollution Cfamily smoking habitsi, diet (a dietary adequacy indexl, and
indoor air pollution at the work place Cemployment in the chemicals or
metals manufacturing sector), are included.—
The issue of excluding possibly relevant variables from the analysis
included outdoor air pollution as well. Oxidants and ozone, because of
insufficient variation in apparent exposures among sample families, have
been disregarded, even though exposure values are present in the
constructed data set. Other important air pollutants, for which data were
85
-------
available such as carbon monoxide, were not even considered because of the
large variations in their instantaneous concentrations within a few
hundreds of feet. Some pollutants that have attracted recent regulatory
and public concern, such as acid sulfates, had no data readily available.
Finally, of the pollutants that were included in the constructed data
set and exploited in the empirical effort, the time series for all except
total suspended particulates were incomplete. Thus, for example, no
information was available on sulfur dioxide concentrations in 1972.
Measurement error is not only an issue in the outdoor air pollution
variables. What some might choose to interpret as measurement error is a
prime feature of the two dependent variables, number of days annually
ill and length of time disabled.^-' Although we have no basis other than
seemingly sensible intuitive interpretations of the form of the questions
asked the respondents Csee the explanations for ACUT and LDSA in Table 5.1),
we choose to interpret the former as acute illness and the latter as
chronic illness. Definitional problems of the distinction between acute
and chronic illness aside, it must be remembered that what is an illness
to one individual is not an illness to another individual. Even the same
individual may differ over time in what he considers to be a state of
illness. Illness is, in part, an idiosyncratic and subjective phenomenon
only partly susceptible to consensus standards of definition. Therefore, if
one prefers a reductionist perspective and wishes to have all phenomena
collapse to, say, a chemical measurement, then the values of the variables
we are trying to explain in this study indeed leave a great deal to be
desired.— Economic analysis, however, presumes that illness and its
costs lie in the eye of the beholder. No laws whatsoever governing choices
are innate in the material objects of ordinary cognition. As has been
emphasized in the introduction to this section of the report, the degree
of illness that afflicts an individual is, in part, often a matter of
purposive choice. Economic principles relate to the subjective desires
motivating individuals to become aware of and perhaps to alter their
environments. Thus no object or status becomes relevant in economic
analysis until humans perceive it can be used for or defeats some
subjective purpose. Illness that is defined in clinical terms but which is
never subjectively realized by the individual who is said to be clinically
ill is of little interest except to clinicians. It is certainly arguable
whether their standards of what constitutes illness should prevail over those
of the individual who professes illness. For this study, we are forced by
circumstances to adopt the latter*s perspective. Fortunately, it fits
readily into economic analysis.
In spite of the preceding argument a type of measurement error does
persist in the two dependent health variables. This type of error is
inherent in the use of any fairly encompassing measure of health status.
Kinds of debilitating acute illness for an individual may range, for example,
from headaches to heel blisters. Chronic illnesses may show similar
variations over body sites and implied debilitating effects for the same
individuals. In effect, therefore, an individual's response to a question
about the number of days he has been ill or the length of time he has been
disabled involves an aggregation of several attributes perhaps sampled, from
some larger population of attributes. The weights the respondent employs
to combine these attributes to obtain the encompassing health measures
86
-------
may differ among individuals. Furthermore, they may not be those weights
that correspond to the contribution of the attribute to some other
parameter of interest, such as hours of work or money wages. Recognition
of the possibility that individuals may employ different weights to
aggregate to the encompassing health measure serves perhaps to deepen
the reader's perception of the subjectivity of our measures of ill-health.
It says only that there may be as many unique measures of ill-health
employed as there are respondents in the sample. The import for our
empirical efforts of discrepancies between the contributions of attributes
to ill-health and to other parameters of interest is greater, since we
shall try to ascertain the impact of air pollution-induced ill-health upon
labor supply and productivity. In particular, the use of the encompassing
measures of ill-health rather than the specific attributes may attenuate
our estimate of the effect of air pollution-induced health effects upon
labor supply and productivity.
As Table 5.1 indicates, all SRC sample individuals not currently
employed or seriously looking for current employment had no information
recorded about the number of days they professed to be acutely ill.
Furthermore, those individuals for whom information on ACUT was recorded
were never sick on weekends: their accute illneses occurred, according to
the data, only on workdays. The ACUT variable may thus be confounded by the
wish of some respondents to legitimatize for the sake of social appearance
or internal self-respect their failure to go to work. In the empirical
efforts regarding ACUT therefore, an actual choice of leisure over labor
could thus be falsely attributed to ill health. Marquis (1978), however
has been unable to discover any basis for this source of bias.
The rather long list of other variables considered can be divided,
somewhat imperfectly, into health state, biological and social endowment,
lifestyle, pecuniary, and environmental variables. For the moment, we will
limit our discussion of the variables not already discussed to the parts
they are expected to play in dose-response functions, reserving the
discussion of labor supply and productivity impacts to a later section.
Only those variables actually used in the estimated dose-response functions
are therefore discussed in this section. A summary table of expected
signs is presented in Table 5.3.
DSAB, the degree of disability is the only included health state
variable not employed as a dependent variable. Since it is ordinally
scaled, its meaning when used as a dependent variable is arbitary. Any
four or five monotonically increasing numbers would have no more and no
less meaning. When entered as an explanatory variable in the chronic
illness production function, its expected sign is unclear. If the individual
continues to live in spite of having a chronic disability, one would expect
the period of recovery, if any, to be lengthier the more severe the
disability. However, in the general population, severe disabilities
perhaps are more likely to lead to earlier death. Thus, those sample
individuals who are severely disabled might be expected to have been
disabled only for a relatively short time span. This would lead one to
expect a negative association between DSAB and LDSA. Which effect would
dominate in any particular sample must be conjectural. In contrast, since
disabilities, both in terms of length and severity, probably cause the
87
-------
Table 5.3
Expected Signs for Explanatory Variables
in Estimated Dose-Response Functions
Acute Illness Chronic Illness
Health States^
DSAB + ?
LDSA + X
Biological and Social Endowments
AGEH + +
CITY ? ?
EDTJC ? ?
FEDU
FMSZ - ?
MARK - ?
POOR + +
RACE
SEXH ? ?
Lifestyles
CHCH
EXER - X
FOOD - -
NCIG + +
RELG
RISK
Precuniary
INSR
Environmen tal
CHEM + +
COLD ? ?
DENS + +
All NOX + +
All SUL + +
All TSP + +
ULTV ? ?
? = unknown
X = irrelevant
88
-------
individual to be more susceptible to common temporary illness, we expect
LDSA and DSAB to contribute positively to ACUT. However, because the
values for DSAB are not monotonically ordered, the magnitudes of the
coefficients for DSAB in both the LDSA or the ACUT expressions should be
disregarded.
No one holds that health states improve with adult age. The adult
human organism suffers natural decay, making the investment necessary to
maintain a given health state progressively more costly. The inclusion of
two additional irrevocable biological attributes, race and sex, can be
justified on at least two grounds. First, susceptibilities to some
diseases differ by race or sex. Men, for example, don't have breast
surgery and whites don't contact sickle cell anemia. The implications of
this for the signs of RACE and SEXH are unclear, however. Second, and
probably most important with respect to race, minorities have frequently
had less preventive and ameliorative medical care available to them and have
perhaps had less opportunity to learn how to use what is available wisely.
The RACE variable might therefore capture some fair portion of past and
present differences in the availability of medical services to individuals.
If this speculation is correct, RACE, which has a value of 1 if the individ-
ual is white and 0 otherwise, should have a negative sign attached for
both illness types.
CITY, FEDU, and POOR are intended to represent differences among
individuals in their childhood environments. If one grew up in a city,
he probably had better access to medical care. On the other hand, he was
probably exposed to more toxics in his everyday environment. The sign to
be expected for CITY is therefore ambiguous. In contrast, the proper
signs to expect for FEDU and POOR are relatively unambiguous. Educated
parents, in addition to their other.knowledge about worldly affairs, will
perhaps be more sensitive to the implications of childhood health
practices for future adult health status of the child. In addition, they
might tend to be better at interpreting signals of health distress and
choosing the medically most effective course of action. If adult health
states are positively influenced by childhood health practices, then the
sign attached to the FEDU coefficients in either acute or chronic illness
dose-response functions should be negative. For similar reasons, the
POOR coefficients are expected to have positive signs.
With one ambiguous exception, EDUC, FMSZ, and MARR contribute to good
health. Many recent studies indicate that among socioeconomic variables,
years of formal schooling completed is frequently the most important
predictor of good health. Grossman (1975) has found empirical evidence of
a causal relationship running from past schooling to current health. The
individual who is married has his wife's time available, as well as his own,
for the protection of his health. At least for acute illness, increasing
family size also implies that certain individuals within the family can
specialize in the production and the protection of other family members'
health. This implies that over some interval there exist increasing returns
to health production specialization within the family, a proposition that
accords neatly with casual observation but for which no strong empirical
evidence appears to exist.
89
-------
The expected sign for FMSZ in a chronic illness dose-response function
is ambiguous because the number of children a family has is, in part, an
investment decision.—' Older children provide more opportunities for
family members to specialize in health production and protection; however,
if a state of chronic disability was suffered by the family head "before the
accumulation of a large family, it would seem that the investment process
in children would be made more costly. The latter statement implies that
fewer children and chronic disability are positively associated, while the
former says that children, once they are able to assume some responsibilities
for family production, contribute to good health. Put in terms of our
concerns in the introduction to this portion of the report, an observed
association between an individual's state-of-health and his family size
could reflect causality running both from family size to health and from
health to family size. This issue could, of course, be resolved by
building an analytical structure in which family size is made a decision
variable. To do so would take us beyond the immediate scope of this
research effort. We have therefore employed family size as an explanatory
variable in our estimated chronic illness dose-response functions without
imposing any sign expectations upon it and recognizing that its presence
could bias the air pollution coefficients.
All of the lifestyle explanatory variables are standard entries in
epidemiological studies of air pollution. There are, however some special
features worthy of note for each variable. NCIG, for example, is not the
number of cigarettes smoked by the individuals but rather the number
smoked per adult family member. It is assumed this serves as a reasonable
proxy for the smoking habits of the individual head. For the cigarette
variable therefore, its estimated coefficient is best considered as an
indicator of the health effects of smoking or not smoking. Little, if any,
credence should be assigned these coefficients as indicators, in the
neighborhood of the average smoking habits of th,e respondent sample, of
the incremental health effects of smoking an additional cigarette; that is,
the sign of the coefficient rather than its magnitude is the result to
inspect.
Biomedical wisdom says that continuing participation in energetic
activities and an adequate diet contribute to good health. Since the SRC
data set contained no information on the respondent's exercise habits
before he became disabled, we have not included EXER in the chronic
illness dose-response function. Otherwise one must face the two-way
causality problem with inadequate data resources to handle it. In
neglecting this variable, however, which proves to be consistently
statistically significant in the acute illness dose-response function,
we raise the spectre of biasing the air pollution coefficients in the
estimated chronic illness dose-response functions. Since, a priori,
energetic activities are expected to reduce the incidence of chronic
illness, the absolute magnitudes of the air pollution coefficients will
be biased downward, causing the effect of air pollution on chronic illness
to be underestimated. However, for those years in which EXER is available
in the SRC data set, the absolute value of the simple correlation between
it and the air pollution variables is generally less than 0.15, The bias
its exclusion introduces is probably therefore minor unless it intrinsically
has a very strong influence on the magnitude of the chronic illness
90
-------
variable.
So as to enhance the creditability of the dietary habits variable, FOOD,
we quote from Survey Research Center Cl972a, p.75):
"Since expenditure on food is a relatively easy to measure proxy
for adequate nutrition and is one of the study's more important
variables, much care has been taken to improve the technique of asking
these questions; several refinements, but no added objectives, have
resulted in a few changes to these questions over the five waves of
the survey."
Accepting the assertion that the amount of food expenditures was one of
the most carefully treated questions in the entire SRC survey effort, the
issue remains as to whether these expenditures, even when stated relative
to food "needs," are capable of providing useful information on the etiology
of illness. Certainly they can provide no information on dietary contribu-
tions to particular diseases unless expenditures on particular food groups
are known. But then we are dealing in any case only with generalized
measures of self-reported health status. As for the use of expenditures on
food rather than actual food consumption, one's comprehension of this
measure is aided if it is viewed as a proxy for a stock variable relating
to the history of the individual's investments in diet. Real capital in
the hospital industry is not measured in terms of gadgets and buildings but
rather as the discounted value of the accumulated investments. Similarly,
dietary adequacy may be measured as the discounted value of the individual's
accumulated expenditures on food. FOOD, which is simply current expenditures
on food relative to a "needs" standard, will generally tend to be positively
related to this discounted value.
The intent of including the CHCH, RISK and RELG variables is to capture
acquired behavioral traits consistent with an out-of-the-ordinary
aversion to health-endangering activities. We hope at least some of those
forms of health-enhancing everyday behavior not otherwise available in the
data set collapse into these variables. Among these forms would be
regulatory getting six to eight hours sleep, a tightly-knit and emotionally
supportive family life, a healthy mix of foods consumed, and the many other
lifestyle factors to which assorted medical commentators variously
attribute the production and protection of good health.
INSR, a dummy variable referring to whether or not the individual is
covered by medical insurance, should be correlated with the individual's
consumption of medical care. The variable should be negatively related
to the price of medical care that the individual faces and therefore
positively related to the quality of medical care he has consumed. If
medical care improves health or maintains good health, then the medical
insurance variable should have a negative coefficient in both the acute
and the chronic illness dose-response functions. Our use of this variable
in a dose-response function might be criticized on grounds that it is
serving as a proxy for the quantity of medical care consumed, where this
quantity and the proxy are the consequence of current period decisions. We
admit the possible validity of this view but nevertheless chose to retain
INSR as our only available proxy likely to be strongly associated with the
91
-------
individual's adult history of medical service consumption. In short, we
assume that the benefits to estimation from including a plausibly
relevant variable (a history of the individual's adult consumption of
medical services) outweigh the losses to estimation incurred by employing
a current period decision variable as an explanatory variable in a single
equation structure.
Among the environmental variables, all the air pollution variables, as
well as DENS and CHEM, are expected to have positive signs for both acute
and chronic illnesses. People who live in crowded conditions are in
closer contact with other individuals, making personal sanitation more
difficult, and increasing the probabilities of contracting whatever
communicable illnesses plague others. The contacts of workers in the
chemicals and metals manufacturing sectors are not so much with carriers
of communicable illnesses, but rather with exposures to toxic substances
in the work place. These exposures are thought to exceed those of the
rest of the population.
Hippocrates, 460-337 B.C. (1939) and the writers of a large literature
descending from those ancient times have asserted a sort of climatic
determinism with respect to health.Z We briefly acknowledge this
literature by considering two climatic variables, COLD, to represent the
extent of freezing weather, and ULTV, to indicate the amount of sunshine.
Although the literature in this area says that climate has an influence on
health, any advice it gives as to whether these climatic parameters are
harmful or beneficial is unsettled. We therefore prefer not to make
assertions about the signs to be expected for the coefficients of these
variables.
A great many more variables for each of our variable classes is
available on the SRC survey tapes. In addition, since the county of
residence is known for each individual respondent for each year of the
survey, additional environmental and general area information could be
combined with the SRC tapes. Many more variables could be constructed from
the basic SRC information. We did initially consider some other
definitions and versions of the variables in Table 5.3, but this list
should provide a reaonable description of the data we had available.
Before proceeding to the presentation and discussion of the dose-
response functions, there are several salient characteristics of the
constructed data set that do not necessarily have clear implications for
the results but which nevertheless provide form and a setting for them.
Tables 5.2 and 5.4 are thus worthy of some attention. The reader is
reminded, however, that these tables are incomplete: they are only
representative of the samples used to estimate the dose-response functions.
Note that three of the characteristics of Table 5.4 are consistent with
a high proportion of the individuals in the sample having lived for long
periods in one locale. People who live within walking distance of
relatives, have always lived in one state, and have never moved to take
a job elsewhere have likely had a long history of exposures to the outside
air pollution of one municipality. In short, the SRC data allow one to
compensate somewhat for the lack of a long data series on the pollution
92
-------
Table 5.4
Proportions of Entire Survey Research Center Sample Processing
a Particular Characteristic During 1971
Characteristic Percent
Asset income <_ $500 81.1
Children <_ 25 years in family unit 51.3
Has relatives living within walking distance 42.6
Employed head 72.7
Unemployed head 2.2
Retired head 16.6
Housewife head 6.7
Student head 1.6
Working wife 33.3
Disabled person in family other than head 3.8
Neighborhood of detached single-family homes or lesser density 65.9
Rents dwelling unit 37.8
Always lived in one state (1970 data)* 40.4
Never moved from a community for a job change (1970 data)* 57.9
Disabled head 21.8
*These proportions are not indicated in the code book describing the
1971 data. It is highly unlikely that they differ significantly from the
1971 proportion.
93
-------
exposures of sample individuals. If one is willing to assume that
relative pollution concentrations among locations have been reasonably
constant over time, then he can at least loosely grasp the effects of
cumulative exposures on differences in health states. These cumulative
exposures might not be terribly relevant with respect to acute illness,
but they can be highly important with respect to chronic illness.
Therefore in all our empirical efforts dealing with chronic illness, we
deal only with sample individuals who have always lived in one state or
who have never moved for a job change. Even though this partitioning by
no means guarantees that we fully capture the cumulative air pollution
exposures of the sample individuals, we believe that it does so to a
substantially greater degree than do most air pollution epidemiology data
sets.
The proportion of sample individuals who profess disabilities
consistently approximates one out of every five. Over the nine year
interval of the data set, it ranges from a low 18.2 percent in 1974 to a
high of 23.6 percent in 1969. In fact, only for the 1974 and 1975 entire
SRC population samples was the proportion disabled below 20 percent (in
1975, the proportion was 18.4 percent). These lower proportions for 1974
and 1975 are probably due to the rather drastic drop in the mean age of
the sample population occurring between 1973 and 1974, which is reflected
in the mean values for the AGEH variable in Table 5.2. The drop causes
the proportion of the SRC sample that reports being disabled to better
approximate the proportion disabled in similar area probability samples
of the U.S. civilian non-institutionalized population. These other
samples generally tend to have ten to fifteen percent of their individuals
suffering from self-reported disabilities.
A glance at Table 5.2 shows that the number of individuals employed in
the chemicals and metals manufacturing sector is usually too small, given
sample sizes of about 400, to estimate reliably the extent to which the
exposures associated with this employment generate illness. As earlier
noted, the 1973 SRC data include information on three-digit occupational
codes by three-digit industry for the sample individuals. If, after
having carefully perused the data to ascertain exactly which occupations in
which industries involve substantial exposures to toxics, the entire SRC
population sample were to be used to estimate an acute or chronic illness
dose-response function, one might have sufficient degrees of freedom
available to obtain reliable coefficients for these manufacturing sectors.
At best, one or two of the samples we employ here have enough sample
individuals employed in these sectors to be slightly suggestive about an
association between exposures in them and acute or chronic illnesses.
Finally, when evaluating the empirical results reported in this study,
one must face the question of the accuracy of respondent recall. Since
there exists no data base referring to contemporaneously observed sample
individual behavior and status, one's judgments about accuracy must
necessarily be more-or-less personal and introspective. The following pair
of facts can aid in the formation of this judgment. First, all respondent
interviews were conducted within 12 months of the year for which respondent
behavior and status was to be reported. Thus the longest interval that
could pass between some respondent event and his reporting of that event
94
-------
was 23 months. In all years, however, the great bulk of the interviewing
was completed by June of the year following the year that was to be
reported. For these respondents, the greatest time lag that occurred
between an event and its reporting was 17 months. The smallest lag that
could occur, since interviewing started in early March of the year following
the year to be reported, was two months ..§/
Perhaps more relevant to the recall issue than the question of lags is
the incentive respondents had to make mental or written note of their
behavior and status to ensure accurate answers when the appointed time for
their interviews arrived. Several points relevant to this incentive
issue can be made. First, as reinterviewing "waves" (this is the SRC's
term) passed, those original respondents who were hostile to the interviewing
process and purpose probably removed themselves from the sample. We
speculate that those who voluntarily stayed in the sample possessed a
substantial incentive for accurate recall. This implies that data from
later years is perhaps more reliable than data from earlier years. Second,
those families that did remain in- the sample became more familiar with
what would be asked them with each reinterviewing wave and would therefore
take more care to make mental or written note of events so that they could
be accurately reported. This too implies that data from later years
tends to be more reliable. Third, the respondents were paid a small sum
($5.00 - $7.00) for participating in the interview. Finally, after
having completed an interview, the respondent was left a postcard that
he was asked to send to the SRC in early January of the following year.
This card informed the SRC of the respondent's current address. Those who
did and did not return the cards were sent a reminder and a postcard in
January, along with a summary explanation of empirical results from the
interviewing of the preceding year. All who returned the postcards,
whether or not reminded, were rewarded with an additional payment of
$5.0.0. The SRC does not report the proportion of those who returned
postcards, but, given the reinterview rate, one can reasonably conclude,
that the return rate must have been fairly high. We judge from this that
respondent interest in the survey must have been substantial, resulting
in an incentive to keep rather careful track of behavior and status.
Aside from the detail of its information, the SRC sample and its
combination with the air pollution data contain little that is remarkable
relative to other data sets that have been used in air pollution epidemiology.
Judging from the general sociodemographic attributes depicted in Tables
5.2 and 5.4, the sample in spite of our disregard of the SRC sample
weights, appears to be close to a random sample of the U.S. civilian
non-institutionalized population. The high proportion of non-whites
does, however, raise some doubt about its exact representativeness.2J
The increasingly better control of sulfur dioxide emissions is clearly
registered in Table 5.2, although control of particulates and nitrogen
dioxide appears not to have exhibited much improvement over the nine-year
interval. Table 5.2, by its failure to show data for variables in some
years that appear in other years, exhibits both changes in the SRC
interview formats as well as our deletion of variables in expressions
estimated for some years when they were not statistically significant
in expressions estimated for samples drawn from other years.
95
-------
5.3 Estimates of Dose-Response Rates for Acute and Chronic Illness
To place any credence in the estimates presented in this section,
one must believe that stochastic factors play a role in dose-response
functions. Stochastic disturbances may have a greater or a lesser part to
play than systematic biological, physical, economic, or social influences,
but they nevertheless have a part. If all influences were entirely
deterministic, the statistical procedures employed here (as well as all of
epidemiology) would be unnecessary and redundant: all one would have to
do to ascertain the values of the influences is go to the laboratory
and perform the relevant measures. In fact, single observations on the
phenomena of interest would suffice: if the observations conformed to
the proposition, one would accept the proposition for now. Otherwise,
it would be rejected. Biomedical research employs both laboratory and
human population studies (and several different variants within each
of these general classifications) to come to grips, most often with less
then iron firmness, with dose-response functions. The use of these
approaches and their variants is an admission that the functions involve
significant stochastic elements.
Reference is made to rates rather than functions in the subtitle of
this section because the empirical results repotted apply only to
changes in measured illness for one-unit changes in the explanatory
variables of interest at the mean values of these dependent and explanatory
variables. These changes could properly describe an entire dose-response
function if and only if that function were linear in the original
variables. Throughout the estimation procedure, we have employed linear
functions for an assortment of reasons, not the least of which is that
there appears to be no strong analytical or empirical precedence for
doing otherwise with the generalized measures of ill-health we are using.
We don't know whether the air pollution dose-health response function is
supposed to be increasing at an increasing or a decreasing rate over a
given interval. A linear function is the best available compromise between
these two possibilities. The linear form is easily interpreted at a
glance and, furthermore, relative to other readily estimated forms such
as the multiplicative, it does not attenuate the potential influence of
observations having extreme values. In the absence of knowledge about the
functional form of the relationship one is estimating, the use of multiplica-
tive and similar forms effectively reduces the variation of the sample
and thus will often allow one to explain a larger proportion of the
variation in the Crescaled) sample. For purposes of the present study,
since we lack prior knowledge of the form of the dose-response functions,
we wish to provide the extremes of good and ill health, and pristine and
filthy air, full rein. This reluctance to reduce the influence of
outliers, when combined with our use of data on individual human being
rather than group averages, means that we reduce, if not completely
deny, our chances of explaining large proportions of .the variation
among our basic observational units in acute and chronic illness.
Tables 5.6a and 5.6b present estimates for household heads of dose-
response relations for acute illness and Tables 5.7a and 5.7b do the same
for chronic illness. So as to reduce the extent to which cumulative
exposures to outdoor air pollutants are unaccounted for, all the estimated
96
-------
chronic illness expressions employ as basic units of observation only
household heads who have always resided in one state. This restriction is
imposed for all chronic illness estimates throughout the chapter.
Substantial care has been taken to assure that all explanatory
variables have either always been outside the household head's domain
of control or have been established by his actions prior to the period
being considered. Thus, variables such as the head's age, where he
grew up, his father's education, and past financial status, his sex and
race, and the cold, air pollution, and the ultraviolet radiation to which
he is exposed at a particular location are matters over which he never
has and never will exercise anything but the most trivial influence. They
are inalterable. Other variables such as the severity of any disabilities
he has, and his education, marital status, and family size were certainly
influenced by his decisions. However, the impact of past decisions on
the current values of these variables will, for nearly all adults,
overwhelm any potential impact of decisions made within any current 12
month period. The economic sector within which one is employed and the
rooms per family members in one's housing are perhaps subject to more
immediate control but, for the great bulk of people, are not very quickly
or readily adjusted. Assertions of predetermination are clearly in-
accurate for most of the life-style variables. One's current cigarette
consumption, exercise, and dietary habits, etc., are quickly adapted to
changing circumstances. Yet one might also reasonably argue that even
these current adaptations are isomorphic to acquired habits, and can
thus be employed as proxies for these predilections. In fact, for
items such as medical insurance, food and cigarettes, there is abundant
evidence in the empirical consumer demand literature that the quantities
individuals consume are quite insensitive to price changes, at least
for the range of price changes likely to occur in a year. Similarly,
these habits tend to persist for some time in the face of substantial
yearly income changes. Finally, introspection says that one's religious
and risk aversion attitudes are the result of the accumulated experiences
and learning of a lifetime rather than a momentary diversion that will
serve only until a new fad comes to one's attention.
A rather large data set like the SRC survey, when joined with a
quite sparse set of a priori propositions with which to restrict the
expressions to be estimated, leads one into temptation. In particular,
using an unchanging set of sample observations, one is tempted to
add and delete variables and try assorted functional forms until a result
is obtained that, on statistical grounds alone, looks good; that is, the
coefficients attached to the explanatory variables all have common sense
or a priori acceptable signs and are generally statistically significant
at high levels. Moreover, summary statistics such as the coefficient
of determination are high and standard errors of estimate are low.
Quite frequently, the results of this "data-grubbing" are reported without
any description of the manipulations lying behind them. As is well-
known, this practice can introduce substantial biases into estimated
coefficients. In the words of Selvin and Stuart (1966, p. 21):
"... any preliminary search of data for a model, even when the
alternatives are predesigned, affects the probability levels of
97
-------
all subsequent teats based on that model on the same data, and
in no very simple way, and also affects the characteristics of
subsequent estimation procedures. The only valid course is to
use different data for testing the model dredged from the first
set of data."
We have not conformed absolutely to this dictum, but have nevertheless
followed it rather closely .iQ./
In Tables 5.6a, 5.6b, 5.7b, each estimated expression is numbered,
with each number in each table corresponding to an entirely new sample
drawn at random from the entire SRC population sample or that portion of the
SRC sample meeting certain imposed conditions. Thus, for example, in
Table 5.6a expressions CIA), (IB), and (1C), are estimated from the same
set of observations but the expressions (1) and the expressions (2)
are estimated from entirely different samples. Since the availability
of variables in the SRC data set can differ greatly from year-to-year,
and the definitions of variables can differ slightly, it is not possible to
exploit formal statistical tests for replication. Nevertheless, if the
different samples do yield similar results for a particular set of
variables, a dimension is added to the estimation procedure that undeniably
adds information and confidence in the results.
Even though a modicum of something resembling data—grubbing is
present in the: estimation of expressions like (1A), (IB), and GLC) in
Table 5.6a, it does not involve anything more than using the same data
set to reestimate expressions in which nothing other than the air
pollution variables has been changed. Thus, though (1) in Table 5.6a
involves three expressions, only three "runs," with one run for each
combination of air pollution variables, was performed.
Table 5.5 is a table of simple correlation coefficients for a
representative sample. These coefficients, of course, differed from one
sample to another, but the table provides a good idea of the general
patterns of intercorrelation among the variables that were estimated
by the various samples. As a glance at the table shows, there is very
little linear association between the air pollution variables and any
single other variable used to explain acute and chronic illness. No
one of these other explanatory variables linearly accounts for more than
23 percent of the variance of an air pollution variable, and, in most
cases, the variance accounted for is considerably below ten percent.
Similarly, the intercorrelation among variables other than the air
pollution variables tends to be very low. This, of course, does not
mean that strong nonlinear associations between single variables are
absent. Neither does it mean that close associations between the air
pollution variables and linear or nonlinear combinations of other
explanatory variables are not present. Although there exist some
statistics that purport to test for these latter two possibilities,
we have not employed them in this report. We thus proceed as if the
fact that linear associations between single explanatory variables are
typically low implies that multicollinearities among all explanatory
variables (except for the air pollution variables) are unlikely to
inflate the standard errors of coefficients, thereby causing certain
98
-------
Table 5.5
Matrix of Simple Correlation Coefficients for a 1971
Representative Dose-Response Function Sample
UlSA
IOSA 1.000
EDUC
CICI
TO*.
FOOD
IIU
tea
KA>
net
(om
mi
svcs
tune
rOOK 0.156
TOO -0.164
4kd -0.160
MIR 0.006
nrr 0.096
*1IW 0.153
TIM 0.12*
HILT -0.002
SOU -0.006
SOU! 0.002
EDUC CICF. EXEI FOOD
-0.139 -0.112 -0.07J -0
1.000 0.001 0.2 JO 0
0.006 0
0
.202
.442
.077
.054
-0.1)7 -0.124 0.0:4 -0.299
0.1M 0.137 0.169 0
0.419 0.306 0.170 0
-0.013 0.023 -0.080 0
.SOI
.732
.289
-0.012 -O.OS4 -0.084 0.044
-0.058 0.079 -0.106 0
-0.024 0.079 -0.119 0
0.053 0.057 -0.126 0
0.113 0.087 -0.129 0
-0'.021 0.04$ -0.142 -0
.050
.016
.018
.072
.009
FEW) MCE ACUT TSFT
root
IUIU
MCE
ACUT
TSPT
•an
nnt
COLT
tout
-0.285 -0.130 -0.094 0
0.326 0.030 0
-0
0
.054
.O94
.071
.155
RISK
-0.1)2
0.454
-0.268
0.134
0.454
-0.133
0.214
0.447
-0.053
O.O42
0.136
0.066
0.069
0.136
0.058
ism
0.067
0.039
0.008
0.074
0.922
tent
0.201
-O.I 55
-0.091
-0.106
0.157
-0.021
0.115
-0.176
0.180
0.026
-0.085
-O.W7
-0.086
"-O.O31
-0.085
-0.044
Tsra
0.056
0.075
0.056
0.096
0.970
0.976
DSA1
0.700
-0.153
-0.062
-0.059
-0.172
-0.200
0.231
0.137
-0.135
-0.136
0.155
-0.043
0.080
0.150
0.066
0.043
0.045
SUIT
0.004
0.039
-0.012
0.119
0.441
0.652
0.622
FMSZ
0.03;
-0.191
0.126
0.038
-0.369
0.173
-0.081
-0.035
0.108
-0.182
-0.235
-0.059
0.034
0.055
0.040
0.021
0.025
0.013
SOU
0.038
0.052
-0.082
0.122
0.742
0.8)7
0.861
O.St-8
SEXH
-0.117
0.217
0.303
0.167
0.311
0.42?
0.018
-0.184
0.081
0.030
0.147
0.353
-0.071
0.110
0.091
0.133
0.156
0.097
0.169
SOLD
0.005
0.065
-0.100
0.122
0.658
0.821
0.800
0.945
0.93»
INSR
-0.301
0.401
0.186
0.151
0.414
0.678
0.001
-0.325
-0.206
0.217
-0.060
0.177
0.413
0.046
0.066
C.OV9
0.047
-0.054
0.042
-0.031
SVCS
-0.179
0.354
0.018
-0.150
0.501
0.04)
0.284
-0.165
-0.188
0.215
0.418
-0.165
0.119
0.414
-0.024
0.155
0.231
0.172
0.108
0.217
0.119
CHID
0.029
0.201
-0.037
-0.024
0.059
-0.032
0.076
-0.024
-0.004
0.033
0.033
0.065
-0.052
-0.012
0.050
-0.018
0.091
(1. 100
0.083
0.015
0.073
0.031
CITY
-0.008
0.057
0.303
-0.025
0.012
0.068
-0.094
-0.048
O.O47
0.088
-0.027
-0.058
0.035
0.076
0.100
-0.017
-0.055
0.042
U.074
0.056
0.072
0.068
0.071
9.2
-------
Table 5.6a
Dose-Response Rates for ACUT: Unpartitloned Samples
Year
Variable
DSAB
LDSA
AGEH
EDUC
MARR
POOR
RACE
SEXH
EXER
FOOD
NCIG
RELG
RISK
INSR
CHEM
DENS
NOXT
NOXM
NOXN
SULT
SULM
SULN
TSPT
TSPM
TSPN
CIA),
B 1967 s
2Q.541
-2.486
4.086
-12.561
-24.264
-87.746*
-17.564
-0.062*
17.943
-12.561
-9.. 392
20.84
1.857*
-0.432
5.862
1.650
13.344
81.9.52
40.419
46.328
87.082
0.039
11.801
81.958
16.670
59,, 05
1.033
0..681
(1B1
B 1967 s
21.140*
-2.068
4.155
-8.362
-24.060
-95.090*
-7.666
-0.063*
18.520
-11.170
15,150
1.488*
-0.442
5.947
1.246
13.540
81.660
40.800
49.95
86.450.
0.033
12.010
17.190
59.31
0.733
0.648
(1C)
B 1967 s
21.520*
-1.895
4.462
-21.280
-26.120
-109 . 900*
-20.370
-0.066*
20.170*
-13.770
13.380
0.722*
-0.120
5.854
1.637
13.300
80.500
40.180
53,220
85.480
0.037
11.760
16.720
60.380
0.372
0.261
(2)
B 1968 s
47.04*
-1.306
16.610
-29.80
-0.056*
16.130*
-17.676*
88.710**
1.518*
-0.963
16.08
1.456
35.560
34.03
0.023
9.844
12.330
47.090
0.925
(3)
B 1969 s
3.252
-1.208
0.065
-52.320*
-66.732*
-0.071
-25.960*
67.510**
1.127
-1.199
0.606 | 1.122*
•
12.290
1.097
29.11
27.030
34.930
0.175
9.668
37.420
7.429
0.951
0.765
o
o
(continued)
-------
Table 5.6a
(continued)
Year
Variable
Constant
R2
S.E.
F
nNOX
nSUL
nTSP
(1A)
- & 1967 s
410.960
0.307
164.745
(13,80) = 4.731
0.308
(IB)
6 1967 s
322.546
0.296
166.030
(13,80) = 4.594
0.353
(1C)
6 1967 s
320.309
0.313
164.108
(13,80) = 4.800
0.544
(2)
6 1968 s
447.874
0.175
317.210
(10,389) = 6.139
0.326
(3)
B 1969 s
283.201
0.182
264.023
(10,389) = 5.473
0.474
(continued)
-------
Table 5.6a
(continued)
Year
Variable
DSAB
LDSA
AGEH
EDUC
POOR
RACE
SEXH
GIGE
EXER
FOOD
NCIG
RELG
RISK
INSR
CHEM
DENS
NOXT
NOXM
NOXN
SULT
SULM
SULN
TSPT
TSPM
TSPN
(4)
6 1970 a
76.490
0.485
-63.200*
18.490
-48.620
-37.120*
9.885
-3.280
2.520*
13.920
1.153
27.360
31.070
30.260
9.872
36.780
55.020
1.104
!
(5)
0 1971 s
47.990*
2.542*
-15.800*
-49.260*
-85.170*
-30.150
-0.030
-21.796*
7.439
2.257
1.453*
14.590
1.199
8.370
26.640
31.090
31.560
0.021
9.876
40.330
2.259
0.764
(6)
0 1972 a
180.800*
1.411
128.100*
4.435
20.740
-99.730
3.529*
-0.972
26.550
1.563
41.550
22.680
43.290
110.300
1.597
0.684
1.782* 0.780
l
(7)
0 1973 s
19.340
0.355
2.550
-14.190
-36.450*
-123.600*
54.410
0.056
0.223*
-0.361
-0.249
14.740
1.051
7.818
28.110
20.460
29.390
76.740
1.075
0.124
3.305
C.314
o
to
(continued)
-------
Table 5.6a
(continued)
Year
Variable
Constant
E2
S.E.
F
n
'NOX
n
SUL
•n
TSP
(4)
0 1970 s
305.260
0.123
262.333
(9,390) = 6.104
0.361
(5)
3 1971 s
172.464
0.123
252.936
(11,388) = 4.926
0.518
(6)
6 1972 s
-78.317
0.169
394.533
(9,390) - 8.836
0.497
(7)
8 1973 s
175.040
0.095
254.413
(11,388) = 4.435
0.618
o
00
*Signifleant at the 0.05 level of the one-tailed t-test,
**Signifleant at the 0.05 level of the two-tailed t-test.
-------
Table 5.6b
Dose-Response Rates for ACUT: Partitioned Samples
Year
Variable
DSAB
LDSA
AGEH
EDUC
MARK
POOR
RACE
SEXH
FOOD
NCIG
RISK
INSR
SULM
TSPM
EXER
DENS
Constant
R2
S.E.
F
NSUL
NTSP
(1)
1967
Always lived in 1 ntate
6 8
42.056*
0.384*
2.716
-17.037
31.832
-60.549
13.327
-0.061
5.643
-4.047
-75.286
-0.992
1.765*
6.538
0.187
2.302
85.185
46.812
53.583
9.005
0.057
3.239*
17.600
70.361
7.631
0.865
121.290
0.152
352.420
(14,306) - 6.621
0.952
(2)
1969
RING - < $7,500
B •
111.200*
2.889
117.800
-116.400
-1.648*
36.940*
32.950
80.820
5.135*
-4.031
37.590
3.488
75.310
78.780
0.559
22.710
27.840
86.440
3.020
3.020
566.723
0.186
443.738
(10,150) - 3.431
0.565
(3)
1969
3 £ NCIC £ 6
e s
17.960
-2.383
35.290
5.323
-0.084
34.030*
-4.700
-71.390*
0.007
-0.594
13.810
1.435
38.710
31.210
0.218
18.620
12.380
42.490
0.831
0.480
165.600
0.076
243.090
(10,268) - 2.191
(4)
1970
1 < DSAB < 3
e a
-94.990*
1.215
56.630
-66.900
-0.168
1.938
-54.560
0.114
1.215
200.600*
-31.710
34.430
99.450
86.310
0.519
35.750
117.000
2.930
2.210
125.600
21.700
482.897
0.122
449.633
(10,114) • 1.585
*Signifleant at the 0.05 level of the one-tailed t-test.
**Signifleant at the 0.05 level of the two-tailed t-test.
-------
Table 5.7a.
Dose-Response Rates for LDSA: Unpartitioned Samples'
Year
Variable
DSAB
AGEH
CITY
EDUC
FEDU
KARR
POOR
RACE
SEXH
FOOD
NCIG
RISK
INSR
CHEM
NOXT
NOXM
NOXN
SULM
SULN.
TSPM
TSPN
Constant
R2
S.E.
F
>X
nSUL
n
nTSP
(1)
B 1967 s
0.003
0.079
0.204
0.188
0.344
0.410 .
-0.7x10
0.023
-0.009
-0.152
0.0036
0.0021
-0.
0.007
0.054
0.284
0.157
0.200
0.297
0.26xlO"J
0.047
0.006
0.245
0.0025
0.0037
636
0.094
0.835
(12,134) - 2.158
(2)
B 1968 s
3.286*
-0.002
0.170
0.135
0.002*
-0.089*
-0.336*
0.0067*
-0.0036
0.227
0.007
0.416
0.163
0.001
0.041
0.218
0.0035
0.0024
0.631
0.371
0.736
(9,390) - 25.580
C3a)
B 1970 s
0.554**
0.005
0.013
-0.044
-0.069
0.072
0.139 .
-0.902
-0.454*
-1.645**
0.0028*
0.035
0.004
0.029
0.037
0.103
0.488
0.114
0.975
0.129
0.575
0.0011
2.980
0.525
0.964
(11,388) - 38.920
0.278
C3b)
B 1970 s
0.550**
0.005
0.001
-0.043
-0.065
0.088
0.132
-0.924
-0.459*
-0.097
0.0018*
0.035
0.004
0.029
0.037
0.103
0.487
0.113
0.973
0.129
0.575
_3
0.66x10
2.924
0.526
0.963
(11,388) - 39.170
0.341
an1." • •
(5A)
B 1971 s
0.808**
0.007*
-0.057
-0.044
0.086
• -0.057
0.233**
-0.13xlO-3
-0.496*
-0.002
0.0019
0.049
0.004
0.030
0.035
0.096
0.119
0.109
0.81x10"^
0.125
•0.916
0.0017
0.265
0.530
0.904
(11,388) - 39.800
0.268
o
Cn
(.continued)
-------
Table 5.7a
(continued)
Year
Variable
DSAB
AGEH
CITY
EDUC
FEDU
MARR
POOR
RACE
SEXH
FOOD
NCIG
RISK
INSR
CHEM
NOXT
NOXM
NOXN
SULM
SULN
TSPM
TSPN
Constant
2
R
S.E.
F
nNOX
nSUL
nTSP
(SB)
0 1971 s
0.809**
0.007*
-0.058
-0.043
0.088
-0.054
0.24Q**
-0.13x10-3
-0.499*
-0.016
0.59xlQ~3
0.049
0.004
0.030
0.035
0.097
0.119
0.109.,
0.81x10
0.125
0.917
0. 73xlQ~3
0.181
0.529
0.9.05
(11,388) = 39.680
(6A)
3 1972 s
0.023*
-0.057
-0.081
0.007
Q.1Q4
-0.272
-0.156
-Q.QQQ7
0.00.28
0.005
0.050
0.045
0.050
0.147
0.160
0.141
0.0017
0.0027
0.701
0.119
1.347
(9,390) = 5.879
0.376
(6B)
@ 1972 s
Q.02Q*
-Q.Q85
-0.125**
0.048
0.116
-0.220
-0.182
•
0.14x10
0.0030*
0.005
0.045
0.043
0.055
0.145
Q.154
0.142
O.'89x!0'3
O.Q013
1.054
0.134
1.315
(9,390) = 6.706
0.630
(continued)
-------
Table 5.7a
(continued)
Year
Variable
DSAB
AGEH
CITY
EDUC
FEDU
MARR
POOR
RACE
SEXH
FOOD
NCIG
RELG
INSR
CHEM
NOXT
NOXM
NOXN
SULM
SULN
TSPM
TSPN
Constant
R2
S.E.
F
nNOX
nSUL
nTSP
(7A)
0 1973 s
0.017*
0.155
-0.122*
0.059
0.050
-0.208
-0.207
0.0033
0.0017
0.044
0.140
0.043
0.052
0.143
0.154
0.141
0.0037
0.0015
0.309
0.106
1.3Q3
(9,390) = 5.785
(7B)
£ 1973 s
0.017*
0.180
-0.128*
O.Q57
0.029
-Q.202
-0.209
Q.QQ3
Q.OQ04
Q.OQ4
0.140
0.043
0.053
0.142
0.155
0.141
0.002
0.0017
0.505
Q.109
1.303
(9,390) - 5.290
(8A)
S 1974 s
0.017*
-0.118**
-0.291
0.300*
-0.001
-0.060
-0.459
-0.161
0.0023
-0.0047
0.0008
0.005
0.049
0.221
0.151
0.230
0.066
0.284
0.327
0.0017
0.0062
0.0028
-0.687
0.118
0.966
(11,214) «= 4.591
0.363
(8B)
6 1974 s
0.017*
-0.111**
-0.287
0.305*
0.005
0.049
0.221
0.151
-0.001 0.230
-0.067
-0.457
-0.131
0.0046*
0.0002
-0.0007
0.067
0.284
0.325
0.0025
0.0022
0.0019
-0.828
0.112
0.964
(11,214) = 4.693
1.143
(continued)
-------
Table 5,7a
(continued)
*Signifleant at the O.Q5 level of the one-tailed t-test.
**Significant at the 0.05 level of the two-tailed t-test.
a
All observations in this table are limited to individuals who have always lived in one state.
o
00
-------
Table 5.7b
Dose-Response Rates for LDSA: Partitioned Samples
Tear
Variable
DSAB
ACER
CITY
EDUC
FEDU
MARR
POOR
RACE
SEXH
FOOD
NCIC
RELC
RISK
IMSR
CKCH
COLD
NOXT
NOXK
NOXS
SULT
SULK
SCLS
TSPT
TSPM
TSPN
ULTV
Constant
,2
§•*•
":iox
nsut
"TSP
(i)
1971
50-cltiea
B *
-0.168**
0.025*
-0.401**
-0.057
-0.048
0.015
0.064
0.050
0.001
0.0047*
-0.0018
0.0078*
-0.51 x 10"5
0.068
0.006
0.190
0.047
0.040
0.019
0.045
0.679
0.002
0.0023
0.0032
0. 0038
0.16 x 10~3
-1.018
0.210
1.563
(14.304) - 5.762
0.470
0.94S
(2)
1969
» *
2.462*
0.163*
0.12 x 10"3
0.028
-0.012
-O.OOS
0.0025*
0.85 x 10
0.108
0.067
0.48 x 10
0.025
0.087
0.067
0.0013
0.20 x Ifl"
0.005
0.624
(9,34oV-662.58
0.608
0.514
<3A>
1972
AGEH > 45
B «
0.028*
-0.007
-0.080
0.001
0.181
-0.263
-0.178
0.0021*
-0.0008
0.008
0.055
0.048
0.060
0.155
0.166
0.153
0.0013
0.0035
-0.378
U.078
1.435
£9,390} - 5.899
0.253
(3B>
1972
ACEH > 45
B s
0.029*
0.031
-0.124**
-0.062
0.112
-0.028
-0.217
0.0017
0.008
0.059
0.045
0.060
0.151
0.169
0.156
0.0012
-0.037
0.083
1.438
(9,390) - 5.899
0.301
(4A>
1972
ACEH > 45 & MILE < 15
B ~ s
0.904**
0.020*
-0.115**
-0.055
-0.035
0.161
0.078
-0.119
0.0021*
0.054
0.006
0.046
0.035
0.046
0.155
0.130
0.119
0.0012
-0.285
0.464
1.101
(10.3«9) . 33.630
0.369
(4B)
1972
AGEH < 45 & MILE <. 15
6 >
0.897**
0.021*
-0.022
-0.045
0.020
0.078
-0.272*
-0.111
0.0013*
-0.0009
0.057
0.006
0.043
0.037
0.047
0.121
0.129
0.120
0.0007
0.0011
0.005
0.439
1.120
(10.389) - 30.490
0.327
•Significant at the 0.05 level of Che one-tailed t-test.
"Significant at the 0.05 level of the two-tailed t-teat.
All observations in this table are United to Individuals who have always lived in one atate, except for the observation* in (2).
These are Halted to individuals who currently llva within walking distance of relatives.
Thai air pollution variables for this axpreaalou refer to arithmetic Men~196S-71 feometric a*an concentrations In MC/B . Th«
referenced 50 cities are JO of the 60 cities used la the aursote swrMllty study that fern « jure of this report.
-------
coefficients to appear statistically non-significant when they are
properly viewed as significant.
There are, however, two very important exceptions to the supposed
absence of a multicollinearity problem: the types of air pollution tend
to be very highly correlated and different moments of the same pollutant
also are closely associated. As Table 5.5 shows, total suspended par-
ticulates and sulfur dioxide appear to have a very high linear association
as do all the moments of a particular air pollutant. If one were to
introduce nitrogen dioxide in Table 5.5, the linear association between
this pollutant and total suspended particulates and/or sulfur dioxide
would also be large, though somewhat smaller than that between the
latter two pollutants. For example, in 19.75, the simple correlation
coefficient between various measures of total suspended particulates and
nitrogen dioxide is never less than 0.5Q and sometimes reaches into the
0.70 or greater range. Given these close linear associations among the
t;ypes of air pollution, we are reluctant to assign a health effect to a
particular pollutant. Instead, it seems preferable to make the assignment
to the outdoor air pollution phenomenon. In addition, when one or more
air pollutants appear as explanatory variables in an estimated dose-
response expression, the standard errors of each will tend to be somewhat
inflated. Thus, a few of the air pollution coefficients to which we do
not attach significance sometimes would be significant if one or more of
the other air pollution variables were removed. Similarly, some of
those air pollution coefficients that are significant would be more
significant with the removal of a companion variable from the expression.
The above discussion does not deal with a dilemma posed by the issues
of bias and multicollinearity. If the different types or moments of air
pollution have separable impacts on health, then one biases the coefficients
of the remaining explanatory variables by deleting one or more of the air
pollution variables. Nevertheless, if one includes the highly collinear
air pollution variables, he reduces the apparent statistical significance
of any one of them. In this study, we do not directly attack the
dilemma by constructing and then applying rigorous criteria for choice.
We choose an easier and less rigorous course by estimating some expressions,
each from a different sample, that include all the types of air pollution,
while including only one type of air pollution in other expressions.
To a very substantial extent, this course was forced upon us by circum-
stances: for some years over the nine-year SRC survey interval, there
was no available information on particular types and moments of the
air pollution variables.
Table 5.5 exhibits one other intercorrelation that is a cause for
concern, namely a simple correlation coefficient of 0.70 between LDSA and
DSAB, i.e., between the duration of a chronic illness and its self-
reported severity. Relative to most other samples of the study, this
intercorrelation is a bit low. For most samples, it is closer to or in
excess of 0.80. Certainly, the length of a disease and its severity are not
identical. In fact, one might expect those who are severely disabled to
have relatively short disease durations: they are more likely to die.
We may thus have increased the intercorrelation between these two variables
by not making DSAB be monotonically increasing. The high intercorrelation
110
-------
arouses suspicions about whether the two variables might be measuring the
same thing, a clearly ridiculous state, if one is trying to explain the
covariation between the two variables. Furthermore, if air pollution is
expected to lengthen the duration of an illness, there is obvious reason
to think that it will also make an illness more severe. More accurately
perhaps, air pollution causes illness and increases the severity of
preexisting illness, thus in a recursive fashion lengthening, for those who
survive, illness duration* This implies that the estimated expressions
which include DSA6 as an explanatory variable are actually reduced form
expressions, where DSAB is determined within the structural system.
As a result, the single equation estimates with DSAB as an explanatory
variable are not asymptotically efficient although they are consistent
since DSAB is the only explanatory variable that would be determined within
the structure of a recursive system. If instead of DSAB being a determin-
ant of LDSA, it is actually another measure of the same thing in respondents'
views, then DSAB must be dropped from the estimated expression. For the
expressions estimated from some samples we include DSAB; for other
samples, we delete it, using whichever of the preceding rationales
conforms to the estimated expression. As we will see, inclusion or
exclusion doesn1t really make much difference to the signs and magnitudes
of the coefficients for the major variables of interest, the air pollution
variables. H/
In estimating dose-response expressions for chronic illness, we have
used LDSA rather than (or in addition to) DSAB because only the former
is stated in cardinal terms. LDSA, however, retains one disadvantage of
DSAB; as presented on the SRC tapes, it takes on only five values.
Although the first four of these values apply to approximate two-year
intervals, the last value might better be termed "a long time," since it
is meant to apply to disabilities lasting eight or more years. If one
interprets, as we shall do in this chapter, this last value to be
equal to exactly ten years, then the dependent variable for chronic
illness has. a measurement error that biases it downward, causing the
effects of the explanatory variables to be underestimated. This could be
a serious source of error since about 40 percent of those who are
disabled in any given SRC survey year, or seven to eight percent of the
total SRC respondent population, profess to have been disabled for eight
or more years. Given this problem, which we disregard until a succeeding
section, it is perhaps preferable to interpret the coefficients attached
to the explanatory variables in the estimated chronic illness dose-
response expressions as the proportion of one of the discrete values
comprising LDSA associated with a one unit change in the relevant
explanatory variable.
Yet another estimation issue is caused by the five discrete values
assumed by LDSA. This small number of discrete values means that
heteroskedasticity could be present in those expressions estimated by
ordinary-least-squares techniques. Ideally, multinomial logit estimation
would be employed; but because the number of parameters with multinomial
logit estimation increases so dramatically when the dependent variable
assumes more than two values, there is an explicit tradeoff between the
misspecification possibly introduced by the use of ordinary-least-squares
and the vastly increased cost and complexity of multinomial logit estima-
111
-------
tion. We have opted here for simplicity and lesser cost while not dis-
missing the heteroskedadicity issue: w.e estimate the chronic illness
dose-response functions by ordinary—least-squares hut peruse the estima-
ted results- by simple graphic techniques to check for the presence of
heteroskedasticity. Even if this undesirable property is present,
it does not fbllovr that our estimates will be biased and inconsistent.
They will not be efficient (they will not have the smallest variance in a
class of unbiased estimators), but they will be unbiased and consistent.
The problem with heterosfcedasdicity is thus not with the estimated co-
efficients themselves but rather with the calculated standard errors.
These standard errors are biased, thus invalidating the tests of signific-
ance for the estimated coefficients.
There are a number of results for acute illness in Tables 5,6a and
5.6b worthy of explicit note:
1) Of the seven different unpartitioned samples used to estimate
acute illness dose-response expressions, statistically significant air
pollution coefficients occur in all of them. Thus, an additional unit of
air pollution, as defined by any of the variety of measures employed here,
was associated with an increase of from one to four hours in average annual
hours of acute illness. Except for 1973, magnitudes of the air pollution
coefficients are quite stable frori one sample to another, even though
the specifications for the expressions often differ substantially. No
tests have been performed to establish whether there are statistically
significant differences in the air pollution coefficients across samples.
2) For the unpartitioned samples, the elasticity, n_, of acute
illness with respect t^o any of the air pollution variables (a unitless
measure of the response of acute illneas to variations in air pollution^
is substantially less than unity. Thik implies that in the immediate
neighborhoods of the sample values of these variables, average annual
hours of acute illness is increasing at 'a decreasing rate with respect to
increases in air pollution.
31 Two of the four partitioned samples in Table 5.6b do not have
statistically significant air pollution coefficients. If air pollution
has any impact upon the frequency of acute illnesses among individuals
who are chronically disabled and who live in families where a pack
or more of cigarettes is smoked, the estimataion techniques and sample
sizes employed here are incapable of capturing it.
. 4) When measures of total suspended particulates and sulfur
dioxide are included as explanatory variables in the same expression, the
coefficient for them usually assumes a negative sign. Generally, total
suspended particulates will take on the negative sign. Similarly, when
sulfur dioxide and nitrogen dioxide are included as explanatory
variables in the same expression, nitrogen dioxide often assumes a
negative sign. For estimated expressions in which total suspended
particulates and/or nitrogen dioxide are used as explanatory variables,
but which do not include sulfur dioxide, both of the former air
pollutants have positive signs. These sign switches could be due
to the high linear associations among the pollution variables.
'112
-------
5) With some exceptions, an increase of one discrete value in
either of the measures of chronic illness tends to increase the
average annual hours of acute illness by from 20 to 40 hours.
6) With the sole exception of the variables for a poor child-
hood and race, the variables representing biological and social endow-
ments fail to play a statistically significant and consistent role in the
acute illness dose-response expressions. It is possible, of course,
and perhaps even likely, that the race and childhood background variables
are capturing many of the effects of low education, etc.
7) The life-style variables in the acute illness dose-response
expressions consistently have the expected signs and are often statistically
significant. This is particularly true for the exercise and nutritional
adequacy variables: they reduce average annual hours of acute illness.
8) Contrary to expectations, the explanatory variable for
availability of medical care, INSR, usually has a positive sign, implying
that people with better access to medical care have more acute illness.
We have no explanation for this other than a pure speculation that
people with better access to medical care are more likely to
recognize the symptoms of acute illness, perhaps because physicicians
provide them with the information to recognize these symptoms. On
the other hand, INSR might simply be a poor measure of the respondents'
access to medical care.
9) Other than air pollution, only two alternative measures
of the respondents' environments were employed as explanatory variables.
These variables were used in only a limited number of samples. DENS,
the number of persons per room in the respondents' residence, increas-
ed average annual hours of illness by more than three in the single sample
where it was statistically significant. The variable for employment
in the chemicals and metals manufacturing sectors had too small a
number of individuals in each sample to yield statistically
meaningful results.
10) Visual inspection of the residuals for expression (1A) of
Table 5.6a and expression (1) of Table 5.6b did not reveal any
serious heteroskedasticity problems.
113
-------
We tentatively conclude from the preceding findings that the life-style
and environmental variables* including air pollution, we have used probably
play a significant role in acute illness. The evidence for the biological
and social background and the access to medical care variables is substan-
tially less clear both because of measurement problems and because racial
differences in educational and childhood environment may be reflected in
simple binary variables for race and a poor childhood. Finally, it should
be noted that none of our expressions "explains" a very large portion of the
variation in acute illness. The coefficients of determination never exceed
0.31 and are often about 0.10. Moreover, the constant term in each expres-
sion nearly always exceeds the sum of the coefficients of the explanatory
variables. This is, of course, partly due to the scaling of the variables,
but, given the number of binary variables (MARK, POOR, RACE SEXH, RELG,
INSR), one might reasonably have not expected quite such a difference. The
relatively unimportant role that many of the most statistically significant
variables play in total variation in annual hours of acute illness is evident
in the following partial coefficients of determination for variables ap-
pearing in various expressions of Table 5.6a: for expression (7), NOXM «
0.004, SEXH = 0.044, and and LDSA = 0.004; for expression (IB), SULM « 0.021,
FOOD - 0.002, RACE - 0.043, NCIG - 0.029, and DSAB = 0.136; and for expres-
sion (5), TSPM = 0.013, POOR = 0.024, DSAB = 0.124. With no more than one or
two exceptions, the two variables for chronic illness, LDSA and DSAB, made
the largest contributions to explaining variations in annual hours of acute
illness.
Tables 5.7a and 5.7b give the estimated dose-response expressions for
chronic illness. The following features stand out in these expressions.
1. Of the twelve different partitioned and unpartitioned samples
present in Tables 5.7a and 5.7b, air pollution coefficients are statistically
significant in nine of them. Not all air pollution coefficients are statis-
tically significant in the samples where more than a single air pollution
variable appears, nor are the signs always positive for those air pollution
coefficients that are statistically nonsignificant. No pattern similar to
the negative signs that are attached to sulfur dioxide or other pollutants
when sulfur dioxide is used as an explanatory variable in the acute illness
dose-response expressions appears here, however. Of the samples having no
air pollution coefficients statistically significant at the 0.05 level or
better of the one-tailed t-test [expressions (1), (5), and (7) in Table
5.7a], all had air pollution coefficients with positive signs and t-values
in excess of 1.0. Two of these samples [expressions (1) and (7)] had air
pollution coefficients statistically significant at the 0.10 level of the
one-tailed t-test. The magnitude (and signs) of the air pollution coef-
ficients for expressions (1), (5), and (7) were similar to the magnitudes
and signs of the air pollution coefficients for the other samples. They
ranged between slightly less than 0.0020 and slightly more than 0.0045,
with the bulk being between 0.0020 and 0.0030. This means that a change
between 0.2 and 0.4 or 0.5 percent in one of the discrete values comprising
LDSA is caused by a one-unit change in air pollution. In elasticity terms,
these discrete values (index) of LDSA appear to be relatively unresponsive
to changes in air pollution. Nearly all the elasticities of the discrete
chronic illness index with respect to air pollution are in the 0.2 to 0.5
114
-------
range, implying that a one percent change in air pollution generally causes
a change in thfa index of substantially less than one-half of one percent.
As was true for the acute illness dose-response expressions, this means that,
in the immediate neighborhoods of tSe chronic illness index values and the
air pollution values present in these samples, chronic illness duration in-
creases at a decreasing rate with respect to increasing air pollution.
2. As earlier noted, translating the coefficients for the explanatory
variables in the chronic illness dose-response expressions is invalid
because the highest value in the index could, in real-time terms, be any-
thing equal to or in excess of eight years. Nevertheless, if one assumes
that the real-time involved in this last index value is equivalent to that
in all the lower values, than the translation can be performed. With this
assumption, the air pollution coefficients imply that an additional unit
of air pollution is, on average, associated with an increase of from one
and one-half to three and one-half days in the duration of chronic illness.
As before, even with the aforementioned assumption, this rate is applicable
only in the Immediate neighborhoods of the chronic illness index values and
the air pollution values present in'the samples.
3. In those unpartitioned expressions where it is employed as an
explanatory variable, the severity of the respondent's disabilities has
a highly significant, positive, and strong effect on the duration of these
disabilities. The partial coefficient of determination of DSAB with respect
to LDSA was consistently about 0.40. The inclusion of DSAB in expressions
did not appear to have an effect on either the magnitudes or the signifi-
cances of theV air pollution coefficients. Similarly, its presence or absence
did not seem to make much difference to coefficients for the other explan-
atory variables.
4. Results for the biological and social endowment variables are
mixed. Only respondent age is consistently significant with the expected
sign. Generally, as expected, the level of the respondent's education is
associated with lesser durations of chronic illness, but it is only occasion-
ally significant. Poor parents tend to be consistently associated with
increased chronic illness durations, but POOR is statistically significant
in only one sample. Otherwise, variables such as CITY, FEDU, MARR, RACE,
and SEXH contributed very little to the expressions. Rarely were they
significant statistically. More importantly, their magnitudes and their
signs proved to be expremely sensitive to whatever specification was
adopted.
5. Because it is not clear that the magnitudes of lifestyle variables
are independent of the duration of chronic illness, fewer of them were used,
and those that were used were used less frequently, than in the acute
illness dose-response expressions. EXER is an obvious case and it has not
entered the chronic illness expressions. In fact, except for RELG, food
adequacy is the only explanatory variable that enters the expressions
estimated for more than one sample. It always has the expected sign but is
never quite statistically significant at the 0.05 level selected for this
study. On the rare occasions when they appear, both cigarette consumption
and fundamentalist religious affiliations have the expected signs. RELG in
expressions (7A) and (7E) just Barely misses Being crowned with statistical
115
-------
respectability. Since religious affiliations seem likely to remain un-
changed whether or not one is disabled, this variable probably should
have been included for the expressions estimated from each sample.
6. The variable representing the availability of medical care,
INSR, performed well for those four samples where it was used. Its sign
was consistent with an interpretation that medical care availability
reduces the duration of chronic illness. Unfortunately, its sign is also
consistent with another interpretation: those who are chronically ill have
difficulty procuring medical insurance. This latter interpretation means
that INSR cduld be a function of LDSA. Given these conflicting interpre-
tations, and having no information on which interpretation is likely to
dominate, we have compromised and included INSR in some expressions while
neglecting it in others. Its inclusion or exclusion does not appear to have
any discernable effects on the coefficients for the air pollution variables.
7. Of the environmental variables, only CHEM seems worthy of comment.
In the one expression where they appear, neither COLD nor ULTV were statis-
tically signficant although COLD did have a positive sign. The statistical
significance of CHEM in expression (3) of Table 5.7a should be disregarded.
Expression (3) was estimated from a sample having only three people employed
in the chemicals and metals manufacturing sector. None of these three
people had a chronic disability.
8. With the exception of DSAB, none of the included explanatory vari-
ables explain substantial proportions of the variation in the index for dur-
ation of chronic illness. The air pollution variables, taken together,
explain no more than two percent of the variation in LDSA; AGEH sometimes
explains as much as five percent and EDUC usually explains around three per-
cent of this variation. As with the acute illness dose-response functions,
we have not been able to account for very much of the sources of variation
in chronic illness.
9. Table 5.7b exhibits the estimated expressions for samples that were
restricted to the values of the variables indicated at the top of each col-
umn. Contrary to similar restrictions placed on the samples for the acute
illness expressions, these restrictions did not alter the explanatory vari-
able coefficients in any noticeable fashion.
10. The patterns of the residuals for several of the expressions in
Table 5.7a have been visually inspected for evidence of heteroskedasticity.
When this problem is present, it appears that the residuals tend to increase
with increasing values of the dependent variable. Because the highest dis-
crete value of LDSA has no upper bound, it is likely that the true variance
of the sample tends to increase with increasing values of LDSA. As Kmenta
(1971, p. 256) shows for expressions with a single explanatory variable, if
the residuals and the sample variance are positively associated, the stand-
ard errors of the coefficients for the explanatory variable will be biased
downward, causing the t-value to be too great. This need not be true, how-
ever, for expressions with multiple explanatory variables. The extent to
which this has resulted in exaggeration or underestimates of the levels of
significance for the chronic illness dose-response expressions is presently
116
-------
Table 5.8
Lagged Effects of Total Suspended Particulates upon Duration
of Chronic Illnesses (LDSA) of Respondents Who,
as of 1975, Had Always Lived
in the Same State
AGEH
EDUC
MARR
POOR
SEXH
FOOD
RELG
CHEM
TSPM5
TSPM4
TSPM3
TSPM2
TSPM1
TSPMO
TSPM9
(1)
Unweighted
e
0. 012*
-0.009
-0.331*
0.150*
-0.012
-0.035*
-0.003
0.249 _4
0.4 x 10
0.001
0.001
0.003
0.008*
0.007
0.006
s
0.004
0.040
0.160
0.110
0.023
0. 021
0.030
0.247
0.061
0.033
0.003
0.016
0.004
0.011
0.006
(2)
Weighted
3
0.017*
-0.103*
-0.237
0.327*
0.046
-0.076
-0.501*
-0.147
0.002
0.001
-0.001
-0.003
-0.003
0.004
0.002
s
0.005
0.050
0.232
0.153
0.235
0.074
0.286
0.332
0.003
0.005
0,004
0.004
0.005
0.005
0.005
Constant
R2
S.E.
F
0.444
0.184
1.032
(12,347) - 6.481
-0.690
0.129
0.969
(15,210) = 4.082
*Statistically significant at the 0.05 level of the one-tailed t-test.
117
-------
unknown. The heteroskedasticity appears to be by far the most prominent
for those estimated expressions having coefficients of determination less
than 0.10.
It is widely thought that pollution-induced chronic illness is usually
the result of cumulative, rather than instantaneous, exposures. Previously
we have taken the position that, if only non-movers are represented in the
sample, air pollution exposures during the year for which the respondent
reports his behavior and status serve as adequate proxies for differences
among respondents in cumulative exposures. If this position is at all
tenuous, we have available the data to remedy it at least partially; that
is, we have available information on respondent residential locations and
air pollution exposures for a number of years. Table 8 presents some pre-
liminary results involving an attempt to estimate the lagged effects of
total suspended particulates upon the duration of chronic illness for 1975
respondents who have always lived in the same state. Since it is unclear
exactly what a lagged effect of pollution upon the duration of an illness
means, we exploit the high intercorrelation between LDSA and DSAB and inter-
pret the expressions in terms of the lagged effects of air pollution upon
the severity of chronic illness. As in earlier tables, the integers attached
to the acronym for mean total suspended particulates refer to the year. Thus,
for example, TSPMO refers to particulate concentrations in 1970.
The expressions presented in Table 8 have involved no tinkering: these
are the first expressions having LDSA as a dependent variable that have
used either of these samples. Expression (1) is an unweighted lag in which
earlier air pollution concentrations are simply entered as additional explan-
atory variables. In spite of the very high simple correlation coefficients
(Z 0.80) among the air pollution values of the various years, at least one
year (1971) is statistically significant. Moreover, the magnitude of the
coefficient increases from 1975 to 1971, and then starts to decline. We
have no explanation for this rather neat pattern and tend to suspect that
its very neatness in an anamoly that would fail to emerge in expressions
estimated from other samples. These other samples have not yet been ex-
ploited .
The air pollution series in expression (2) has more structure imposed
on it. In particular, the series is assumed to follow a geometric lag
distribution where the coefficients decline in fixed proportions, causing
the impact of more distant air pollution concentrations to become pro-
gressively smaller. Clearly, expression (2) does not accord any importance
to total suspended particulates. However, this does not mean that all
weighted lag structures will give similar results. Estimation techniques
are available that allow one to fit polynomial structures of any degree.
These techniques have not been applied here.
In concluding these remarks about dose-response functions, we must
make explicit a feature of the SRC data set that could readily cause the
morbidity effects of air pollution and other negative health influences
to be biased downward. This possible bias is due to ;the retrospective
feature of the SRC data: living individuals are questioned about their
behavior and status during the preceding year. The problem arises because
118
-------
some potential respondents who were alive during the preceding year are
dead by the time the interview occurs. Presumedly, those who died would
tend to be those who were most seriously ill. If air pollution and other
negative health influences contribute to this seriousness, or if those
who are most seriously ill are most sensitive to air pollution, then the
health impact of air pollution will be understated. Thus, the dose-response
functions presented here are relevant only for those individuals who man-
aged to survive over the time interval which the interviews described and the
calendar date at which the interviews occurred. This qualification applies
to all sections of this report where the SRC data is exploited. It is not
a minor qualification since approximately five percent of the respondents
died between interview years.
5.A Recursive Estimates of the Effect of Air Pollution Upon Health, Labor
Earnings, and Hours of Work
In the past decade, a number of empirical studies have appeared that
describe the effect of health status upon labor productivity, where pro-
ductivity effects are measured in lost earnings and work-time.-^' At the
same time, numerous epidemiological studies that.attempt to associate health
status with air pollution have been published J^£' Thus far, no one has tried
to combine the two study objectives in order to grasp the effect of air pol-
lution upon either of the aforementioned measures of labor productivity.
This section is a first attempt to do so. Labor productivity effects have
never been explicitly included in quantifications of the benefits of national
air pollution control efforts. Our results suggest that these productivity
effects could constitute a significant portion of these benefits and are
certainly worthy of further study.
In spite of a number of limitations which will later be exposed, the
section has at least three unusual, if not utterly novel, features. First,
although it treats health status as an exogenous rather than endogenous
variable, a structural equation for health status is specified. This
contrasts with nearly all epdemiological studies, where the analysis is
confined to reduced-form health status, making any direct assignment of
health effects to air pollution an extremely tenuous operation. Second, the
health parameters in this section are estimated in the context of structural
expressions for hourly earnings and annual hours of work. Finally, possible
differences in effects of air pollution upon crude measures of acute and
chronic generalized health status are recognized. The null hypothesis is
that air pollution, by enhancing initial susceptibility and by making re-
covery more difficult, causes acute and/or chronic health problems. This,
of course, was the theme of the previous section. In this section, we
wish to ascertain the impact, if any, of these air pollution-induced health
adversities upon earnings rates and hours worked. Thus through the inter-
mediary of any health problems it induces, air pollution can be said to
indluence labor productivity.
Even though health is treated as being exogenously determined, the Gross-
man (1972) model of health production can serve as the analytical foundation
of the expressions to be estimated.1A' This model views the individual as
the producer, via his selections of mixes of market-purchased goods and his
own time, of health status. Within the context of this approach, earnings
119
-------
Table 5.9
Simple Correlation Coefficients Between Labor Supply and
Certain Other Variables for a 1970 Sample
WORT
&DALO
UHK
UIOR
MHC
XCTK
ACOT
DSAB.
LDSA
ACEH
CXTT
EDOC
1H»
rasz
KXK
IACX
SXXH
DEER
FOOD
BISK
OS*
CH£M
SDLT
S01M
SULK
TSPt
TSPM
T«n
WAGE
0.085
0.235
-0.038
-0.039
0.465
-0.421
-0.042
-0.134
-0.141
0.017
0.094
0.165
0.044
-0.038
-0.114
-0.014
0.072
0.072
-0.007
0.139
0.088
-0.012
-0.037
-0.038
-0.056
0.002
0.046
0.058
WORK
1.000
-0.629
0.012
-0.468
-0.441
-0.174
0.016
0.323
0.131
-0.046
-0.116
0.008
0.448
0.161
-0.078
0.235
0.505
-0.033
-0.174
-0.137
-0.109
0.081
-0.005
0.009
BDALO LTWK
0.287 0.123
1.000
0.070
0.108
0.656
-0x167
-0.170
-0.156
-0.143
0.197
0.018
0.493
0.244
-0.424
-0.126
0.139
0.360
0.193
-0.058
0.538
0.439
-0.082
-0.163
-0.113
-0.077
0.087
0.086
0.122
ICTR UION
-0.629 0.101
-0.167
0.155
-0.131
-0.268
1.000
-O.102
0.325
0.303
0.156
-0.057
-0.172
-0.132
0.165
0.094
-0.199
-0.284
-0.150
-0.239
-0.138
-0.413
0.040
0.085
0.083
0.048
0.066
0.044
0.046
RING
0.479
0.656
0.054
0.070
1.000
-0.268
-0.079
-0.227
-0.190
0.107
0.092
0.465
0.148
0.094
-0.058
0.018
0.480
0.217
-0.061
0.427
0.440
-0.022
-0.183
-0.134
-0.127
0.075
0.130
0.170
120
-------
rates depend on various forms of investment in human "capital" (e.g., edu-
cation, prior lifestyles, and medical inputs) and labor market conditions;
and the time supplied to the labor market depends on the individual?s hourly
earnings and the quantities of goods and time desired for household pro-
duction and consumption. Health states depend on the prior resources the
individual has devoted to their production.
Except for certain of the environmental variables, the data used" to
estimate the model consist of four distinct samples drawn from the 1969,
1970 and 1971 SRC interview data. Several variables, defined in Table 5.1,
are used in this section that were not used in the preceding section. For
one of the samples, Table 5.9 provides the simple correlation coefficients
between these additional variables and some of the other previously used
variables. Representative means and standard deviations for the additional
variables are available in Table 5.2.
Table 5,9 gives little attention to LTWK and UION because our major
interest in them is their association with WORK, WAGE, and RING. Absenteeism
was checked in this sample but apparently none of the respondents would
admit to being absent from work for reasons other than sickness. As was
noted in Table 5.4, where 81.1 percent of the respondents had annual asset
incomes of no more than $500, most of the respondents' annual incomes not
earned during the current year appear to be governmental transfer payments.
This accounts for the negative and high correlations between ICTR and RINC
and WAGE. Note also in Table 5.9 that the simple correlations between the
two chronic illness measures, DSAB and LDSA, and WORK and RINC are quite
high.
The household head's annual number of work hours, WORK, and his hourly
earnings, WAGE, are used as the empirical representations of the endogenous
variables in the model. Remember from the definitions of Table 5.1 that
WAGE is an approximation of the marginal, rather than the average, wage
rate. Annual number of work hours is used as the sole measure of labor
supply because the sample contains no information on the seasonal distri-
bution of hours when working. Neither vacation time nor sick time is in-
cluded in annual hours worked, even if the individual was paid during these
times.
The system to be estimated for each sample consists of four expressions:
a chronic illness expression; an acute illness expression; a wage expression;
and a labor supply expression. A representation, in implicit form, of this
structural system is as follows:
1. LDSA = f(Biological and social endowments, Lifestyles, Medical
care, Environmental). (5.1)
2. ACUT = g(LDSA, Biological and social endowments, Lifestyles,
Medical care, Environmental). (5.2)
3. WAGE = h(LDSA, ACUT, Cost-of Living, Experience, Biological and
social endowments). (5.3)
121
-------
4. WORK = k(WAGE, LDSA, ACUT, Transfer income, Wealth). (5.4)
As structured, this system is obviously recursive.
A great deal of research is available [e.g., Lazear (1976)] showing
that earnings are positively related to formal and informal schooling.
Good health is here viewed as having effects on earnings analogous to the
effects of increased schooling; that is, good health increases the individ-
ual's marginal value productivity and therefore raises his marginal earnings.
In addition, previous good health may have had an indirect effect on earn-
ings, by easing the task of achieving schooling success and thereby ultimately
improving the individual's productivity and associated earnings. The EDUC
and LOCC variables in (5.3) are intended to capture the effects of training
upon earnings. They may also reflect, in part, the influence of past health
status. The health status variables, ACUT, DSAB, and LDSA, in (5^3) regis-
ter the effect of current health status, via the effect on productivity,
upon earnings. Since chronic illnesses reflect long duration, as opposed
to temporary, reductions in productivity, we expect wages to exhibit greater
responsiveness to the chronic illness variables than to the acute illness
variable.
In addition to the aforementioned variables, the marginal earnings
expression includes variables representing the 1970 cost-of living in the
county of residence as well as variables representing the individual's race
and sex. If, as is frequently asserted, being non-white or female negatively
influences marginal earnings, either labor market discrimination or less
market productivity in the current period could account for the influence.—'
The structural system we employ is incapable of distinguishing between the
two possible influences.
Cost-of-living, BDAL, in the county of residence is accounted for in
(5.3) because it is real marginal earnings, rather than money earnings,
that limit the extent to which the individual is able to satisfy his
cravings and yearnings.
As Mincer (1970) and others have shown, earnings expressions similar
to (5.3) should be semi-logarithmic, where the dependent variable is the
logarithm of the earnings term. In this paper, we presume the earnings
expression to be linear in the original variables. This presumption was
adopted in order to obtain a sample of individuals possessing reasonable
variability in the values of the health variables, earnings, and hours
worked. If, in order to avoid having to assign positive earnings to indi-
viduals who really had zero earnings, only individuals who actually had
positive earnings were included in the sample, the variability of the
chronic disability measures would have been substantially reduced, thus
requiring that inferences about the influence of air pollution on health,
earnings, and hours worked be drawn from the relatively few remaining indi-
viduals whose health status and work patterns differed substantially from
the mean. Moreover, dropping individuals with zero earnings from the
sample would have meant that those individuals with long-standing and/or
severe chronic health problems would be excluded.
122
-------
Expression (5.4) the annual hours worked or labor supply expression,
is consistent with the treatments of health capital in Grossman (1972).
Improvements in health states increase the total time available for work
and for consumption. With real earnings and consumption opportunities
held constant, the consumer would be inefficient, assuming he was initially
in equilibrium, if he allocated all this additional time solely to consump-
tion. This is because the ratio of consumption time to work would rise,
causing the marginal value of consumption time to become less than the
marginal earnings that could be obtained. To recover equilibrium the indi-
vidual would have to devote the additional time to both work and consump-
tion. We therefore expect the amount of work time to increase with improve-
ments in health status.
In addition, since health status is assumed to be exogenous, an
improvement in health would increase the wage rate as well as the pecuniary
equivalent of time spent in consumption. In terms of the household produc-
tion approach to consumer theory, "full income" would be increased. The
health improvement therefore would constitute a pure income effect, causing
the individual to increase the value he attaches to any unit of consumption
time. This increase in the value of consumption time would cause the indiv-
idual to increase his demand for those marketed goods permitting him to use
this more highly valued consumption time with greater effectiveness. The
purchase of these marketed goods requires that he obtain more income, and
therefore that he increase his work time.
An increase in income not earned in the current period, ICTR, would
also result in a pure income effect. However, because the additional income
is not a consequence of improvements, in work productivity, the value of work
time relative to consumption time decreases, assuming the wage rate and
health status to be invariant. The result is that with an increase in
income not earned in the current period, the individual must reduce work
time in order to restore equilibrium.
The preceding remarks indicate why the sign of the marginal hourly
earnings variable, WAGE, in (5.4) is ambiguous. An increase in marginal
hourly earnings would increase the value of work time relative to the
value of consumption time, causing the former type of time to be substi-
tuted for the latter. However, the increase in marginal hourly earnings has
simultaneously increased the individual's "full income," causing the value
he attaches to any given unit of consumption time to increase. Whether the
increase in the value of consumption time exceeds the increase in the value
of work time is an empirical question.
Since the immediately preceding remarks refer only to real marginal
hourly earnings, (5.4) includes BDALO, the cost-of living index, in order
to control differences in real earnings among counties of residence.
The four-equation system, in which acute and chronic illnesses are
exogenously determined, represents a strictly recursive system. First,
health status is determined independently of hourly earnings and hours
worked, and then health status is used to determine hourly earnings and
hours worked. Similarly, hourly earnings are determined independently of
123
-------
Table 5.10a
a b
Empirical Results for a 1971 Sample '
Recursive Labor Supply
1. LDSA = -1.018 + 0.06(NCIG) - 0.17(DSAB)* + O.OS(RELG) - O.AO(CITY)*
(0.04) (0.07) (0.68) (0.19) ..
- O.OS(FEDU) + 0.06(EDUC) + 0.15(FOOD) + 0.025(AGEH)*
(0.04) (0.05) (0.19) (0.006)
+ O.OOl(COLD) + O.OOl(ULTV) - 0.002(SULM) + 0.005(NOXM)*
(0.002) (0.002) (0.003) (0.002)
+ 0.008(TSPM)*
(0.004)
R2 - 0.21; F(13, 305) - 5.76; S.E. = 1.56
2. ACUT - 35.397 + 0.25(NCIG) - 0.38(DSAB) - 4.98(LDSA) - 47.39(EXER)
(6.20) (9.40) (7.59) (35.76)
+ 5.14(EDUC) - 0.36(AGEH) + 0.06(COLD) - O.Ol(ULTV) - 0.38(SULM)
(4.85) (0.87) (0.27) (0.02) (0.44)
+ 0.06(NOXM) + 0.49(TSPM)
(0.31) (0.52)
R2 - 0.15; F(ll, 307) - 0.43; S.E. = 215.15
3. WAGE - -5.619 + 0.08(BDALO) + 0.02(ACUT) - 156.70(SEXH)* + 33.46(LOCC)*
(0.06) (0.10) (44.41) (10.81)
- 3.00(DSAB) - 41.73(LDSA)* + 20.31(EDUC)* + 50.80(RACE)
(14.35) (15.72) (10.20) (32.08)
R2 = 0.20; F(8, 310) = 9.72; S.E. = 367.66
4. WORK - 2011.671 - 0.12(BDALO) - O.Ol(ACUT) - O.OS(ICTR)* + 123.40(SVGS)*
(0.15) (0.23) (0.01) (26.35)
- 10.55(DSAB) - 212.00(LDSA)* + 0.50(WAGE)*
(34.26) (36.52) (0.13)
R2 = 0.35; F(7, 311) = 23.68; S.E. - 865.51
(continued)
124
-------
Table 5.10a
(continued)
a
Standard errors are in parentheses.
The sample includes only respondents who resided in 50 large U.S. cities.
*Significant at the 0.05 level of the one-tailed t-test.
125
-------
Table 5.10b
Empirical Results for a 1970 Sample3
Recursive Labor Supply
1. LDSA » 2.980 + 0.554(DSAB)** + 0.005(AGEH) + 0.013(EDUC) - 0.044(FEDU)
(0.035) 0.004 0.029 . 0.037
- 0.069(POOR) + 0.072(RACE) -f 0.139(SEXH) - 0.902(FOOD) - 0.454(lNSR)*
0.103 (0.488) (0.114) (0.975) (0.129)
- 1.645(CHEM)* + 0.0028(TSPM)*
(0.575) (0.0011)
R2 - 0.525; F(ll,388) = 38.920; S.E. - 0.964
2. ACUT = 165.208 + 39.52(LDSA)* - 1.421(AGEH) - 16.92(SEXH) - 0.086(CIGE)b
(13.34) (1.312) (39.16) (0.118)
- 78.40(EXER)* - 0.105(FOOD)* - 38.84(RISK) + 187.0(INSR)** + 0.623(TSPM)*
(40.11) (0.033) (13.26) (47.47) (0.317)
R2 - 0.195; F(10,389) = 6.139; S.E. = 204.462
3. WAGE = -132.318 - 25.930(LDSA)* + 24.070(EDUC)* + 15.370(DSAB)
(14.440) (8.5780) (18.260)
+ 26.88d(FMSZ)* + 42.380(BDALO)* + 52.950(LOCC)* - 7.163(LTWK)
(6.079) (6.138) (22.130) (33.88)
+ 66.090(UION)* + 47.60(RACE)
(34.580) (34.22)
2
R = 0.408; F(ll, 388) = 24.28; S.E. = 258.908
4. WORK = 1266.680 - 163.900(LDSA)* + 0.354(WAGE)* + 44.260(FMSZ)*
(27.220) (0.130)
+ 519.800(SEXH)* - 0.272(1CTR)* + 23.060(BDALO) - 0.074(ACUT)*
(80.27) (0.022) (15.200) (0.031)
R2 = 0.551; F(6, 393) = 80.41; S.E. = 663.196
Standard errors are in parentheses
Annual family expenditures on cigarettes in dollars
*Significant at the 0.05 level of the one-tailed t-test.
**Significant at the 0.05 level of the two-tailed t-test.
126
-------
Table 5.10c
a
Empirical Results for a 1971 Sample
Recursive Labor Supply
1. LDSA = 0.265 + 0.808(DSAB)** + 0.007(AGEH)* - 0.057(EDUC)* - 0.044(FEDU)
(0.049) (0.004) (0.030) (0.035)
+ 0.086(POOR) - 0.057(RACE) + 0.233(SEXH)** - 0.138xlO~^FOOD)*
(0.096) (0.119) (0.109) (0.81 x 10 4)
- 0.496(INSR)* - 0.002(CHEM) + 0.0019(TSPM)
(0.125) (0.916) (0.0017)
R2 = 0.530; F(ll,388) = 39.800; S.E. = 0.904
2. ACUT = 99.839 + 0.985(AGEH) + 55.55(INSR)* - 67.50(EXER)* - 0.052(FOOD)*
(1.038) (27.69) (33.34)
- 10.59(RISK) + 21.784(LDSA) + 1.177(TSPM)*
(11.29) (12.637) (0.676)
2
R = 0.091; F(10, 389) = 4.095; S.E. = 236.224
3. Acute illness, ACUT, is assumed not to effect marginal hourly earnings.
Marginal hourly earnings expressions that include ACUT as an explanatory
variable have been estimated from three different samples. In each
case, ACUT has proven to be statistically nonsignificant. See, for
example, expression (3) of Table 5.10a.
4. WORK = 682.263 - 0.078(ACUT)* - 50.119(LDSA) - 154.20(DSAB)*
0.032 (34.073) (46.490)
+ 30.460(FMSZ)* + 515.000(SEXH)* - 0.2771(ICTR)* + 8.969(BDALO)
(14.02) 76.190 (0.022) 7.148
R
2 = 0.562; F(7, 392) = 72.34; S.E. = 654.473
Standard errors are in parentheses.
*Significant at the 0.05 level of the one-tailed t-test.
**Sij>nificant at the 0.05 level of the two-tailed t-tost.
-------
Table 5.10d
Si
Empirical Results for a 1969 Sample
Recursive Labor Supply
1. LDSA = -0.223 + 0.041(NCIG)* - 0.090(INSR) + 1.964(DSAB)*
(0.019) (0.104) (0.109)
+ 0.1212(POOR) - 0.098(EDUC) + 0.10 x 10~^(FOOD) + 0.003(AGEH)
(0.078) (0.199) (0.52 x 10 ) (0.003)
+ 0.0013(TSPM) + 0.0018(SULM)
(0.0011) (0.0021)
R2 = 0.478; F(9,390) = 39.69; S.E. = 0.736
2. ACUT = 447.874 +16.61(MARR) + 16.13(NCIG)* - 88.71(INSR)*
(35.56) (9.844) (47.09)
+ 47.04(LDSA)* - 29.80(POOR) - 0.564(FOOD)* - 7.676(RISK)
(16.08) (34.03) (0.231) (12.33)
- 1.306(AGEH) - 0.963(TSPM) + 1.518(SULM)*
(1.456) (0.706) (0.925)
R2 = 0.095; F(10,389) = 3.139; S.E. = 317.201
3. WAGE = 49.305 + 1.275(FMSZ) -I- 28.20(LOCC)* - 12.07 (LDSA)*
(2.869) (4.312) (7.203)
+ 34.98(UION)* - 24.16(EDUC) + 136.6(RACE)* -f 116.9(SEXH)*
(15.73) (38.13) (16.95) (17.75)
R2 = 0.411; F(7,392) = 39.03; S.E. = 143.265
4. WORK = 1779.540 - 0.623(ACUT)* + 25.87(FMSZ)* - 0.077(ICTR)*
(0.082) (10.15) (0.026)
+ 143.8(SVGS)* - 15.02(LDSA) - 0.277(WAGE)* + 394.8(SEXH)*
(59.63) (25.90) (0.165) (66.31)
R2 = 0.253; F(7,392) = 18.95; S.E. = 514.153
a
Standard errors are in parentheses.
*Significant at the 0.05 level of the one-tailed t-test.
128
-------
Table 5.1la
Labor Supply Effects of Air Pollution-Induced
Chronic and/or Acute Illnesses
From Tab_le__iga!_ Air Pollution Induced Chronic Illness Only
Effect of a One Unit Increase in
Air Pollution Upon Labor Supply
Direct Effect
Indirect (via WAGE) Effect
Total Effect
NOXM
-1.0600 hours
-0.1044 hours
-1.1644 hours
TSPM
-1.6960 hours
-0.1669 hours
-1.8629 hours
Sum of total effects from Table IQa. expressions <• -1.1644 - 1.8629 - -3.0273
hours.
From Table
Air Pollution Induced Chronic and Acute Illnesses
Effect of a One Unit Increase in Air Pollution
Upon Labor Supply via Direct Impact
of Chronic Illness
Direct Effect
Indirect (via WAGE) Effect
Total Effect
TSPM
-0.458 hours
-0.026 hours
-0.484 hours
Effect of a One Unit Increase in Air Pollution
Upon Labor Supply via Impact of Chronic
Illness on Acute Illness
Direct Effect
Indirect (via WAGE) Effect
Total Effect
TSPM
-0.017 hours
Zero, by assumption
-0.017 hours
(continued)
129
-------
Table S.lla
(continued)
Effect of a One Unit Increase in Air Pollution
Upon Labor Supply via Direct Impact
of Acute Illness
Direct Effect
Indirect (via WAGE) Effect
Total Effect
Sum of total effects from Table lOb expressions -
hours.
TSPM
-0.046 hours
Zero, by assumption
-0.046 hours
-0.484 - 0.017 - 0.046 - 0.547
From Table IQc; Air Pollution Induced Acute Illness Only
Effect of a One Unit Increase in Air Pollution
Upon Labor Supply via Direct Impact
of Acute Illness
Direct Effect
Indirect (via WAGE) Effect
Total Effect
TSPM
-0.092 hours
Zero, by assumption
-0.092 hours
From Table IQd: Mr Pollution Induced Acute Illness Only
Effect of a One Unit Increase in Air Pollution
Upon Labor Supply via Direct Impact
of Acute Illness
Direct Effect
Indirect (via WAGE) Effect
Total Effect
TSPM
-0.9457 hours
Zero, by assumption
-0.9457 hours
130
-------
Table 5.lib
Value of Labor Supply Effects of Air Pollution-Induced
Chronic and/or Acute Illnesses for Pollution
Concentrations Two Standard Deviations
Removed from the Mean Concentration
From Tables IQa and lla
Mean air pollution + two standard deviations
NOXM = 95.320 + 82.470
TSPM = 115.818 + 65.756
Labor supply effects
NOXM - (-1.164 hours)(+ 82.470) = 95.9951 hours
TSPM - (-1.8629 hours)(+ 65.756) = 122.4975 hours
Total Effects 218.4926 hours
Value of labor supply effects:($2.92)(215) = $638.00
From Tables IQb and lla
Mean air pollution + two standard deviations
TSPM = 74.837 + 87.864
Labor supply effects
TSPM = (-0.547 hours)(+ 87.864) - 48.062 hours
Value of labor supply effects:($3.23)(48) = $155.00
From Tables IQc and lla
Mean air pollution + two standard deviations
TSPM - 89.210 + 55.938
Labor supply effects
TSPM - (-0.092 hours)(55.938) = 5.146 hours
Value of labor supply effects-' ($3.59) (5.146) •= $18.47
(continued)
131
-------
Table 5.lib
Value of Labor Supply Effects of Air Pollution-Induced
Chronic and/or Acute Illnesses for Pollution
Concentrations Two Standard Deviations
Removed from the Mean Concentration
From Tables IQd and lla
Mean air pollution ± two standard deviations
SULM = 24.583 ± 46.690
Labor supply effects
SULM = (-0.9457 hours) (46.690) = 44.155 hours
Value of labor supply effects: ($3.32) (44.155) - $146.59
132
-------
hours worked. Similarly, hourly earnings are determined independently of
hours worked and then hours worked are determined from hourly earnings. As
Kmenta (1971, p. 585) shows, estimation of a recursive system by ordinary
least squares is equivalent to estimation by full information, maximum
likelihood.
At this juncture, we wish to emphasize that the use of a single air
pollution health effect, or effect of health on wages and/or hours worked,
may be somewhat misleading. These effects may differ, for example, with
age and numerous other variables. As one gets older, it may be that air
pollution-induced health effects become progressively more severe, implying,
for given levels of training and work experience, that the absolute effect
of air pollution upon hourly earnings and hours worked increases with age.
Ideally, this possibility makes it worthwhile to estimate separate expres-
sions for different age groups. Otherwise, one obtains, as we do, a coef-
ficient representing effects for neither old nor young people but simply
a weighted average of the two from which it is impossible to disentangle
the separate contributions of each group effect. In essence, in addition
to all the other caveats that must be applied to the empirical results set
forth here, one cannot blindly transfer these estimated air pollution-
induced health, hourly earnings, and hours worked effects to other samples
of individuals unless their age distribution is similar to the age distri-
bution in these samples. If air pollution-induced effects also differ by
other demographic attributes such as race and sex, a similar caution applies.
Tables 5.10a, 5.10b, 5.10c, and 5.10d present estimates of the chronic
illness dose-response expressions, the acute illness dose-response expres-
sions, the marginal earnings expressions, and the labor supply expressions.
The samples of individuals used to estimate these expressions include house-
wives, retirees, and students, all of whom were assigned zero hours of acute
illness by the Survey Research Center. These individuals constitute about
twenty percent of the sample, thus imparting what is probably a substantial
downward bias for these labor supply calculations in the estimated effects
of air pollution upon acute illness. Failure to include these groups would
have resulted, however, in the removal from the sample of a disproportion-
ately high number of individuals with chronic illnesses.
Table 5.11a provides estimates of the direct and indirect effects upon
labor supply, as measured by annual hours worked, of air pollution-induced
acute and/or chronic illnesses. Assuming that the marginal hourly wage is
an accurate representation of the market value of the worker's marginal
productivity, these reduced work hours are valued in Table 5.lib at the
marginal wage applying before the reduction in work hours. Apart from any
issues dealing with the estimation procedures used to obtain each expression,
the reader should be sensitive to the fact that assumptions stating that
illness is unaffected by work-hours and/or wages underlie the calculations
in these two sets of tables.
Detailed description of the calculation procedures in Tables S.lla and
5.lib is both tedious and repetitious. In order to inform the reader of the
procedure, we describe that applied to the material in Table 5.10a, leaving
the reader the responsibiliy to invent for himself the procedures we have
133
-------
applied to Tables 5.10b, 5.10c, and 5.10d, which have resulted in the labor
supply effect estimates set forth in Tables S.lla and 5.lib.
Of the three air pollution variables in the chronic illness dose-
response expression of Table 5.10a, two. NOXM and TSPM, have a positive
sign and are statistically significant.—' Making the already acknowledged
dangerous assumption that each discrete interval of IDSA is slightly more
than two years, or 830 days, the coefficient attached to NOXM implies that,
on average, each unit increase in annual geometric mean concentrations of
ambient nitrogen dioxide increases the length of chronic illness by 4.15
days.—' Similarly, on average, each unit increase in annual geometric mean
concentrations of ambient total suspended particulates increases the length
of chronic illness by 6.64 days. Calculated at the arithmetic means, the
elasticity of LDSA with respect to NOXM is 0.47, while the elasticity for
TSPM is 0.95.
The signs of the coefficients for the non-health variables in the hourly
earnings expression, (3), in Table 5.10a are in accord with a priori expec-
tations. Except for BDALO and RACE, all are statistically significant at
generally accepted levels. As for the health-related variables, neither
acute illness nor the severity of disability appears to have an effect upon
hourly earnings. However, the length of time over which the individual has
been disabled has a substantial and statistically meaningful effect. . An
increase of two years in the length of time the individual suffers from a
chronic illness reduces hourly earnings, on average, by 41.73 cents. When
calculated at the means, the elasticity of WAGE with respect to LDSA is
-0.17, implying that within the ranges of chronic illness time length and
hourly earnings considered here, the response of hourly earnings to chronic
illness is rather sluggish.
Using the above results for the effect of LDSA on WAGE, and the earlier
results for the effect of NOXM and TSPM on LDSA, one can calculate the
average effect of each of the two air pollutants upon hourly earnings. The
4.15 day effect of an additional unit of NOXM on LDSA is 0.50 percent of the
830 days said to constitute one unit of LDSA. Since a one unit increase in
LDSA reduces hourly earnings by 41.73 cents, the average effect of an
additional unit of NOXM on hourly earnings is (0.005)(-41.73) = -0.2087
cents. Performing the same calculations for TSPM, the average effect of
an additional unit of total suspended particulates on hourly earnings is
(0.008)(-41.73) = -0.3338 cents.
Among the non-health variables in the labor supply expression, (4) of
Table 5.10a, only BDALO fails to be statistically significant. The coeffic-
ient for WAGE has a t-value slightly less than four, and it implies an
elasticity of WORK with respect to WAGE of 0.12. This means that the sub-
stitution effect of a change in real earnings exceeds the income effect.
The highly significant and negative coefficient attached to 1971 income
secured by means other than 1971 labor, ICTR, is consistent with a sub-
stantial income effect that causes the individual to substitute consumption
hours for work hours. The elasticity of WORK with respect to ICTR, when
evaluated at the means of the variables, is -0.18.
134
-------
The positive and statistically significant coefficient attached to
WAGE implies that the length of time the individual has been chronically
ill, LDSA, has an indirect as well as a direct effect upon the annual hours
of workl the individual supplies. This occurs because, as was observed in the
references to (3) of Table 5.10a, LDSA lowers hourly earnings as well as
having a powerful direct effect, according to (4), upon labor supply. Table
S.lla exhibits the direct, indirect, and total effects of NOXM and TSPM upon
labor supply, as measured by annual hours worked. - The total effect is an
estimate of the coefficient for LDSA in a reduced form expression.
Assuming the average work day to be eight hours long, a one unit in-
crease in LDSA directly brings about a 212 hour or 26.50 day reduction in
annual working time. As earlier noted, 0.5 percent of a one unit change in
LDSA is attributable to NOXM, while 0.8 percent of a similar change is due
to TSPM. The direct effect of an additional unit of NOXM upon annual hours
worked is therefore (0.5 x 10 2)(-212) = -1.06 hours, while the direct
effect of TSPM is (0.8 x 10~2)(-212) - -1.6960 hours.
The indirect effect of air pollution upon labor supply is obtained by
first recognizing that in (4) of Table 5.10a, each one cent change in hourly
earnings generates an average change of the same sign of 0.50 in annual
work hours. As was noted in the discussion of the empirical results for
(3), an additional unit of TSPM reduces hourly earnings by 0.3338 cents.
The indirect effect of an additional unit of TSPM upon annual work hours is
then (-0.3338)(0.50) = -0.1669 hours; the indirect effect of an additional
unit of NOXM on annual work hours is then (-0.2087)(0.50) = -0.1044.
On average, the total reduction in ,labor supply caused by a one unit
increase in TSPM is 1.8629 hours, while the reduction for a one unit increase
in NOXM is 1.1644 hours. Assuming the health of the representative individ-
ual in this sample to be exogenously determined, and that no potential
interviewee died between the year for which behavior and status is recorded
and the time of the interview, the total reduction in his annual hours
worked caused by simultaneous one unit increases in NOXM and TSPM is then
3.0273 hourss i.e., approximately three hours. This last figure assumes
that the effects of NOXM and TSPM are additive. Making the exceedingly
strong assumptions that the effects of these two air pollutants upon hourly
earnings and annual hours worked are constant over all ranges bating consid-
ered and that the effect of hourly earnings upon annual hours worked is also.
constant, those individuals living in cities having air pollution concen-
trations two standard deviations removed from the mean concentration of the
cities considered in this paper will have changes in annual hours worked
of 95.9951 hours due to NOXM, and 122.4975 hours due to TSPM; that is, an
individual who works and resides in an extremely clean city might work 218
hours more a year than the individual who works and resides in a city with
average air pollution concentrations. Valuing these 218 hours at the marginal
wage applying before the reduction in work hours, we have a loss in average
total earnings of (218) ($2.92) or $638 per individual, a figure which, in
spite of the grossness of our assumptions, is not in great discord with
intuitive possibilities. Given our linearity assumption about the response
of labor supply to air pollution, this results in $1,276 in lost wages for
an individual living in an extremely dirty location as compared to that same
individual living in an extrenely clean locftion.
135
-------
In the preceding paragraphs, we have calculated:
rjACEfdWORK > m 3 Illness , 9 WORK . SWAGE . 3Illness
^Pollution' 3Pollution 3WAGE " 3llness 3Pollution
As an alternative, we could readily have calculated:
d»
ness. This is reflected in the example from Table 5.10c as well as that
from Table 5.10b. In the latter, although air pollution does significantly
affect acute illness, its effect, via acute illness, upon labor supply is
overwhelmed by the effect of air pollution-induced chronic illness. The
sample of Table 5.10c must depend for its labor supply effects upon acute
illness alone. Its magnitude is trivial relative to the air pollution
induced chronic effects of Tables S.lOa and 5.10b. Note, however, that the
money value of the labor supply effects of the air pollution-induced acute
illness in Table S.lOd are nearly one-quarter of the total effects of the
air pollution induced illnesses in Table S.lOa.
The empirical results set forth in this section suggest that air pol-
lution, mainly via its influence on chronic illness, affects labor produc-
tivity, that at least the order of magnitude of the effect can be estimated
within the Immediate neighborhood of existing air pollution concentrations
and health states, and that the estimates can be given meaning within a
rigorous analytical framework. Nevertheless, the estimates we have obtained
are basically reduced form estimates: the causally subsequent expressions
relating to chronic and acute illnesses and marginal hourly earnings are
simply substituted into the labor supply expression to obtain the total of
the direct and indirect effects of air pollution induced health effects upon
labor supply. This may be too extreme. We allow the individual's state-
of-health to influence his earnings and his annual hours of work, but we do
not permit these hours of work or earnings to influence his state-of-health.
136
-------
Yet some empirical evidence exists that' long hours of strenuous physical
work may generate fatigue and thereby initiate or accentuate air pollution
induced health effects..!"/ Moreover, presumedly in order to try to capture
socioeconomic and Background influences for which they have no overt
measures available, epidemiologists have often included earnings as an
explanatory variable in dose-response functions. Even economists [e.g.,
Grossman (1972) and Cropper (1977)] have included wages or earnings in
analytical statements of health production functions.
In a succeeding section, we attempt to establish empirically whether
reciprocal relations exist between health states, work hours, and wages for
a sample of respondents in the SRC data. Before doing so, however, we
present an analytical model of consumer behavior which enables us to provide
some a^ priori structure for these reciprocal relations. In particular, with
this model we are able to interpret the estimated relations as demand func-
tions for avoiding acute or chronic illnesses and predict the behavior of
several of the function parameters. To the best of our knowledge, the model
set forth in the next section is the first to conform to the common sense
notion that health status is a direct source of utility as well as a factor
that influences the efficiency of production and consumption activities.
5.5 A Model of the Effect of Air Pollution on the Demand for Health—
Let an individual obtain utility from two commodities: H, the dis-
counted flow of health services in each period i, h . ; and Z, the present
value of the stream of services per period of a composite commodity, z . .
Thus:
U = U(H,Z) (5.5)
where
I I
H = I «h., and Z = E °^z.,
i=0 1 i=0 ± 1
andtt is the individual's discount factor for the ith period.
Presume that the individual has an initial health endowment, H , that
was provided instantaneously in period 0. However, due to natural aging,
this initial health stock depreciates exogenously over time as given by
(5.6), where B. is the proportion of H remaining in the ith period.
H. = B.H (5.6)
i i o
The h, and z. are produced by linear homogeneous production functions
f . (j = H,ZJ whose inputs are goods, X.., and time in each period i. Air
pollution and other environmental gooJs are included among the X . . In
general 3h./8X., when i is pollution.
-V- (5-7)
137
-------
zi = ^zi-v' (5-8)
where T is the time allocated specifically to health, care, and T is
leisure time. In the 2L . , no distinction is made between ameliorltive and
preventive medical care, since, if the ameliorative care returns the indiv-
idual to his former health status, he is dropped back into the same risk
pool he was in before receiving the ameliorative care.
We make a distinction between the time-based wage rate and an incentive
payment based on the flow of productive services the individual provides.
The latter is viewed as a supplement to the time-based salary. It is a
reward varying directly with the effort the individual expends over and
above that minimum expenditure necessary for him to keep his job. This
distinction between time-based salary and incentive payments for non-pre-
scribed effort expenditures allows us to discriminate between acute and
chronic health effects insofar as they influence the efficiency of production
and consumption activities. Acute health effects do not alter total earnings
except when they reduce time on the job, whereas chronic effects alter both
time on the job and total earnings for any given amount of time on the job.
Total incentive payments, M , are given by (5.9), where g(') is a
twice-differentiable, decreasing returns-to-scale production function, P
is the incentive payment, and E and e are respectively stock and flow non-
health environmental variables (e.g., schooling, services of a mate, air
pollution that directly affects productivity, rather than via health, coffee,
air conditioning, etc.) that may influence the ability to put forth effort.
The c's are their respective unit prices. Note that % varies directly with
the amount of output the individual's efforts produce, rather than the
amount of effort he expends.
Mi = ^i'WV - CEEi - CeV (5-9)
In (5.9) T represents time expended on other work activities in the the
period, including household production. These activities are presumed to
dissipate energies that could otherwise be devoted to work. Alternatively,
one could include T ., work time, rather than T in (5.9) on the presumption
that, beyond some positive time expenditure, additional work time causes
fatigue and/or ennui. —
The individual's ith period time constraint is given by (5.10) where 9
is Becker's (1967) "full-time," and TW± is work time.
If p , p are the price indices of the goods used in the production of
h and z, and If x, ,x are the average (= marginal) composite purchased good
coefficients of h.anS z., then the individual's budget constraint over his
planning horizon can be represented as:
J0 Yi = Twiw + Mi - VhV s Wi = °' (5'n)
138
-------
where Y is the ith period flow of non-earnings income, and W is the time-
based wage rate.
Upon combining (5.10) and C5.ll), assuming W represents the shadow-
price of time, one obtains the "full" intertemporal wealth constraint, (5.12)
mh>ht
(5.12)
The optimal levels of H and Z, the optimal uses of stock and flow non-
health environmental variables, and the utility-maximizing time allocations
in each period are obtained by maximizing (5.5) subject to (5.12) with non-
negativity constraints on H , Z, E, e, and T . There are thus 31+2 first-
order conditions including 8he full-wealth constraint.
I I
S «U +A[S «(3 P - 3.[ P.X. + WT.])] < 0; (5.13)
1=0 x H 1=0 1 1 8h±
U + X[- £=. (P X + WT )] < 0; (5.14)
Z 1 Z Z Z
P - W < 0; (5.15)
Orp
Di
5 0; (5.16)
Pg - ce < 0; (5.17)
ei
Assuming internal solutions, expression (5.13) can be rewritten to form
(5.18):
1TCJ - s tt-^p^ = s I:L H« ^5
i=0 h ±=0 x i °h± ±mQ x
which says that the optimal state-of -health occurs where the present value
of health is less than the capitalized cost by the value of the marginal
utility of the health stock. Thus, the net price of health as an unput into
the work process is the horizon period consumption price, Ia.g (P 2L + WT»)»
less the pecuniary equivalent of marginal utility.
Upon combining (5.13) and (5.14), one obtains:
139
-------
I I
T TT Z «.« (p X, + WT. ) - Z «6.P
1 uw -i-n--1-1- hni h *-n i-i-8|,
7 cc /_Ji\ _ x u izP. ltf>
a, ^ j _ i
i=0 X UZ x
- £ « (P x + WT )
•f ^ *7 9
±=Q * Z Z Z
s c./c
h z
which states that the marginal value product of health in work offsets the
predetermined consumption price component. Thus, one consequence of the
dual role of health is that, even though the time-based wage rate is fixed
and the household production functions are linear homogeneous, the full
shadow price of health in production or consumption is endogenous, dependent
on the state-of-health demanded since the marginal product of better health,
Pg, , and the marginal utility of better health, U 7X, will decline as H
h. Ho
increases.
To ascertain the response of health states demanded to changes in the
parameters specified in the model and to formulate a demand function for
health states, the first-order conditions (5.13) - (5.17) must be totally
differentiated and the relevant partials for H calculated.
The response of health demand to own predetermined price, 2^3. (I
WT ) can be decomposed into compensated substitution and (full) income
effects:
(5
3[Z«B.(P \ + WT )] ~ 9[SaiPi
-------
Y = (I «WT )/(c = p x + WT ) (5.23)
Z 1 Z Z Z Z Z
In (5.21) a compensated increase in the time-based wage rate reduces
the demand for the absence of acute health effects (causing the value of
freedom from air pollution exposures to be reduced) if the individual's
production of freedom from acute health effects is more time-intensive than
is his production of other goods from which he obtains utility. This is
because the second-order conditions require that e*c < 0. Although we
H H |
can only speculate, activities such as daily exercise programs and the care-
ful preparation of healthy menus do seem more time-intensive than reading a
novel or eating at the local fast-food emporium. Even if the consumption
price time intensities are equal, i.e., YH = Y7» an increase in W might
still reduce the demand for freedom from acute health effects, since, from
(5.22) and (5.23), YR > YZ as CR > ^.
The second-order conditions imply that there will exist a discrepancy
between the observed income elasticity of health status and the "true"
income elasticity. In fact, the former is likely to be less than the latter
because the jdata used to calculate the observed elasticity.will frequently
be unable to distinguish between the time-based and the incentive payment
components of the total wage. These two components imply that the individ-
ual's budget constraint will be nonlinear since chronic health status in-
fluences the ability of the individual to provide those productive services
rewarded by incentive payments. This downward bias further implies that
estimates of the demand for the absence of air pollution induced chronic
health effects will also be biased downward whenever the data do not allow a
distinction between the two earnings components. If an exogenous reduction
in air pollution increases the optimal degree of absence of chronic illness,
the marginal productivity portion of the full shadow price of health dimin-
ishes, assuming that the supply of effort is negligibly reduced by the ad-
ditional earnings. The shadow price of the health stock therefore rises.
A second general consequence of the contribution of freedom from chronic
illness to incentive payments is that changes in education and similar
factors related to the provision of productive services will influence the
shadow price of health by altering horizon period productivity. In turn,
these factors will affect the value the individual attaches to the absence
of air pollution-induced chronic illness. In short, the individual's demand
for freedom from air pollution exposures will be related to his education,
job experience, and other influences on his productivity.
The uncompensated elasticity of freedom from chronic health effects
with respect to the price, c., of any of the aforementioned factors related
to the provision of productive services is ambiguous, however. This
elasticity is given by (5.24), where q. refers to one of these productive
services.
141
-------
c. .=0 c.
The sign of this expression depends on whether the factor in question is a
substitute for (cj> > 0, as with education), or a complement of ( < 0 as
perhaps with comfortable job surroundings) freedom from chronic illness.
For example, assuming non-inferiority (e > 0), if freedom from chronic
illness and the services of a mate are (imperfect) substitutes in the pro-
vision of productive services, then a compensated increase in c. would
raise the demand for health; the sign of the uncompensated effect, however,
would depend on the magnitude of e and the share of the costs of the
services of a mate in full income.8
The effect of a change in the price, P, of the output of productive
services is also ambiguous. Expressed in elasticity terms, this effect is:
I I
GHD = ~GHCH E I^SI/CH + 2 2 *H + S P8-i/Rep-
Hp H H i-0 ± ± i H j i-0 Cj i=0 ± R
While an increase in P raises the marginal value product of good health,
thus lowering c , and increases incentive-based income, the value of the
output contributions of the other input factors in g(») also rises. The
sign of the compensated substitution effect will thus depend on the com-
plementarity-substitution relations between freedom from chronic health
effects and other inputs.
Accounting for the preceding development, we can express the demand for
freedom from chronic and acute illnesses in terms of two functions dif-
fering according to whether we are considering acute or chronic illness.
Both of these functions will involve arguments, however, relating to pre-
determined variables that influence the price of time, in addition to
variables that relate to production and consumption activities. Thus, for
the willingness to accept chronic illness, we can write the demand function
as:
1L . = y (Time-based wage, Incentive payment, Non-earnings
income, Environmental variables, Cost-of-living,
Endowment variables).
In the case of the demand for acute illness, the demand function, y9(*)»
for HArni_ is similar to HrnCA above, except that the term for incentive
A.CUX. * i ^ * LiDSA
payments is deleted.
5.6 Some Empirical Results; The Demand for Freedom from Air Pollution-
Induced Acute and Chronic Illness
The model of the preceding section implies that changes in the willing-
ness to accept acute illness will result in changes in work time alone,
although the extent of the change will depend on other parameters such as
the time-based wage rate, transfer income, and assorted Background variables.
142
-------
In contrast, the wage rate is endogenous in the demand for freedom from
chronic illness, since the extent of chronic illness determines, in part,
the wage rate. Thus, although the wage rate is determined outside the
system in the demand for freedom from acute illness, it is determined within
the system in the demand for freedom from chronic illness. This implies
that we can treat the demand to avoid acute illness as a single expression,
but must account for the simultaneity Between the wage rage and chronic
illness when estimating the demand to avoid chronic illness.—' In the
latter case, we must resort to simultaneous equation estimation procedures.
Here we adopt two-stage least squares .-?±/
The appropriate expressions to calculate the pecuniary amounts the
individual would have to receive to be willing to pay to avoid an increase
in acute or chronic illness are, respectively, (5.21) and (5.24) of the
previous section. Calculation of these expressions is clearly rather com-
plex. As an alternative, we have calculated this willingness to accept as:
o£ time> (Ulness time)
, P
d (Pollution) d (Pollution)
Upon reflection, this proposed method of calculation seems no different
than the procedure employed to calculate the pecuniary equivalent of the
recursive effects of air pollution upon labor supply. A somewhat subtle
difference does nonetheless exist. In particular, a difference exists in
the definition of illness time and its response to pollution variation:
The recursive estimates dealt only with the physical effects of air pol-
lution, while illness time in the above expression represents the individ-
ual's utility-maximizing illness time. When estimating dose-response
expressions, we included as explanatory variables only predetermined vari-
ables either that described the individual's current health status or were
a. priori physical determinants of changes in this status. In contrast, when
estimating the individual's demand expression for willingness to pay to
avoid illness, we include variables such as the time-based wage rate,
transfer payments, incentive payments, etc., that influence the sacrifices
the individual is willing to make in order to avoid illness time. For
consistency, and only when we have no alternative, we even sometimes re-
interpret the meanings of identical explanatory variables that appear in
both the dose-response expressions and the demand expressions. Thus, INSR,
which was conveniently interpreted as a proxy for the availability of medical
care in the dose-response expressions, will be interpreted in the demand
expressions as a proxy for the price that the individual faces for a given
quantity of medical care.
In the analytical model of the preceding section, increased air pol-
lution reduces the flow of health services, and, as a consequence, reduces
utility and usually increases the marginal product of particular health
investments. These effects are opposing, causing the sign to be expected
for the coefficients attached to the pollution variables to be ambiguous.
However, pollution also causes the cost of supplying a given health status
to increase. The result is that the income the individual is willing to
forego to avoid pollution-induced illness is positive. We therefore expect
the signs attached to the pollution coefficients in the demand expressions
to be unambiguously positive.
143
-------
Table 5.12 below presents three estimated demand expressions relating to
acute illness for two different samples drawn from the 1571 SRC data. These
samples include housewives, retirees and students, all of whom were assigned
zero hours of acute illness by the SRG. The expressions are linear in the
original variables. Expressions (1) and (3) were estimated from the same
example. Only in the first two expressions is at least one of the air pol-
lution variables statistically significant. The individual's time-based
wage, which was measured as his hourly earnings on his regular job, appears
to have no influence on his demand for avoiding increased hours of acute
illness. Neither does annual work hours nor cigarette expenditures. As
previously noted, substantial measurement error is involved in GIGE. People
who participate in energetic activities and have adequate diets tend to have
greater demands for the avoidance of acute illness, as do tho&e who are ridk
averse. Older people and those who face lower prices for medical care seem
less willing to pay to avoid additional acute illness. As in the dose-
response expressions for.acute illness, the sign attached to INSR is puzzling.
Additional income, the acquisition of which does not involve any current
time, increases the demand for acute illness avoidance.
In expressions (1) and (2), each additional unit of TSPM results, respec-
ively, in an additional 1.212 and 0.796 additional optimal acute annual hours
of illness. In expression CD of Table 5.12, the arithmetic mean of WAGE is
$3.62,,meaning that the representative individual would, on average, be
willing to pay an additional $4.39 annually to avoid one additional unit of
TSPM. The arithmetic mean of WAGE for expression C2) in Table 5.12 is $3.58.
Thus, the representative individual in this sample would be indifferent
between paying $2.85 and an additional unit of TSPM. In expression (2), the
arithmetic mean TSPM is 87.315 and 54.749 units of TSPM is two standard
deviations removed from this mean. Assuming a linear extrapolation of the
preceding marginal (= average) willingness to pay of $2.85 for avoiding an
additional unit of TSPM to be valid, the representative individual in
expression (2) would be willing to pay $312 annually to avoid the additional
hours of acute illness associated with living in a location where TSPM is
extremely high as opposed to being extremely low. A similar calculation for
the representative individual in expression (1) indicates that he would be
willing to pay $457.97 in 1971 dollars annually in order to avoid a similar
fate.
The basic calculations from the willingness to pay to avoid chronic
illness expressions in Tables 5.13a and 5.13b are identical to the pro-
cedures used for the willingness to pay to avoid acute illness expressions
of Table 5.12. The sole difference is the use of the arithmetic mean value
rather than WAGE. Table 5.13a holds no special surprises except for the
sign attached to the statistically significant coefficients of DSAB. None-
theless, the sign is consistent with a finding of Hamushek and Quigley (1978)
that disabilities appear to affect negatively the earnings of the blue-
collar workers but have little, if any, effect on the earnings of (presumedly)
higher paid white-collar workers.
The estimates in Table 5.13b indicate a reduced quantity demanded of
chronic illness avoidance with an increase in age, and an increased quantity
demanded with reduced prices for medical care. The significance of the
144
-------
Table 5.12
Willingness to Pay to Avoid Acute Illness
Sample
Variable
WORK
WAGE
GIGE
EXER
FOOD
RISK
AGEH
INSR
ICTR
TSPM
SULM
Constant
2
R
S.E.
F
(1)
3 1971 s
0.007
0.047
-0.057
-66.990*
-0.052*
-10.460
0.955
54.85**
-0.244*
1.212*
-0.610
0.018
0.032
0.094
33.320
0.024
11.250
1.034
27.58
0.022
0.668
0.419
99.057
0.091
245.647
(10,391) = 3.094
(2)
$ 1971 s
-0.007
-0.016
-0.108
-30.033
-0.115*
-40.020*
-0.506
161.800**
-0.278*
0.796*
0.010
0.020
0.118
40.019
0.033
13.420
1.286
47.230
0.022
0.384
182.339
0.086
267.306
(9,390) - 4.112
(3)
& 1971 s
0.012
0.039
-0.067
-60.520*
-0.052*
-12.680
1.246*
63.480*
-0.233*
0.500
0.018
0.052
0.095
33.620
0.024
11.360
0.742
27.890
0.021
0.478
128.082
0.089
258.336
(9,390) = 3.475
*Statistically significant at the 0.05 level of the one-tailed t-test.
**Statistically significant at the 0.05 level of the two-tailed t-test.
145
-------
Table 5.13a
Two-Stage Least Squares Estimates of WAGE
Expressions for Chronic Illness
Sample
Variable
EDUC
WORK
DSAB
FMSZ
BDALO
HMPNb
LTWK
ABSNa
UION
RACE
LDSA
Constant
S.E.
F
CD
g 1970 s
31.730*
0.016
179.200**
33.610*
40.470*
0.554**
-17.430
-5.401
87.320*
41.310
-255.600*
8.735
0.021
50.230
6.293
6.075
0.218
33.520
44.010
34.620
33.780
58.880
-59.852
255.199
(11,388) = 26.020
(2)
g 1971 s
23.740*
0.0017*
35.670**
63.790*
14.610*
0.642
-35.160
-
29.880
68.430
-69.940*
5.307
0.001]
17.220
37.980
3.447
0.927
32.070
-
19.920
81.210
30.530
-28.345
159.234
(10,389) = 13.685
*Statistically significant at the 0.05 level of the one-tailed t-test.
**Statistically significant at the 0.05 level of the two-tailed t-test.
«j
ABSN refers to the frequency with which the individual missed work for
reasons other than illness.
HMPN refers to annual hours of home production, e.g., car repairs,
house additions and repairs, etc.
146
-------
Table 5.13b
Two-Stage Least Squares Estimates
of Chronic Illness Expressions
(LDSA)
.Sample
Variable
RISK
AGEH
(1)
£ 1970 s
-0.030
0.029*
INSR ! -1.475*
CHEM ; -6.804*
CITY
POOR
FEDU
ICTR
TSPN
stjLN
WAGE
Constant
S.E.
F
0.052
0.500*
-0.036 o
-0.17x10 *
0.0021
-0.001
0.005*
0.052
0.006
0.257
2.479
0.129
0.150
0.044 -
0.05x10
0.0020
0.004
0.002
0.521
1.168
(11,388) = 9.733
(2)
0 1971 s
-0.016
0.031*
-0.553*
0.268
0.050
0.345*
-0.028 .
-0.80x10 *
0.0039*
-0.0007
0.005*
0.048
0.005
0.170
0.703
0.134
0.135
0.046,
0.16x10
0.0010
O.OC14
0.001
0. 033
1.193
(11,388) = 13.250
*Statistically significant at the 0.05 level of the one-tailed t-test.
**Statistically significant at the 0.05 level of the two-tailed t-test.
147
-------
coefficient for CHEM in expression (1)_ is undoubtedly an anamoly since only
one person worked in the chemicals and metals manufacturing sector. Those
respondents who were poor when growing up demand less chronic illness avoid-
ance, perhaps Because their health status is initially less and they there-
fore must invest more to reach a given health status level. WAGE, and there-
fore WAGE, is defined here as the individual's marginal hourly earnings.
This need not be his hourly earnings without overtime on his primary job.
In Table 5.13b, only expression C2) possesses a statistically signifi-
cant air pollution coefficient. Assuming as in previous sections that each
unit of LDSA is slightly more than two years, or 830 days, in length, that
each of these days is a potential workday, and that the average workday is
eight hours long, then an additional unit of TSPN in expression (2) of 5.13a
causes the individual's utility-maximizing number of days of chronic illness
to increase by 3.25 days over his lifetime. We have no idea, however, how
these additional days will be distributed over his lifetime, nor can we
treat 3.25 additional days for someone who is already chronically ill as
similar to 3.25 additional days for someone who is not now chronically ill.
Assume our representative individual currently has no chronic illness, and
further assume that perpetual exposure to an additional unit of TSPN will
cause him to acquire immediately a "chronic" illness. The arithmetic mean
for WAGE in 1971 is $3.72 per hour. Since our representative individual
works eight hours per day, and since he will now find that 3.25 days of his
worktime will at some time no longer be available, he would be willing to
pay an undiscounted amount of $96.72 in a single lump sum. The arithmetic
mean of TSPN in sample (2) is 156.185, and 127.574 units of TSPN is two
standard deviations removed from this mean. Assuming the validity of a
linear exprapolation of the preceding marginal (= average) willingness to
pay to avoid the chronic illness induced by perpetual exposure to an addi-
tional unit of TSPN, we find that the representative respondent would be
willing to pay an undiscounted lump sum of approximately $25,000 ($24,678)
to avoid the chronic illnesses associated with spending the rest of his life
in an extremely high TSPN location as opposed to an extremely low TSPN
location.
5.7 Overview of Empirical Results
We view the empirical results of this chapter as tentative and ongoing
rather than as definitive and final. The SRC interview data that we employ
is a random sampling of the civilian, noninstitutionalized population of the
United States. Extrapolations of results to the entire population are there-
fore fairly reasonable, even though we have not employed the SRC sampling
weights. However, caution must be exercised in doing so: our measures of
illness are substantially less than ideal. In particular, the measure of
chronic illness is rather discrete and its uppermost value is unbounded.
Moreover, individuals who died between the reference year of the interview
and the time of Interview are not Included. Both factors probably cause the
health impact of air pollution to be underestimated. Nevertheless, we feel
that we have provided an example of some of the things that can be done with
microepidemiological data on health status, endowments, and time and budget
allocations. In the bulk of the dose-response expressions we have estimated,
most of which were estimated from distinct random samples, air pollution is
associated with increased time spent being acutely and/or chronically ill.
148
-------
Air pollution, in addition, appears to influence labor productivity, /where
the reduction in productivity is measured in the earnings lost due to reduc-
tions in salable skills and in worfc-time. The reduction in productivity due
to air pollution-induced chronic illness- seems- to overwhelm any reductions
due to air pollution-induced acute illness.
The following examples involve linear extrapolations of estimated labor
productivity effects and willingnesses—to—pay at arithmetic mean air pol-
lution concentrations. The linear exprapolattona extend two standard devi-
ations from the means- of the frequency distributions of these concentrations.
Geographical locations residing in the upper tails of these distributions
might reasonably be regarded as extremely dirty while those along the ex-
tended portion of the lower tails are bathed in extremely clean air. The
representative individual who is instantaneously and painlessly removed
from an extremely dirty location to an extremely clean one might expect to
acquire about $20 (In 1970-71 dollars) in additional annual earnings from
reductions in air pollution-induced acute illnesses. This same individual
would annually acquire several hundred 1970-71 dollars (approximately $100
to $600 in our empirical tests) by the reduction in chronic illness he would
obtain from a similar removal. Both these results assume that wage rates
are not adjusted in response to a cleaner environment.
The willingness of the representative individual to pay for the annual
hours of acute illnesses he could avoid by being in a clean rather than a
dirty environment is, for the two samples for which we obtained estimates,
between $300 and $500 annually in 1970-71 dollars. For chronic illness
avoidance, we calculated, under some extremely'crude assumptions and on the
basis of only ja single sample, that the representative individual would be
willing to pay an undiscounted lump sum of $25,000 to be in the clean rather
than the dirty environment.
149
-------
FOOTNOTES
— The Survey Research Center possesses the exact addresses of the sample
families, but does not include them in its data tapes.
2/
— This "errors in variables" problem is usually handled by using instru-
mental variables which are highly correlated with the variable measured with
error but are uncorrelated with the error. We were unable to think of a
variable having these properties.
— SRC interviews for 1973 behavior and status include a three-digit
occupational code corresponding to the coding used in U.S. Bureau of the
Census, 1970 Census of Population Alphabetical Index of Industries and Oc
cupations, Washington, D.C.: USGPO (1971). This means that information is
available in the SRC data set on nearly the exact kind of job held by the
family head and/or his wife. This rather magnificent store of information
obviously has many research possibilities which remain completely unexploited
in this study.
4/
— Other measures of ill-health are available in the SRC data set,
particularly the severity of the disability, if any, and the number of weeks
missed from work due to sickness. Because of its qualitative nature, the
decision was made to use the first of these entirely as an explanatory, rather
than as a dependent variable.
— Expressions of discomfort with the reductionist perspective are now
fairly common in the biomedical literature. See, for example, Syme and Berk-
man (1970) and Engel (1977). More importantly, there is empirical evidence
that variations in self-reported health status reflect correct variations
in clinically objective measures of health. See Grossman (1975, p. 168) for
a review of this literature as well as some additional empirical evidence.
—The literature which views children as an investment is surveyed in
several papers in a supplement to the March/April 1973 issue of the Journal
of Political Economy.
— The 18th century French jurist and philosopher, Montesquieu (1947,
p. 245), succinctly stated the central theme of much of this literature:
"The nations of hot countries are timorous like old men, the nations in
colder regions are daring like youngsters." Recent efforts have been con-
siderably less elitist and self-congratulatory.
8/
— A fair amount of work appears to have been done to ascertain the dis-
crepancies, if any, between self-reported and clinically evaluated health
status. Survey Research Center (1977, pp. 7-10) states that the bulk of
studies conclude: (1) as the time between an interview and an event lenghtens,
there is increased underreporting about the magintude of the event; (2)
important events are less likely to be incompletely and inaccurately reported;
and (3) self-reported events are likely to be biased in what the respondent
considers to be a socially acceptable direction. Marquis (1978), however,
disputes these conclusions because all studies either check self-reported
health status against clinical records or check clinical records against
status. He shows that a statistically correct test of bias requires both
150
-------
checks. When he performed this check with a sample of individuals from
Dayton, Ohio, he found that "...there is little or no average reporting bias
in hospital admission/discharge data obtained by household interviews." (p.
42).
97
— This high proportion of non-whites is probably caused by the fact
that 40 percent of the original 1967 sample was composed of families pre-
viously interviewed by the U.S. Bureau of the Census for the 1966 Survey
of Economic Opportunity.
— Wallace (1977) has surveyed a number of recently evolved tests
enabling the investigator to ascertain the extent to which Selvin's and
Stuart's (1966) data-dredging alter the trustworthiness of later estimates.
We have disregarded the Wallace (1977) tests in this study in favor of
drawing entirely new samples each time a new expression is estimated.
— There is another alternative: each of the following structural
expressions could be estimated:
a) DSAB = f(Air pollution, lifestyle, . . ., etc.)
b) LDSA - g(DSAB, . . .)
where the DSAB in expression (b) is the estimated value of DSAB. However,
since DSAB is measured in ordinal and discrete terms, either a multinomial
logit or a basic logit specification using maximum likelihood estimation
methods would have to be employed. In the latter case, four different
versions of (a) would have to be estimated since DSAB involves four dis-
crete ordinal measures.
127
— See, for example, Grossman and Benham (1973), Thaler and Rosen (1975),
and Parsons (1977).
13/
14/
137
A review of recent work is available in Lave and Seskin (1977).
In Grossman's (1972) notation, the sick time production function is:
^t = bO + bl[It + 6)Ht- I1
where TL represents chronic or acute sick time, H is the stock of health
capital, I is current health investments, and 6 is the rate at which the
health stock decays. The term in parentheses is the stock of health capital
written in terms of the past stock of health capital and current investment
in health. Thus, for example, we treat such variables as POOR, DSAB, and
FEDU as determinants of H , and FOOD, NCIG, TSPM, etc., as components of
I and £ . Grossman (1972) chosses a multiplicative form for this expression,
whereas we adopt a linear form. Most inportantly, Grossman (1972) makes both
the wage rate and the health state endogenous by making the former a function
of the latter and the latter a function of the former. We treat the health
state as exogenously determined while retaining the dependence of the wage
upon the health state.
151
-------
— This currently lesser productivity could readily be due to past
discrimination in the labor market and /or education as well as fewer past
opportunities for investment in physical health.
-^— In this case, it is unlikely that multicollinearity has seriously
inflated the standard errors of the air pollution variables. The highest
simple correlation coefficient between an air pollution variable and another
explanatory variable was r » C.TTTVT = 0.65. All other simple correlation
loir bULiM
coefficients were less than 0.20.
— The 830-day interval is a weighted arithmetic mean established by
taking the midpoint of each of the time equivalents of the SRC index
measures for LDSA and weighting by the proportion of the entire SRC sample
in 1971 having a particular LDSA index value. Ten years was treated as the
midpoint for the uppermost LDSA index.
•jo/
—'See Crocker and Horst (1977).
19 /
— Ideal generalization of this model would have: (1) the flow of health
services rather than the stock of health entering the individual's utility
function; and (2) the opportunity cost of time not be assumed equal to the
wage rate but rather derived from the model to be equal to the wage rate
weighted by the shadow price for expenditures on inputs into the production
of health and the composite commodity.
20/
— The time expenditure at which fatugue and/or boredom sets in on a
particular job and the rate at which it changes is itself likely to be a
function of the individual's state-of-health and education. We have not
tried to capture this either in this model or in the subsequent empirical
effort that accords with it. One might argue that various attitudinal
measures such as job satisfaction, aspiration and ambition, and others
readily available in the SRC data would serve as adequate proxies for
fatugue and boredom.
21 /
— Simultaneity is implied by the model in the demand for acute illness.
In particular, although we considered it only in passing, the time expended
in other work activities is an endogenous variable, which, in turn, implies
that work time is endogenous. We have, infact, tested this simultaneity
by treating work as endogenous and estimating the systme by two-stage least
squares. The results, which we do not bother to report here, differed only
trivially from the ordinary least squares estimates that we do report.
— The reader should be aware that by adopting a TSLS estimation pro-
cedure, we are giving up some efficiency in estimation in order to enhance
the consistency of our estimation. The cruelty of this tradeoff is due to
the quite low coefficients of determination involved in OLS estimates of the
freedom from chronic illness demand function.
152
-------
Chapter VI
AN ESTIMATE OF NATIONAL LOSSES IN LABOR PRODUCTIVITY
DUE TO AIR POLLUTION-INDUCED MORBIDITY
6.1 Introduction
In this brief chapter, we use what we consider to be the most repre-
sentative of the recursive labor supply estimates in Table 5.10 to speculate
what the aggregate gains in U.S. labor productivity could be from a reduction
in air pollution-induced acute and chronic morbidity. Due to the preliminary
and exploratory nature of our work, we are most anxious that the reader
wishing to employ or to communicate these calculations be careful always to
make highly visible the set of assumptions in which the calculations are
embedded. Otherwise, he will be unable to make an informed judgment about
the extent to which the world represented in the text corresponds to reality.
Figure 6.1 is a hueristic representation of the structure forming the
basis of our estimate. Air pollution is viewed as increasing directly both
chronic and acute illness. In addition, it causes an indirect increase in
acute illness via its positive effect on chronic illness. Acute illness
reduces hours worked, but, because of its passing nature, it has no impact
upon the worker's long-term productivity that determines the level of his
wages. However, chronic illness, which does reduce long-term productivity,
exerts a direct negative influence on both wages and hours worked. It also
influences hours worked in an indirect manner through its effect upon wages.
Figure 6.1
A Representation of the Effect of Air Pollution
Upon Labor Productivity
Chronic Illness
153
-------
6.2 The Assumptions
Table 6.1 is a succinct list of the major assumptions underlying our
empirical implementation of the structure depicted in Figure 6.1 and its
extrapolation to a national aggregate. We divide these assumptions into
four classes: specification, measurement, estimation, and aggregation. The
table also indicates the probable direction of bias, if any, the assumption
introduces. However, we do not .now know the sensitivity of our estimates
and calculations to any particular assumption or to the entire set of
assumptions. Upon reviewing Table 6.1, the judicious reader will immed-
iately become aware that our listing is sufficiently strenuous to raise
some questions about whether our estimates and calculations are yet suf-
ficiently compelling to warrant their serious use.
In spite of the lengthy listing of assumptions, we emphasize that our
treatment of the system in Figure 6.1 has several positive distinguishing
features. To balance any negative impressions established from Table 6.1,
we list these positive features in Table 6.2. Our estimates of the system
in Figure 6.1 is presented in Table 6.3. As a result of a one-unit (yg/m3)
increase in air pollution, we estimate that the representative person in
Table 6.3 will have his annual work hours reduced by 0.547 hours. Of this
reduction, only 0.046 hours will be due to acute illness. The loss in labor
productivity suffered by this person can be calculated by (where A stands
for change):
A (Work hours • Wage) _ A (Work hours) . Wage + A (Wage) . Work hours
A(pollution) ~ A(Pollution) A(Pollution)
Upon performing this calculation, we obtain:
= (0.547)($3.225) + ($0.071)(1560.895)
= $2.86
That is, a one-unit reduction in air pollution would have increased this
representative person's 1970 earnings by $2.86. Only $0.15 of this sum
represents the gain from a reduction in acute illness.
The above $2.86 sum represents our "best" estimate at this point of the
representative person's gain in 1970 earnings from a one-unit reduction in
air pollution. Lower and upper bounds for this estimate can be established
by making use of the confidence intervals for the effect of pollution on
chronic and acute illness; that is, we wish to calculate the gain in earnings
when the pollution coefficient in (1) is 0.0028 + 0.0011, and when the
pollution coefficient in (2) is 0.623 ± 0.317. At least for the chronic
illness expression, this confidence interval captures nearly all the range
of the values for the pollution coefficients in the chronic illness expres-
sions estimated in the previous chapter. Upon performing this calculation
for the lower bound, we obtain $1.88, and for the upper bound, we obtain
$3.84.
Assume that the average exposure of the U.S. 1970 urban population to
annual geometric mean total suspended particulates was 100 yg/m^ and that
154
-------
Table 6.1
Major Assumptions Limiting Generality of Results
Specification
1) Air pollution affects only the duration of chronic illness. Our
inattention to the severity of chronic illness tends to reduce the estimated
impact of air pollution on labor productivity.
2) Occupational exposures to hazards and environmental pollutants other
than air pollution do not influence either acute or chronic illness. If air
pollution is moderately and positively associated with these hazards and
pollutants, this assuption tends to increase the estimated impact of air
pollution on labor productivity.
3) Annual geometric mean ambient concentrations of total suspended
particulates serve as an adequate proxy for all forms of air pollution.
The effect of this assumption upon the estimated effect of air pollution
on labor productivity is unknown,
4) All relationships depicted in Figure 6.1 are linear. It is unknown
what effect this assumption has on the estimated effect of air pollution on
labor productivity.
5) Air pollution-induced health effects do not cause the voluntary
substitution of leisure for work. This assumption tends to reduce the
estimated impact of air pollution on labor productivity.
Measurement
6) Air pollution exposures for each individual in the sample are
adequately represented by a single annual average of ambient concentrations
obtained at a single monitoring station within the individual's county of
residence. Since pollution monitoring stations in the early part of the
1970's were predominantly in downtown urban locations, individuals' air
pollution exposures probably tend to be exaggerated. This will reduce the
estimated health effects of air pollution.
7) The duration of any air pollution-induced chronic illness cannot
exceed ten years. This will reduce the estimated effect of air pollution
upon the duration of chronic illness.
8) Housewives, retirees, and students, who together constitute about
twenty percent of our samples, do not contract air pollution-induced acute
illnesses. This assumption will tend to reduce the estimated impact of air
pollution upon labor productivity.
9) Air pollution-induced chronic and acute illnesses are a constant
proportion of all illnesses. The effect of this assumption is unknown.
(continued)
155
-------
Table 6.1
(continued)
10) The quantity of preventive and ameliorative medical care an
individual consumes is adequately measured By whether or not he has medical
insurance. This assumption has an unknown effect upon our estimates.
11) Relative air pollution concentrations across the U.S. have been
fairly constant. This assumption has an unknown effect upon our estimates
of air pollution-induced chronic illness.
12) When interviewed, the individuals in the sample had no incentive
to bias their answers nor did they have difficulty accurately recalling
their personal medical histories of the previous twelve to sixteen months.
The effect of this assumption upon our estimates is unknown.
13) No individual who would otherwise have been included in the sample
died between the time for which information was to be gathered and the time
of the interview. In fact, about five percent of the potential respondents
died each year. The effect of this assumption is to reduce the effects .of
air pollution upon labor productivity.
Estimation
14) With the available data, classical linear regression procedures
provide consistent and unbiased estimates of the structure depicted in
Figure 6.1. The effect of this assumption upon our estimates is unknown.
Aggregation
15) The response of the health state of each individual in the U.S. to
any given change in ambient air pollution is a constant. The effect of this
assumption upon the calculation for the aggregate effect of air pollution
upon labor productivity is unknown.
16) The response of the health state of every individual in the U.S.
to ambient air pollution changes is identical. The effect of this assump-
tion upon the calculation for the aggregate effect of air pollution upon
labor productivity is unknown.
156
-------
Table 6.2
Distinguishing Features that Enhance the Generality of Results
1) The acute illness and chronic illness dose-response estimates used
to calculate the aggregate impact of air pollution-induced morbidity upon
U.S. labor productivity are representative of estimates obtained from many
different independent samples drawn from the same data set. In effect,
substantial quasi-replication of the dose-response estimates has been
performed.
2) The system is estimated only for people who have always lived in
one state. We believe this restriction enhances the extent to which we
capture the effect of the history of air pollution exposures upon the chronic
illness dose-response function. :
3) Our estimated expressions for wages and hours worked are very
similar to those obtained by other economists.
4) We include more information on life-styles and genetic and social
endowments than is usually included in dose-response expressions estimated
from epidemiological data.
157
-------
Table 6.3
Estimated Expressions to be Used to Calculate the Effect of
Air Pollution—Induced Illness on LaKor Productivity3
(1) 830 day years chronically ill = 2.980 + 0.554 (illness severity)** +
(0.035)
0.005(age in years) + 0.013(years of school) - 0.044(father's years of
(0.004) (0.029) (0.037)
school) - 0.069(poor when growing up) + 0.072(Caucasoid) + 0.139(male)
(0.103) (0.488) (0.114)
- 0.902(diet adequacy) - 0.454(has medical insurance)* - 1.645(works
(0.975) (0.129) (0.575)
in chemicals/metals industries)b + 0.0028(mean total suspended
(0.0011)
particulates)*
R2 = 0.525; S.E. = 0.964; F(11,388) = 38.920.
(2) Annual hours acutely ill = 165,208 + 39.52(years chronically ill)*
(13.34)
-1.421(age in years) - 16.92(inale) - 0.086(cigarette expenditures) -
(1.312) (39.16) CO.118)
78.47(gets strenuous exercise)* - O.lOSCdiet adequacy)* - 38.44(degree
(40.11) (0.033) (13.26)
of risk aversion)* + 187.70(has medical insurance)** - 85.56(works in
(47.47) (191.20)
chemicals/metals industries) + 0.623(mean total suspended particulates)*
03.317)
R2 = 0.195; S.E. = 204.462; F(10,389) = 5.721.
(3) Wage in cents - -132.318 - 25.930(years chronically ill)* + 24.070(years
(14.440) (8.578)
of school)* + 15.370(illness severity) + 26.880(family size)* + 42.380
(18.260) (6.079) (6.138)
(cost-of-living)* = 52.950(years on current job)* - 7.163(often late
(22.130) (33.88)
for work) + 66.090(union member)* + 47.60(Caucasiod)
(34.580) (34.22)
R2 = 0.408; S.E. = 258.908; F(ll,388) = 24.28.
(continued)
158
-------
Table 6.3
(continued!
C4) Annual hours worked = 1266.68 - 163.9Q(yeara chronically 111}* + 0.354
C27.22) CO.130)
Cwage in cents)* + 44.26(family size)* + 519.80(male)* - 0.272(dollars
(16.68) (80.27) (0.022)
Of transfer income)* + 23.06(cost^-of-living) - 0.074(annual hours
(15.20) (0.031)
acutely ill)*
R2 = 0.551; SVE. = 663.196; F(6,393) = 80.41.
aExact variable definitions are available in Table 5.1.
bThe number of people in these industries was too small for this coefficient
to be meaningful.
*Statistically significant at the 0.05 level of the one-tailed t-test.
**Statistically significant at the 0.05 level of the two-tailed t-test.
159
-------
the standard deviation of these exposures was 30 yg/m . Throughout this
study, total suspended particulate measures have been highly correlated
with other air pollutants so that total suspended particulates probably
serve as an adequate proxy for all air pollution. Further assume that the
national urban population is approximately 150 x 10^ people, each of whom
is or will be a family head. After age 20, each of these family heads has
a life-span of 50 years and any air pollution-induced chronic illnesses he
contracts are distributed rectangularly over the 50 years. The earnings he
loses due to the presence of an acute or chronic illness do not vary over
the years. Given these and earlier assumptions, a 60 percent reduction in
air pollution would, in June 1978 dollars, increase the value of 1970
U.S. labor productivity by the amounts shown in Table 6.4. Most of the
gain would accrue due to reductions in air pollution-induced chronic illness.
It must be strongly emphasized that the magnitudes exhibited in Table
6.4 are extremely sensitive to the assumptions we have made. Nevertheless,
given any reasonable set of assumptions about air pollution exposures, size
of the population exposed, etc., the estimates of labor productivity gains
in Table 6.4 are much larger than previous estimates of all types of annual
gains from air pollution control in the United States. No gains in labor
productivity, via reductions in air pollution-induced health effects, have
previously been developed. It thus appears that the economic gains from
the morbidity effects of air pollution control have been greatly under-
valued, perhaps because most prior research efforts have concentrated upon
mortality rather than morbidity.
A more conservative but equally tenuous way of calculating the effects
in Table 6.4 might proceed as follows. Assume that the 75 percent, or 112
x 10" million people of the 150 x 106 urban population are 16 years or
older. At age 16, each of these adults has a lifespan of 56 years and any
air pollution-induced chronic illnesses he contracts are distributed rectan-
gularly over the 56 years. The annual earnings he loses due to the presence
of an acute or chronic illness do not vary over the 56 years. If the median
household size is 2.0, there are then 56.25 x 106 urban household heads.
There is thus a $160.88 x 106 = C$2.86) (56.25 x 106) gain in the labor
productivity for household heads from a one unit reduction in air pollution.
If two-thirds of the household heads are married, if 35 percent of
these households have working wives, and if working wives earn 60 percent as
much as their male counterparts, there would then be a $22.58 x 10^ =
($2.86) (0.6) (13.13 x 106) gain in the labor productivity of working wives.
If the value of household services provided by all household members
in each urban household is 40 percent of the household head, there would
then be a $64.35 x 106 » C$2.86) CO.4) C56.25 x 106) gain in the household
labor productivity of all urban households. Adding the results for house-
hold heads, working wives, and household labor, we obtain a $247.81 x 10^
gain in labor productivity for a one unit reduction in air pollution. A 60
percent reduction in 1970 air pollution would then, in August 1978 dollars,
increase the value of 1970 urban labor productivity by $25 x 109 dollars.
This is a "best" estimate. Its upper and lower bounds are, respectively,
$34 x 109 and $16 x 109. If one performs these identical calculations in
precisely the same fashion for a 1977 U.S. total population of 216.1 x 106,
one obtains a "best" estimate of $36 x 109.
160
-------
Table 6.4
Estimated Per Capita Aggregate Gains in 1970 U.S. Labor Productivity Due to
a 60 Percent Reduction in Air Pollution
(June 1978 Dollars)
Per
Capita Aggregate
Lower Bound $189.50 28,426 x 106
"Best" Estimate $288.29 43,243 x 106
Upper Bound $387.07 58,061 x 10
161
-------
REFERENCES
Becker, G.S., "A Theory of the Allocation of Time," Economic Journal 75
(September 1965), 493-517.
Blumquist, G., "Value of Life: Implication? of Automobile Seat Belt Use,"
Unpublished, March 1977.
Conley, B., "The Value of Human Life in the Demand for Human Safety,"
American Economic Review 66, (March 1976), 45-57.
Crocker, T.D. and Horst, R.L, Jr., Oxidant Air Pollution and Work Performance
of Citrus Harvest Labor, Research. Triangle Park, N.C.: USEPA
Publication, 600/5-77-013 (September 1977).
Cropper, M.L., "Health, Investment in Health, and Occupational Choice,"
Journal of Political Economy 85 (December 1977), 1273-1294.
Engel, G.L., "The Need for a New Medical Model: A Challenge for Biomedicine,"
Science, (1977), 129-136.
Grossman, M., "On the Concept of Health Capital and the Demand for Health,"
Journal of Political Economy 80 (March/April 1972), 223-255.
Grossman, M., and Benham, L., "Health, Hours, and Wages," in M. Perlman,
(ed.), The Economics of Health and Medical Care, New York: Halstead
Press C1973), 205-233.
Grossman, M., "The Correlation between Health and Schooling," in N.E.
Terleckyj (ed.), Household Production and Consumption, New York:
Columbia University Press (1975), 147-211.
Hanushek, E.A., and Quigley, J.M., "Implicit Investment Profiles and Inter-
temporal Adjustments of Relative Wages," American Economic Review 68
(March 1978), 67-79.
Hippocrates, 460-377 B.C., "On Airs, Waters, and Places," in F. Adams, (ed.),
The Genuine Works of Hippocrates, Baltimore (1939).
Kneese, A. V., and Schulze, W., "Environment, Health and Economics - The
Case of Cancer," American Economic Review 67, (February 1977), 26-32.
Kmenta, J., Elements of Econometrics, New York: Macmillan Publishing
Company (1971).
Lave, L. and Seskin, E., Air Pollution and Human Health, Baltimore: Johns
Hopkins Press (1977)
Lazear, E., "Age, Experience, and Wage Growth," The American Economic Review
66 (September 1976), 548-558.
162
-------
Marquis, K. H., Record Check. Validity -of Survey Responses: A Reassessment
of Mases in Reports of Hoapltalizatlons, Report R-2319-HEW, Santa
Monica, California: The Rand Corp. (May 1978).
McCarthy, M.D., "Notes on the Selection of Instruments for Two Stage Least
Squares and K Class Type Estimators of Large Models," Southern Economic
Journal, (January 1971), 251-259.
Mincer, J., "The Distribution of LaBor Incomes: A Survey with Special
Reference to the Human Capital Approach," Journal of Economic Liter-
ature 8 (March 1970), 1-26.
Mishan, E.J., "Evaluation of Life and Limb: A Theoretical Approach,"
Journal of Political Economy, Vol. 79, (December 1971).
National Academy of Science, Nitrates; An Environmental Assessment,
Environmental Studies Board, NAS, Washington, D.C., 1978.
Schwing, R.C. and McDonald, G.C., "Measures of Association of Some Air
Pollutants, Natural Ionizing Radiation and Cigarette Smoking with
Mortality Rates," presented to the International Symposium on Recent
Advances in the Assessment of the Health Effects of Environmental
Pollution, Paris, France (June 1974).
Schultz, T.P., The Estimation of Labor Supply Functions for Secondary
Workers, Report R-1265-NIH/EDA, Santa Monica, California: The Rand
Corporation (February 1975).
Selvin, H.C. and A. Stuart, "Data-Dredging Procedures in Survey Analysis,"
The American Statistician 20 (1966), 20-23.
Smith, R., "The Feasibility of an 'Injury Tax' Approach to Occupational
Safety," Law and Contemporary Probleirts, (Summer-Autumn, 1974).
Stigler, G.J., "Imperfections in the Capital Markets," Journal of Political
Economy 75 (June 1967) 291.
Survey Research Center, University of Michigan, Experiments in Interviewing
Techniques; Field Experiments in Health Reporting, 1971-1977,
Washington, D.C." USDHEW Publication No. (HRA) 78-3204 (Nov. 1977).
Survey Research Center, A Panel Study of Income Dynamics; Study Design,
Procedures, Available Data, Ann Arbor: Institute for Social Research,
University of Michigan (1972a).
Syme, 'S.L. and Berkmani L.E., "Social Class, Susceptibility and Sickness,"
American Journal of Epidemiology 104 (1976), 1-8.
Thaler, R. and Rosen, S., "The Value of Saving a Life: Evidence from the
Labor Market," in N.E. Terleckyj, (ed.), Household Production and
Consumption, New York: Columbia University Press (1975), 265-297.
163
-------
Waddell, I.E., The Economic Damages of Air Pollution, Washington, D.C.:
Socioeconamic Environmental Studies Series, IJSEPA (19741,
Wallace, T.D., "Present Estimation in Regression: A Survey," American
Journal of Agricultural Economics 59 (August 1977), 431-443.
164
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
I. REPORT NO.
EPA-600/5-79-001a
3. RECIPIENT'S ACCESSION NO.
1. TITLE AND SUBTITLE
Methods Development for Assessing Air
Pollution Control Benefits: Volume I, Experiments in
the Economics of Air Pollution Epidemiology
5. REPORT DATE
February 1979
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Thomas D. Crocker, William D. Schulze, Shaul Ben-David,
and Allen V. Kneese
J. PERFORMING ORGANIZATION NAME AND ADDRESS
University of Wyoming
Laramie, Wyoming 82071
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO.
1HA616 and 630
11. CONTRACT/GRANT NO.
R805059-01
12. SPONSORING AGENCY NAME AND ADDRESS
Office of Health and Ecological Effects
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460
13. TYPE OF REPORT AND PERIOD COVERED
Interim Final. 10/76-10/78
14. SPONSORING AGENCY CODE
EPA-600/18
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This volume employs the analytical and empirical methods of economics to develop
hypotheses on disease etiologies and to value labor productivity and consumer losses
due to air pollution-induced mortality and morbidity.
In the mortality work, 1970 city-wide mortality rates for major disease
catagories have been statistically associated with aggregate data from sixty U.S.
cities on physicians per captia, per capita cigarette consumption, dietary habits,
air pollution and other factors. The estimated,effect of air pollution on mortality
rates is about an order of magnitude lower than some other estimates. Nevertheless,
rather small but important associations are found between pneumonia and bronchitis
and particulates in air and between early infant disease and sulfur dioxide air
pollution.
The morbidity work employed data on the generalized health states and the time
and budget allocations of a nationwide sample of individual heads of household. For
the bulk of the dose-response expressions estimated, air pollution appears to be
significantly associated with increased time being spent acutely or chronically ill.
Air pollution, in addition, appears to influence labor productivity, where the
reduction in productivity is measured by the earnings lost due to reductions in work-
time.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
cos AT I Field/Group
Economic analysis
Air pollution
Epidemiology
Public health
Economic benefits of
pollution control
13B
18. DISTRIBUTION STATEMENT
Release unlimited
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
175
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
OU.S. GOVERNMENT PRINTING OFFICE: 1979 620-007/3769 1-3
------- |