United States
Environmental Protection
Agency
Office of Policy
Planning and Evaluation
Washington DC, 20460
August 1989
EPA-230-08-89-065
Estimating and Valuing
Morbidity in a Policy
Context:
Proceedings of June 1989
AERE Workshop

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EPA 230-08-89-065
AERE Workshop
Estimating and Valuing Morbidity
in a Policy Context
Proceedings
Workshop Sponsors
The Association of Environmental and Resource Economists
U.S. Environmental Protection Agency
National Oceanic and Atmospheric Administration
Session Chairpersons
Session I
Chair: Ann Fisher, U.S. EPA
Session II
Chairs: Richard Williams, FDA
Allen Basala, U.S. EPA
Session III
Chair: William H. Desvousges, RTI
Research Triangle Ftark, North Carolina
June 8-9, 1989

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The information in this document has been funded in part by the
United States Environmental Protection Agency (EPA) under
Cooperative Agreements CR-812056 and CR-815869. It has been
subjected to the Agency's peer and administrative review, and
approved for publication as an EPA document. Mention of trade
names or commercial products does not constitute endorsement or
recommendation for use.

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CONTENTS
Session I: Estimating the Amount of Illness and Inury Associated with
Specific Causes
The Role of Epidemiology in Developing Useful Data for Public Health Policy
Daniel A Hoffman (to be provided at workshop)
Acute Health and Variable Air Pollutants
James C Murdoch, Mark A Thayer, William N Weirick
Estimating Skin Cancer (Melanoma) Deaths from Sunlight Exposure
Hugh M Pitcher
Session II: Valuation of Changes in Illness and Injury
Pricing Environmental Health Risks Survey Assessments of Risk-Risk and Risk-Dollar
Trade-offs W, Kip Viscus, Wesley A Magat, and Joel Huber
The Social Costs of Chronic Heart and Lung Disease
Maureen L. Cropper and Alan J. Krupnick
Estimating the Value of Avoiding Morbidity and Mortality from Foodborne Illnesses
Josephine A Mauskopf and Michael T French
Utility-Adjusted Impairment Years: A Low-Cost Approach to Morbidity Valuation
Ted R. Miller, Charles Calhoun, and W Brian Arthur
Valuing Nonmarket Goods: A Household Production Approach
Mark Dickie and Shelby Gerking
Valuation of Morbidity Reduction Due to Air Pollution Abatement Direct and Indirect
Measurements
Mordechai Shechter
Risk, Self-Protection and Ex Ante Economic Value
Jason F Shogren and Thomas D Crocker
The Economics of Quarantines: An Application to Pesticide Regulation
Erik Lichtenberg, Robert C Spear, and David Zilberman

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THE ROLE OR EPIDEMIOLOGY IN DEVELOPING
USEFUL DATA FOR PUBLIC HEALTH POLICY
by
Daniel A Hoffman

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The Role of Epidemiology in Developing
Useful Data for Public Health Policy
Daniel A. Hoffman, Ph.D.
Centers for Disease Control
Atlanta, Georgia
INTRODUCTION
In the last two decades, the role of epidemiology in
providing data for public health policy makers has become
more prominent than any time in the history of this
discipline. Its greatest advantage is that it provides
direct human evidence of the health outcomes from various
environmental exposurs, unlike animal models. However,
there are many caveats that need to be attached to these
data. The objective of this paper is to review some of
the basic limitations to the epidemiologic method, both
in study design and in interpretation of the data. The
perspective that I will present is that of an
epidemiologist in a public health agency. The Centers for
Disease Control does not engage in the development of
regulations or have a large program in risk assessment.
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Our principle function is to serve the state and local
health departments by offering advice and assistance when
necessary through field investigations of potential
public health problems-in our case,
environmentally-induced disease. This involves the
identification of study hypotheses, designing the study,
developing the necessary survey instruments, collecting
health data, analyzing this data, and finally offering
our interpretation and recommendations. Basically we
engage in the classical epidemiologic method of
hypothesis generation and testing through field
investigations. Consequently, my talk today is focused on
the techniques involved in acquiring these data, and
examining the strengths and weaknesses of these data as
they relate to various interpretations of their meaning
for use in risk assessments, regulatory actions, or
public health policy decisions.
DESCRIPTION OF EPIDEMIOLOGIC METHODS
The assessment of effects on humans of various
environmental exposures relies heavily upon the results
from testing of animal models and clinical and
epidemiological studies. However, the most important
advantage that epidemiological studies have over animal
investigations is that they provide direct evidence of
the effects of toxic exposures in humans. Conversely,
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human studies are difficult to conduct properly and the
interpretation of the results from these studies makes
life difficult for both regulators and policy makers.
Part of the problem in interpretation stems from the
design of these studies which can be very complex.
Another problem is dealing with the inherent biases which
inevitably creep into the interpretation of the data, no
matter how thoroughly these have been addressed either in
the study design or analysis. This stems from the fact
that, with the execption of clinical trials,
epidemiological studies are observational by nature, not
experimental . Not only do humans vary widely in their
response to toxic agents but they vary also in their
capacity for response as well as in their exposure to
factors such as alcohol and tobacco, which may may
greatly modify the nature or severity of their responses
to toxic exposures. One example would by the relation
between radon exposure and cigarette smoking which could
either be additive, submultiplicative or mulplicative
depending upon which data is reviewed and which model is
applied to that data.
Despite these difficulties, techniques for the evaluation
of data from human studies have been developed and
refined. The epidemiological method has matured to the
point that it has withstood the criticism that it is
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incapable of establishing the etiology of disease.
Epidemiological inferences have been sustained and
corroborated by the results of toxicological and
biochemical studies, and epidemiology has proven to be a
powerful tool for the exploration of both qualitative and
quantitative cause-and-effect relationships between
environmental exposures and human disease. However, there
is still much to be done, especially at the rather low
levels of exposures that most human populations
experience, to further refine the tools of epidemiology.
I would now like to briefly discuss some of the various
study designs used in epidemiology. Next I will address
some of the sources of bias in epidemiologic data, and
conclude with a discussion on interpretations of
causality based on data derived from epidemiological
studies. Two areas of study which I will not discuss in
any detail today are the appropriateness of animals models
as they apply to risks in humans and the use of
biomarkers as indicators of risk in epidemiologic
studies. The majority of our experience at CDC has been
concerned with collection and interpretation of
epidemiologic data so the principal focus of my talk will
be on that process.
The most commonly used designs in epidemiology are: 1)
case reports; 2) ecological or correlational studies; 3)
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cross-sectional studies; 4) case-control studies; and 5)
cohort studies.
1 . CASF. REPORTS
Case reports identify one or more cases of a disease that
have been detected by clinicians, by company or union
officials, or by through active surveillance or passive
reporting such as cancer registries. The first recorded
case studies of environmental disease were Sir Percival
Pott's observations of scrotal cancer among chimney
sweeps in London. Publication of such case reports often
constitutes the first recognition that a problem of
environmnetally induced disease exists, and subsequent
epidemiological assessment proceeds from this
recognition. A more recent example includes the first
recorded cases of AIDS by clinicians at UCLA medical
center in 1978. In a case series, an inference of causal
association between causation and an environmental agent
is based on the plausibility of the following
considerations: clustering of the cases in a limited time
frame; the relative rarity of the types of diseases
observed; a history of common environmental exposure; an
the apparent strength of the association. The most common
use of case reports are hypothesis generation,
surveillance, and case registries
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Survei 11ance
The case report has historically been an important"
surveillance tool, especially for recognition of
infectious diseases. Occupational case reporting has been
useful in terms of reporting occupational injuries for
workman's compensation, but not so much for occupational
diseases due to the long latency period between exposures
and disease. A more recent use of case reports as a
surveillance tool is for the identification of senital
health events. These are cases of disease associated with
well-characterized causes whose appearance signals a
breakdown in mechanisms for disease prevention. This
method has been applied with success in the reduction of
maternal and infant mortality and has been extended to
such environmental illnesses as lead poisoning.
Case Registries
Other surveillance systems relying on case reports
include case registries, such as the CDC Dioxin Registry
or workers suspected of having been exposed to dioxin.
These exposure registries perform the task of grouping
potentially high-risk populations for future
epidemiological studies.
An advantage of case reports over most other types of
epidemiological studies is their low cost. In addition, a
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short lag time between identification of cases and
dissemination of information is more typical of case
reports. However, relying on case reports as an early
warning system is less useful when:
1)	the cases are sporadic;
2)	the relative risk is low;
3)	the outcome is a common disease or a symptom
with multiple common etiologies such as lung
cancer or heart disease;
4)	there is a long latent period between exposure
and effect; and
5)	there is a continuum of disease and health and
no clear distinction between cases and noncases is
possible, for example, premalignant dysplasia and
carcinoma in situ.
In addition, case reports can provide only a rough
estimate of disease frequency, in that they give no
information on the size of the population at risk and
thus make it impossible to calculate a disease rate.
Finally, case reports are difficult to generalize to a
population since the population from which the cases are
identified is not usually well defined.
2. CORRELATIONAL OR ECOLOGIC STUDIES
Another type of descriptive tool used by epidemiologists
is the so-called correlational or ecologic study, which

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uses data from entire populations to compare disease
frequencies between different groups during the same
period of time or in the same population at different
points in time.
As an example of the former, correlational studies have
suggested that various dietary components, in this case
per capita meat consumption, may be risk factors for
colon cancer. Figure 1 shows the correlation between per
capita consumption of meat and rates of colon cancer in
women from a large number of countries. As apparent from
this figure, the rates of colon cancer are lowest in
countries with the lowest per capita meat intake and vice
versa.
Figure 2 illustrates the change in disease frequency
within the same population over time. In this slide, the
difference between tge approximately 820,000 deaths from
coronary heart disease that would have been expected in
the United States if the 1968 rates had continued to
apply and the approximately 630,000 deayhs actually
observed. Such data suggest two possible explanations: 1)
that the decline in deaths from coronary heart disease
could be due to prevention due to improvements in
life-style habits and consequent risk factor reduction,
and 2) that while the rates of CHD did not decline,
persons were surviving longer due to improvements in
medical management of CHD.
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While correlational studies are useful in developing
hypotheses for study, they cannot be used to test them
because of a number of imitations inherent in their
design.
1)	Correlational studies refer to populations
rather than to individuals. Therefore, it is not
possible to link an exposure to occurrence of
disease in the same person.
2)	The distribution of other risk factor's which
may account for different rates of a disease, may
be differentially distributed among populations.
This is known as the "ecologic fallacy".
3. CROSS-SECTIONAL STUDIES
Another type of descriptive study design is the
cross-sectional survey, in which the status of an
individual with respect to the presence or absence of
both exposure and disease is assessed at the same point
in time. For example, the Health Interview Survey is a
national cross-sectional study that periodically collects
extensive information by questionnaire from a sample of
over 100,000 persons throughout the United States. These
studies often rely on personal interviews or
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questionnaires to obtain demographic information,
symptomatic, and exposure data on clinical evaluations
based on physical examinations and laboratory and
environmental sampling data to identify the
characteristics of the sample population and to
quantitate exposure to potential risk factors. An
advantage of the cross-sectional survey is the rapid
estimation of numerator values for determining frequency
or prevalence rates of both exposure and effects.
Limitations of this method include the inability to
distinguish whether the exposure preceeded the
development of disease or whether the presence of disease
affected the individual's level of exposure, since
exposure and disease are assessed at the same point in
time. Cross-sectional approaches have limited usefulness
in cancer studies because of the usual low prevalence of
cases. It is also extremely difficult to quantify
exposure in cross-sectional studies. However, for factors
that remain unaltered over time, such as sex, race or
blood group, the cross-sectional survey can provide
evidence of valid associations.
Five common pitfalls can be found in the cross-sectional
method. These are:
1) Selection bias, in that a nonrepresentative
sample of the population may be surveyed, limiting
the generalizability of the survey results;
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2)	Confounding bias, which can result for factors
related to both exposure and outcome, such as age;
3)	Inadequate sensitivity of the survey
instruments. This includes specificity, which is
the ability to detect "true" negatives, and
sensitivity or the ability to detect "true"
positives;
4)	Lack of standardization of the instruments used
for data collection, which may prohibit the
pooling of data from multiple surveys; and
5)	Inadequate validation of either exposures of
health outcomes, resulting in misclassification of
either category.
Summarizing, in general, cross-sectional studies are
useful for raising the question of the presence of an
association rather than testing a hypothesis.
The next two types of epidemiologic studies are
observational in design. These are the case-control study
and the cohort study.
In theory, it is possible to test a hypothesis using
either design strategy. In practice, however, each design
offers certain unique advantages and disadvantages. In
general, the decision to use a particular design is based
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on the features of the exposure and disease, the current
state of knowledge^nd logistic considerations such as
available time and resources.
4 . CASE-CONTROL STUDIES
In the case-control study, a case group or series of
patients who have a disease of interest and a control or
comparison group of individuals without the disease are
selected for investigation, and the proportions with the
exposure of interest in each group are compared. Lung
cancer patients, for example, can be compared to persons
without that disease for differences in exposures, such
as cigarette smoking, occupational exposures, and radon
levels in the home.The relative frequency of
distribution of the exposure in the case and control
groups is usually evaluated by computing an odds ratio
which is defined as the product of the number of exposed
cases and unexposed controls divided by the product of
the unexposed cases and exposed controls. This is also
somtimes known as the cross-product odds ratio because of
the manner in which it is calculated.
Case-control studies can be conducted relatively rapidly.
Many simultaneous exposures can be evaluated in relation
to even the rarest disease. Howver the sequence of
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exposure-health event is often difficult to assess if the
case population includes patients selected from
historical records. If the disease studied is rapidly
fatal, interviews with surrogate respondents may be
required which may result in misclassification of
exposures. The individual exposure status is often
difficult to quantify with any precision, especially in
environmental studies, and control of possible
confounders may require a complex design or analysis.
Consequently, only environmental exposures with a high
prevalence and relative strong toxic effect are
effectively studied by the case-control method.
5-	COHORT RTTTDTF.S
In a cohort or follow-up study, the study population is
divided on the basis of exposure status. For example, in
a recent study of the health effects of volatile organic
compounds in Michigan, we assembled study cohorts on the
basis of whether or not VOC'S were detected in their well
water and if they had lived for a specified period of
time in the study area. Residents who had moved away
prior to the initiation of the study were still eligible
for inclusion in either the exposed or unexposed cohorts.
Once the exposure status of the study cohorts has been
determined, which is sometimes quite complex and can
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result in misclassification of exposure status thus
biasing the study outcome towards the null hypothesis of
finding no effect, the history of disease is determined
in both the exposed and unexposed groups. The rate of
disease in the exposed group is compared to that in the
unexposed group resulting in a relative risk of disease
which could be due to the exposure being studied. This is
also called the rate ratio since it is simply the ratio
of two incidence rates. Both of these measures of
association include a factor for follow-up time known as
the person-year. This is simply defined as the interval
from the time exposure began to the date of diagnosis of
disease, death, loss-to-follow-up or, if disease-free, an
arbitrary date.
The strengths of the cohort approach include the
following:
1) the sequence of exposure and health outcome can
be studied;
) many health outcomes can be evaluated with
regard to the one exposure of interest (although
this may have become a problem in some studies as
multiple comparisons inevitably lead to at least
one "significant" finding);
3) the initial exposures can be quantified through
historical records or even more so if there is a
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biologic marker of exposure such as blood or bone
lead levels;
4)	rare exposures can be studied;
5)	collection and analysis of potential
confounding factor is possible; and
6)	absolute risks may be calculated for use in
public health prevention strategies.
Some of the drawbacks to the cohort approach are the
expense and difficult logistics of these studies, the
potential for misclassification of exposure and disease
outcome resulting in a biased estinate of risk, and the
inability to study rare disease because of the very large
populations necessary for study. This latter drawback is.
important in studying the effects of low-level
environmental exposures. Because the anticipated risk of
these exposures is low, very large numbers of exposed
persons are required for study if the outcome is to have
any decent statistical power.
PROBLEMS IN CURRENT STUDY DESIGNS
From the previous discussions, four areas of major
problems become evident: 1) the assessment of the
exposure-response sequence; 2) quantification of
exposure; 3) recognition of bias and confounding; and 4)
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quality and validity of data. Clearly, a very complex
study design may be required to yield useful results.
Measures to improve the usefulness of human studies for
risk assessment purposes include the extension of the
duration of follow-up time, assessing the time component
in exposure and disease diagnosis, focusing on
potentially high-risk populations for study, and quality
assurance of information on exposure and disease. While
most of these measures are in the area of logistics and
funding, an important exception is improvement of the
quality of the exposure data.
In the past decade, development of environmental exposure
mesures has been very rapid. Detection limits for
chemicals in environmental media have dropped by three to
four orders of magnitude, and the progress of tests for
some chemicals in biological media is almost as
impressive. The detection limits for dioxin in sera, for
example, is now measured in parts per quadrillion.
Unfortunately, little progress to date has been found to
be of practical use in epidemiologic analysis and risk
estimation. For instance, issues of background levels,
biological persistence, adaption mechanisms, absorption
kinectics, saturation of metabolic pathways, and the
impact of an individual's characteristics on the
pathogenetic process have not been addressed in most
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epidemiologic study designs, and, for the most part, have
yet to enter the area of regulatory risk assessment.
There are other practical exposure issues that need to be
addressed such as noncontinuous or fluctuating exposures,
the cause of interspecies differences, and whether or not
an observed dose-response relationhip is stable over a
wide range of dose levels. We will also see an increasing
demand to incorporate quality assurance and quality
control in epidemiologic studies with regard to matters
other than laboratory work. For example, it is of utmost
importance to make certain that the disease of concern is
following and not pre-dating exposure. Finally, there is
the issue of the quality of the diagnostic criteria for a
case or a non-case.
The quality of diagnosis becomes a very central issue
when it comes to scenarios of localized environmental
pollution, for example, at a chemical dump site, and
residents with nonverifiable and subjective complaints,
which may be real to them, sucah as headache, fatigue,
nausea, chest pain, and loss of libido. Currently, there
is an inclination among epidemiologists to ignore or
disqualify this so-called "dump-site syndrome" from
serious study. However, such an attitude is usually
followed by a deterioration of a conflict situation
between citizens and authorities. There are many
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instances where eventually epidemiologists have been
forced by heavy and relentless public and political
pressures to conduct studies of such perceived illnesses.
In doing so, they will have to derive methods to cope
with non-verifiable health outcomes, while maintaining
scientific integrity and credibility. In theory, it
should be possible to either solve the problems with
statistical tools, or by developing tests for the kinds
of complaints often described as emotional or
behavioral. CDC staff are currently developing and
applying such tools to several large studies.
Statistical methods usually fail since the situation at a
dump site is inherently associated with an abundance of
negative publicity, usually in the direction of stating
the association of voiced complaints with exposure, or
even just living near a dump site, as a fact. This
scenario often results in serious reponse biases for
persons who perceive they may be exposed. I do not forsee
that behavioral toxicology, an exciting new field of
research, can provide us in the near future with the
appropriate scientific tools to address currently
nonconfirmable complaints.
DEVELOPMENT OF MOLECULAR EPIDEMIOLOGY
A special problem, both in animal and human studies, is
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that current designs deal with observed disease, which is
a more or less advanced stage of a toxic effect. In
animal studies, most diseases are observed in moribund or
sacrificed animals. In humans, disease detection is
usually in an earlier phase by virtue of man's ability
for detailed communication. However, even common diseases
such as cancer, arthritis, hypertension, and diabetes
still pose unresolved problems in assessing the date of
onset. Estimates of this date may differ by many years,
and this would offset greater accuracy in exposurement.
The logical response to this problem is to develop
techniques to diagnose the disease in the earliest
possible stage. But the question then arises: "What is
earliest possible?" An aggressive biopsy regimen for
diseases such as cancer and kidney disease may shift the
date of diagnosis from months to years earlier. Certain
inborn metabolic disorders can now be detected
prenatally. The use of electron microscopy has brought us
closer to the early onset of renal disease.
Unfortunately, these striking improvements in early
diagnosis require invasive procedures. This is a serious
handicap to epidemiologic studies, especially those
involving environmental rather than clinical or
occupational exposures. This explains the increasing
interest of epidemiologists and risk assessors in the use
of biomarkers indicating past exposures or early stages
of tissue dysfunction, for example, DNA-adducts.
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VALADIATION OF ASSUMPTIONS FROM EPIDEMIOLOGIC STUDIES FOR
REGULATORY PURPOSES AND PUBLIC HEALTH POLICY DECISIONS
Finally, I would like to discuss the interest of
epidemiologists in the validation of a number of
assumptions used in risk assessments for regulatory
purposes or public health policy decisions. One of these
is the assumption that the presence of a toxic chemical
in the environment automatically implies exposure, and
that that body dose is proportional to environmental
concentrations. This assumption leads to the often-used,
but nevertheless incorrect practice of assuming that the
concentration of a chemical in media such as soil, air or
water is a direct measure of the amount of chemicals
absorbed in the human body. Worse, without much thought
it is often considered identical to the challange to the
organ or tissue interest when determining acceptable
exposure levels. Studies into the relation between
environmental presence, human exposure, and
organ-specific dose are increasing in number.
The findings from these studies have sometimes been
contrary to expectation. For example, at the CDC, studies
have shown that the concentration of arsenic, PCB'S,
mercury, and lead in the soil of a neighborhood is only
partly related if at all to the levels in the biologic
specimens of residents. In this light, it is important to
recognize the importance of well-conducted research with
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negative findings. Such research is critical to our
understanding of the effects of toxicants on human
biology. Moreover, such findings help concerned
scientists to inform the public of true risks and allay
undue anxiety. Indeed, despite the abundance of available
data to date, the relation between environmental
concentrations of chlorinated hydrocarbons such as DDT,
dioxin, and PCB'S, and human sera or adipose samples,
remains unclear, and the relation of these levels of body
burdens to clinical disease remains uncertain.
To date, epidemiologic studies almost never prove cause
and effect, though in a few instances, reasonable people
would accept some of them as such. For example, in
looking at the pathway of exposure and body burden, the
association of the reduction of lead used in gasoline
production and the reduction of mean blood lead levels in
the U. S. population is striking. Over a 4-year period
when the lead phasedown in gasoline was occurring, we
were conducting a study of blood lead levels in the U. S.
population using data from the Second National Health and
Nutrition Examination Survey or NHANES-2, an example of a
cross-sectional study. Two things, declining blood lead
levels and lead used in gasoline production were highly
correlated. We removed over 100 potentially confounding
variables from this association in the analysis and the
coefficient of correlation did not appreciably change.
Yet many epidemiologists stated that this did not provide
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adequate evidence of cause and effect. The only way to
unequivocally prove cause and effect in this situation
would be to conduct an experimental study where children
were placed in chambers and breathed air with different
lead levels and then measure their blood lead levels.
This experiment, of course, would be entirely unethical
and would not be supported by society. Studies conducted
in humans must use only inadvertent exposure or natural
experiment s" such as that occurred with water
fluoridation and dental carries.
Proper use of epidemiologic data can lead to important
collective public health benefits. On the other hand, to
press such data into service to respond to causal effects
for an individual's disease holds high potential for
misuse of the data.
We will continue to respond to specific incidents of
human exposure to toxic or hazardous substances. We will
also continue our efforts, through epidemiologic
techniques, to measure both the immediate and long-term
health effects and to make sound recommendations for the
attenuation of these potential risks.
Although the results of such epidemiologic investigations
may not provide the conclusive answers about health risks
from environmental exposures, which are now in such
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demand and so prevalent in the media, we have hope that
we can study and detect these associations where they
exist, so that prudent public health actions can be
taken. Thus, we see the ultimate role of epidemiology as
one of prevention, which is the most effective public
health policy to implement.
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SUGGESTED READINGS
1.	Brunekreef, B., Noy, D., and Clausing, P.:
Variability of exposure measurements in environmental
epidemiology. Am J Epidemiol 1987; 125:892-898.
2.	Lilienfeld, A. M.: Practical limitations of
epidemiologic methods. Environmental Health Persp
1983;52:3-8 .
3.	Schneiderman, M. A.: Extrapolation from incomplete
data to total or lifetime risks at low doses.
Environmental Health Persp 1981;42:33-38.
4.	Dinman, B. D. and Sussman, N. B.: Uncertainty,
risk, and the role of epidemiology in public policy
development. J Occup Med 1983;25:511-516.
5.	Glass, R. I.: New prospects for epidemiologic
investigations. Sci ence 1986;234:951-956.
6.	Stein, Z. and Hatch, M. : Biological markers in
reproductive epidemiology: prospects and precautions.
Environmental Health Persp1987;74:67-75.
7.	Einarson, T. R., Leeder, J. Steven, and Koren, G.:
A method for meta-analysis of epidemiological studies.
Pharmacoepidemiology 1988;22:813-823.
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800
800
Expected
191,500
Deaths
700
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Observed
(/>
= 600
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in 1968)

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DRAFT
AERE Conference
June 8, 1989
Malignant Melanoma Death Rates,
Outdoor Recreation
and
Sun Screens
Hugh M. Pitcher
Economic Studies Branch
Office of Policy Analysis
US EPA
May 18, 1989
Disclaimer: This paper reports interim results on research which
is still in process. It presents the personal opinions of the
author. It has not been reviewed by EPA and does not represent an
official EPA position.

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Ab s t r a c t
Previous work has shown that there is a six fold increase in
the risk of death from melanoma for white males born in the 1940's
when compared to white males born in the 1880's and 1890's. For
women the same ratio is slightly less than three. Accepting the
hypothesis that most melanoma is caused by exposure to solar
radiation, an investigation of changes in residence patterns,
occupation, and outdoor recreation is made to see if the changes
in cohort risk can be explained by changes in factors related to
exposure patterns. Household access to automobiles turns out to
be the best potential measurable factor explaining outdoor
recreation patterns. While no conclusive findings are reached,
support is developed for the hypothesis that intense exposure of
skin which has not developed natural defenses under low to moderate
exposure is the primary risk factor for melanoma. The introduction
of sun screens" is associated with reductions in this risk. Since
lifetime incidence rates for white males in the 1940's cohorts will
approach 2.5 percent with death rates of about .6 percent, melanoma
is a significant public health problem. The paper's results
suggest that a risk communication policy should be aimed at
modifying sun exposure habits to reduce intensity of exposure.
The association of the automobile with problem exposure behavior
suggests a strategy of keeping sun screen in the glove compartment.
The payoff from such a policy could be a dramatic reduction in
melanoma incidence and death.

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INTRODUCTION
Cutaneous malignant melanoma is the most rapidly rising cause
of cancer death for white males and the second only to lung cancer
for white females.^" In response to this, there has been much
2
investigation of potential causes. Because melanoma cannot be
induced in small laboratory animals by ultraviolet radiation alone,
the ability of laboratory research to settle etiologic issues has
been sharply limited.	Epidemiologic results have been
inconsistent, with less melanoma observed on frequently exposed
parts of the body, and death rates increasing with latitude in
4 5
Europe. ' Occupations involving outdoor exposure have been found
to be mildly protective. ® It has been difficult to develop a model
which can comfortably explain all of these results. Thus, despite
all the work on melanoma to date, there is still a clearly
understood feeling by the research community that this is a disease
g
whose etiology is not at all well understood.
The first part of the paper reviews some basic biological and
epidemiological results. The next section reports on previous
results obtained in this research project. The project has been
centered around factors affecting melanoma death rates for US
whites between 1950 and 1984. County death rates have been
agregated into Standard Metropolitan Areas(1980 definition) and
merged with census data on sociodemographic characteristics of the
1980 population, weather data for each city, and model based
3

-------
4
g
estimates of exposure. This data set has been used to investigate
the response of death rates to potential exposure, the cohort
structure of death rates, and the response of death rates to
individual components of the ultraviolet spectrum. For this paper,
the data set is used to predict cohort levels of risk, which serves
as the basis for the analysis of changes in ecologic risk factors.
The third part of the paper then precedes to examine how
factors such as outdoor recreation, outdoor work, and residence
have varied over the period for which cohort risk of death of
melanoma can be inferred from the data set. First, some measures
of how these factors have changed are developed. These are then
compared to the summary risk measures for each cohort. Out of this
there emerges a fairly clear picture of the kinds of exposure
factors that can be related to the observed change in risk. These
factors can explain the rise and stabilization of the cohort risk
factors. They cannot explain the downturn in risk seen in the
youngest cohorts.
The next section looks at available data on sun screens to see
if they are a potential cause of the downturn. It is shown that
sunscreens can be an explanation of the decline only under the
hypothesis that it is control of intense exposure of skin which has
not developed natural protection which is important if risk is to
be reduced. Usage levels are too low for them to have been a factor
if control of all exposure is necessary to reduce risk. The last
section developes some of the potential benefits of a risk

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5
communication strategy developed along the lines suggested by the
results of the previous sections.
BACKGROUND
This section reviews some basic biology, some of the little
that is known about how the skin develops natural protection, and
some results about how exposure changes as a function of latitude,
time of year, and time of day.
Melanoma arises in the melanocyte, the cell which produces
melanin, the compound responsible for skin color. ^ The precise
process by which the transformation to a tumor takes place is not
known. ^ The tumor is normally highly antigenic--meaning the
immune system will attack it--and one of the clinical markers for
an early lesion is a red iritated area around the lesion. 12 since
UV radiation is known to suppress some aspects of the immune sytem,
immune suppression via this route is thought to play some role in
13
the disease.	However, this role remains to be worked out in
detail. The tumor metastizes readily once it penetrates the
surface of the skin and it is the metastases which are responsible
for the mortality associated with melanoma. ^ On the other hand,
five year survival rates for melanomas removed before the dermis
15
has been invaded are about 95 percent. Thus early diagnosis and
removal are critical to effective treatment of the disease.
Incidence and death rates from melanoma have been growing very
rapidly.16 Figure 1 shows death and incidence rates for whites in
the US. In 1984 total deaths from melanoma in the US were 5377.
of these deaths 5264 were whites and 113 were non whites. Age

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6
adjusted death rates were 3.11 for white males, 1.65 for white
females, .37 for non-white males and .41 for non-white females.
This is a world wide pattern, indicating that melanoma is primarily
a disease of white populations. For non-whites, melanoma almost
always arises in the non-pigmented portion of the body, either
under the nails or on the soles of the feet.^ Thus pigmentation
is protective. This is true even within the white population, with
southern Europeans such as Spanish and Portuguese much less likely
18
to get melanoma than those of northern European origin.
The hypotheses that melanoma might be solar related stems from
the fact that non-melanoma skin cancers seem to be clearly sun
19
related.	Non-melanoma cancers occur most frequently on the
exposed portion of the body, and are much more frequent on those
with lots of outdoor activity--thus they clearly are a function of
2 0
lifetime exposure.	Melanoma, on the other hand does not follow
21
this pattern. Less exposed parts of the body, such as the trunk
in males, and the legs in females, are the predominate place where
melanoma is found. This clearly indicates the need for some
modification of the solar hypothesis. The second problem stems
from the results for Europe, which show that the expected decrease
of melanoma incidence and death rates with latitude does not
22
occur.	Rather rates are lower m southern Europe than m
northern Europe. This may be due to the pigmentation variations
discussed earlier. Later results in the paper on the possible
role of recreation, occupation and residence patterns may also
help explain the anomaly.

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Existing results also point to the role of early exposure as
• , 23,24
being critical.	Again, the results are not unambiguous, and
in some cases depend on quite small samples. Finally, due to the
lack of an animal model, the exact portion of the spectrum
O R
responsible for carcmogenisis is not clear.	The hypothesis is
that the UVB part of the spectrum is responsible, since this is the
part of the spectrum where damage to DNA occurs. Due the lack of
a widely distributed network of instrumentation capable of
individual waveband measurement, there has been no confirmation of
this by epidemiological studies. Thus the potential role of
sunscreens as a protective device has been difficult to determine
since the major chemicals are effective only in the UVB part of the
,	26
spectrum.
Exposure to the sun elicits the production of melanin and the
development of a thicker stratum corneum, the outermost layer of
27
cells on the skin. . Both of these factors reduce penetration of
UV radiation to the growing layer of cells. While it is difficult
to determine the exact extent of the protection induced by these
factors, the tanning process does increase the length of time
necessary to produce erythema(sunburn) by at least a factor of
28
three.	Black skin reduces the level of radiation reaching the
29
melanocyte by about a factor of 10.	Perhaps obviously, the
incident angle of radiation is also very important, since radiation
entering the skin at a sharp angle must travel much further before
reaching the growing layer of cells. Thus, most work activities

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8
expose substantially less of the skin to intense doses than do
activities like sunbathing, where the body is prone.
Ultraviolet radiation present at ground level starts at about
290nm and increases by about 5 orders of magnitude in intensity by
325 rati. From this wavelength to 400 nm, the lower end of visible
spectrum, radiation is rougly constant in intensity and varies in
the same manner as visible light. The large variation in intensity
between 290nm and 325nm is due to absortion by ozone in the
stratosphere. Figure 2 shows variation in DNA weighted radiation
by latitude for a clear day in the peak month of the year and for
total radiation during the year. Note that there is little
variation in peak values between the equator and 30 degrees,
latitude. Figure 3 shows DNA and Erythema weighted radiation
measures during the year for Washington DC. Note that DNA weighted
radiation varies more than does erythema weighted radiation.
Figure 4 shows variation during speak day in July. Note again
that DNA radiation varies more during the day than does erythema.
The relevance of these differences in behavior will become clear
later in the paper.
PREVIOUS RESULTS FROM THIS PROJECT
The work already done on this data set bears on a number of
the open questions discussed above.	First, it shows that
variations in intensity of ultraviolet radiation are associated
with higher death rates.JU A one percent increase in peak(clear
summer day) DNA weighted radiation yields a .85 percent increase
in the death rate for males and a .58 percent increase in the death

-------
9
rate for females. Controls for socioeconomic variables do not
affect the results while including the effect Qf ethnic origin
reduces the responsiveness of death rates by about 20%.
The second area of work with this data set suggests that it is
exposure in the UVB part of the spectrum which is responsible for
• • 31
the carcmogenisis.	The exposure measures used in previous
epidemiology on melanoma have been simple latitude(which is a non-
linear function of exposure as figure 2 illustrates), hours of
sunlight, or an integrating meter(known as the Robertson Berger
meter) which gives a single measure of UV radiation. 32 The
exposure measure used in this study is developed from a model which
incorporates satilite measures of ozone into a radiative transfer
model to predict ground level UV radiation. These predictions can
either be in the form of wavelength weighted measures where the
weights are the inverse of the biological effectiveness of
different wavelengths, or as individual waveband energies. jn this
particular work, individual waveband energies from 295-299 through
330-334 for a clear day in June were used as exposure measures.
Table 1 presents the estimates for different wavebands. Deaths
were modeled as a poisson process and estimation was done using
iteratively reweighted least squares to get maximum liklyhood
estimates. The results show a positive relationship between
radiation below 320, with a negative and significant relationship
above 330 for males. For females that pattern is similar, but the
results are not significant above 330nm.	Because of high
correlations between different wavebands, it is not possible to

-------
10
introduce more than two wavebands simultaneously into the
equations. The second part of Table 1 shows the results using 295-
299 and 300-304 as the short waveband with various wavebands used
as the long waveband. This indicates the upper range for positive
response to radiation lies at about 315 nm or at the upper end of
the range where radiation damages DNA.
These results rely heavily on variations in specific parts of
the spectrum. Since the model has only been tested with aggregate
mesures produced by the Robertson-Berger meter, more work is needed
to baseline the model. However, the overall pattern of variation
is dependent only on variations in measured ozone and very basic
radiative principles. Thus while there may be measurement error,
it is unlikely to be systematic in nature, and thus, in this simple
model, the expected result would be to bias the estimated
coefficients toward zero.
The third set of analyses done with this data look at cohort
33
experiences.	As seen m Figure 5, there is a very systematic
structure to a plot of the log of the national cohort death rates
against age. Cohorts are defined as those who are 0 to 4 years of
age for a five calender year interval. This results in a median
birth year equal to the initial calender year of the period. This
definition was required because death data were only available in
five year age groups in the source data set. The labels on the
plot refer to the median birth year for each cohort. The parallel
slopes of the cohort death rate curves above the age of thirty
suggest that it is early exposure which is critical to the

-------
11
potential risk. Statistical analysis	confirms that the curves
above the age of 30 have equal slope.	For men this slope is 7
percent per year and for women it is	five percent per year. As
Figure 5 shows, there is no slope to	the death rate experience
before age 10. Clinical experience indicates these deaths are due
. 34
to congenital nevi.	Therefore, it seems reasonable to assume
that the rate for 0 to 9 year olds is constant, and all the
variation in cohort risk is due to variation in how the death rate
changes between age 10 and age 30. Table 2 presents estimates for
a model which includes DNA weighted exposure, individual cohort
estimates for 7 < Age < 32, and a common age effect above age 32.
These results suggest that variations in some aspect of exposure
across time for the age group less than 30 are at the root of the
varying coefficients for the cohort specific age variable.
Using a much simpler procedure, estimates at age specific
rates at age 32 can be made for chorts born between 1865 and 1970.
For the 35 years of data available, average ratios for each five
year differential are computed. These averages are used to
extrapolate from the nearest available death rate to the age 32
death rate. Table 3 gives the results of these forecasts for each
birth cohort. White males show marginally greater than a ten to
one variation while white females show about a five to one
variation. Interestingly, there is a predicted downturn in the age
specific rates for cohorts born after 1950. As seen in figures 5
and 6, these reductions are already seen in these cohorts at
35
younger ages.	Next to the differential rates for blacks and

-------
12
whites, this is the largest variation seen in experience with
melanoma. Thus any explanation of melanoma aetiology must deal
with this experience. The next section of the paper looks at some
potential explanations for these large cohort effects.
COHORT VARIATIONS IN DEATH RATES
Given the small number of degrees of freedom across cohorts
and the very limited quantity and quality of data on recreation in
particular, the analysis in this section is more qualitative in
nature that the analysis in the previous sections. The essential
question to be addressed is what changes have occurred in exposure
habits and opportunities between 1880-84, when the oldest cohort
in the study was 15-19 years old and the 1980-84 period, when the
1965 cohort was 15 to 19 years of age. There are a number of
hypothesis which could be suggested for the variation across this
period of time. Here only solar related hypotheses are considered
since there is little indication in the literature of any other
cofactor besides genetic predisposition as a potential cause of
melanoma. (This is not to say one might not exist--but only that a
creditable one has not been found so far) .
The first potential hypothesis is that changes in place of
residence during the critical exposure years might have changed so
that average intensity of exposure is higher. However, as Table
4 shows, DNA relevant radiation weighted by state populations
between 15 and 24 for every five years between 1890 and 1985
increases by only 2.8 percent in intensity(average exposure in 1980
is 3.25) . Since this would amount to only an 2.5 percent change

-------
13
in risk at age 32 for males and a 1.65 percent change in risk at
age 32 for females, this does not explain the very large changes
in lifetime risk seen in Table 4.
Likewise, occupational exposure is not the explanation. The
two major occupation groups with extensive sun exposure are farming
and construction. As Table 5 shows, these have fallen sharply in
relative size, and even in absolute size during the 1880-1985
period. Also occupation is less apt to be a risk factor for those
under the age of 20 since labor force participation rates are
relatively low and have been quite static in the 50 to 60 percent
range for white males between 14 and 19 and between 20 and 30
percent for white females in the same age group.
A third potential hypothesis centers around outdoor
recreational exposure. This can at best be a partial explanation
of the changes in melanoma risk. Around 1900, forty percent of the
population lived on farms and participation in outdoor recreation
was about 4 hours per capita per year(see Table 7), while the
lifetime risk of death from melanoma was only about 1 in 1000 for
both males and females. In 1960, eight percent of the population
lived on farms, per capita participation in outdoor recreation had
risen to almost 120 hours, and the lifetime risk of death from
melanoma had reached 6 per thousand for males and 2.7 per thousand
for females. From 1960 to 1985, farm population fell to about 2.5
percent of total population, per capital outdoor recreation hours
by 2 and one/half fold, but the risk of melanoma has decreased.
While the results between 1900 and 1960 are suggestive of a role

-------
14
for outdoor recreation, the 1960 to 1985 results suggest(as always
with melanoma it seems) that if there is a role for recreational
exposure it is not a simple one.
One can make sense of the role of recreation if what matters
is not the extent of participation, but simply participating at
all. Under this hypothesis one would expect to see a stabilization
in participation rates in sun intensive activities beginning in the
sixties. Unfortunately, data on a comparative basis does not
exist. What can be examined is a number of proxy variables for
participation. One proxy for recreation behavior is the percent
of the labor force not at work due to vacation (see Table 8) . While
comparable data is not available before World War 2, data given in
Clawson and Knetch indicate weeks of vacation per worker rose from
.37 in 1929 to 1.09 in 1959, suggesting percent participation rose
during the 1929-1946 interval also.
A second indicator of percent participation comes from noting
that over ninety percent of outdoor recreation involves automotive
^ • XX
transportation.	Assuming that most recreational activity
involving automotive transportation is family oriented, the
critical variable controlling access to outdoor recreation is
household motor vehicle ownership. Table 9 gives this data for
the post war period. Table 10 extends this back before WW II as
mean vehicles per household. Comparison with Table 9 indicates
that mean vehicles oer household is roughly double the percentage
of households owning at least one car. What is clearly interesting

-------
15
about this variable is the apparent saturation on a per household
basis which occurs in the early 1960's.
These two variables suggest that a case can be made that the
breadth of participation in outdoor activity stablized in the
1960's. Several surveys of participation in outdoor activities
were done between 1962 and 1982-83. While summary results from
these surveys are not in a format that makes comparison across time
possible, the latest survey(1982-83) does indicate that all but 11
percent of the general population participate in some form of
outdoor recreation. For those between 12 and 24, all but 3 percent
of the population participate. The next step in this process is
to get the source level documents and see if a more coherent
picture can be developed.
The other aspect of changes in recreational exposure which is
important to understand is that activities associated with intense
exposure have increased over time.	Swimming, especially
sunbathing, is typically associated with more intense exposure than
hiking or bicycling. Further, in the northern part of the country,
the outdoor swimming season does not begin until the intensity
level is within ten percent of the peak level it will achieve
during the year. One illustration of the increase in intensity is
that the number of muncipal swimming facilities per capita
increased more than seven fold between 1910 and 1965.
The issue of when expsoure begins, alluded to in the previous
paragraph, is also important. There have been very significant
changes in the time at which exosure begins for the critical age

-------
16
groups. In the 1880's, they typical student attended school for
only 80 days a year, and stoped school after the eighth grade.
Today, the typical student attends school twice as long and in
excess of 95 percent of the 5-17 year old population is in school.
Given the shortness of the typical school year before 1900, we can
suppose that the real pattern for farm children, especially those
in the early teens, was to be outside helping with farm work
beginning in the spring and continuing through the fall. This is
not a pattern of limited sun exposure. It is a pattern which leads
to the development of a tan prior to the period of peak intensity.
As Table lb shows, if the participation in farm work begins in
March or April, the exposures levels are much lower than those
found beginning in late May or June, the typical time at which
school closes in the modern era and outdoor recreation starts.
Thus we have a potential hypothesis explaining the increase in
melanoma as a function increase in the effective intensity at the
time when sun exposure begins for the season. Under this
hypothesis, the stabilization of rates occurring in the 1930's to
1950 for females and in the 1950's for males is explained by
stabilization in the percent of the population getting intense
exposure. The large increase in recreation behavior since the
sixties is one of more extensive participation by each individual,
rather than a broader participation. If this is in fact the case,
and more work is needed on this score, then a consistent pattern
can be found which explains the growth of melanoma by an increase
in the effective intensity of radiation brought about by changes

-------
17
in education and work patterns which delay the onset of outdoor
exposure until the period of peak insolation, and the spread of
activities such as swimming, which expose much of the body to
sunlight, especially parts of the body which rarely receive any
prior exposure.
This would explain the markedly lower rates seen for the head
neck and hands for melanoma, since these parts of the body are
exposed year round and thus have always developed some level of
natural protection. It does not however, explain the decrease in
melanoma rates seen in cohorts born since the 1950's. One possible
explanation, consistent with the solar hypothesis, is that sun
screens have played a role. This is discussed in the next section.
SUNSCREENS
Under the intensity hypothesis, to be effective in reducing
risk, sunscreens do not have to be used all the time, but only
during the period of initial exposure. The question is whether the
total use Of Sunscreens, given in Table 12, is sufficiently high
to have possible been effective in reducing risk. To provide
adequate protection at the rated level, about one ounce of product
X X
is required. Typical applications to	the entire body seem to be
at about half this rate. xx This rate	is still enough to produce
a very significant reduction in risk.	Thus the actual number of
applications available is about twice the number of ounces sold.
This yields about three applications	per individual, which is
probably a minimum level of protection	for one day on the beach,
but not enough to get all potentially	exposed individual through

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18
the period of developing a tan without getting an intense dose.
Thus it is unlikely that sun screens are the potential explanation
for the declining risk seen in the younger age cohorts. Only if
all sunscreen use were concentrated in the younger cohorts would
this be possible. In fact, anecdotal evidence suggests it is the
younger cohorts which are least apt to use sunscreens. Thus some
other explanation for the decline must be sought. This does not
mean that a policy of increased use of sun screens would be
ineffective. The potential of such a policy is discussed in the
next section.
FOUNDATION OF A RISK ASSESSMENT POLICY
The intensity hypothesis suggests that a policy is possible
which might be very effective in reducing melanoma. The primary
goal of the policy would be to limit exposure very carefully during
the period before the skin has a chance to develop its natural
defenses of thickenign of the stratum corneum and tanning. Since
these processes both take time, this would imply either the careful
use of sunscreens or a significant limitation on activity during
a vacation taken by somebody who starts exposure when natural
intensity levels are high or travels to a sunny area during the
winter.
How much might such a prevention program be worth. No
strategy could probably return us to the results of the 1900 era.
There is simply too much intense radiation present in modern
recreational activities and use of sun screens is unlikely to be
universal. However, it might be reasonable to reduce risk by 60

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19
percent. The results of a policy with this level of effectiveness
are illustrated in Table 12. Since we have a fairly detailed sense
of the death rate pattern for melanoma, the table looks at years
of life saved rather than reductions in mortality. The figures are
for a cohort group of 100,000. The total reduction in melanoma
mortality, in a given year, under steady state cohort behavior,
would be 368 lives per 100, 000 males, and 162 lives per hundred
thousand females. At currently typical white birth cohort sizes
of about 1.75 million each for males and females, this yields a
total reduction of better than 9000 melanoma related deaths. Total
associated incidence would be about four times these levels, giving
reduced incidence of about 36,000 cases. it should be emphasized
that these are long run numbers and do not take account of whatever
is currently acting to reduce death rates. They do suggest that
a policy to moderate sun exposure habits has a very high potential
public health payoff.

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Skin Melanoma Trends Among Whites in the United States
20-1
CL
O
CL
o 10
O
o
*
o
o
<
ai
'S
on
<
Q
z
<
(/)
(/)
ZD
o
CD
V)
ZD
—>
Q
<
I
LJ
O
<
1-
tncldence
Mortality
Legend
MALES
FEMALES
0.H i—"—f
1950
-i—|—«—>"
1955
-i	1	1	1	r-
1960
-I	1	1	1	I	r
1965
YEAR
—i—i—i—i—i—|—i—i—i—i—i—i—i—i—" i
1970	1975	1980	1985

-------
Skin Melanoma Mortality by Birth Cohort
Among WHITE MALES
100
10:
Q.
O
Q.
O
O
O
m
O
0
1
tKL
1:
0.1:
0.01:
1895—99
1925-29
1945-49
° 00'' £	&*'
n -\K <\°> rr
AGE GROUP

-------
Skin Melanoma Mortality by Birth Cohort
Among WHITE FEMALES
lOOq
10:
a.
o
a.
o
o
o
*
o
o
f
OH
h
0.1
0.01:
\ /
1925-29
1895-89
0 001 /<> Jb1 \K' \9' oN1 o?' ^	*'
AGE GROUP

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20
Table la
Ultraviolet Radiation Variation by Latitude
Latitude Clear Day	Annual
DNA Weighted	DNA Weighted
0 5.45	1162.5
10 5.39	1181.6
20 4.59	989.1
30 4.14	658.0
40 3.31	370.7
50 2.33	204.0
60 1.67	124.3
Table lb
Clear Day UV Radiation by Month
Month	DNA Weighted	Erythema Weighted
Jan 15
.25
31. 0
Feb 15
. 50
57 . 9
Mar 15
1.01
108 . 7
Apr 15
1. 85
186.8
May 15
2 .51
246.5
Jun 15
3 . 14
299. 6
Jul 15
3 .40
318 . 3
Aug 15
2 . 91
274 . 6
Sep 15
2 . 03
196.2
Oct 15
1.09
110 . 9
Nov 15
.46
51. 2
Dec 15
.24
28 . 9
Source: Model based estimates using satelite data on ozone.
Units are not comparable.

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21
Table lc
UV Radiation on July 15 (Clear Day)
Time of Day	DNA Weighted	Erythema Weighted
6-6:30 am
. 0055
.78
6:30-7 am
. 0129
1. 66
7-7:30 am
. 0259
3 .06
7:30-8 am
. 0456
5.03
8-8:30 am
. 0723
7 . 55
8:30-9 am
. 1050
10 . 53
9-9:30 am
. 1419
13 .77
9:30-10 am
. 1800
17 . 05
10-10:30 am
.2162
20 . 10
10:30-11 am
.2469
22 . 66
11-11:30 am
.2693
24.51
11:30-12 am
.2811
25.48
12-12:30 pm
.2811
25.48
12:30-1 pm
.2693
24.51
1-1:30 pm
.2469
22 . 66
1:30-2 pm
.2162
20 . 10
2-2:30 pm
. 1800
17 . 05
2:30-3 pm
. 1419
13 .77
3-3:30 pm
. 1050
10 . 53
3:30-4 pm
. 0723
7 . 55
4-4:30 pm
. 0456
5 . 03
4:30-5 pm
. 0259
3 .06
5-5:30 pm
. 0129
1. 66
5:30-6 pm
. 0055
.78
6-6:30 pm
. 0020
.30
6:30-7 pm
. 0006
.09
All radiation values from radiative transfer model
incorporating satelite measurements of ozone.

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22
Table 2a
Wavelength Specific Estimates
of Exposure Effects*
Mai e s
Wavelength
Coefficient
Standi
2 95-2 9 9nm
.142

. 0104
3 0 0-304 rati
.148

. 0108
3 0 5-309nm
.153

. 0115
310-314 rati
. 145

. 0125
315-319nm
.112

. 0132
32 0-324 ran
. 055

. 0139
32 5-32 9nm
. 0014

. 0143
3 3 0-334 nm
- . 028

. 0143
3 3 5-339nm
- . 044

. 0136
3 5 5-359nm
- .064

. 0138


Females

2 95-2 9 9nm
. 0817

. 0123
3 0 0-304 nm
. 0871

. 0128
3 0 5-309nm
.0923

. 0135
310-314 nm
.0912

. 0144
315-319nm
. 0765

. 0152
32 0-324 nm
. 0458

. 0157
32 5-32 9nm
. 0159

. 0158
3 3 0-334 nm
- . 00090

. 0158
3 3 5-33 9nm
- .0106

. 0149
3 5 5-359nm
- . 0204

. 0152

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23
2 95-2 9 9nm
315-319nm
2	95-2 9 9nm
32 0-324 rati
3	0 0-304 rati
32 0-324 ran
Table 2b
Multiple
Mai e
. 151
( .0182)
-. 0255
( .0197)
. 150
( .0114)
- .0298
( .0152)
.166
( .0124)
-.0472
( .0158)
Waveband
Female
. 0709
( .0219)
. 0197
( .0225)
. 0804
( .0136)
. 0012
( .0176)
.0908
( .0147)
- . 0091
( .0182)
* All units have been converted to standard deviation form so that
coefficients can be directly compared.

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24
Table 3

Age and Exposure Model
Coefficients
Vari able
Mai e

Female

Coef St.Dev.
Coef.
St. Dev.
Constant
-3.99 .118
-3 . 90
.117
DNA expos.
.263 .0125
. 188
. 0137
Age 65
.0730 .0430
.074
. 0405
Age 6 0
.146 .0153
. 126
. 0162
Age 5 5
.154 .00859
.143
.00874
Age50
.155 .00583
.142
.00597
Age4 5
.150 .00523
. 140
.00528
Age4 0
.149 .00493
. 138
.00496
Age35
.143 .00480
. 139
. 00476
Age30
.143 .00469
. 139
.00465
Age2 5
.139 .00463
.132
.00460
Age2 0
.131 .00462
. 126
.00458
Age 15
.125 .00463
. 120
.00460
Age 10
.117 .00467
. 117
. 00463
Age 0 5
.110 .00469
. Ill
.00466
AgeOO
.102 .00473
. 107
.00471
Age95
.0962 .00478
. 105
. 00475
Age 9 0
.0921 .00480
. 100
.00478
Age8 5
.0837 .00483
.092
8 .00482
Age 8 0
.0806 .00487
.0920 .00486
Age>32
.0653 .000817
.0538 .000882
Sum of Squares



Regression
4273 . 7

2655.3
Error
200 . 7

153 . 0
Total
4474 . 4

2808 . 4
About Mean
4199.7

2577 . 1
The agexx variables denote a variable
which for cohort xx
0	if Age < 7
age - 7 if 7 < Age < 32
25	if Age > 32
and 0 for all other cohorts. Cohorts are denoted by the last two
years of their median birth date and run from 1965 back to 1880.
The Age>32 variable is 0 if Age < 32 and Age - 32 otherwise.

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25
Table 4
Predicted Rates at Age 32
Median Birth Year White Males	White Females
1865	.146 .238
1870	.194 .234
1875	.222 .311
1880	.257 .330
1885	.309 .313
1890	.398 .424
1895	.419 .441
1900	.438 .460
1905	.553 .494
1910	.643 .593
1915	.907 .693
1920*	.986 .857
1925*	1.224 .969
1930*	1.555 1.109
1935*	1.482 1.116
1940*	1.509 .998
1945*	1.690 1.051
1950*	1.866 1.155
1955	1.690 .998
I960	1.330 .954
1965	.800 .807
1970	.795 .395
* denotes observed value for that cohort. Other values are
predicted from the nearest observed value and the average ratio
between age 32 and the observed value at that age.

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26
Table 5
Population(Age	15-24) Weighted Measures of Exposure
Year	DNA Exposure
1890	3.185
1900	3.201
1910	3.194
1920	3.205
1930	3.212
1940	3.212
1950	3.225
1960	3.239
1970	3.238
1980	3.263
1985	3.276
* Data on population from US Historical Statistics and various
issues of US Statistical Abstract. UV measures are mean of SMSA
spectific measures within each state.

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27
Table 6
Farming and Construction Employment
Year
Total
Farming
Construction
Perc
1880
17390
8920
900
56.5
1890
23320
9690
1510
48 . 0
1900
29070
11680
1665
45 . 9
1910
37480
11770
1949
36.6
1920
41610
10790
1233
28 . 9
1930
48830
10560
1988
25 . 7
1940
56290
9575
1876
20 . 3
1950
63377
9926
2364
19.4
1960
71489
7057
2926
14 . 0
1970
84889
4596
3588
9.6
1980
108544
3705
4346
7 . 4
1985
117167
2941
4673
6.5
* Data from 1950 are not strictly comparable to earlier data.
Data from 1880 to 1940 are from US Historical Statistics, US
Dept of Commerce, Washington DC 1975 (Series D167, D170 and
D17 3) . Data from 1950 to 1985 are from Economic Report of the
President, Council of Economic Advisors, Washington, DC,
1989(Tables B32, B43, and B98) .

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28
Table 7
Per Capita Hours of Recreational Activity
Year
Hours
1900
1910
1920
1930
1940
1950
1960
1970
4
7
20
43
59
80
1985
1980
116
211
272
304
*Data through 1960 are adapted from Clawson and Knetch, The
Economics of Outdoor Recreation. From 1970 to 1985, they are
extended by computing an index based on visits to National
Parks, National Forests, State Parks, Personal Consumption
Expenditures for Gardening, and Travel to the Carribean and
South America.

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29
Table 8
Percent Participating in Vacation
Not at Work by Reason of Vacation
(annual average, 1000's)
Year
On Vacation
Percent
1985
3338
34 . 2
1980
3320
36.7
1975
2815
35.4
1970
2341
33 . 1
1965


1960
1576
26.5
1955
1268
22 . 7
1950
1137
21. 5
1946
662
13.8
* Percent assumes everybody counted during the year as being not
at work due to vacation is distinct and multiplys not at work by
12 to get an estimate of total fraction of the work force which
takes a vacation.

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30
Table 9
Household Ownership of Motor Vehicles
Year Total Percent	Percent
One Car	Two or More
1948	54
1950 59 52	7
1955 70 60	10
1960 77 62	15
1965 79 55	24
1970 82 54	28
1977 84 47.5	36.5
Source: US Historical Statistics 1948-1970, Motor Vehicle
Facts and Figures, 1978.

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31
Table 10
Access to Motor Vehicles
Year
1890
1895
1900
1905
1910
1915
1920
1925
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
Cars
(1,000's!
0
0
8
77
458
2332
8132
17440
22973
22495
27372
25695
40191
51961
61420
74909
88775
106077
120866
129329
Total
(1,000's!
0
0
8
79
469
2491
9239
19941
26532
26230
32035
30638
48567
61949
72887
89090
106808
130919
153358
167342
Per
Capita
0
0
0.00011
0 . 00094
0.0051
0 . 025
0 . 087
0 . 17
0.22
0.21
0.24
0.22
0 . 32
0 . 37
0040
0.46
0.52
0 . 61
0 . 67
0 .70
House-
holds
(1,000's!
12690
14341
15992
17939
20183
22501
24467
27540
29997
31892
35153
37503
43554
47874
52799
57251
63401
71120
80776
86789
Per
HH
0.0
0.0
0.0005
0.0044
0 . 023
0 . 11
0 .38
0.72
0 .88
0.82
0 . 91
0.82
1.12
1
1.
1,
1.
1.
1
1.
29
38
56
68
84
90
93

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32
Table 11
Sales of Sun Protection Products
(Real 1988 $, 1,000,000's)
Year	Total	SPF > 8
Sales	Ounces	Sales Ounces
1960	85.6	57.1
1965	115.8	77.2
1970	155.3	103.6
1975	193.9	129.3
1980	238.9	159.3	80.0	53.3
1984	249.0	189.5	103.3	68.9
Source: I am indebted to Jim Murdoch and Mark Thayer for
providing the original data.

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33
Table 12
Potential Mortality Impacts
of Reducing Acute Exposure
Males-1940 Birth Cohort
Age	Baseline Reduced Difference
Mortality Mortality
0-4
.28
.07
.21
5-9
.26
.07
.19
10-14
.51
.20
.31
15-19
1.04
.42
.62
20-24
2 . 05
.82
1.23
25-29
4 .06
1. 63
2 .44
30-34
8 . 00
3.20
4 .80
35-39
11.27
4 .51
6.76
40-44
15 .77
6.31
9.46
45-49
22.39
8 . 96
13 . 43
50-54
30 . 93
12 . 37
18 .56
55-59
42 . 02
16.81
25.21
60-64
55 . 68
22 .27
33.41
65-69
71.09
28 .44
42 . 65
70-74
85 . 72
34 .29
51043
75-79
95 . 00
38 . 00
57 . 00
80-84
93 . 35
37 . 34
56.01
85 +
75 . 98
30 .39
45.59
Expected Total
Li fetime
Add.

Yrs .
70 . 7
14 .85
65 . 8
12 . 50
60 . 9
18 .88
56.1
35 .01
51. 4
63 .22
46.8
114.00
42 . 2
202.56
37 . 5
253.58
32 . 9
311.30
28 . 4
381.53
24 . 2
449.10
20 . 2
509.28
16. 6
554.57
13.3
567.30
10 . 5
540.04
8 . 0
456.00
6.0
336.06
4 . 5
205 . 15
Total
615
247
5025

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34
Table 12 Continued
Females-1940 Birth Cohort
Age
Baseline
Reduced
Di f ference
Expected
Tota^

Mortality
Mortality

Li fetime
Add.





Yrs .
0-4
.26
.10
.16
77 . 4
12 . 07
5-9
.24
.10
.14
72 . 5
10 .44
10-14
.45
.18
.27
67 . 6
18 .25
15-19
.85
.34
.51
62 . 7
31 . 98
20-24
1.57
.63
.94
57 . 8
54 .44
25-29
2 . 92
1. 17
1.75
53 . 0
92 . 86
30-34
5 .40
2 .16
3 .24
48 . 1
155 .84
35-39
6. 95
2 .78
4 . 17
43 . 3
180.56
40-44
8 .89
3 .56
5 . 33
38 . 5
205.36
45-49
11.51
4 . 60
6. 91
33 . 9
234.11
50-54
14 . 63
5 . 85
8 .78
29.4
258.07
55-59
18 . 43
7 . 37
11.06
25 . 0
276.45
60-64
22 . 95
9. 18
13 .77
21. 0
289.17
65-69
28 . 04
11.22
15 . 12
17 . 2
289.37
-J
0
1
-J
33 . 30
13 . 32
19. 98
13 . 6
271.73
75-79
37 .81
15 . 12
22 . 69
10 . 5
238 .20
80-84
39.81
15 . 92
23.89
7 . 7
183.92
85 +
36.05
14 . 42
21.63
5 . 6
121.13
Total
270
108

2924

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35
FOOTNOTES
Forthcoming at the Conference

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36
BIBLIOGRAPHY
Two basic citations--detailed bibliography available	at the conference.
1.	Longstreth, JD ed., Ultraviolet Radiation	and Melanoma, US
Environmental Protection Agency, EPA 400/1-87/001D,	December, 1987.
2.	Gallagher, RP ed., Epidemiology of Malignant	Melanoma, Springer
Verlag, New York, 1986.

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Acute Health and Variable Air Pollutants
By
James C. Murdoch
Auburn University at Montgomery
Mark A. Thayer
San Diego State University
William N. Weirick
Northeast Louisiana University

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2
I . Introduction
Previous epidemiological studies [4,5,6,8] have established
an empirical relationship between measures of urban air pollution
(the dose) and human illness (the response) . The results from
these studies are interesting to policy analysts because they
can, in principle, be used to predict the impacts of proposed air
pollution control policies on urban populations. These aggregate
dose-response predictions are credible to the extent that they
seem to confirm the association between air pollutants and
illness that has been found in clinical studies [2,7].
Nevertheless, the sensitivity or robustness of the predictions
from the estimated dose-response functions to alternative
specifications, datasets, and estimation strategies remains an
important issue [2] .
This paper addresses two methodological issues in estimating
air pollution dose-response functions. Both concern accuracy in
measuring the air pollution dose.
The first involves the intracity variation in the pollution
data and the location of respondents. Previous studies have not
assigned respondents different location codes over the day. Yet
many people, especially those working, get a different dose
during the day, when compared to the evening when they are at
home. The dataset analyzed here facilitates a work and home
assignment of air pollution to individuals within a city. This
allows us to compare the responses of individuals to air
pollution at their workplace with their responses to air

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3
pollution at home. By modeling more of the variation in the
pollution data, we measure the "real-world" dose; hopefully,
improving the accuracy of the estimates of the influence of air
pollution on human health.
The second issue concerns the intralocation variation in air
pollution. Since air pollution in an urban area can vary from
hour to hour, we hypothesize that the dose is more appropriately
modeled as variable over a day. Even when an individual does not
change locations, he or she will experience different doses as
the air pollution varies from hour to hour. Therefore, the air
pollution dose depends on where and when a person is exposed.
The air pollution doses used in previous studies have been based
on a periodic (either one year or two weeks) average. By
averaging the pollution data, the intraday variation in the data,
which may influence human health, has been ignored. This can
cause specification error bias, owing to left out and incorrectly
measured variables in the dose-response function.
The remainder of this paper is organized into four sections.
In Section II, we present a brief review of the relevant
literature on estimating the relationship between air pollution
and human morbidity. The empirical models, data, and basic
estimation methods are described in Section III. The results are
presented in Section IV, while the last section contains
concluding remarks.
II. Air Pollution and Morbidity: Previous Studies
The design of this paper is most closely related to the

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4
studies by Ostro [4,5], Hausman et al. [3], and Portney and
Mullahy [6] . These authors use the Health Interview Survey
(HIS), an annual health survey of people in various locations
throughout the U.S., to study the empirical relationship between
air pollution and human morbidity. Morbidity is measured by a
variable that reflects the changes in the normal activities,
owing to health impairments, of the survey respondents during the
2-week recall period of the HIS. Several pollutants are
analyzed, including measures of the atmospheric concentrations of
total suspended particulate (TSP), ozone, fine particulate, and
sulfates. In addition to including several socio-economic and
weather measures in their models; these authors examine numerous
subsamples based on sex, working status, and smoking status,
attempting to hold constant as many confounding influences as
possible.
In Ostro [4], the variation in the air pollution data comes
from the pooling of respondents from different cities. Doses
were measured by the annual average of total suspended
particulate (TSP) and sulfates (S04) and ignore the intrayear
and intraday variation in the pollution data. The morbidity
measures reflect the number of "work loss days" (WLD) and the
number of "restricted activity days" (RAD) that survey
respondents reported during the two-week recall period. The TSP
term is significant and has the expected relationship to RAD and
WLD. The S04 term is not significant, which may not be surprising
since S04 is more localized than TSP.

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5
In his follow-up piece, Ostro [5] uses a Poisson distribution
to model the relationship between the number of RADs and the
contemporaneous (with the survey) two-week average of fine
particulate. Fine particulate are estimated from airport
visibility and TSP data. The two-week average of fine
particulate is significant over several different samples and
years.
Hausman et al [3] concentrate on WLD and specifically
control for intrayear variation in pollution. Additionally, they
estimate models with alternative lags of the two-week (in
contrast to the annual) average of TSP, although no formal tests
to choose among the specifications are presented. Like the Ostro
studies, intracity variation in the pollution exposure (within a
period) is ignored and the S04 measure is not significant.
Hausman et al provide some empirical support for the Poisson
specification; i.e., the pollution coefficients were robust when
the Poisson assumption that the variance equal the mean was
relaxed and when a fixed effects model was estimated.
Portney and Mullahy [6] estimate a Poisson model with the
number of respiratory related RAD as the dependent variable and
various measures of ozone and sulfates for the exposure
variables. Portney and Mullahy's ozone exposure measures are
probably better suited to test acute health effects because they
average over the daily maximum of ozone during the two-week
recall period. Moreover, by matching respondents to the
pollution monitoring stations closest to their census tract (and

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6
within a 10 and a 20 mile radius of their census tract) , Portney
and Mullahy analyze some of the within city variation in the
pollution data. They find that the estimates for the ozone
coefficients do not vary greatly among these different assignment
strategies, meaning that the intracity variation is not
empirically important in their data. As in the aforementioned
studies, sulfates do not perform in an _a priori expected manner.1
III. Methodology and Data
The methodology and data used in this study were constructed
in order to examine the robustness of acute health predictions.
In particular, we propose to compare the predicted health
responses from a "traditional" specification to specifications
where the pollution measures and assignments more accurately
reflect real world exposures. This comparison exercise will
provide information for policy makers as well as future research
efforts.
Define the following notation:
H. = the health response of individual i in time period t.
X. = a vector of individual specific covariates.
W = the weather in time t.
POL.^(L) = the pollution exposure experienced by i in time
period t. The exposure is a function of i s location (L)
over the time period.
Then,
H = f (X. , W , POL . (L) )	(1)
it	i t	it

-------
7
is a hypothesized dose-response function.
To estimate a model like (1) , requires data on H^_ , X. , W^_ ,
and POL. (L) and a functional form for the model. The necessary
it
data were obtained from a health survey, the Weekly Weather and
Crop Bulletin, and the SAROAD system data tapes. The functional
form for the model was specified to be consistent with previous
studies.
The health survey data
During 1978-1980, Geomet Technologies, Inc. administered a
health survey to the members of 2,594 households in the greater
St. Louis area. Households were enrolled in the survey in groups
of about eighty per week beginning June 4, 1978 and ending May
27, 1979. The respondents maintained daily logs of their
activities, locations, restrictions in activities, and the
reasons for any restrictions in activities. The logs were kept
over four two-week periods; thus, the dataset includes the
restrictions on activities and the locations for each respondent
for 5 6 days.
The structure of the survey also facilitated the collection
of extensive data on socioeconomic conditions, lifestyle choices,
work environment, medical care, and health.2 A complete
description of the data and the datafiles are available from the
authors upon request.
The appropriate measure of the health response depends on
the focus of the study. Here, we are particularly interested in
acute respiratory health responses. As an empirical measure of

-------
8
H , we used the number of RADs reported by the respondent in the
it
time period, owing to a respiratory disorder or symptom (NRRAD^_ ) .
Given this type of limited dependent variable, a
reparameterization of the Poisson distribution is a particularly
attractive statistical model for equation (1) .
As shown elsewhere [6], the expected value of NRRAD^_ under
the Poisson model is given by
E (NRRAE^. ) = exp(X^fl + W V + P0Lit(L)5)	(2)
where the fl,	and 6 represent parameter vectors that are
estimated via maximum likelihood methods. Using equation (2), a
prediction for a small change in a POL (L) variable (or any
it
other) is a straightforward computation.
The variables in X. should include measures on i's age,
income, living arrangements, working conditions, personal health
habits, and personal health status. Since an incorrect
specification of the X could bias the estimates of the
i
relationship between H and POL (L) , we included several
it	it
covariates. Moreover, the data were limited to people between
the ages of 16 and 65 who are non-smokers and working outside of
the homes
A brief description and summary statistics of the X
i
covariates, the weather covariates, and NRRAD are presented in
Table 1.
Pollution Data
The pollution data were obtained from the U.S. Environmental
Protection Agency's SAROAD system. The data tapes contain hourly

-------
9
observations, collected at 14 monitoring sites, on numerous
pollutants in the St. Louis Air Quality Control Region.4 The
pollution data were matched to the survey respondents by time, as
described below, and location vis-a-vis the monitoring stations.
The respondents averaged about three miles from a monitoring
site.	The pollutants analyzed here, ozone and sulfur dioxide
(S02), were chosen for two reasons. First, the data for these
two pollutants were collected at all of the monitoring stations
over the time period of the health survey. For the other air
pollution measures, for example, total suspended particulate and
N02, the data are not available for several weeks during the
survey period or they were not collected at each site. Second,
S02 tends to be more localized than ozone. This contrasting
nature of the two pollutants provides a natural "laboratory" for
measuring the appropriateness of our measures and assignments of
pollution.
The pollution measures differ from the X. and the W because
an individual's exposure to pollution is not constant over t.
Pollution exposure can varyas individuals change locations over
the day. Even when an individual is stationary, their exposure
changes as the pollution varies over the course of the day.5
In defining the measures of air pollution dose, our
objective was to preserve as much variation in the pollution data
as possible. The format of the health survey means that, for
each enrollment week, there are four associated two-week periods.
Since we used the survey data from weeks 1 through 41, there are

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10
164 two-week periods. However, within each two-week period, we
grouped the data into "day-time" observations (the hours 11:00 am
through 5:00 pm) and "night-time" observations (the hours 5:00 am
through 10:00 am and 6:00 pm through 12:00 pm).* The pollution
data were, therefore, initially grouped into 328 subperiods.
Each day-time subperiod contains 98 observations, while the
night-time subperiods consist of 182 observations.
For each subperiod, we computed the following sets of
parameters:
(i)	The mean and standard deviation. if the data are normally
distributed, then these parameters fully describe the
distribution of the pollution.
(ii)	The mean and standard deviation of the natural logarithm of
the data. If the data are lognormally distributed, which may be
more plausible than normality, then these parameters characterize
the distribution of the dose.
Also, to facilitate a comparison with previous models, the two-
week mean and the average over the daily maximums were computed.
Two methods were developed for investigating the sensitivity
of the dose-response function to the individual's pollution
exposure. Both address the variability in air pollution doses.
The impact of locations changes on pollution measures
For an individual who lives in one location and works in
another, we are uncertain about the correct assignment of the
pollution dose. With the data analyzed here, each respondent has
two location codes; a home code and work code. The home location

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11
pollution, the work location pollution, or some combination of
the two could seemingly be used to assign pollution exposures to
the individuals. Moreover, the pollution data reflect different
times of the day; thus, the home code may be more appropriate for
night-time exposures and the work code more appropriate for day-
time exposures. Since we are uncertain about the correct
assignment, one possibility is to let the data determine it.
Let 9^ be the fraction of the total exposure time to air
pollution experienced during the day at work. Similarly, let 0^
be the fraction experienced at home during, our definition of,
the night-time. Finally, let 0^ be the fraction of exposure time
experienced at home during the day. We assume that 0^ + ^2 + ^3
= 1, implying that all of the exposure is experienced in the
manner hypothesized.
The 0's, if assumed to be unknown, can be estimated given
some criterion. the correct mean exposure experience by a
respondent is a weighted average of the means at each location
for each time period, where the weights are the 0's. Let
WDPOLMU = the mean of pollution calculated from the day-time
data at the work location code,
DPOLMU = the mean pollution calculated from the day-time
data at the home location code, and
NPOLMU = the mean pollution calculated from the night-time
data at the home location code.
Then,
POLAVE = 8 WDPOLMU + 8 DPOLMU + 0 NPOLMU	(2)
X	z	o

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12
is the weighted average pollution experienced by the respondent.
We use a grid search over the 0's to find the set that maximizes
the likelihood function.
As reference points, we alternatingly let each of the 8*s
have a value of 1. Additionally, we assumed 112 hours of
exposure per week; 40 at work, 56 at home during the night-time
hours, and 16 at home during the day-time hours. These
assumptions give 0^ = 40/112, 0^ = 56/112, and 0^ = 16/112.
The impact of intradav variation on pollution measures
Some intraday variation in the pollution data is captured by
using the day-time and night-time means. However, there does not
seem to be any theoretical reason for using the mean of the
pollution distribution to measure the dose. In fact, a simple
example illustrates that using the mean imposes a linear
restriction on the dose-response function. Assume that the
pollution exposure for some individual is variously POL1, POL2,
and POL3 over the time period. Let the probability of each level
occurring be fl, f2, and f3, respectively. Then, the mean equals
fl*POLl + f2*POL2 + f3*POL3. Next, let the dose -response
function be linear in parameter space. Write it as
H = 6q + 6 (fl*POLl) + 52(f2*POL2) + 63(f3*POL3)
for some individual in some time period. If 6. = 5,. = 6 , then
«L	M	W
using the mean is equivalent to entering the probability
distribution. On the other hand, different 5's would indicate
that a mean model incorrectly restricts the health response to
changes in average pollution; i.e., the response depends on how

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13
the mean changed. The problem with this method is that we have
no guidance on the number of 6's to specify. Still, this type of
analysis may provide insights into the health response of
distributions of air pollution.
IV. Empirical Results
The impacts intradav variability in Pollution exposures
In Table 2 we display the parameter estimates from several
models. Only data from the first follow-up period was used to
estimate the parameters. While the qualitative conclusions are
similar for the second follow-up period, we could not
statistically pool the data from the first two periods. The
estimates based on the third and fourth period observations were
quite different than those obtained from the first two. In
particular, most of the parameter estimates were sensitive to the
alternative specifications. This problem is apparently
symptomatic of some type of survey bias, perhaps because
respondents lost interest after the first two periods.
The specifications presented in Table 2 differ in the type
of pollution measures entered. Several other independent
variables could be selectively entered into the specifications.
Those presented here are representative of the literature. The
pollution coefficients are not particularly sensitive to any of
the measures, except the seasonal dummies and, the weather
variables. Selectively dropping these variables can change the
sign of the pollution measures in some of the specifications.
The weather variables and the seasonal dummies are statistically

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14
significant in each specification, however.
The first specification represents a "traditional" air
pollution dose-response function. The air pollution is assigned
to the respondents home location code. The variable labels
represent average ozone (OZMU) and average S02 (SOMU), where the
average is computed using data from the entire day. Fourteen of
the eighteen coefficient estimates exhibit p-values of less than
.05. As in other studies using a sulfur-oxide term, SOMU has a
negative sign but is insignificant.
The remaining coefficient estimates are remarkably stable
across different specifications. They show, all else equal,
that:
older respondents have fewer expected restricted activity
days due to respiratory symptoms and disorders [E(NRRAD)],
•	years of education do not affect E(NRRAD),
•	the E (NRRAD) is lower for males,
respondents in higher income classes have a lower E(NRRAD),
respondents with good perceived health have a lower
E(NRRAD),
previous smokers have a greater (or insignificant) E(NRRAD),
cooler temperatures and more rain increase E(NRRAD),
when respondents are exposed to irritants at work, E(NRRAD)
diminishes,
respondents who exercise regularly, reduce E(NRRAD), and
the greatest E(NRRAD) occurs during weeks 17-24, which is
from the end of September to the middle of November.

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15
One of the most interesting estimates is the coefficient on EXER.
If individuals can reduce their expected number of respiratory
related activity days by "expenditures" on regular exercise, this
may give analysts an avenue for assessing the benefits of a
cleaner environment.
Specifications (2), (3), (4), (5), and (6) illustrate the
impacts of using different assignment methodologies (or weights)
for the pollution terms. As indicated above, the actual dose is
hypothesized to be some combination of the air pollution at home
during the day (DOZLMU and DSOLMU) , the air pollution at home
during the night (NOZLMU and NSOLMU) , and the air pollution at
work during the day (WDOZLMU and WDSOLMU).
We used the mean of the natural logarithm of ozone and S02
(all variable end with "LMU") because the log of the data
appeared to be more normally distributed than the levels; thus,
using the mean of the logs is a better measure of "the central
tendency in the data.*
The impacts of changing the 0's are dramatic on the
estimated coefficients for ozone and S02. In specification (2),
0 =0=0 and 0 =1. The respondents are assigned the mean
JL	O	«
pollution at their homes computed over the day-time hours (11:00
am - 5:00 pm). The coefficient on DSOLMU remains insignificant,
but becomes positive, and the likelihood function rises (the
negative falls) slightly. Since the maximum reading usually
occurred during this time interval, this specification is similar
to [6], who used the average of daily maximums.

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16
The third specification shows that, when the respondents are
assigned a dose based on their home location pollution average
over the night-time hours (5:00 am - 10:00 am and 6:00 pm - 12:00
pm), the ozone influence remains stable and the S02 coefficient
remains insignificant. The S02 coefficient estimate jumps
noticeably in magnitude, however, and the likelihood function
continues to rise.
e
1 = 1 and ®2 = = ® ~"~n specification (4) . The S02 term
is significant and of similar size to the one exhibited in (3) .
The coefficient estimate on the ozone term is also significant
and about the same size as the estimate in (2) and (3) .
Specifications (5) and (6) show the impact of non-zero 8's.
The 0'S are constructed a priori in specification (5), while in
six they are estimated using a grid search. The log of the
likelihood functions are the same up to the second decimal point.
When comparing the coefficient estimates in (5) and (6) to the
estimates obtained with the other models, we see that the impact
of the pollution terms increases as the measures approach "real
world" exposures.
The empirical significance of the alternative models is
displayed in Table 3. Predictions of the expected value of NRRAD
from each specification for one thousand identical individuals
are shown. The predictions differ by the, type of change in ozone
and S02.

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17
A change in just ozone (Predict2) can change the prediction
on E(NRRAD) by from 1.928 per thousand to 10.671 per thousand; a
difference of over 400%. Similarly, a change in just S02
(Predict3) can change the E(NRRAD) per thousand from .356
(or -2.393, using specification 1) to 9.246; over 2000%.
Clearly, the choice of the pollution measure can have a dramatic
impact for policy analysts.
An analysis of non-mean models
As noted above, it is possible to test the mean
specification. Based on the mean and standard deviation
estimates of the logged data and assuming both pollutants were
lognormally distributed, we computed the probability that the
pollutants would fall into various categories. For ozone, we
chose four categories; 0-5, 5.01-20, 20.01-60, and greater than
60. For S02, we used 0-5, 5.01-10, 10.01-25, and greater than
25. The probabilities were computed for each of the
distributions used above (i.e., day-time work, day-time home, and
night-time home) and then averaged using the maximum likelihood
estimates for the 0's. The specifications with the probabilities
entered as dependent variables did not significantly improve the
model. * This was true for both ozone and S02, indicating that
the exposure time weighted mean model can not be rejected.
Evidently, the distributional aspects of the air pollutants are
adequately captured by specification (6) for the data analyzed
here.

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18
V. Conclusions
The primary conclusion of this paper is that predictions
from alternative estimated dose-response functions differ
substantially, depending on how pollution exposures are measured
and assigned to individuals. The exposure varies because
individuals" locations and air pollutants are not constant
throughout a day. Dose-response specifications that use a
weighted average of pollution experienced during the day at home,
during the day at work, and during the night at home
statistically outperform more traditional models. Moreover, the
weighted average models indicate that the pollutants adversely
affect human morbidity more than traditional models.
Our results indicate that sulfur-dioxide adversely affects
human health. This finding is different from previous studies.
The apparent reason for the difference is our treatment of the
variable nature of the pollution. This particularly appealing,
in the case of S02, because S02 is more localized than ozone.
Hence, too much aggregation in the pollution data would mask the
strength of the influence. By disaggregating the data, we have,
hopefully, uncovered the true relationship.

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References
1.	S. Gerking and L. Stanley, An economic analysis of air
pollution and health: the case of st. louis. Rev. Econ Statist.
68, 115-121, (1986).
2.	D. Hammer, et al, Los angeles student nurses study: daily
symptom reporting and photochemical oxidants, Arch. Environ.
Health. 28, 255-260 (1974).
3.	J. Hausman, B. Ostro, and D. Wise, Air pollution and work
loss, NBER Working Paper No. 1263 (1984).
4.	B. Ostro, The effects of air pollution on work loss and
morbidity, J. Environ. Econ. Management, 10, 371-382 (1983).
5.	B. Ostro, Air pollution and morbidity revisited: a
specification test, J. Environ. Econ. Management. 14, 87-98
( 1987) .
6.	P. Portney and J. Mullahy, Urban air quality and acute
respiratory illness, J. Urban Econ.. 20, 21-38 (1986).
7.	S. Vedal, et al, Daily air pollution effect's on children's
respiratory symptoms and peak expiatory flow, Amer. J. Public
Health. 77, 694-698 (1987).
8. A. Whittemore and E. Korn, "Asthma and air pollution in the
los angeles area, Amer. J. Public Health. 70, 687-696 (1980) .

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20
Endnotes
1.	Portney and Mullahy find nonlinearities in the dose-response
function. The marginal responses to increases in ozone are greater
when equations are estimated with the data reflecting higher
(greater than .05 pphm) ozone concentrations. They also find that
the elasticity of the expected value of the respiratory RAD is not
constant with respect to changing ozone as implied by the simple
poisson distribution.
2.	Survey respondents provided information on the number of visits
to a doctor, the travel time to the doctor, visits to emergency
rooms, and other "cost" measures. Gerking and Stanley [ ] use
these data to estimate a willingness to pay for reduced air
pollution expression that is based on an averting behavior model
of consumer choice.
3.	A statistical test indicated that the smokers could not be
pooled with the non-smokers using a dummy variable to reflect
smoking status.
4 . An independent benchmark, the Regional Air Monitoring System
(RAMS ) data, was used to assess the quality of the SAROAD data.
The RAMS data, which were collected in the late 1970s, but not
during the time of the health survey, were subjected to extensive
quality control and more accurately measure airborne pollutants.
During the time that both systems were operational, the ozone
readings between RAMS and nonRAMS data exhibit zero order Pearson
correlations in the range of . 3 to . 6 for the hourly data. These
correlations improve substantially as the data are aggregated to
the daily and weekly level. Hence, there is every reason to expect
that our use of the SAROAD data over a two-week period accurately
measures the air pollution dose.
5.	We did not model the weather as changing over the course of
the day. It probably should be. However, the methodology proposed
here facilitates a comparison to previous studies.
6.	We computed Chi-square tests of distributional independence for
all possible aggregations of the daily data by monitoring station.
In the vast majority of cases, we cannot reject the hypothesis that
the 11 am - 5 pm data come from the same distribution. Similarly,
we cannot reject the hypothesis that the 5 am - 10 am and 6 pm -
12 pm data come from the same distribution. The hypothesis that
all the daily .observations are generated by the same distribution
was rejected in most cases, however.
7.	The p-values are based on the variance-covariance matrix
computed directly from the maximum likelihood estimates. They do
not reflect a correction like in [6] or [3] .

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21
8.	To identify the appropriate distribution of the data, we
estimated the "transformed" mean and standard deviation and the
transformation parameter. These parameters are based on the
powernormal distribution, which utilizes the Box-Cox power
transformation. The Box-Cox transformation facilitates a test
between normal and lognormal distributions. In the majority of
cases for S02, the lognormal distributional assumption could not
be rejected. With respect to ozone, we found that, usually, both
the normal and lognormal distributions could be rejected. However,
the transformation parameter was closer to 0 ( indicating
lognormal), than to 1.
9.	We tested the probability model three ways. Firstly, by
entering the probabilities for just ozone. Then, by entering the
probabilities for just S02, and, finally, by entering both. None
of the Chi-squares, comparing twice the difference in the log
likelihood values, indicated rejecting the linear constraint
imposed by the mean specifications.

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Table 1.
Variable Descriptions and Summary Statistics
Non-smokers, First Follow-up Period.
(Observations = 597)
Variable
Description
Mean
StDev.
Minimum
Maximum
AGE
Age in years
38.88
13.37
18
65
EDUC
Years of school
13.32
2.93
0
24
SEX
1 if male
.49
.50
0
1
WHITE
1 if white
.78
.43
0
1
INCOME
Income category
6.06
1.48
1
8
PHEALTH
1 if perceived health good
.93
.30
0
1
PSMOKE
1 if previous smoker
.18
.39
0
1
TEMP
Average temperature
60.40
20.84
13
83
RAIN
Average rainfall
.63
.57
0
2.15
IRR
1 if irritants at work
.34
.47
0
1
EXER
1 if exercise regularly
.11
.31
0
1
SI
1 if weeks 1-8
.26
.44
0
1
S2
1 if weeks 9-16
.30
.46
0
1
S3
1 if weeks 17 - 24
.13
.34
0
1
S4
1 if weeks 25 - 32
.17
.38
0
1
NRRAD	Number of respiratory related restricted activity days during follow-up
period two.
Frequency for NRRAD
Value of NRRAD Frequency
0
558
1
39
2
9
3
7
4
6
5
2
6
3
7
4
8
1
9
0
10
0
11
1
12
0
13
0
14
0
Mean = .241

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Table 2.
Alternative Coefficient Estimates of the Dose-Response Function
Dependent Variable = NRRAD
Variable
(1)
(2)
(3)
(4)
(5)
(6)
AGE
-.033*
-.032*
-.036*
-.030*
-.034*
-.033*
EDUC
-.018
-.024
-.015
-.024
-.021
-.022
SEX
-.083*
-.121
-.048
-.118
-.060
-.074
WHITE
.617*
.676*
.798*
.734*
.704*
.692*
INCOME
-.203*
-.199*
-.188*
-.164*
-.192*
-.191*
PHEALTH
1.146
1.266*
1.201*
1.326*
1.268*
1.284*
PSMOKE
.219*
.238
.181
.129
. 185
. 188
TEMP
-.054*
-.042*
-.038*
-.037*
-.040*
-.041*
RAIN
.853*
.957*
.716*
.956*
.982*
1.031*
IRR
-.302*
-.319*
-.214
-.273
-.229
-.245
EXER
-.888*
-.863*
-.800*
-.819*
-.854*
-.861*
SI
-2.441*
-2.681*
-2.321*
-2.536*
-2.867*
-2.941*
S2
1.318*
.773
1.421*
.796*
.853*
.719*
S3
1.565*
1.268*
1.575*
1.107*
1.516*
1.446*
S4
.841*
1.036*
1.057*
1.086*
1.410*
1.424*
OZMU
.037*





SOMU
-.028





DOZLMU

.951*




DSOLMU

.065




NOZLMU


.989*



NSOLMU


.407



WDOZLMU



.905*


WDSOLMU



.367*


0ZLAVE1




1.692*

S0LAVE1




.587*

0ZLAVE2





1.708*
S0LAVE2





.571*
CONST
1.043
-2.442*
-2.858*
-3.568*
-5.560*
-5.705*
8
1
na
0
0
1
40/112
.4
e
2
na
1
0
0
56/112
.4
6
3
na
0
1
0
16/112
.2
-L like
270
269.5
268.8
269.4
264.5
264.5
~Indicates that the p-value is less than .05.

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Table 3.
Predicted Reductions in the Expected Value of NRRAD
Per 1000 People by Specification
(1)
(2)
(3)
(4)
(6)
Predictl
Predict2
Predict3
.637
2 .290
-2.393
2.197
1.928
.356
14.294
8.188
8.119
5.418
3.089
3.022
16.351
10.671
9.246
12.940
8.546
7.186
Notes: The predictions are based on the following initial values: AGE=40, EDUC=12, SEX=1,
WHITE=1, INCOME=6, PHEALIH=1, PSMOKE=0, TEMP=70, RAIN=.5, IRR=0, EXER=0, Sl=l, S2=0, S3=0,
and S4=0. The initial value for ozone is 40, while the initial value for S02 is 20. The
predictions are per 1000 people, where:
Predictl is based on reducing ozone to 30 and S02 to 10,
Predict2 is based on reducing ozone to 30 and maintaining S02,
Predict3 is based on reducing S02 to 10 and maintaining ozone.

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Pricing Environmental Health Risks:
Survey Assessments of
Risk-Risk and Risk-Dollar Trade-offs*
by
W. Kip Viscusi
Wesley A. Magat
and
Joel Huber
Revised, April, 1989
*This research was supported by EPA Cooperative Agreements to
Northwestern University (CR-814478-01-0) and Duke University (CR-
814388/01-0) . We would like to thank our contract officer, Dr.
Alan Carlin, and his colleagues at EPA for helpful suggestions
with respect to our study's focus and survey design.

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Ab s t r a c t
This study develops a methodology for measuring the values
that individuals place on morbidity risk reductions and applies
it to the measurement of the benefits from reducing the risks of
contracting chronic bronchitis. The survey methodology involves
the use of an iterative computer program that presents
respondents with a series of pairwise comparisons which are
individually designed to measure respondents' marginal rates of
substitution for chronic bronchitis risk reduction. The approach
is innovative in that it measures the rates of trade-off for
chronic bronchitis risk reduction in terms of the risk of an
automobile accident fatality, as well as in dollars. Since it
generates estimates for each individual, it can reveal
distributions of benefit measures rather than simply a population
mean estimate. The resulting rates of trade-off for chronic
bronchitis and auto fatality risks suggests that the risk of a
chronic bronchitis case is worth 32% of the comparable risk of
death, as measured by the median trade-off rate. When risk
reduction for chronic bronchitis is compared to a cost of living
increase, the median rate of trade-off is $457,000, whereas the
comparison between automobile fatality risk reductions and cost
of living increases yielded a median rate of trade-off of $2.29
million. The results across different risk-risk and risk-dollar
trade-offs were internally consistent.

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1. Introduction
Over the past decade economists have devoted substantial
attention to the implicit valuation of health outcomes. These
analyses of risk-dollar trade-offs have relied in large part on
market-based data.^" For example, wage-risk trade-offs have been
used to analyze the implicit value of fatalities and the average
nonfatal job accident risk. Similarly, economists have analyzed
the trade-offs implied by seat-belt usage decisions to infer a
value of life.2
Although studies using market data provide useful benchmarks
for health risk valuation, they do not resolve the issue of how
government agencies should attach benefit values to health
outcomes for which we do not have good market data. This
omission is particularly important for government agencies, such
as the U.S. Environmental Protection Agency (EPA), which
generally focus on policy contexts in which market forces are
believed to not be fully effective. For these situations, no
useful market trade-off data may be available. Nevertheless,
economic analysts would like to select the efficient project mix,
and some benefit measure is required to perform such an analysis.
In recent years, a large number of studies have addressed these
benefit issues using non-market techniques, thus greatly
expanding the range of benefit components that can be valued.
This study makes several contributions to the literature on
non-market techniques for benefit valuation. First, we develop a
methodology for measuring the benefits of reducing the risks from
various types of morbidity effects. The methodology uses an

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2
iterative computer program to ascertain the points of
indifference for consumers who are asked to trade off the reduced
morbidity risk with increases in other attributes of a location
decisions, such as an area's cost of living and the risk of an
automobile fatality.^
Second, we apply the methodology to an important health
benefit valuation problem, that of estimating the value of
reductions in the risk from chronic bronchitis, one central type
of chronic obstructive pulmonary disease alleged to be a major
adverse effect of ozone pollution exposure. Most previous
studies of health valuation focus on acute health effects, such
as accidental death, rather than chronic diseases whose effects
are more difficult to communicate to potential victims.
Third, our approach yields the entire distribution of
consumer values for chronic bronchitis risk reduction, rather
than just the mean valuations which can be derived from market-
based approaches to the problem. This information is important
for policy makers in situations where consumers place, widely
divergent values on reducing risk.
Fourth, because chronic disease effects are difficult to
communicate to potential sufferers, it is important to use a
methodology that adapts to whether subjects understand the
valuation task being asked of them. By administering the
questionnaires interactively on a computer, our approach allows
us to build in several tests of task comprehension that, if
failed, provide additional information before proceeding with the
questionnaire .

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3
Finally, our methodology produces values for morbidity risk
reduction in terms of trade-offs with several other metrics
besides money. In our chronic bronchitis application, we measure
trade-offs with the risk of automobile fatalities, as well as
with a dollar measure derived from changes in the cost of living.
Many policy-makers are hesitant to base decisions on benefits
denominated in dollars, and they may be more willing to
implicitly consider benefit values when measured in units of a
common risk such as death. Converting all health outcomes into
death risk equivalents facilitates cost-effectiveness analysis by
calculating the cost per statistical life equivalent saved, and
it addresses concerns with respect to dollar pricing. Even if
the morbidity valuations are elicited in terms of trade-offs
between risks, they can still be converted into dollar values by
using hedonic measures of the value of the comparison risk if
that comparison risk is death (with the appropriate application
of sensitivity analysis to the assumed values of life used to
make the translation).
There are reasons to suspect that consumers may have fewer
difficulties with the task of specifying rates of trade-off of
one risk with another, as opposed to trading off a risk with a
certain dollar amount. The risk-dollar trade-off task sometimes
produces alarmist responses from subjects who cannot envision
that they would voluntarily subject themselves to a higher risk
of a serious morbidity effect for a finite amount of additional
income. ^ Dollar valuation tasks also are difficult to design in
ways that subjects will find analogous to real choice situations,

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4
and they may offer biased responses to questions that do not
force them to pay for the risk reduction being valued. There is
a final reason to prefer the risk-risk trade-off approach. To
the extent that consumers are equally adverse to the risks from
different types of risks, asking them to trade off one risk
against another produces rates of trade-off which measure the
relative value to them of the two risks without regard to the
risk aversion which enters in trading off uncertain health risk
with certain dollars. in this sense the risk-risk trade-offs
provide values which are not as heavily influenced by the
consumers' attitudes towards facing risks per se.
The outline of this paper is as follows. Section 2 provides
an overview of the study design and the sample. Section 3
describes the risk-risk trade-offs whereby respondents put their
chronic morbidity valuations into auto death equivalents. In
Section 4 we describe the direct estimates of risk-dollar trade-
offs for chronic bronchitis obtained by asking respondents to
trade off chronic bronchitis risks with either the area's cost of
living or property damage from storms. As a check of the
validity of the approach, we provide evidence on auto fatality
risk-dollar trade-offs in Section 5. These implicit value of
life numbers are tested against those in the literature to assess
the valibity of the survey approach. In Section 5 we also
convert all of our results for the value of chronic bronchitis to
dollar equivalents. Section 6 concludes the paper.

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5
2. Study Design and Sample Description
Genera 1	Approach
We used a sample of 593 shoppers from a blue-collar mall in
Greensboro, North Carolina to measure willingness-to-pay values
for reducing the probability of contracting chronic bronchitis.
The subjects made four series of pairwise comparisons of
different locations where they could live with the locations
differing in two attributes. In most of these comparisons, one of
the locational attributes varied was the probability of
contracting chronic bronchitis.
The first series of questions yielded a rate of trade-off
between decreases in the risk of chronic bronchitis (CB) and
increases in the risk of an automobile fatality, thus providing
what we call a "risk-risk" trade-off. The second series of
questions determined a "risk-dollar" trade-off, where the
reduction in the risk of CB was achieved at the expense of a
location with a higher cost of living.
If subjects were found to more easily trade off a reduced CB
risk with a higher auto fatality risk than with a cost of living
increase, we wanted to sort out whether this result was due to
the fact that the cost-of-living differences were measured in
dollars or that they were given with certainty (that is, with no
risk involved over dollar gambles) . Thus , our third series of
questions asked subjects to trade off reductions in the CB risk
with increases in a lottery on dollar losses expressed as a risk
of storm damage, where if a storm were to occur, it would cause
$2,000 of damage to the subject's home and belongings. Finally,

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6
in order to compare the CB risk--auto fatality risk trade-offs
with the risk-dollar trade-offs, it was useful to obtain a dollar
measure of the value of reducing the risk of automobile
fatalities. This fourth series of questions provided a rate of
trade-off of risk reduction in automobile fatalities to increases
in a location's cost of living.
The results from these four series of questions allows us to
address the following questions:
*	What is the distribution of CB risk--death risk trade-offs?
*	What is the distribution of CB risk-- (certain) dollar trade-
offs?
*	What is the distribution of CB risk-- (uncertain) dollar trade-
offs?
*	Which of these three trade-offs is easier to elicit accurately
from consumers?
*	What is the distribution of death risk--(certain) dollar
trade-offs?
*	How does the distribution of CB risk-- (certain) dollar
trade-offs compare with the distribution of CB risk--dollar
trade-offs derived from combining the CB risk--death risk
trade-offs with the death risk--(certain) dollar trade-offs?
*	How does the distribution of CB risk-- (certain) dollar trade-
offs compare with the distribution of CB risk--dollar trade-
offs derived from combining the CB risk--death risk trade-offs
with the values of life derived from wage hedonic studies?
It should be noted that the first question is the most
important one to answer because it addresses the use of an

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alternative metric to dollars for measuring morbidity risk
willingness-to-pay values, that of another health risk, namely
death. For cost-effectiveness purposes, it is not necessary to
go beyond the death risk metric, as alternative policy
initiatives can be compared on the basis of this metric rather
than dollars. However, if the CB risk values measured in death
risk units translate closely to the direct dollar valuations of
reducing CB risks that we obtain, policy makers can be more
confident in the reasonableness of the risk-risk valuations.
In order to understand our empirical results that allow
responses to the questions above, it is first necessary to
carefully describe the design of the survey and sample.
Methodology
The task of eliciting individuals' valuation of chronic
bronchitis is not straightforward. The first problem is that few
individuals fully understand the health effects of chronic
bronchitis. Second, once given this information, they may not
have sufficient experience in dealing directly with such trade-
offs to give meaningful valuation responses. To accommodate
these difficulties, we developed an interactive computer program
that would inform consumers as well as elicit trade-off
information.
Three different questionnaires were used, but for
concreteness let us focus on what we will designate Questionnaire
A. After acquainting the respondent with the computer, the
program elicits information regarding the respondent's personal
characteristics (e.g., age) . A substantial portion of the

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8
questionnaire (about 40 questions) is then devoted to acquainting
the respondent with the health implications of chronic bronchitis
and the nature of the trade-offs that would be encountered.
These questions elicit the respondent's familiarity with chronic
bronchitis, information on smoking history, and provide a
detailed summary of the health implications of chronic
bronchitis .
The thirteen principal health implications of chronic
bronchitis are summarized in Table 1. The chronic bronchitis
disease classification includes a variety of illnesses of
differing severity. Our intent was not to value each possible
combination of systems, but rather to establish a methodology
that could be used to value this and other adverse health
effects. Consequently, our valuation procedure pertains to the
set of symptoms summarized in Table 1, but the broader purpose of
our analysis is to develop a methodological approach that is more
generally applicable to other patterns of chronic bronchitis, as
well as to different diseases such as cancer.
Since chronic bronchitis takes many forms, this study
focused on the most severe chronic morbidity effects. ^ Thus, the
survey's focus is on the adverse health outcomes at the extreme
and of the cluster of diseases within the chronic bronchitis
grouping. Because a quick overview of these effects may not be
fully comprehended by respondents, in each case subsequent
questions ascertain the respondents' assessed disutility ranking
of each outcome in a linear 49-point scale. The purpose of these
questions is not to establish attribute-based utilities, but to

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9
Table 1
Health Implications of Chronic Bronchitis
1.	Living with an uncomfortable shortness of breath for the
rest of your life.
2.	Being easily winded from climbing stairs.
3.	Coughing and wheezing regularly.
4.	Suffering more frequent deep chest infections and pneumonia.
5.	Having to limit your recreational activities to activities
such as golf, cards, and reading.
6.	Experiencing periods of depression.
7.	Being unable to do the active, physical parts of your job.
8.	Being limited to a restricted diet.
9.	Having to visit your doctor regularly and to take several
medications.
10.	Having to have your back mildly pounded to help remove
fluids built up in your lungs.
11.	Having to be periodically hospitalized.
12.	Having to quit smoking.
13.	Having to wear a small, portable oxygen tank.

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10
encourage respondents to think carefully about the health
implications of chronic bronchitis and their own view of the
effect of this disease on their well-being.
At this point in the questionnaire, the respondents confront
the first of two set of trade-off questions. Individuals are
presented with a choice of moving to one of two alternative
locations which differ in terms of their chronic bronchitis risk
and automobile accident risk. To ensure that respondents would
be willing to consider making such a move at all, they were told
that these two locales posed a lower risk of both outcomes than
their current place of residence.
Since risk levels differ across individuals, the program
elicits information regarding individual activities that are
likely to influence their person-specific risks, such as smoking
habits (for chronic bronchitis) and mileage driven per year (for
auto accident deaths). The program then informs the respondents
that the probabilities presented in subsequent questions are
calculated based on their responses to the earlier risk-related
activity questions, even though the same risks are actually
•	ft
presented to all subjects. This procedure increases the extent
to which the stated risk levels are taken at face value, while
facilitating the comparison of risk trade-offs across subjects
because they all responded to the same risks.
To ensure that respondents understand the task before
proceeding to questions in which one location is lower in one
risk but higher in the other risk, they are first presented with
a dominant choice situation. Let the notation (x,y) denote a

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11
locale where the chronic bronchitis probability is x/100,000 and
the automobile death risk is y/100,000. The actual survey did
not present the choices in such abstract terms, but this notation
9
makes the exposition of the survey structure simpler.
To ascertain whether respondents understand the task, they
are first asked whether they prefer Area A with risks per 100,000
population of (75, 15) or Area B with risks (55, 11) . Since each
of the Area B risks is lower, this alternative is dominant.
Respondents who do not comprehend the task and incorrectly answer
that they prefer Area A are sent through a series of questions
that explain the structure of the choice in more detail.
The performance with respect to the dominance question was
quite good. Over four-fifths of the sample gave a correct
response to the dominance questions on their initial attempt.
After being given additional information, fewer than one percent
of them gave an incorrect answer, and these respondents were
excluded from the sample since they did not understand the
interview task.
The program then proceeds with a series of pairwise
comparisons in which the attributes are altered based on the
previous responses until indifference is achieved. The computer
program used tabular summaries, but for expositional purposes we
will consider the abstract formulation of the trade-offs.
&	Model	Ql	State-Dependent	TTti 1 i ti es
Consider the following model of state-dependent utilities.
Let subscript a denote Area A and b denote Area B. Also, let
U (CB) be the utility of a case of chronic bronchitis, U(D) equal

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12
the utility of an auto accident death, and U(H) equal the utility
of being healthy (i.e., having neither CB nor an auto accident).
To simplify this exposition, we assume that contracting CB and
dying from an automobile accident are mutually exclusive events.
Also, let Xa denote the probability x/100, 000 for Area A and Ya
denote the probability y/100, 000 for Area A, and let Xb and yb be
defined similarly. The survey continually modifies the choice
pairs until subjects reached the situation where
(1)	XaU(CB) + YaU(D) + (l - xa - Ya)UtH)
= XbU(CB) + YbU(D) + (1 - Xb - Yb)U(H).
Our general objective is to establish the death risk
equivalent of chronic bronchitis. If we assume for concreteness
that Xa > Xb and Yb > Ya (no loss of generality) , then
(2)	(Xa - Xb)U(CB) - (Yb - Ya)U(D) + (Xa - Xfa + Ya - Yb)U(H),
"*b-*a	*b-Ya
(3)	U(CB) - 	 U(D) + (1 - 	)U(H) .
xa-xb	xa-xb
If we define the rate of trade-off between CD and D as	SO
that
(4)	tx -
Yb-Ya
xa~xb
we obtain the result that
(5)
U (CB)
= t-^U(D) + (1
- t1)U(H)

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13
The utility of CB cases has been transformed into an equivalent
lottery on life with good health and death, for which we have a
well-developed literature.
Survey Structure
Now consider the first set of paired comparison questions
presented in Questionnaire A after the dominant choice question
described above. In this case, respondents are given the choice
between Area A with risks (75, 15) and Area B with risks (55,
19). Suppose that Area B is preferred in this example. Area B
has the lower chronic bronchitis risk and higher auto accident
risk; therefore, in subsequent questions the program raises the
CB risk in the preferred Area B until indifference is achieved.
If in the original choice the subject prefers Area A, in
subsequent questions the program lowers the auto death risk in
Area B until the point of indifference is reached.
Suppose that after considering a series of such comparisons
the subject reaches indifference where he views the risk (75, 15)
as being equivalent to (65, 19) . Using equations 4 and 5 above,
this would imply that
19-15
t, = 	 = 0.4
75-65
and
U (CB) = 0 . 4U (D) + 0 . 6U (H) .
The second set of paired comparison questions in
Questionnaire A focuses on the more traditional risk-dollar
trade-off involving CB and cost of living. Area A has the same

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14
cost of living as the respondent's present residence, but Area B
has a cost of living that is $80 higher, yet poses a lower CB
risk Xb. If in the initial question Area B is preferred, Area
B's CB risk is increased until indifference is achieved.
Similarly, if Area A is preferred, Area B's cost of living is
reduced until reaching the point of indifference.
In the context of a state-dependent utility function with
two arguments, health status and income, we have
XaU(CB) + (1 - Xa)U(H) - XbU(CB,-$80) + (1-Xb)U(H,-$80).
If utility functions are additively separable in money and
health, then
XaU(CB) + (1 - Xa)U(H) - XbU(CB) + (l-Xb)U(H) + U(-$80),
which simplifies to
(Xa - Xb)U(CB) = U(-80) + (Xa - Xb)U(H),
or
U(-$80)
U(CB) - 	 + U(H) .
(Xa-Xb)
If we assume that utility is linear in money (with a coefficient
equal to one) in establishing our health valuation scale, then we
have
U (CB) = -L + U (H) ,
i.e., CB is equivalent to being healthy and suffering a financial
loss tantamount to L dollars, where

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15
-$80
L » 	 .
xa"xb
This procedure to establish a risk-dollar trade-off rate
involves two assumptions regarding the structure of utility
functions. First, we assume additive separability with respect
to money and health. Second, we assume that the dollar
magnitudes treated are sufficiently small that utility is
approximately linear in money. Since even risk-averse utility
functions meet this test for small monetary changes, ^ we
selected our health-risk levels so that the dollar magnitudes
involved be small.
The structure of Questionnaire B is similar to Questionnaire
A except the certain $80 loss in terms of living costs has been
replaced by a lottery on $2000 storm damage loss. -*-n this case,
respondents must specify the storm damage probability that
establishes an equivalent CB-storm damage pair. If we assume
that respondents are risk-neutral, then the storm damage loss can
be replaced by its expected value. The possible advantage over
the cost-of-living approach is that respondents may be able to
make more meaningful comparisons of two different lotteries
rather than having one attribute -- the dollar payoff -- being
non-stochastic. As with the first set of questions in
Questionnaire A, if the consumer prefers Area B in the initial
question, the program leads the consumer to indifference by
increasing the CB risk of Area B until indifference is achieved.
Similarly, when the consumer initially prefers Area A, the

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16
program reduces the storm damage risk in Area B until reaching
the point of indifference.
Questionnaire C repeats the first part of Questionnaire A,
and these samples are pooled in the analysis below. The second
set of questions addresses the more traditional death risk--
dollar trade-off using auto deaths and cost-of-living trade-offs.
The structure is similar to that of the second set of questions
in Questionnaire A except that CB has been replaced by auto
fatality risks so that respondents must reach the point that
U(D) = -L + U(H),
where
-80
h + 	
xa"xb
as before. This portion of the study provides a direct
comparability test with the literature on market-based values of
life. The fatality risk--dollar trade-offs will also be used in
conjunction with the chronic bronchitis--fatality risk trade-offs
to establish a chronic bronchitis--dollar trade-off rate.
Table 2 summarizes the structure of the 3 questionnaires
described above.
Sample Description
The interviews of the subjects were all done through an
interactive computer program, thus avoiding problems of
interviewer bias and promoting honest revelation of preferences.
Response rates to sensitive questions, such as income level, were

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1
Table 2
Summary of Survey Structure
Questionnaire A
Trade-Off
1. Chronic bronchitis
auto deaths
Units of Measurement
Auto deaths per chronic
bronchitis case
Procedure
In the area with the
higher auto accident
risk, increase the
bronchitis risk (to
make that area less
desirable) or reduce
the auto accident
risk (to make that
area more desirable)
until reaching in-
di f ference.
2. Chronic bronchitis
cost of living
Dollar value per
1/100,000 reduced
risk of bronchitis
In the area with
lower bronchitis
risk, increase the
bronchitis risk (to
make that area
less desirable) or
decrease the cost of
living (to make that
area more desirable)
until reaching in-
di f ference.
Questionnaire B
1. Chronic bronchitis
storm damage
Reduced probability of
$2000 storm damage
that is equivalent to
one bronchitis case
prevented
In the area with the
higher storm damage
risk, increase the
bronchitis risk (to
make that area less
desirable) or reduce
the storm damage
risk (to make that
area more desirable)
until reaching
indi f ference.

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18
Table 2 (cont'd)
Summary of Survey Structure
Questionnaire C.
1. Chronic bronchitis
auto deaths
Auto deaths per chronic
bronchitis case
!Same as Questionnaire A - Part 1]
In the area with the
higher auto accident
risk, increase the
bronchitis risk (to
make that area less
desirable) or reduce
the auto accident
risk (to make that
area more desirable)
until reaching in-
di f ference.
2. Auto accidents -
cost of living
Dollar value per
1/100,000 reduced
risk of an auto
accident
In the area with
lower auto accident
risk, (to make that
area less desirable)
or decrease the cost
of living (to make
that are more
desirable) until
reaching indif-
ference .

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19
much higher than those usually achieved with face-to-face
interviews. In addition, subjects were not concerned with
whether their responses impressed the interviewer. Use of a
computer also made it possible to ask a sequence of questions to
ascertain the appropriate marginal rates of substitution.
The sample was recruited for the study by a professional
marketing firm at a mall intercept in Greensboro, North Carolina.
This locale has a representative household mix and is used as a
test marketing site for many national consumer brands. This firm
and locale have been used successfully in two previous studies by
the authors. ^ Use of such a consumer sample also yields more
reliable responses to issues such as the valuation of property
damage from storms than would a student sample or a sample from a
city with an unrepresentative population, such as the college-
oriented cities of Evanston, Illinois, or Chapel Hill, North
Carolina.
Table 3 provides a glossary of the variables and the
associated sample statistics. Questionnaires A and C had a
similar mix of respondents, with a mean age in the low thirties,
a even split between males and females, two years of college
education, a 50 percent married rate, about 0.6 children under 8
years old, a household size of 2.7 - 2.8, and a household income
in the mid-range of thrifty to forty thousand dollars.
Questionnaire B has a somewhat different mix because of the
difference in the times at which the samples were recruited
(e.g., week-end shoppers differ from day-time weekday shoppers).
The Questionnaire B sample is about 10 years older, more likely

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Table 3
Summary of Sample Characteristics
Mean and Std. Deviations
Questionnaire
Demographic
Variables
A
AGE, in year
33 .74
(12.42)
43.47
(12.68)
33 . 07
(11.66)
MALE, sex dummy
vari able
0 .50
0 . 42
0 .51
EDUCATION, years of
schooling
14 . 02
(2.23)
14 . 32
(2.47)
13 .79
(2.66)
MARRIED, married
dummy variable
0.49
(0.50)
0 .79
(0.41)
0 .49
(0.50)
KIDS, number of
children under 8
0 .56
(1.00)
0.83
(1.04)
0 . 65
(1.07)
HOUSEHOLD, number of
people in household
2 .71
(1.25)
3 . 00
(1.16)
2 .80
(1.23)
INCOME, annual	35,386.60	45,367.65	37,153.85
household income	(19,009.95)	(20,335.54)	(21,333.80)
in dollars
194
204
195

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21
to be married, and with a household income about $10,000 greater.
As the last row of Table 3 indicates, each of the three samples
had about 200 respondents, with combined sample for the study of
593.
3. Risk-Risk Trade-Offs
Table 4 displays the means and standard deviations of the
trade-off rates implied by the indifference points of the subject
responses. To go beyond these summary statistics, consider first
set of trade-offs between CB and auto accident deaths. For this
analysis Questionnaires A-l and C-l are pooled since the
questions are identical.
Establishing a death risk metric for CB enables respondents
to think in risk terms, avoiding the comparability problems that
might be encountered if monetary attributes were introduced.
Similarly, for policy purposes EPA can establish a death risk
equivalent and establish cost-effectiveness ratios in terms of
the cost per statistical death prevented. As indicated in
Viscusi (1986), this cost-effectiveness index will provide a
comprehensive measure of the policy impact and also avoid the
political sensitivities of placing dollar values on all health
outcomes. Once a uniform health metric is established, one can
then compare the cost per life equivalent saved with various
value-of-life reference points and decide whether the policy
should be pursued if one wishes to take a benefit-cost approach.
Unlike market-based studies of the value of life, the survey
technique yields information on the entire distribution of the
valuations. Table 5 reports the deciles of the distribution for

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22
Table 4
Rates of Trade-off Implied by Indifference Points
Means and Std. Deviations
Part B
Trade-off Rates
CB-Auto (A-1 & C-l),
auto deaths per CB case
CB-Cost of Living (A-2),
dollar value per
1/100,000 CB risk
CB-Storm Damage (B-l),
number of $2,000 storms
equal to one CB case
Auto-Cost of Living (C-2), -
dollar value per 1/100,000
reduced auto accident risk
A
0. 68
(0.82)
8 . 83
(12.501
Questionnaire
852.60
'1064.20)
C
0 .70
(0.95)
81.84
'168 . 54'
Sample Size
194
204
195

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23
Table 5
Distribution of Chronic Bronchitis
Auto Death Trade-Offs
Auto Death Equivalents per Chronic
	Bronchitis Case	
Decile
.10	0.12
.20	0.20
.30	0.23
.40	0.27
.50	(median) 0.32
.60	0.40
.70	0.80
.80	1.00
.90	1.33
1.00	4.00
Mean	0.68
(St.	error of mean) (0.06)

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24
respondents who gave consistent answers that converged to a
particular trade-off value. Subjects whose responses indicated
that they did not fully comprehend the valuation task were
excluded from our sample.
Specifically, we excluded subjects who failed one of the
following consistency checks:
1)	they started the series of paired comparison questions by
preferring one area, say Area A, and as Area B was made
more desirable in subsequent comparisons they continued to
prefer Area A, even on the last question of the series in
which Area B dominated Area A on both attributes;
2)	like inconsistency #1, they continued to prefer Area A in
each comparison until the last one in which Area B dominated
Area A in both attributes, yet on this last question they
indicated indifference between Area A and Area B;
3)	they indicated preference for one area, say Area A, on the
first and all subsequent questions in the series (including
the last one in which Area B dominated Area A) , then when
confronted with this inconsistency and asked to repeat the
series of questions chose Area B in the first question
(despite have selected Area A the first time they were given
this question);
4)	they indicated preference for one area, say Area A, on all
questions in the series except the last one in the series (in
which Area B dominated Area A) but including the next-to-last
question (for which Area B easily dominated Area A on one
attribute and Area A just barely dominated Area B on the

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25
other attribute) , thus making it impossible to interpolate
between the trade-offs implied by the last two questions to
obtain an indifference point (because the last question
yields no rate of trade-off) ; or
5) they expressed indifference between all pairs of areas in the
series of questions, despite wide variation in their
attributes.
Individuals who failed one of these inconsistency checks either
did not understand the choice task, were not responding honestly,
attached no value to one of the two attributes, or have non-
monotonic preferences for one of the attributes. we assume that
neither of the last two preferences attributes are possessed by
any subjects, thus implying that answers which fail any of the
five inconsistency checks do not represent the subjects' true
preferences .
The requirement that the response pattern to the series of
paired comparisons be internally consistent will lead to more
meaningful estimates than if no such checks were imposed. About
two-thirds of the sample converged to an indifference situation
and had consistent responses, where this percentage was similar
across all questionnaires. ^ These consistency checks
distinguish our approach from the usual contingent valuation
method in which respondents' answers are taken at face value
without such formal tests of whether the subjects understood the
valuation task and displayed consistent choices.
In evaluating the distribution in Table 5, first consider
the respondent at the tenth percentile. This person viewed a

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26
chronic bronchitis probability as being just as severe as a risk
of an auto accident that was 0.12 as great. Thus, this
individual would view a chronic bronchitis risk of 100/100,000
risk of 100/100, 000 per year as being equivalent to the annual
chance of being involved in an auto accident of 12/100,000.
Now examine the respondent at the other end of the
distribution. This individual views a chronic bronchitis risk as
being four times as severe as a risk of death, so that a
100/100,000 risk of CB would be viewed as comparable to a
400/100,000 risk of death. He or she gave consistent responses
to the questions, but opted for the choice reflecting the highest
CB valuation.
Many studies in the survey valuation literature exclude the
tails of the distribution since they are tainted by extreme
respondents such as this. Rather than discard such information
altogether, we report the entire distribution, recognizing that
the top and bottom deciles may be affected by a lack of complete
understanding of the interview task. The reported distributions
enable readers to assess how important outliers are within the
context of the study and by focusing primarily on the median
responses rather than the mean we avoid the distortion of our
results by these outliers.
The response pattern in which CB was more highly valued than
auto death risks was exhibited by the top two deciles for each
questionnaire's response distribution. Such a pattern is not
necessarily implausible. In addition to possibly
misunderstanding the interview task, two explanations can be

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2
offered. First, individuals might legitimately believe that such
a severe chronic illness is a worse outcome than death. The
health outcome described in Table 1 is quite serious and will
have substantial duration. Their normal activities would be
curtailed, medical interventions including hospitalization and
possible reliance on a portable oxygen tank would accompany
severe cases of CB, other illnesses would be more likely, and
they would experience periods of depression.
The second possible explanation is that the respondents were
establishing equivalences between different average risks in an
area rather than different risks to themselves. The CB risk was
characterized as an involuntary risk not under their control
except for smoking, whereas the auto accident risk differs
depending on one's driving habits and skills. Other studies
suggest that individuals may have overly optimistic assessments
of risks influenced by their actions, such as auto death risks,
as discussed in Viscusi and Magat (1987) . If this were the case,
the perceived person-specific risk would be below the stated
risk, causing an upward bias in the results in Table 5.
The median CB valuation is equivalent to 0.32 auto deaths.
Because of the skewed nature of the responses, the mean value of
0.68 is more than double the median response. Regression
analysis of the CB-auto death trade-off rates indicate no
significant variation across subjects with respect to either
demographic factors such as age, income, and education, or
personal characteristics such as smoking habits. This result is
neither surprising nor disturbing. Most individual attributes,

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28
such as household income, should affect the CB valuation and the
value of life similarly, and thus be unrelated to variation in
the CB--auto death trade-off rates across subjects. Because
there are no systematic differences among individuals in their
risk-risk trade-offs, we can aggregate them into meaningful
summary measures such as medians and means without the risk of
drawing misleading conclusions from an unrepresentative sample.
The general implications of these results is a follows.
Most, but not all, people regard the risk of chronic bronchitis
as a less severe outcome than the risk of death. However, the
prospect of a sustained chronic illness is viewed as a very
severe outcome. Based on the median responses, the death risk
equivalent of CB is. 0.32, and based on the mean response it is
0.68. The general order of magnitude of both the median and the
mean is the same and is just below that of fatalities. As will
be indicated in Section 5, these statistics can be transformed
into dollar valuation equivalents using established value-of-life
statistics.
4. Risk-Dollar Valuations of Chronic Bronchitis
The second approach that we employed to value chronic
bronchitis was to establish risk-dollar trade-offs. The two
approaches used were to establish the chronic bronchitis risk
equivalent of a higher cost of living and to determine the
relationship between chronic bronchitis risks and storm damage
risks.
Consider first the cost-of-living results in Table 6. The
first column of Table 6 lists the decile of the distribution.

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29
Table 6
Distribution of Chronic Bronchitis
Cost of Living Trade-Offs
Decile
Trade-Off Levels
Dollar Value per
1/100,000 Reduced Risk
of Chronic Bronchitis
(A-2)
Implicit Dollar
Value per Case
of Chronic
Bronchitis
, 10
.20
.30
.40
.50 (median)
. 60
.70
.80
.90
1.0
Mean
(St. error of mean)
1.50
3.00
3.50
4 . 00
4.57
5.33
6.40
8 . 00
20 . 00
80 . 00
8 . 83
(1.14)
$150,000
$300,000
$350,000
$400,000
$457,000
$533,000
$640,000
$800,000
$2,000,000
$8,000,000
$883,000
($114,000)

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30
Column two presents the increased dollar value in the annual cost
of living that the respondent was willing to incur per 1/100,000
reduction in the annual probability of chronic bronchitis. If we
multiply the results in column 2 by 100,000, we obtain the
implicit dollar value per statistical case of chronic bronchitis.
As in the case of the risk-risk results, the response
pattern is skewed so that the upper tail of the responses
generates a mean valuation estimate in excess of the median. The
results here indicate the average dollar value of chronic
bronchitis is $883,000, with an associated standard error of
$114,000. The $457,000 median of the distribution is just over
half of the mean. Each of these values is below the usual
estimates of the implicit value of life, which are reviewed in
Viscusi (1986). These results follow the expected pattern, given
the CB--auto death risk trade-off results reported above.
As in the case of the risk-risk trade-offs, the upper bound
of the chronic bronchitis valuation estimates exceeds most
estimates of the value of a fatality, as $8 million exceeds some
but not all estimates of the value of life. More precise
comparisons of all of the results using a dollar metric will be
undertaken in Section 5.
The second set of CB risk-dollar trade-offs, which is
reported in Table 7, uses storm damage risks as the dollar
counterpart so that respondents must compare monetary lotteries
and health status lotteries rather than certain monetary (cost of
living) differences with health status lotteries. The first
column of results gives the value of y for which a storm causing

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31
Table 7
Distribution of Chronic Bronchitis
Storm Damage Trade-offs
Decile
Equivalent $2000
Damage Probability
(xlOO,000)
Implicit Dollar
Value per Case
of Chronic
Bronchitis
, 10
.20
. 30
.40
.50 (median)
.60
.70
.80
.90
1. 0
Mean
(St. error of mean)
175.00
228.57
266.67
266.67
400.00
533 . 33
800.00
1,333.33
2,000.00
4,000.00
852.60
(91.93)
$350,000
$457,140
$533,340
$533,340
$800,000
$1,066,660
$1,600,000
$2,666,660
$4,000,000
$8,000,000
$1,705,200
($183,860)

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32
damage of $2000 with a probability of y/100,000 is equivalent to
a chronic bronchitis probability of 1/100,000. A more meaningful
metric is the expected storm damage that is equivalent to each CB
case. This figure is obtained by multiplying the first column of
results by the $2000 damage per storm damage event. The second
column of results gives the dollar value per statistical case of
chronic bronchitis, where these dollar values have been obtained
using the storm damage costs.
A comparison of the distributions of implied CB valuations
in Tables 6 and 7 suggests that the subjects may have found the
storm damage lottery comparison to have been more difficult to
make than the comparison with a non-probabilistic cost-of-living
increase. The distribution derived from the storm damage lottery
comparison stochastically dominates the distribution from the
cost-of-living comparison, with both its median and mean almost
double that of the cost-of-living distribution. Based on a
comparison with the dollar values of avoiding automobile accident
fatalities reported in next section, the CB avoidance values
derived from the storm damage lottery questions appear to be
somewhat high. Further, the standard error of the mean is about
50 percent higher for the distribution derived from the storm
damage distribution than for the cost-of-lived based distribution
of CB values. In any event, these results do not suggest that
expressing dollar trade-offs in probabilistic form, as in the
storm damage lottery, aids people in making risk-dollar trade-
offs, which was our original hypothesis.

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33
5. Trade-Offs Between Auto Deaths and Cost-of Living
A useful check on the survey methodology is to ascertain the
implicit value of life using a direct fatality risk-dollar trade-
off. This is done using automobile accident risks and cost of
living in Questionnaire C-2, and the results of this exploration
are reported in Table 8.
The median response of $2,286,000 is quite reasonable in
view of the similar (in 1987 dollars) market-based estimate by
Blomquist (1979), but the mean value of $8,184,000 seems rather
large. The high mean estimate was generated by a portion of the
sample with value of life estimates as high as $80, 000, 000. Such
implausibly large estimates can occur because of the difficulty
of the comparison task. Respondents are being asked to establish
an equivalence between some annual chance of chronic bronchitis
x/100,000 that is equivalent to an $80 cost-of-living increase.
This is a difficult comparison to make. in contrast, the risk-
risk questions focused on chronic bronchitis--auto accident risk
comparisons of x/100,000 and y/100,000, where most respondents
did not believe that the severity of outcomes differed by more
than an order of magnitude.
The implicit dollar value of CB can be obtained by chaining
the responses to questionnaire part C-l, which gives the CB-auto
death trade-off, and part C-2, which gives the auto death--
dollars trade-off. These results appear in Table 9. The median
dollar value of each chronic bronchitis case is $800,000. The
mean is much greater because there is one outlier with a $320
million value. This individual expressed extreme responses on

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34
Table 8
Distribution of Auto Accident --
Cost of Living Trade-Offs
Dollar Value per	Implicit Dollar
1/100,000 Reduced	Value of
Decile	Risk of an Accident	an Accident
. 10
10 . 00
$1,000,000
.20
17 .50
$1,750,000
.30
17 .50
$1,750,000
.40
20 . 00
$2,000,000
.50 (median)
22.86
$2,286,000
. 60
26. 67
$2,667,000
.70
40 . 00
$4,000,000
.80
80 . 00
$8,000,000
.90
177 .78
$17,778,000
1. 0
800.00
$80,000,000
Mean
81.84
$8, 184, 000
(St. error of mean)
(14.40)
($1,440,000)

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35
Table 9
Implicit Valuation of Chronic Bronchitis
Implied by CB--Auto Death and Auto Death --
Cost of Living Trade-offs
Questionnaire C
Fracti 1e s	Inferred CB Value
.10	$200,000
.20	$350,000
.30	$522,449
.40	$646, 154
.50	$800,000
.60	$1,066,667
.70	$2,133,333
.80	$3,555,556
.90	$12,800,000
.99	$71,111,111
1.00	$320,000,000
Mean	$6,962,364
(Std. Error of Mean)	($2,977,373)
(N = 112)

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36
each component part, valuing each CB case at four times the
amount of each death and having an implicit value of an auto
fatality of $80 million. In each case, these were the highest
values in the sample and the highest permitted by the Program,
which indicates that this individual probably did not understand
the valuation task.
As instructive summary of the results is provided in Table
10. For the results creating CB/auto death risk equivalents, the
numbers have been transformed into implicit value-of-life terms
using three different reference points: a $2 million value of
life; a $3 million value of life; and a $5 million value of life.
The $2 million figure is comparable to the median auto death risk
valuation within the survey so that this estimate provides an
internal comparison of the results. The $3 million figure is
included since the recent estimates by Moore and Viscusi (1988)
indicate that the labor market value of life is in the $2-$3
million range using BLS data, and this was the "best estimate" of
the value of life in earlier work by Viscusi (1983) . The $5
million reference point is the value of life figure obtained
using new NIOSH data on job fatality risks, which Moore and
Viscusi (1988) view to be superior to the BLS data.
The pattern displayed by the results is fairly similar. In
each case mean valuations are at least double the value of the
median. Although one would not expect symmetry in a distribution
truncated at zero, the very high end responses observed appear to
be due to response errors.

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Table 10
Summary of Risk-Dollar Equivalents
Direct
Valuation
Estimate
CB Estimate
Using
$2 Million
CB Dollar
E s timate
Using
$3 Million
CB Dollar
Estimate
Using
$5 Million
Value of Life Value of Life Value of Life
CB/Auto Fatality:
A-1 & C-l (Median)
A-1 & C-l (Mean)
$640,000
$1,360,000
$960,000
$2,040,000
$1,600,000
$3,400,000
CB/Cost of Living:
A-2 (Median)	$457,000
A-2 (Mean)	$883,000
CB/Storm Damage:
B-l (Median)
B-l (Mean)
$800,000
$1,705,200
CB/Dollars (Derived from CB/Auto Fatality and Auto/Cost of Living)
C-l & C-2
C-l & C-2
$800,000
$6,962,364
Auto/Cost of Living:
C-2 (Median)
C-2 (Mean)
$2,286,000
$8,184,000

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38
The most clearcut divergence from plausible patterns is the
mean value of life of $8, 184, 000 for the auto death\cost-of-
living trade-off. Whereas the mean CB/auto values were roughly
double the median, the mean auto/cost of living values were
almost four times the size of the median, indicating a much more
skewed distribution. As noted in the discussion of Table 8, this
mean value was influenced in part by individuals with implied
values of life as high as $80 million. These outliers suggest
that for some People making meaningful trade-offs involving small
cost-of-living differences and low risks of auto accident
fatalities is a task they cannot handle effectively.
The valuation of chronic morbidity across the difference
questionnaire approaches is quite similar for the case in which
we use a $2 million value of life figure to transform the death
equivalent statistics into meaningful dollar estimates. The
median value for the CB/auto death risk trade-offs is $640,000,
as compared with a median value of $457, 000 for the CB/cost of
living trade-off and a median value of $800,000 for the CB/storm
damage results. These results are similar to the $800,000 median
CB value that was obtained by chaining the CB/auto and auto/cost
of living responses. Even with a higher value of life of $3
million, the CB/auto median of $960, 000 is not out of line with
the CB/cost of living and CB/storm damage results.
Once we move to the case where a $5 million value of life is
used, the median dollar valuation of each CB case prevented is
greatly increased to the $1, 600, 000. if EPA were to rely on, for
example, the CB/cost of living results to value CB and then use a

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39
value of life of $5 million without also using an appropriately
adjusted CB value, this procedure could potentially understate
the value of the CB cases prevented by a factor of three. By
converting all outcomes to a health risk equivalence scale using
a death risk metric, EPA avoids any distortion in the mix of
targeted illnesses that might otherwise occur if the value of
life number selected was incorrect.
6. Conclusion
Although market evidence remains our most reliable guideline
for assessing the shape of individual preferences, such evidence
is unavailable for many outcomes that are either not traded
explicitly in markets or traded implicitly but in a market for
which available data are not rich enough to identify the
pertinent trade-off rates. Analysis of risk-risk and risk-dollar
trade-offs using various types of simulated market choices
provides a useful mechanism for establishing such values.
This study has developed a methodology for deriving
morbidity valuation estimates based on the trade-off with another
well-known risk, rather than forcing individuals to express
trade-off rates between morbidity rate reductions and dollars, a
task which is unfamiliar to most people. We presented several
conceptual reasons why consumers should be able to more
accurately convey risk-risk trade-offs than risk-dollar trade-
offs, and the application of our methodology to the valuation of
reductions in the risk of chronic bronchitis indicate that most
individuals can make risk-risk trade-offs, even with a disease as

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complicated and unfamiliar to healthy people as chronic
bronchitis.
Although for the purpose of cost-effectiveness analysis
there is no need to measure risk reduction value in terms of
dollars, when we translated our risk-risk estimates into risk-
dollar estimates using either survey results on auto accident
risk reduction values or published value-of-life estimates, the
distributions compared favorably, thus providing additional
confidence in the reasonableness of the results derived from our
methodology. While this study applied the approach to the
valuation of only two risks, that of chronic bronchitis and an
auto accident fatalities, the favorable results suggest that the
methodology may be more widely applicable to other morbidity
risks, such as various forms of cancer.

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41
Footnotes
¦'•See Viscusi (1986) for a review of the market trade-off
literature.
See analysis by Blomquist (1979) for an inventive use of
seatbelt usage data to infer a value of life.
3
Survey studies of various health and environmental risks
include the seminal work by Acton (1973) as well as more recent
studies often grouped under the designation "contingent
valuation. " These recent analyses include: Brookshire, Thayer,
Schulze, and d'Arge (1982) ; Cummings, Brookshire, and Schulze
(1986);	Fischhoff and Furby (1988); Gerking, de Haan, and Schulz
(1988); Smith and Desvousges (1987); Viscusi and Magat (1987);
Viscusi, Magat, and Forrest (1988); and Viscusi, Magat, and Hube
(1987)	; and Fisher, Chestnut, and Violette (1989) .
^ In designing our survey, we used software from Sawtooth
Software, Inc.
5
For an important recent study of the valuation of health
risks rather than mortality, see Berger et al. (1987) .
®For example, see Viscusi, Magat and Huber (1987), pages
477-478 .
7
See Petty (1985) for a discussion of the distinction
between chronic bronchitis, the related disease emphysema, and
the broader disease category called chronic obstructive pulmona
disease. The authors selected the type of chronic bronchitis
described in Table 1 after consulting closely with two lung
specialists at Duke University Medical Center and visiting the
Medical Center rehabilitation program for patients with severe
lung diseases.
Q
At the end of the interview, subjects were carefully
debriefed about this use of average rather than person-specific
risks.
9
Our past studies suggest that presenting the risk in terms,
of the number of cases for a large base population is more
comprehensible than giving risk levels such as 0.00075.
10See Arrow (1971).
i:LSee Viscusi and Magat (1987) and Viscusi, Magat, and Hube
(1987) .

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42
12
Problt analysis was used to identify personal
characteristics that explain the division of subjects between
those giving consistent and inconsistent responses. The only two
significant variables in the equation are AGE and SMOKER, with
older respondents less likely to give consistent responses and
smokers more likely to respond consistently. These results may
reflect the difficulty that older subjects have with the new
interview technology (computers) and the greater thought that
smokers have given to the implications of chronic bronchitis.

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43
References
Acton, Jan, Evaluating Programs to Save Lives: The Case of Heart
Attacks (Santa Monica: Rand Corp., 1973) .
Arrow, Kenneth J. F.ssavs in the Theory of Risk-Rearing (Chicago:
Markham, 1971) .
Berger, Marck C., Glenn C. Blomquist, Don Kenkel, and George S.
Tolley, "Valuing Changes in Health Risks: A Comparison of
Alternative Measures," Southern Economic Journal, Vol. 53
No. 4 (1987), pp. 967-984.
Blomquist, Glenn, "Value of Live Saving: Implications of
Consumption Activity, " Journal of Political Economy, Vol. 87
(1979), pp. 540-558.
Brookshire, David, Mark Thayer, William Schulze, and Ralph
d'Arge, "Valuing Public Goods: A Comparison of Survey and
Hedonic Approaches, " American Economic Review, Vol. 72
(1982), pp. 165-177.
Cummings, Ronald, David Brookshire, and William Schulze, Valuing
Environmental	Goods :		Assessment	of	£il£	Conti nent
Valuation Method (Totowa, N.J.: Rowman and Allanheld,
1986) .
Fischhoff, Baruch, and Lita Furby, "Measuring Values: A
Conceptual Framework for Interpreting Transactions with
Special Reference to Contingent Valuation of Visibility,"
Journal of Risk and Uncertainty, Vol. 1, No. 2 (1988), in
press.

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Fisher, Ann, Lauraine Chestnut, and Daniel Violette, "The Value
of Reducing Risks of Death: A Note on New Evidence,"
Journal of Policy Analysis and Management. Vol. 8, No.
1 (1989), pp. 88-100.
Gerking, Shelby, Menno de Haan, and William Schulze, "The
Marginal Value of Job Safety: A Contingent Valuation Study,"
Journal of Risk and Uncertainty, Vol. 1, No. 2 (1988), in
press.
Moore, Michael, and W. Kip Viscusi, "Doubling the Estimated Value
of Life: The Implications of New Occupational Fatality
Data," Journal of Policy Analysis and Management. Vol. 7,
NO. 3 (1988), pp. 476-490.
	, and 	( "The Quantity-Adjusted Value
of Life," Economic Inquiry. vol. XXVI, No. 3 (1988), pp.
369-380.
Petty, Thomas L., Chronic Obstructive Pulmonary Pi sease (New A
York: Marcel Dekker, 1985).
Smith, V. Kerry, and William Desvousges, "An Empirical Analysis
of the Economic Value of Risk Changes,tt Journal of Political
Economy. Vol. 95 (1987), pp. 89-114.
Viscusi, W. Kip. Risk bv Choice: Regulating Health and Safety in
the Workplace (Cambridge: Harvard University Press. 19831,
	, "The Valuation of Risks to Life and Health:
Guidelines for Policy Analysis," in Bentkover, et. al. ,
Benefit Assessment: The State of the Art (Dordrecht,
Holland: Reidel Publishers, 1986), pp. 193-210.

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45
Viscusi, W. Kip and Wesley A. Magat, Learning about Risk:
Consumer and Worker Responses to Hazard Information
(Cambridge: Harvard University Press, 1987).
	f Wesley A. Magat and Anne Forrest, "Altruistic
and Private Valuations of Risk Reduction," Journal of Policy
Anal vsi s	and	Management. Vol. 7, No. 2 (1988), pp. 227-245.
, and Joel Huber, "An
	 I 	 '	'
Investigation of the Rationality of Consumer Valuations °f
Multiple Health Risks, " Rand Journal of Economics", Vol. 18,
No. 4 (1987), pp. 465-479.

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THE SOCIAL COSTS OF CHRONIC HEART
AND LUNG DISEASE
by
Maureen L Cropper
University of Maryland
and
Alan J. Krupnick
Resources for the Future

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THE SOCIAL COSTS OF CHRONIC HEART AND LUNG DISEASE
Maureen L. Cropper and Alan J. Krupnick
University of Maryland and Resources for the Future
INTRODUCTION
To value a program that reduces the probability of contracting a
chronic disease, one would like to know what a person who does not have the
disease would be willing to pay to reduce his probability of getting it.
The sum across individuals of these willingnesses to pay, plus the expected
costs of the disease that are not borne by these individuals, comprise the
theoretically correct measure of social benefits from reducing incidence of
the disease.
In this paper we measure the medical costs and lost productivity
associated with various chronic heart and lung diseases. Our justification
for focusing on these components of the social cost of illness is that
medical costs and lost earnings are often not borne by individuals
themselves and, hence, are unlikely to be reflected in willingness to pay
figures. Therefore, they must be added to willingness to pay estimates to
compute the total benefits of reducing the incidence of a disease.
Effects on Earnings
Our estimates of the effects of chronic illness on labor force
participation and on earnings differ in two respects from those available
in the literature (Bartel and Taubman, 1979; Salkever, 1985). First, our
dataset—the Social Security Survey of Disabled and Non-Disabled Adults-
-allows us to distinguish the effects of individual diseases (e.g.,
emphysema, chronic bronchitis) rather than disease categories (chronic
respiratory illness). As one might expect, there is significant
variation in the effects of individual diseases within broader categories:
Emphysema, for example, has a large negative effect on earnings whereas
chronic bronchitis does not. Hypertension has no significant effects on
1. The diseases studied are: allergies, asthma, chronic bronchitis,
emphysema, other chronic lung disease, arteriosclerosis, heart attack,
hypertension, other chronic heart disease and stroke.

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2
probability of participation or on earnings, whereas a heart attack
occurring between 45 and 54 reduces both.
Second, we examine how the effect of each disease varies with age of
onset and duration. It is generally believed (Bartel and Taubman, 1979)
that, other things equal, a person is more likely to participate in the
labor force at any age the earlier in life he contracts a chronic disease.
The argument is that the benefits of making adjustments to the disease
(retraining, changing occupations) are larger the earlier in life the
disease begins. Thus, the earlier the age of onset the more likely it is
that adjustments will be made. It is not, however, clear that the human
capital argument applies to the diseases examined here, most of which are
contracted later in life. Since one seldom witnesses changes in occupation
after age 45 it is unlikely that small variations in age of onset matter
after this age. Indeed, age of onset may have a positive effect on
participation if a disease is more serious when contracted at an earlier
age.
It is also of interest to see how the duration of a disease alters
labor market behavior. For two persons who contracted emphysema at age 45,
are effects on earnings greater for a person currently 50 or for a person
currently 60? Holding age of onset constant, this is equivalent to asking
whether the disease has a greater effect on participation and earnings when
one has had the disease for five years or for fifteen years. One might
hypothesize that the longer one has had a disease the longer he has had to
adjust to it; hence, labor market effects should diminish with duration.
On the other hand, for progressive diseases, e.g., emphysema, the longer
one has had the disease the more serious it is likely to be.
We find that the tendency of chronic disease to reduce labor force
participation and earnings does not increase with age of onset. Indeed,
for emphysema, heart attack, arteriosclerosis and stroke, an age of onset
between 45 and 54 significantly reduces the probability of working at all
future ages, but an age of onset between 55 and 65 does not. It might seem
that this result occurs because people who contract a disease earlier will,
on average, have had it for a longer time than persons who contracted it

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3
later in life. For emphysema this appears to be true. When duration is
held constant, it is having the disease for 6 or more years that affects
labor market behavior rather than contracting it at age 45. For heart
attack, arteriosclerosis and stroke, however, the duration of the disease,
holding age of onset constant, has no effect on participation.
Medical Costs
Our estimates of medical costs, which come from the National Medical
Care Expenditure Survey (NMCES), have two advantages over existing
estimates of medical expenditures (National Heart, Lung and Blood
Institute, 1982; Hartunian et al., 1981). The National Heart, Lung and
Blood Institute allocates aggregate costs, such as hospital costs and
doctor costs to diseases based solely on a disease's proportion of total
activities, e.g., hospital days and total doctor visits, respectively.
This approach has two shortcomings: (1) it assumes that the average cost
of, say, a hospital day or doctor's visit is the same for all diseases, and
(2) it does not allow one to examine the distribution of medical costs per
person. An alternative "engineering" approach is to multiply the number of
hospital days or doctor visits attributable to a condition by the typical
price for a hospital day or typical price for a doctor visit for that
condition (see e.g., Freeman (1976)). This approach circumvents the first
objection raised above but not the second.
By using individual data on medical costs, collected over a one-year
period for over 40,000 persons, we are able to examine the distribution of
medical costs per person by disease. Our most interesting results pertain
to the size distribution of medical costs. For the five diseases whose
medical costs we study—bronchitis, emphysema, hypertension, ischemic heart
disease and non-specific heart disease—the distribution of annual costs
per person is highly skewed. For emphysema, ischemic heart disease and
non-specific heart disease median expenditures are less than one-tenth of
mean expenditures. For bronchitis and hypertension median expenditures are
about one-fourth of mean expenditures.
Because NMCES contains information on source of payment, it is also
possible to see to what extent individuals and their families bear the

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4
medical costs of these diseases. For emphysema, ischemic heart disease and
non-specific heart disease only about 10% of aggregate medical costs are
borne by patients' families. The percentages are somewhat higher for
bronchitis (34%) and hypertension (23%). The percent of cost borne by the
patient's family differs, however, by size of cost. As noted above, the
majority of persons with the diseases studied here incur small annual
medical expenses. Averaging across individuals, the fraction of medical
costs paid for by one's family is 2/3 for hypertension and bronchitis and
half for emphysema, ischemic heart disease and non-specific heart disease.
This implies that, on average, individuals (or their families) pay a higher
fraction of small medical expenditures than of large ones.
THE EFFECT OF CHRONIC ILLNESS ON LABOR FORCE PARTICIPATION AND EARNINGS
The Model
In modelling the effects of various diseases on earnings it is
standard practice (Bartel and Taubman, 1979; Mitchell and Butler, 1986) to
distinguish the effects of each disease on participation from its effects
on earnings given that one participates. Debilitating diseases such as
emphysema and stroke may force a person to drop out of the labor force
because he is physically unable to work, or may reduce earnings to the
point where they fall below the reservation wage. If a person continues
working he may curtail hours (if free to do so) or suffer a drop in pay
because he changes jobs or because his productivity falls. This implies a
drop in earnings, conditional on working.
The decision to participate, and earnings, conditional on
participation, constitute a two-equation system. The individual
participates if the decision function, 1^, is non-zero. Earnings, Y^f
are observed only if the individual participates.
1^ - - et	Participation decision	(1)
Participate if 1^ > 0,
m	Earnings in labor market	(2)

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5
Yt observed if I > 0
Y not observed if It < 0.
Equation (1) can be viewed as a reduced-form equation that results
from comparing the utility received from income and leisure, conditional on
working, with the utility received from income and leisure given that the
individual does not work. If income and leisure in each state are replaced
by their exogenous determinants, one obtains equation (1).2
Because earnings in (2) are observed only for working persons,
estimation of (2) involves a classic selectivity problem: persons for whom
earnings data are available are in the lower tail of the error distribution
in equation (1). As long as the errors in equations (1) and (2) are
correlated, applying least squares to (2) results in inconsistent parameter
estimates since E(ut|Zt« > et) * 0.
To obtain consistent estimates of this system we follow the two-stage
approach outlined by Lee (1983) [see also Maddala (1983)]. We assume that
the error term in the participation equation has a logistic distribution
F(et) - l/[l+exp(-ZtS)], and estimate a logit model of labor force
participation. The error term	can be transformed to an error term
e* with a standard normal distribution,
e* - J(et) - ~"1(P(et)),
-1
where ~ is the inverse of the standard normal distribution function.
Assuming that e* and u are bivariate normally distributed with
2
correlation coefficient p and V(u^) ¦ a , expected earnings are a linear
function of X plus a term that represents the density of e*
conditional on working,
E(Xt0+ ut|et 
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6
Applying OLS to (3) yields consistent estimates of the parameters fi and
3
op.
The Data
The Sample. The data used to estimate our model come from the 1978
Social Security Survey of Disability and Work (U.S. Department of Health
and Human Services, Social Security Administration, 1981). The survey,
which was designed to examine issues relating to eligibility for disability
benefits and the effects of disabilities on labor force participation,
consists of two samples, a stratified random sample of 6,853 persons from
the 1976 Health Interview Survey, and a sample of 4,886 persons from the
population of recipients of Social Security Disability Insurance who were
declared eligible for benefits no earlier than 5 years before the survey.
Our sample consists of 2,218 men between the ages of 18 and 65 from the
4
Health Interview Survey portion of the Social Security Survey.
Earnings Equation. To avoid transitory fluctuations during the survey
week, earnings are measured as wages and salaries received from all jobs
during 1977. (All earnings are measured in 1977 dollars.) The independent
variables entering the earnings equation X , are listed in Table 1.
Earnings are assumed to depend on education (measured by a series of dummy
variables), experience (proxied by a series of age dummies), experience
squared, marital status, family size, race, locational dummies and the
health variables described below and in Table 2.
Labor Force Participation Equation. As with earnings, participation
is defined based on behavior throughout the 1977 calendar year. An
individual is considered to have been in the labor force if he worked 30 or
more weeks during the 1977. Men who did not work at all during 1977 are
classified as not participating in the labor force. Men working between
3.	The two-stage estimation procedure, including	asymptotic standard
errors (Maddala, 1983), was programmed by the	authors using the SAS
matrix language.
4.	There are a total of 2,626 men between 18 and	65 in the HIS portion of
the Social Security survey. 408 of them were	eliminated because they
appeared to change labor force status during 1977, the year for which
participation and earnings were measured.

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7
one and 29 weeks were eliminated from the sample on the grounds that these
persons were either students or changed labor force status.
Since the decision to participate in the labor force is made by
comparing the utility of income and leisure when in the labor force with
income and leisure when out of the labor force, the variables in Z^
should include all those entering the earnings equation, plus variables
that would affect income conditional on not participating, and variables
that would affect the utility of leisure time. The only such variables
available in the survey that are not included in are (1) whether the
individual is aware of Social Security disability benefits and (2) whether
the individual is a veteran, both of which might affect income received if
the individual did not participate. A third variable included in Z^ to
capture motives for working is the size of the respondent's debt.
Health Variables. The survey contains two types of information about
chronic illness. Respondents were asked whether they had ever been
diagnosed by a doctor as having any one of the 35 chronic diseases listed
in Table 2, as well as when the disease first began to bother them (age of
onset) . They were also asked whether they were functionally limited by any
of the diseases. Functional limitation questions include whether the
respondent had difficulty walking, climbing stairs, lifting heavy objects,
etc. Respondents were also asked whether they experienced symptoms such as
pain, fatigue, swelling and shortness of breath.
In both the earnings and participation equations the severity of
chronic disease is measured by dummy variables that indicate the presence
of a chronic condition. Pleasures of functional limitation, while possibly
useful as indicators of the severity of disease, are not associated with
specific diseases and, hence, cannot be used to measure the severity of
individual diseases.^
5. In addition to collecting these measures of functional limitation, the
survey also asks respondents if they "have a disability that limits the
type or amount of work [they] can do?" This variable, which is
included in addition to the chronic disease dummies in Mitchell and
Butler's (1986) analysis of the labor market effects of arthritis, was
excluded from our analysis for two reasons. First, the answer to this
question is not an exogenous measure of health but reflects the
Footnote 5 continued on next page

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8
In measuring the effect of particular diseases on participation and on
earnings we would like to distinguish effects by age of onset and by
duration of the disease. The extent to which this is possible depends on
the disease studied. Table 3 gives the distribution of age of onset for
persons in our sample for each of the 10 respiratory and circulatory
diseases studied. In our sample few cases of emphysema, arteriosclerosis,
or stroke occur before age 45. For this reason these diseases are
represented by only two age of onset dummies indicating that the disease
was contracted between the ages of 45 and 54 or between the ages of 55 and
65.
Chronic bronchitis and other chronic lung disease occur earlier in
life than emphysema; however, the small numbers of persons in our sample
with these conditions restrict us to only two age of onset categories for"
each disease: before age 45 and after age 45. Allergies, asthma, heart
attack, hypertension, and other chronic heart disease occur frequently
enough and early enough in life that we can distinguish between 3 and 5 age
of onset categories for each disease, as indicated in Table 2.
We have attempted to distinguish between duration of disease and age
of onset only for those diseases that appeared to have a significant effect
6
on labor force participation when age of onset alone was measured. These
included emphysema, arteriosclerosis, heart attack, stroke and other heart
disease. Each disease was significant only when age of onset was 45 or
older. The fact that these diseases occur later in life, together with a
maximum sample age of 65, means that we can distinguish only two duration
categories: persons who have had the disease 0-5 years and persons who have
had the disease 5-10 years.^
Footnote 5 continued from previous page
decision to stop/continue working. Second, the variable may capture
effects of multiple diseases that we wish to capture using disease-
specific dummies.
6.	Throughout the paper "statistically significant" means significant at
the 5% level, one-tailed test.
7.	Chronic bronchitis beginning between ages 25 and 44 significantly
decreased the probability of labor force participation; however, there
were too few persons who had had chronic bronchitis for more than 10
years to permit using additional duration dummies for this disease.

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9
Results
Labor Force Participation. The more serious respiratory and
circulatory diseases examined—chronic bronchitis and emphysema;
arteriosclerosis, heart attack, stroke and other heart disease-
-significantly reduce the probability that a man participates in the labor
force, other things equal. Table 4 presents coefficients obtained from the
logistic participation equation for the respiratory and circulatory disease
variables listed in Table 2. [The coefficients of other variables in the
participation equation appear in the appendix to this paper.] The table
indicates that the less serious diseases—allergies, asthma, other chronic
lung disease and hypertension—have no significant effects on
participation. To calculate the effect of each disease on probability of
participation its coefficient must be multiplied by P(l-P), where P is
the probability of participation. Since P = 0.670 for our sample, the
coefficients in Table 4 imply that contracting emphysema between ages 45
and 54 reduces the probability of participating in the labor force by an
average of 23.3 percentage points. Arteriosclerosis reduces probability
of participation by 15.6 percent, while having a stroke between 45 and 54
reduces subsequent probability of participation by 57.3 percent.
What is somewhat surprising is the effect of age of onset on
participation. For emphysema, arteriosclerosis, heart attack and stroke,
an age of onset between 45 and 54 significantly reduces probability of
working at all future ages, but an age of onset between 55 and 65 does not.
Such a result runs counter to the standard argument that, the earlier the
onset of a disability, the more likely it is that the individual will
adjust to it by retraining and/or switching jobs. One reason that the
standard argument may not apply is that, for the diseases studied here, a
diagnosis at age 45 may indicate a more severe case of the disease than a
diagnosis at age 60 (a heart attack at age 45 is often more devastating
than a heart attack at age 60).
A second possibility is that for progressive diseases such as
emphysema and arteriosclerosis, persons who contract the disease earlier
will, on average, have had it for a longer time than persons who contract
it later in life. To the extent that severity increases with the duration

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10
of the disease, persons who have had the disease longer will be less likely
to work. The results in Table 4 may thus be due to the fact that age of
onset is directly correlated with the number of years the individual has
been bothered by the disease.
To test this hypothesis the age of onset categories in Table 2 were
subdivided to distinguish duration of disease from age of onset. Persons
with an age of onset between 45 and 54 were divided into two categories:
those who had had the disease for 0-5 years and those who had had the
disease for 6-10 years. For persons with an age of onset between 55 and 65
9
only the 0-5 year duration category was used.
The estimated coefficients of the age of onset/duration dummy
variables appear in Table 5. These coefficients suggest that controlling
for duration alters the effect of age of onset only in the case of
emphysema. For emphysema, when duration is held constant at 0-5 years, age
of onset has no effect on participation. Having the disease for 6-10
years, however, significantly reduces the probability of participation. In
the case of arteriosclerosis, heart attack and stroke, however, the main
effect on labor force participation is caused by age of onset, with onset
between 45 and 54 making participation less likely, and onset between 55
and 65 having no significant effect. These results suggest that the effect
of age of onset and duration are, in general, disease-specific.
Earnings. The results for our earnings equations suggest that, for
the respiratory and coronary diseases studied here, most labor market
effects occur through reductions in participation rather than reductions in
earnings. Table 6 presents coefficients of the disease dummies in an
earnings equation in which diseases are distinguished by age of onset and,
8.	One could, of course, argue that persons with very severe cases of the
disease die soon after diagnosis; hence duration may not measure
severity.
9.	Persons with an age of onset between 55 and 65 with duration greater
than 5 years thus had a value of zero for all health dummies, as did
persons without the disease.

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11
in the case of emphysema, by duration. The only respiratory and
circulatory diseases studied that significantly reduce earnings are
emphysema and heart attack. Having emphysema for 6-10 years reduces
earnings by 65%. Having a heart attack between the ages of 45 and 54
reduces earnings by 45%.
The Magnitude of Expected Earnings Losses. The expected loss in
earnings to a person who contracts a chronic disease is the sum of the
effects of the disease on probability of participation, and on earnings,
given that one participates. Specifically, the expected loss in earnings
is the sum of the change in probability of participation times pre-illness
earnings, plus the reduction in earnings caused by the disease times the
post-illness participation rate,
Expected Loss in Earnings * AP(EarningSQ) + P^( AEarnings).	(4)
This loss begins at age of onset and continues until the age that
retirement would occur in the absence of the disease.
Tables 7 and 8 present estimates of the first term in (4), expected
earnings losses due to non-participation. The effect of each disease on
probability of participation, AP, is determined by multiplying the
coefficient of the disease in the participation equation, 6^, by P(l-P),
where P is the probability of being in the labor force. Table 7 presents
estimates of fiP, the fraction by which pre-illness earnings are reduced due
to non-participation. In the tablet P is estimated at each age from
Bureau of Labor Statistics data on labor force participation rates (U.S.
Department of Labor, Bureau of Labor Statistics, 1988) . In Table 8 AP
has been multiplied by average 1987 earnings of all male workers to produce
annual earnings losses, by age, due to non-participation.
In both tables earnings losses due to increased probability of not
working peak between 55 and 65, because P(l-P) is maximized in this
10. Because fewer chronically ill people appear in the earnings equation
than in the participation equation it was necessary to eliminate
certain age of onset categories from the earnings equations.

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12
interval. The maximum annual expected reduction in earnings ranges from
15.5% for heart attacks to 57.1% for strokes. Bronchitis and emphysema
each reduce expected earnings (through effects on participation) by at most
25%.
For emphysema, arteriosclerosis, stroke and other heart disease
earnings losses due to reduced probability of participation constitute the
total change in expected earnings. For emphysema and heart attack the
second term in equation (4) must be computed. This term, in $1977, appears
in Table 8 together with expected earnings losses due to non-participation.
Comparison with Previous Work. The only study of the labor market
effects of chronic respiratory and circulatory diseases of which we are
aware is Bartel and Taubman (1979). Using data from the NAS Twins Panel,
Bartel and Taubman examine the effects of each of several disease groups on
labor force participation and on earnings, conditional on participation.
Unfortunately the diseases groupings used by Bartel and Taubman do not
correspond exactly to the diseases used in our study. They combine
bronchitis, emphysema and asthma into a single disease category (BRON) , and
heart disease and hypertension into another category (HH). The effect of
each disease category, is examined for various ages of onset; however,
emphasis is placed on diagnoses that occurred between 1962-67, when
respondents were in their early forties. Because emphysema,
arteriosclerosis and stroke are rare at this age, it is unlikely that BRON
and HE capture these more severe diseases.
When they examine the effects of a diagnosis at age 40 on
participation at age 50 Bartel and Taubman do not find any significant
effects of respiratory or circulatory diseases on labor force
participation. This is in sharp contrast to the results presented in Table
7, which indicate that chronic bronchitis, emphysema, arteriosclerosis,
heart attack, stroke, and other heart disease reduce the probability of
labor force participation between 6 and 57 percentage points. The
difference in findings may be due in part to the relatively young age of
their sample. The disease variable used in the participation equation
represents the effects on participation at (mean) age 50 of a diagnosis

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13
that occurred at (mean) age 40. For the diseases we study the most
significant effects on participation correspond to an average age of onset
of 50.
Regarding effects on earnings, Bartel and Taubman find that a
diagnosis of respiratory illness (BRON) at age 40 reduces earnings by 25%
at age 50 and that heart disease/hypertension (HH) , diagnosed at age 40,
reduces earnings by 8.5% at age 50. By contrast, we find that having
emphysema for at least 6 years reduces earnings by an average of 65% for
persons who continue working. The corresponding reduction in earnings due
to having a heart attack between 45 and 54 is 45%. We thus find greater
effects on earnings than do Bartel and Taubman, but for more narrowly
defined diseases. The difference between our results and theirs reflects
the fact that their disease categories include less severe diseases, such
as bronchitis and hypertension, as well as more debilitating ones.
MEDICAL EXPENDITURES AND SERVICES UTILIZATION
The medical costs of a chronic disease to society are the costs of the
detection, treatment, and rehabilitation of the disease, as well as a
portion of research, training, and facilities costs. In this section we
present measures of medical expenditures for individuals for five target
diseases: hypertension, ischemic heart disease, non-specific heart disease,
chronic bronchitis, and emphysema. These measures were computed from self-
provided cost of treatment data for persons in the 1977-78 National Medical
Care Expenditure Survey (National Center for Health Services Research,
1981) .
There are three reasons why our measures of medical expenditures do not
measure the true social costs of medical treatment. First, medical
expenditures are computed using market prices, which may not reflect
marginal productivities due to the absence of competition in the market for
medical services. Second, because the data are specific to individuals
with chronic diseases, the costs of detection are not included. In
addition, because medical care providers are a minor source of research and
medical training, these cost components are likely to be greatly
underestimated (if included in overhead charges) or ignored completely.

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The National Medical Care Expenditure Survey
To estimate the medical costs of chronic respiratory and heart disease
we used the 1977-78 National Medical Care Expenditure Survey (NMCES).
NMCES presents data on health care utilization and expenditures for
approximately a one year period for 14,000 households (40,320 persons)
selected randomly from the civilian noninstitutionalized U.S. population.
Each of these households was provided with a calendar diary for recording
their use and cost of medical services. Each was interviewed six times
over this period, with responses in prior periods provided to the household
for verification.
Each time a person in the NMCES suffered an activity limitation,
disability day, visited or called a doctor, vent to the hospital or
purchased medication a record was created for an illness episode.
Information on the number and cost of illness episodes and on the cause of
each illness episode comes from the household survey. Medical costs are
thus self-reported costs. ^ The diseases associated with each illness
episode were reported by households, and translated into ICDA codes by
interviewers.
The five respiratory and circulatory diseases we examine, their ICDA
codes, and the number of persons reporting episodes involving each
condition appear in Table 9.
Allocation of Medical Costs Among Multiple Conditions
To calculate the costs associated with a target condition one must add
the costs associated with the condition across all illness episodes. This
would pose no problem if all episodes of illness were associated with only
a single disease. If, however, an illness episode is associated with more
11. To check on the accuracy of these costs, the household survey was
supplemented by a survey of physicians and facilities that provided
medical care to persons in the household sample period and by a survey
of employers and insurance companies responsible for the health
insurance coverage of responding households. A close correspondence
was found between reported and actual costs.

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15
than one condition, the cost of the episode must be allocated among
conditions.
Table 10 indicates the extent of the joint cost allocation problem.
The table indicates that of the 3,479 persons with at least one episode of
hypertension, 71% (2,476) had episodes that involved hypertension alone.
[In the language of NMCES an episode involving only a single condition is a
"simple" episode.] For these persons the problem of cost attribution does
not arise. Thirteen percent of persons (426 persons) with hypertension
episodes have "related to" episodes—episodes that involve hypertension and
some other condition. In these cases the respondent attempted to allocate
costs among the related conditions; however, in cases where no attribution
was possible, for example, the case of hospital room charges, the costs
were duplicated for each condition. "Same as" episodes, involving 7% of
all persons with hypertension, mean that the individual attributed the
episode to hypertension and a condition that was the "same as"
hypertension—although it was assigned a different ICDA code. In this case
no allocation of costs among the multiple conditions is possible; instead,
the total costs of the episode are associated with each condition. "Same
as " episodes thus lead to double counting of medical costs, and "related
to" episodes may involve some double counting.
The number of persons with "multiple episodes" are found by subtracting
those with 'single episodes from the total (e.g., for hypertension, 314
persons had multiple episodes). In general, persons with more than one
episode involving the same disease have other than "simple" episodes that
may involve double-counting problems.
Results
Magnitude of Expenses, by Disease. Table 11 shows the frequency
distribution of annual medical expenses for each of our target diseases, as
well as mean and median expenses. [All figures are in 1977 dollars. ] As
one would expect, the highest average expenditures are associated with
ischemic heart disease ($1256) and non-specific heart disease ($1041).
Emphysema is associated with a mean expenditures of $633. The average

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16
annual costs of hypertension and bronchitis are considerably less: $216 and
$97, respectively.
In each case the distribution of annual expenses is highly skewed:
median expenses are one-quarter of mean expenses for bronchitis and
hypertension and approximately one-tenth of mean expenditures for
emphysema, ischemic heart disease and non-specific heart disease. For all
diseases but ischemic heart disease at least half of all persons have
annual expenditures of $75 or less. [For ischemic heart disease 41% of all
persons have annual expenditures of $75 or less.]
Categories of Expenses. Table 12 shows how expenditures are
distributed across categories for each disease. NMCES allocates expenses
to three major categories: medical contacts (primarily doctor visits),
hospital expenses, and drugs. There are several minor categories that are
omitted from the table.
As would be expected, hospital expenses are the largest category of
expenses for all conditions, even when people with no hospital expenses are
included in the averaging computation. The maximum hospital expenses per
person exceed $20,000 for the heart diseases and are in the $10,000 range
for the other target diseases. Expenses on medical contacts are the next
largest category of expenses for all conditions.
Comparison With Other Studies. The NHLBI (1982) estimates annual
expenditures on chronic bronchitis and emphysema using the "top-down"
approach described above while Freeman et al. (1976) use an engineering
approach with aggregate data to estimate annual expenditures on emphysema.
Table 13 provides the NHLBI and Freeman estimates of total and per person
expenditures adjusted to 1977 dollars using the medical price index.
The NHLBI estimates of expenses per case, at $118 and $102 for chronic
bronchitis and emphysema, respectively, contrast sharply with ours, at $97
and $633. Nevertheless, because of the top-down nature of the NHLBI
approach, their estimates may differ from ours if different estimates of
disease prevalence are being used. In fact, the NHLBI prevalence estimates

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17
for these diseases (which are taken from the Health Interview Survey (HIS))
are 3.5 and 1.0 percent of the civilian, noninstitutionalized population of
the U.S. in 1979 (216 million people) for chronic bronchitis and emphysema,
respectively. Our estimates of prevalence, which are conditional on the
occurrence of some medical event (i.e., a restricted activity day, some
cost incurred, or some service used (including a phone call to the
doctor)), are far lower — 1.1 and 0.5 percent for chronic bronchitis and
emphysema, respectively, for 1977.
The underestimate of prevalence implied by this conditionality implies
that our sample would under-represent, relative to the NHLBI, people with
zero medical costs. This implies, in turn, that the NHLBI estimate of
expense per case should be lower than ours. Instead, the NHLBI estimate
for chronic bronchitis, the disease for which the highest proportion of
sufferers in our sample has zero costs, actually exceeds our estimate.
Freeman et al, using data on health care utilization and average prices
for 1970, estimate expenses on emphysema in 1977 dollars of $233.5 per case
annually. These estimates are over double those of the NHLBI but still are
far lower than ours.
Sources of Payment. NMCES provides information on five sources of
funding for medical expenses: family, medicaid, medicare, personal
insurance, and other. In addition to being of intrinsic interest,
information about sources of funding suggests the extent to which medical
costs are likely to be internalized in willingnesses to pay to avoid
disease. In theory, willingness to pay should take into account the
medical costs of the condition paid for by the family, but not those costs
borne by others. Thus, the portion of expenses paid by others should be
added to the bid as part of the social cost of each of the target
conditions.
Table 14 identifies these funding sources by condition for males 20
years of age and older, the group to which our labor market analysis
applies. For each disease the second row of the table gives the percent of
total costs paid for by each source. Even for hypertension and bronchitis,

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18
the least serious diseases studied, families pay a minority of total costs,
23% and 34%, respectively. For emphysema and the heart diseases families
pay less than 15% of total costs. What are the most important sources of
funding? Personal insurance is the most important source of funding for
ischemic heart disease (46 percent), reflecting the high proportion of
expenses for the hospitalization component and the high degree of coverage
afforded this type of expense by health insurance plans. The insurance
share for emphysema is large (28 percent) for much the same reason.
Coverage for non-specific heart disease, the condition with the least
family funding, is not dominated by insurance. Rather, because the
population with this condition tends to be older than that for ischemic
heart disease, the largest funding share comes from medicare (36 percent).
Finally, it is curious that medicaid funds less than one percent of
expenses for ischemic heart disease while funding from 7 to 17 percent of
the expenses for the other target conditions.
Although a minority of total medical costs are paid for directly by
patients and their families family funding is the q most important source of
payment for a majority of patients. This is because most patients incur
small expenses (see Table 11) and families bear a larger percent of small
expenses than of large expenses. For each disease the third row of Table
14 computes for each individual the percentages of funding received from
various sources and then averages these percentages across individuals for
each source. As can be seen, the average percentages for the family source
(in brackets) are much higher than the aggregate percentages for the family
source (in parentheses), the former ranging from 52 to 70 percent, while
the latter ranges from 13 to 36 percent. This difference implies that
relatively large numbers of people have episodes with small expenses that
they pay for themselves. This may reflect deductibility clauses, the
exclusion of drugs from coverage for some policies, or other factors.
Age Distribution of Expenses. To permit comparison of the labor
market effects of chronic respiratory and circulatory diseases with medical
costs, Table 15 presents average medical costs for males, by age. Mean
annual expenses appear generally to increase with age, up to the A60's or

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19
70's for bronchitis, emphysema and hypertension. Expenses for those with
heart disease (heart attacks), however, peak in the MO's.
A comparison of average medical expenses with the labor market effects
of each chronic disease (see Table 8) suggests that the labor market costs
of chronic respiratory and circulatory diseases are generally greater than
the medical costs. Exceptions to this result are hypertension, which has
no effect on labor force participation or on earnings, and heart disease
before the age of 45, which also appears to have no significant labor
market effects.

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20
Table 1. Non-health Variables Entering Earnings and Participation
Equations

Mean
Standard
deviation
Maximum
Minimum
Earnings, 1977*
14,362.
77045.
50000.
0
In labor force, 1977
0.670

1
0
Married3,
No. in household3
No. children < 5
No. children 5-18®
No. children > 18
0.718
3.294
0.190
0.670
0.184
0.45
1.732
0.512
1.174
0.482
1
15
5
8
3
0
1
0
0
0
Age dummies:
18-24
35-44
45-54
55-65
0.141
0.174
0.222
0.261
0.348
0.379
0.416
0.440
1
1
1
1
0
0
0
0
Highest educ. level:
Elementary school
High school
College
0.193
0.487
0.229
0.394
0.500
0.421
1
1
1
0
0
0
Non-white
0.124
0.330
1
0
Regional dummies3:
Northcentral
South
West
0.265
0.335
0.178
0.441
0.472
0.383
1
1
1
0
0
0
Lives in7Urban Area3
(Age-16)
0.679
888.25
0.467
730.23
1
2401
0
4
Veteran
0.452
0.498

0
Aware of disability
benefits
0.407
0.491
1
0
Debt3
2116.9
8858.00
200800 •
0.
~Average based on 1486 persons in labor force
Measured as of interview date

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21
Table 2. Health Variables in Earnings and	Participation Equations
Each of the following variables assume	a value of 1 if the respondent
contracted the disease at the age indicated	and a value of 0 otherwise:
RESPIRATORY AND CIRCULATORY DISEASES
Age of Onset Categories (Sample Size)
Allergies
0-17
(35)
18-34
(37)
35-65
(18)
Asthma
0-17
(40)
18-34
(14)
35-65
(19)
Chronic Bronchitis
25-44
(18)
45-65
(21)


Emphysema
45-54
(49)
55-65
(23)


Other Chronic Lung Dis.
18-44
(17)
45-65
(26)


Arteriosclerosis
45-54
(55)
55-65
(24)


Heart Attack
25-44
(28)
45-54
(57)
55-65
(42)
Hypertension
25-34
(57)
35-44
(79)
45-54
(148
Other Chronic Heart Disease
0-34
(23)
35-44
(34)
45-54
(51)
Stroke
45-54
(17)
55-65
(20)


55-65 (66)
55-65 (22)
OTHER CHRONIC DISEASES
Sample Size
Arthritis or rheumatism
Other trouble with back or spine
Deformity of foot, leg, arm, hand
Nervous or emotional problems
Deformity of back or spine
Deafness
Stomach ulcer
Diabetes
Hernia or rupture
Difficulty reading (with glasses)
Kidney stones or kidney trouble
Other chronic stomach trouble
Tumor, cyst or growth
Hissing arms, hands or fingers
Gallbladder or liver trouble
Paralysis
Alcohol or drug problems
Cancer
Epileptic seizures
Mental illness
Blindness
Thyroid trouble or goiter
Hissing legs or feet
Tuberculosis
Multiple sclerosis
367
296
228
209
154
133
130
113
92
86
76
64
52
46
40
35
25
24
24
20
19
18
14

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22
Table 3. Distribution of Respiratory and Circulatory Diseases by Age of
Onset
Number of persons in sample with
age of onset
0-17 18-24 25-34 35-44 45-54 55-65
Allergies
35
18
19
10
4
4
Asthma
40
5
9
7
9
3
Chronic Bronchitis
15
2
13
5
15
6
Emphysema
0
1
4
3
49
23
Other Chronic Lung Diseases
1
4
7
6
20
6
Arteriosclerosis
0
0
7
11
55
24
Heart Attack
2
0
5
23
57
42
Hypertension
12
23
57
79
148
66
Other Chronic Heart Disease
18
5
10
34
51
22
Stroke
1
0
2
2
17
20

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23
Table 4. Effects of Chronic Diseases on Labor Force Participation
by Age of Onset
Age of
onset
Coefficient
t-Ratio
Asthma
0-17
18-34
35-65
00093
0.625
0.093
0.22
0.75
0.16
Allergies
0-17
18-34
35-65
-0.061
0.505
-0.565
0.13
0.95
0.91
Chronic Bronchitis
25-44
45-65
-1.229
-0.816
1.69
1.17
Emphysema
45-54
55-65
-1.053
-0.683
2.55
1.21
Other Chronic Lung Disease
18-44
45-65
-0.218
-0.528
0.29
0.95
Arteriosclerosis
45-54
55-65
-0.707
0.134
1.72
0.26
Hypertension
25-34
35-44
45-54
55-65
-0.435
-0.131
0.189
-0.112
1.16
0.38
0.78
0.34
Heart Attack
25-44
45-54
55-65
-0.463
-0.720
0.507
0.94
1.94
1.15
Stroke
45-54
55-65
-2.593
-1.530
2.38
1.41
Other Heart Disease
0-34
35-44
45-54
55-65
-0.393
-0.184
-0.896
-1.462
0.90
0.40
2.39
2.04

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24
Table 5. Effects of Chronic Diseases on Labor Force Participation
by Duration of Disease and Age of Onset
Duration	Onset Coefficient t-Ratio
Asthma 0-17	0.017	0.04
18-34	0.780	0.92
35-65	0.029	0.05
Allergies 0-17	-0.040	0.09
18-34	0.542	1.02
35-65	-0.479	0.78
Chronic Bronchitis 25-44	-1.254	1.70
45-65	-1.013	1.46
Emphysema 0"5 45-54	-0.230	0.35
5-10 45-54	-1.299	2.04
0-5 55-65	-0.370	0.62
Other Chronic
Lung Diseases 18-44	-0.465	0.65
45-65	-0.670	1.19
Arteriosclerosis 0-5 45-54	-0.389	0.57
5-10 45-54	-0.252	0.41
0-5 55-65	0.659	1.11
Hypertension 25-34	-0.418	1.12
35-44	-0.151	0.44
45-54	0.084	0.35
55-65	-0.088	0.27
Heart Attack 25-44	-0.449	0.91
0-5 45-54	-1.003	1.70
5-10 45-54	-1.069	1.85
0-5 55-65	0.371	0.79
Stroke 0-5 45-54	-1.503	1.25
5-10 45-54	-7.551	0.38
0-5 55-65	-0.900	1.06
Other Heart Disease 0-34	-0.352	0.81
35-44	-0.165	0.36
0-5 45-54	-1.119	1.75
5-10 45-54	-0.007	0.01
0-5 55-65	-1.273	1.73

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25
Table 6. Effects of Chronic Diseases on Ln (Earnings) by Age of Onset
Age of
Onset Coefficient T-Ratio
Asthma
-
-0.232
1.020
Allergies
-
-0.061
0.318
Chronic Bronchitis
-
-0.023
0.065
Emphysema
0-5\
6-10
0.229
-1.038
0.641
2.009
Other Chronic Lung Disease

-0.511
1.294
Arteriosclerosis
45-54
55-65
0.279
-0.624
0.680
1.510
Hypertension
25-34
35-44
45-54
55-65
0.207
-0.041
0.193
0.311
0.916
0.188
1.211
1.167
Heart Attack
25-44
45-54
55-65
0.056
-0.590
-0.376
0.151
1.706
1.141
Stroke
-
0.843
1.386
Other Heart Disease
35-44
45-54
0.302
0.055
1.008
0.165
denotes duration of disease rather than age of onset.

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26
Table 7. Effect of Respiratory and Circulatory Diseases on Probability of Participation
by Age of Onset
Disease
Change in probability of participation at each age
Age of Onset	25-34	35-44
45-54
55-65
65 +
Chronic Bronchitis
25
45
-0.067
-0.067
-0.111
-0.084
-0.288
-0.218
-0.180
0.136
Emphysema
45
-0.099
-0.256 -0.159
45
-0.060 -0.157 -0.098
Heart Attack
45
-0.059
-0.155
-0.096
Stroke
45
55
-0.220 -0.571 -0.356
-0.327 -0.204
Other Heart Disease
45
-0.075 -0.196 -0.122
55
-0.324
-0.202

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i. /
Table 8. Annual Change in Expected Earnings at Each Age Due to Various Chronic Diseases ($1977)
Annual Change Due to Reduced Probability of Participation
(Change Due to Reduction in Earnings if Working)
Disease
Age of onset
25-34 3 5 - 4 4
45-54
55-65
65+
Chronic Bronchitis	25
45
$-870.2 $-1226.3 $-2229.1 $-4860.9 $-1680.4
-1689.6 -3684.4 -1273.7
Emphysema'
a
45
-1978.4
-4314.3
-10891.)
-1491.5
-6044 .7)
Arteriosclerosis
45
-1210.6 -2639.9
-912.6
Heart Attack
45
-1197.7
-8949. 6)
-2611.8
(-7515.8)
-902.9
-4171.2;
Stroke
45
55
-4415.8
-9629.5
-5511.0
-3328.9
-1905.2
Other Heart Disease	45
55
-1513.7 -3301.0 -1141.2
-5455.6 -1886.0
Effects on Earnings do not begin until duration is greater than or equal to 6 years.

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28
Table 9. Sample size by condition, NMCES.
Disease	ICDA codes	Persons
Total	4789
Hypertension	401-404	3479
Ischemic heart disease	410-414	378
Non-specific heart disease	429	884
Chronic bronchitis	490-491	430
Emphysema	492	222

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29
Table 10. Distribution of single vs multiple episodes types.
Number of persons with	Percent
single episodes	with
only
One*	one
Total One	One	related-to/ single
Disease	persons simple same-as stand-alone episode
Hypertension
3479
2476
227
462
91.0
Ischemic
378
195
34
80
81.7
Non-specific heart
CO
CO
501
104
166
87.2
Chronic bronchitis
430
272
49
63
89.3
Emphysema
222
130
21
42
86.9
*In each of these cases there is only one 'stand alone' episode to analyze
that is associated with our target disease.

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Table 11. Frequency Distribution of Annual Expenses per Person, by Condition.
Unweighted.
Total Expense
Percentage of Sample in Each Expense Category
Bronchitis	Emphysema	Hypertension
xpei
777
($19
$ 0
0-25
25-50
50-75
75-100
100-150
150-200
200-300
300-400
400-500
500-750
750-1000
1000-1500
1500-2000
2000-3000
3000-4000
4000-5000
5000-10000
10000-20000
20000+
N
Hean Expense
Median Expense
17.4
36.3
19.8
8.4
4.7
5.1
1.6
3.0
0.7
0.5
0.9
0.2
0.5
0.2
0.2
0.2
0.2
430
$96.74
$23.27
20.7
23.0
7.7
5.4
4.5
8.6
4.1
5.4
1.8
0.9
2.7
1.4
3.6
4.1
1.4
0.9
1.4
1.4
1.4
222
$632.76
$42.63
6.7
21.8
19.2
13.2
8.7
11.2
5.5
5.1
2.4
1.2
1.3
0.6
1.1
0.4
0.6
0.2
0.1
0.5
0.1
0.1
3479
$215.79
$53.51
Ischemic HD
9.0
15.9
10.3
5.6
6.3
9.5
6.9
9.3
2.6
2.4
2.4
2.6
2.9
2.4
1.3
2.9
0.3
3.4
2.6
1.3
378
$1257.55
$116.26
Nonspecific HD
12.9
19.2
11.5
6.8
5.1
7.0
4.6
7.6
3.2
1.6
2.5
1.5
2.6
1.9
2.6
3.1
1.4
2.9
1.1
0.9
884
$1041.26
$73.90

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31
Table 12. Average
: Expenses Per Person By Disease
and Category
($1977) .


Mean Expense
Std Dev
Maximum
CONDITION
Expenses



Bronchitis
(n=430)
Medical Contact
Hospital
$38.87
41.30
$117.30
499.76
$1683.00
9635.00

Drugs
14.65
44.60
605.27

Total Expense
96.74
537.54
9712.00
Emphysema
(n=222)
Medical Contact
Hospital
72.06
498.40
179.13
2073.30
1683.00
18832.00

Drugs
46.43
94.72
730.01

Total Expense
632.76
2171.28
19563.78
Hypertension
(n=3479)
Medical Contact
Hospital
51.88
111.65
127.12
1278.68
2854.89
57940.00

Drugs
41.62
55.89
970.45

Total Expense
215.79
1377.29
60588.00
Ischemic HD
(n=378)
Medical Contact
Hospital
96.23
1069.38
273.83
3653.32
3977.33
35910.00

Drugs
68.88
105.86
791.32

Total Expense
1257.55
3831.66
36462.00
Nonspecific HD
(n=884)
Medical Contact
82.45
220.92
4074.04
Hospital
859.10
3479.98
49638.00

Drugs
44.71
83.18
1094.67

Total Expense
1041.26
3736.60
49743.00

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32
Table 13. Medical Expenses on Chronic Bronchitis and Emphysema from the
NHLBI (1982) and Freeman et al (1976). (1977 $'s)
NHLBI
Hospital Doctor Drugs Total
Chronic Bronchitis
(millions of $'s)
$285 $162 $432 $879
Per Person
(38.1)
157.8) (21.7) (117.7'
Emphysema
(millions of $'s)
152
48
219
Per Person
(71.0) (22.5) (8.7) (102.1;
Freeman et al
Emphysema
(millions of $'s)
$174
$71 $59 $304
Per Person
1133.4)
:54.5) (45.6) (233.5;

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JJ
Table 14. Funding Source by Condition for Males 20 Years of Age or Greater.
Veighted.






Personal


Mean Expense
Pamily
Medicaid
Medicare
Insurance
Other
CONDITION







Bronchitis
478447
$205.24
$69.01
$4.25
$57.58
$62.38
$12.02



<3«>d
(2*)
(28*)
(30*)
(6*)



[65X1
[1*1
[4*1
[25*1
[4%]
Emphysema
766736
726.78
100.54
96.62
172.74
165.93
190.95



(14*)
(13*)
(24*)
(23*)
(26%)



I5U]
[3*1
[12*1
[18*1
[ 13%]
Hypertension
6644606
268.87
60.96
14.44
94.03
48.57
50.87



(23*)
(5*)
(35*)
(18*)
(19%)



(68*]
[3*1
[4*1
[16*1
[9%]
Ischemic HD
1184816
1739.77
180.77
186.23
287.79
840.05
244.93



(10*)
(11*)
(17*)
(48*)
(14%)



[50*1
[4*1
[9*1
[28*]
[8%]
Nonspecific HD
2019627
1662.99
164.38
72.77
685.51
493.92
246.41



(10*)
(4*)
(41*)
(30*)
(15%)



[51*1
[6*1
[12*1
[18*]
[13%]
Complex Multiple Episode excluded (see text).
^Mean does not include observations reporting zero.
(*
Percentage of Mean Expense.
^Percentage of Expense by Source, Averaged Over All Individuals.

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Table 15. Average Medical Expanses for Males, by Age. Weighted.
CONDITION
Bronchitis
Emphysema
Hypertension
Ischemic HD
Wean Expense Std Dev
Maxinua
Total
Expense
(Billions $)
Age Group





0-9
438016
$59.59
$109.84
$626.45
$26.1
10-19
160828
33.55
51.83
270.00
5.4
20-29
89507
84.99
148.34
514.00
7.6
30-39
60767
46.86
63.46
197.56
2.8
40—49
65470
96.40
140.54
446.05
6.3
50-59
67189
141.66
186.04
654.60
9.5
60-69
125470
249.56
781.04
4251.16
31.3
70-79
58254
485.20
2061.74
9712.00
28.3
80-89
11790
60.22
51.36
116.00
0.7
_> 20
478447
180.94
841.34
9712.00
86.6
Avars?*
1077291
109.60
569.05
9712.00
118.1
40-49
50017
562.54
672.46
1647.00
28.1
50-59
164485
884.41
2481.30
13535.82
145.5
60—69
341324
371.82
1639.63
17615.01
126.9
70-79
168861
580.66
2667.20
19563.78
98.1
80-89
39177
1474.26
1585.82
4854.75
57.8
90-99
2872
2.19
0.00
2.19
0.01
> 20
766736
595.16
2079.27
19563.78
456.3
Average
766736
595.16
2097.27
19563.78
456.3
0-9
17632
37.16
51.85
132.14
0.7
10-19
42691
241.54
436.87
1186.45
10.3
20-29
266550
74.09
199.29
1852.00
19.7
30-39
563863
• 96.74
369.69
6427.20
54.6
40-49
1000099
183.71
627.80
5504.85
183.7
50-59
1720562 '
264.21
1502.78
22771.07
454.6
60-69
1763206
486.97
3950.75
60588.00
858.6
70-79
1025353
115.82
428.34
9144.00
118.8
80-89
343210
176.83
358.22
2391.58
60.7
90-99
21317
80.95
63.68
140.70
1.7
100+
5215
37.80
0.00
37.80
0.2
> 20
6709375
261.22
2192.97
60588.00
1752.6
Average
6769698
260.15
2183.48
60588.00
1763.6
10-19
4014
0.00
0.00
0.00
0.0
30-39
21589
102.33
99.31
239.82
2.2
40-49
138574
4691.54
8048.54
23840.63
650.1
50-59
416557
1346.61
2772.72
14697.77
560.9
60-69
381771
1556.08
4631.68
23413.50
594.1
70-79
187042
769.57
2370.64
12571.90
143.9
80-89
74932
1174.44
3013.67
11320.83
88.0
> 20
1220465
1670.91
4400.88
23840.63
2039.3
Average
1224479
1665.43
4394.70
23840.63
2039.3
0-9
4451
0.00
0.00
0.00
0.0
10-19
18671
402.77
763.10
2009.00
7.5
20-29
41827
974.21
1958.24
4966.51
40.7

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35
30-39	20574	1063.75
4P-49	204956	2032.02
50-59	524168	1375.39
60-69	595206	1274.62
70-79	426144	2224.78
80-89	202381	589.05
90-99	37315	276.94
100+	5215	73.30
> 20	2057786	1475.72
Avara?*	2080908	1462.93
1614.51
3543.00
21.9
4906.42
23883.04
416.5
5077.84
38375.75
720.9
4634.08
43326.75
758.7
7825.51
49743.00
948.1
2070.29
15360.86
119.2
450.81
1194.00
10.3
0.00
73.30
0.3
5353.93
49743.00
3036.7
5325.98
49743.00
3044.2

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36
REFERENCES
Bartel, Ann and Paul Taubman. 1979. "Health and Labor Market Success: The
Role of Various Diseases, " Review of Economics and Statistics vol. 61
no. 1 (February), pp.1-8.
Freeman, Robert A., et al. 197 6. ''Economic Cost of Pulmonary Emphysema:
Implications for Policy on Smoking and Health," Inquiry, vol. 13, pp.
15-22 .
Hartunian, N.S., C.N. Smart, and M.S. Thompson. 1981. The Incidence and
Economic Costs of Major Health Impairments (Lexington, Massachusetts,
D. C. Heath and Co. )
Lee,. Lung-Fei. 1983. "Generalized Econometric Models with Selectivity,"
Econmetrica vol. 51, no. 2 (March), pp.507-512.
Maddala, G. S. 1983. Limited-Dependent and Qualitative Variables in
Econometrics (Cambridge, Cambridge University Press) .
Mitchell, Jean M. and J. S. Butler. 1986. "Arthritis and the Earnings of
Men," Journal of Health Economics vol. 5, pp.81-98.
Oster, Gerry, Graham A. Colditz, and Nancy L. Kelly. 1984. The Economic
Costs of Smoking and Benefits of Quitting (Lexington, MA: Lexington
Books).
Salkever, David, S. 1985. Morbidity Costs: National Estimates and Economic"
Determinants, U.S. Dept. of Health and Human Services, Publication No.
(PHS) 86-3393, (Washington, DC: USGPO).
U. S. Department of Health and Human Services, Social Security Administration.
1981. Users' Manual, 1978 Survey of Disability and Work.
U. S. Department of Labor. Bureau of Labor Statistics. 1988. Employment and
Earnings vol. 35, no. 1 (January) .
U.S. National Center for Health Services Research. 1981. NMCES Household
Interview Instruments. Publication No. (PHS) 81-3280, (Washington, DC:
USGPO).
U.S. National Heart, Lung and Blood Institute. 1982. Tenth Report of the
Director, National Heart, Lung, Blood Institute. Volume 3: Lung Disease.
NIH Publication No. 84-2358 , (Washington, DC: USGPO).
U.S. Social Security Administration. 1982. 1978 Survey of Disability and
Work. Technical Introduction. SSA Publication No. 13-11/45, (Washington,
DC: USGPO).

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37
APPENDIX

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38
Table A.l Coefficients of Non-Health Variables in Participation Equation
Coefficient | t-Ratio
Married
No. in householda
No. children <5
No. children 5-18
No. children > 18
Age dummies:
18-24
35-44
45-54
55-65
Highest educ. level:
Elementary school
High school
College
Nonwhite
a
Regional dummies :
Northcentral
South
West
Lives in-Urban Areaa
(Age-16)
Veteran
Aware of disability
benefits
Debt3
0.8989	5.89
-0.1290	2.58
0.4072	2.56
0.1060	1.34
0.3216	2.23
-1.2822	5.92
1.1440	4.28
1.5330	3.75
2.2198	3.55
-0.2006	0.84
0.1312	0.65
0.0386	1.38
-0.5886	3.39
0.3662	2.17
-0.1020	0.64
-0.0808	0.45
0.1852	1.46
-0.00160	4.54
-0.1077	0.81
-1.0358	8.68
0.00004	2.56
Measured as of interview date

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Table A. 2 Coefficients of Remaining Health Variables in Participation Equation
Disease	Coefficient	t-Ratio
Arthritis or rheumatism
-0.2791
1.65
Other trouble with back or spine
-0.4597
2.79
Deformity of foot, leg, arm, hand
-0.3741
1.89
Nervous or emotional problems
-0.8574
4.10
Deformity of back or spine
-0.7925
3.53
Deafness
-0.2624
1.08
Stomach ulcer
-0.2714
1.11
Diabetes
-0.1334
0.49
Hernia or rupture
0.005837
0.02
Difficulty reading (with glasses)
-0.2017
0.65
Kidney stones or kidney trouble
-0.1528
0.48
Other chronic stomach trouble
-0.2896
0.85
Tumor, cyst or growth
0.1030
0.27
Hissing arms, hands or fingers
-0.5395
1.42
Gallbladder or liver trouble
-1.1440
2.40
Paralysis
-1.9011
3.49
Alcohol or drug problems
-1.4264
2.46
Cancer
-0.82301
1.56
Epileptic seizures
-1.5235
2.18
Mental illness
-1.0498
1.60
Blindness
0.1043
0.16
Thyroid trouble or goiter
-0.2380
0.39
Missing legs or feet
-0.5794
0.84
Tuberculosis
0.1099
0.09
Multiple sclerosis
-2.3758
1.78

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40
Table A. 3 Coefficients of Non-Health Variables in Earnings Equation
Coefficient T-Ratio
Married	0.267	2.439
No. in household	-0.071	1.736
No. children <5	0.050	0.634
No. children 5-18	0.058	1.117
No. children > 18	0.003	0.034
Age dummies:
18-24	- 0.421	2.771
35-44	0.230	1.601
45-54	0.229	0.936
55-65	0.364	0.941
Highest educ. level:
Elementary school	-0.096	0.644
High school	0.004	0.036
College	0.294	2.271
Nonwhite	-0.195	1.550
Regional dummiesa:
Northcentral	0.111	1.136
South	0.011	0.113
West	- 0.025	0.231
Lives iruUrban Areaa	0.117	1.527
(Age-167	-0.0002	0.806
^Measured as of interview date
Note: Dependent variable is In(earnings) .

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41
Table A.4 Coefficients of Remaining Health Variables in Earnings Equation
Disease	Coefficient	t-Ratio
Arthritis or rheumatism
-0.051
0.415
Other trouble with back or spine
-0.033
0.296
Deformity of foot, leg, arm, hand
0.043
0.301
Nervous or emotional problems
-0.208
1.075
Deformity of back or spine
-0.297
1.597
Deafness
-0.226
1.257
Stomach ulcer
-0.031
0.174
Diabetes
-0.300
1.690
Hernia or rupture
0.059
0.290
Difficulty reading (with glasses)
-0.136
0.520
Kidney stones or kidney trouble
-0.341
1.409
Other chronic stomach trouble
0.242
0.954
Tumor, cyst or growth
-0.327
1.368
Hissing arms, hands or fingers
0.354
1.340
Gallbladder or liver trouble
0.290
0.604
Paralysis
-2.931
4.518
Alcohol or drug problems
0.355
0.594
Cancer
-1.003
2.215
Epileptic seizures
-1.865
2.795
Mental illness
-0.010
0.015
Blindness
-0.001
0.002
Thyroid trouble or goiter
-0.044
0.100
Missing legs or feet
0.356
0.580
Tuberculosis
0.184
0.246
Multiple sclerosis
0.653
0.506

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ESTIMATING THE VALUE OF AVOIDING MORBIDITY AND MORTALITY
FROM FOODBORNE ILLNESSES
Josephine A. Mauskopf, PhD
Michael T. French, PhD
Center for Economics Research
Research Triangle Institute
Research Triangle Park, NC 27709
May 1989

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ESTIMATING THE VALUE OF AVOIDING MORBIDITY AND MORTALITY FROM
FOODBORNE ILLNESSES
I INTRODUCTION
All foods produced for human consumption in the United States are regulated for
composition, quality, safety, and labeling under the Food, Drug, and Cosmetic (FD&C) Act of
1938 and its subsequent amendments. One of the chief goals of the FD&C Act is to reduce the
presence of contaminants or adulterants in domestic and imported foods. Consuming foods that
contain illegal contaminants or adulterants increases the risk of foodborne illness and decreases
consumer welfare. The Food and Drug Administration (FDA) is empowered to ensure
compliance of the FD&C Act for all domestic and imported food products. FDA's compliance
monitoring program and enforcement activities reduce the probability of violative products
reaching consumers and causing welfare losses.
FDA's objective is to maximize social welfare subject to a given compliance monitoring
budget. The optimal solution is to allocate program resources across different inspection and
enforcement activities to the point where the incremental value per unit expenditures for all
activities are equal. To develop such an efficient compliance monitoring program, FDA must
consider the costs and benefits of different alternatives. The costs of such programs consist
primarily of the value of resources used to inspect and test products, and ensure compliance. The
benefits of compliance monitoring activities depend on:
•	the impact of compliance activities on the probability that violative products will
reach the consumer,
•	the probability that each violation will lead to various adverse health effects (e.g.
salmonellosis, botulism cancer, or chemical poisoning), and
•	the value of the welfare losses associated with each adverse effect.
Figure 1 shows how estimates of the three factors noted above can be combined to
estimate the benefits of different compliance monitoring options. Calculating these values is not
a straightforward task, however, and requires careful analysis. For example, the impact of
compliance activities on the probability of a violative product reaching the consumer depends
both on the initial probability of the product violating the FD&C Act as well as on how
effectively the compliance monitoring and enforcement activity reduce this probability. The
probability of a product violating the Act may vary overtime and with country of origin.
1

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The probability that any violation of the Act adversely affects a consumer will depend on
the type and degree of the violation. Food contaminated with salmonella will be more likely to
have an adverse effect on a consumer if the level of contamination is high, if the typical portion
size is large, and if the product is eaten without further cooking. Furthermore, the relationship
between dose and the probability of an adverse response may vary for different violations of the
Act. For example, the probability of an adverse health effect associated with frequently ingested
levels of salmonella or botulinum toxin may be high, while the probability of cancer as a result of
ingesting carcinogenic pesticides above the permissible levels may be much lower.
Finally, the value to consumers of avoiding the welfare losses associated with adverse
health effects depends on how soon the effect occurs after they consume the violative product
and the magnitude of the expected welfare losses.
This paper develops a methodology for estimating the value of the welfare gains
associated with avoiding statistical cases of morbidity and mortality from foodborne illnesses.
We demonstrate the methodology for botulism, salmonellosis, chronic hepatitis, and bladder
cancer. The methods and results from this research can be combined with information on the
costs of enforcement, dose-response relationships, and changing probabilities of violations to
guide FDA in developing an efficient compliance monitoring program.
II BACKGROUND
Consumers derive value from a food inspection and monitoring program through lower
risks of adverse health effects. When a compliance monitoring program detects and removes a
violative product from distribution, it reduces the risk of consumers suffering adverse health
effects and corresponding welfare losses. The value of reducing the risks of adverse health
effects could be easily measured by market clearing prices if there were markets for health risks.
With the exception of wage premiums for occupations with higher than average risks of on-the-
job death or injury, health risks are not a market commodity. Thus, analysts must develop other
methods to estimate the value of reducing food-related health risks.
One of the earliest approaches used to estimate directly the costs associated with different
illnesses is the cost-of-illness (COI) methodology. In its simplest form, the COI methodology
calculates the dollar cost of illness or disease as the sum of the present values of the medical
resources used to diagnose and treat the disease and the individual productivity losses it causes.
The COI methodology is a practical simplification of the more comprehensive human capital
approach to valuing illness. Cooper and Rice (1976) and Rice, Hodgson, and Kopstein (1985)
2

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have used the COI method to estimate the costs of many different diseases. Hartunian et al.
(1981) employed the COI model to value the costs of coronary heart disease, stroke, cancer, and
motor vehicle injuries.
The COI method is well-suited for estimating many of the tangible costs of illnesses, but
it does not address any of the intangible or disutility costs. Nor does it distinguish between
avoidance of identified cases of illness and reduction in the risk of adverse health effects. Utility
is a conceptual device used primarily by economists to measure the amount of well-being and
pleasure an individual experiences. Utility declines with deteriorating health status, as well as
with increased risk of illness. Since the benefits of a government regulation are best described in
terms of statistical cases of illness avoided, we fist estimate the value of utility gains from
decreased risks of statistical illness.
While utility is a useful construct in theory, it is unobservable in practice. Thus, we need
to derive proxy measures for utility changes such as monetary values. The concept of
willingness to pay (WTP) has gained acceptance in the economics profession as a dollar
equivalent to utility changes. The WTP approach is based on macroeconomic utility theory and
has been used extensively to estimate the value of utility improvements and the cost of utility
reductions. For example, the WTP approach imputes the cost of adverse health consequences by
measuring how much individuals are willing to pay for small reductions in the risk of those
effects. By measuring the value individuals place on small changes in the probability of
mortality and morbidity, economists and health professionals have extended the analysis to
measure the disutility cost of a statistical mortality and morbidity case.
Although dollars may bean imperfect measure of a consumer's valuation of avoided
utility losses, within a certain range of preferences, people are familiar with the process of
expressing values for goods and services through prices. Furthermore, dollar values provide a
benchmark by which a wide variety of foodborne illnesses can be measured and compared.
We present a methodology for estimating the dollar value of avoiding morbidity and
mortality from foodborne illnesses using both the willingness-to-pay approach and the cost of
illness approach. We demonstrate our methodology and derive valuation estimates for avoiding
statistical cases of botulism, salmonellosis, chronic hepatitis, and Madder cancer.
Ill METHODS AND RESULTS
The empirical model presented here was developed using publicly available data. We
used the model as part of a larger study to estimate the value of avoiding both health and
3

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nonhealth adverse effects from consuming foods that violate the FD&C Act (Mauskopf et al.
1988). In this paper, we only describe and implement the method for estimating the value of
avoiding adverse health effects.
The method we use to compute the dollar value for avoiding foodborne illnesses
associated with violations of the FD&C Act consists of the following seven steps and is
illustrated in Figure 2:
•	Identify the foodborne illnesses of concern.
•	Describe the adverse health effects of each foodborne illness on an individual
consumer.
•	Translate these health effects into time spent in specific health states.
•	Estimate the gains in quality-adjusted life-years (QALYs) associated with avoiding a
case of each foodborne illness.
•	Estimate the value of a QALY.
•	Compute the willingness-to-pay estimate for avoiding each foodborne illness by
combining the estimates of the QALYs avoided and the dollar value of a QALY.
•	Use the estimated adverse health effects to compute the cost-of-illness estimates for .
each foodborne illness.
We discuss each step of the analysis in the following sections.
Identify Foodborne Illnesses
In the first step of the analysis, we use available human and nonhuman data to identify
illnesses likely to be associated with violations of the FD&C Act (FASEB, 1988). In some cases,
a cause-and-effect relationship between a violation and an illness is well-established, such as that
between botulinum toxin and botulism. In other cases, this relationship maybe less understood,
such as that between pesticide residues and risk of cancer.
To facilitate the later steps in the estimation procedure, we subdivide foodborne illnesses
into three categories:
•	acute illnesses, which occur with no latency period after exposure, have a well-
defined duration, and end in either death or complete cure;
•	chronic illnesses, which have no (or a short) latency period after exposure, a
prolonged duration, and end in death; and
4

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• cancers, which have a prolonged latency period, short or prolonged duration, and end
in either death or complete cure.
Most foodborne illnesses can be assigned to one or more of these categories. Table I
presents some examples of violations of the FD&C Act and their associated foodborne illnesses.
Botulism is caused by botulinum toxin in a food product and is classified as an acute illness.
Survivors of a severe case of botulism might also suffer from residual chronic illness, but this is
not included in our analysis. Salmonellosis is caused by a bacterium and is a common disease in
its less severe forms. Chronic hepatitis may persist throughout an individual's life after an attack
of acute foodborne hepatitis. Certain pesticide residues and food coloring agents may be
associated with an increased risk of bladder cancer.
Describe the Health Impact an Consumers
In general, foodborne illnesses can occur at various levels of severity, each of which
affects the consumer to a different degree. To simplify the analysis, we chose three levels of
severity for each illness: mild, moderate, and severe. We define the severity category for the
acute and chronic illnesses based on well-defined clusters of symptoms, resource use, and/or
mortality risk The severity levels are used for all illnesses except cancers, which we define as
local, regional, and distant.
For each level of illness severity, we describe the impact on consumers in terms of patient
symptoms, mortality rates, duration of treatment and recovery, frequently used medical
treatment, and functional status during treatment and recovery. Functional status during the
illness is defined as either in a hospital, in bed at home, or at home not in bed. Table II illustrates
an impact profile for botulism salmonellosis, and chronic hepatitis. Table III illustrates the
impact profile for bladder cancer. We obtained the data for these impact descriptions from the
medical and clinical literature.
Determine Time Spent in Specific Health States
Adverse health effects from foodborne illnesses can cause both short- and long-term
changes in health status. We classify the length and degree of health status changes by the time
spent in specific health states. Health states can be defined broadly or narrowly depending on the
conditions and purpose of the analysis. Several studies in the biomedical literature have
developed health states or health status index scales to describe and categorize the adverse health
consequences from illness and disease.
5

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For this analysis, we use the set of health states defined by Rosser and Kind (1978). But
analysts can use any set of health states general enough to be applied to all foodborne illnesses
and for which relative utility weights have been estimated. In our comprehensive study for FDA
(Mauskopf et al. 1988), we also used the Bush et al. (1981) health status index and the health
status index developed for a study of vaccines by the Institute of Medicine (1985). Table IV
presents the Rosser and Kind health state definitions. They express health status in terms of two
dimensions: objective disability and distress.
After choosing a set of health states, we describe the adverse health effects from each
foodborne illness in terms of time spent in the specific health states. The descriptions are
presented for botulism, salmonellosis, and chronic hepatitis in Table V and for bladder cancer in
Table VI using the Rosser and Kind health states. For example, we estimated that a mild case of
botulism would result in severely limited ability to work for five days with mild distress. In
contrast, we estimated a serious case of botulism would result in 90 days confined to bed in
severe distress, 30 days confined to a chair in moderate distress, and 60 days unable to work in
mild distress.
Estimate Losses in Quality-Adjusted Life-Years
To estimate the QALYs lost as a result of a foodborne illness, it is necessary to make a
series of assumptions including age at exposure to the violative product, latency period after
exposure for the illness to appear, remaining life expectancy at time of illness, and health status
at onset of illness and for remaining lifetime. We assume the following baseline conditions:
•	age at exposure is 30 years,
•	a 20-year latency period for cancer, but no latency period for acute or chronic effects,
•	remaining life expectancy at age 30 and at age 50 is 46 years and 26 years
respectively,
•	individuals are in perfect health and, in the absence of foodborne illness, would
continue in perfect health for their remaining lifetime.
Lipscomb et al. (1983) have shown that this last assumption results in overestimates of the losses
associated with illness of about 5 percent.
Using the assumptions noted above, the estimated time spent in specific health states for
each foodborne illness, and the relative utility (well-being) weights shown in Table VII for the
Rosser and Kind index, we computed the losses in QALYs associated with each illness.
6

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Table VIII presents the estimated losses in QALYs for botulism, salmonellosis, chronic hepatitis,
and bladder cancer.
For botulism, the estimated losses in QALYs are much larger for those who die from the
disease (25.5 QALYs discounted at 3 percent or 46 QALYs undiscounted) than for those who
have a severe case and survive (0.647 QALYs). For chronic hepatitis, the losses in QALYs are
assumed to continue for the rest of the individual's lifetime. We estimate that approximately 50
percent of the people with bladder cancer die. In addition to suffering premature death, those
individuals who die from bladder cancer suffer significantly greater losses from morbidity (0.31
undiscounted QALYs) than those who survive (0.07 undiscounted QALYs).
Estimate the Value of a Quality-Adjusted Life-Year
We use willingness-to-pay estimates for reductions in morbidity and mortality risks to
assign a dollar value to a QALY. The process follows a series of steps. First, we explored the
literature and chose a representative willingness-to-pay estimate for the value of a statistical life.
We selected $5 million. This value was estimated by Viscusi and Moore (1988) in a recent study
of wage premiums paid to workers in risky occupations with an average age of 40 years. Five
million dollars serves as the willingness-to-pay estimate to avoid the index state (death) from a
previous condition of perfect health. We assume that the remaining life expectancy for a 40-
year-old worker is 36 years. Using a value estimated for a statistical life (death) is appropriate,
because FDA monitors and enforces programs that reduce the risk of foodborne illness for the
general population, thus preventing statistical, not identified, cases.
Equation 1 illustrates the formula we use to compute the undiscounted value of a QALY
from the estimated value of a statistical life.
Alternatively, for a discount rate of 3 percent, we first convert remaining life expectancy to total
discounted life-years (TDLYs) through the following calculation:
$QALY (0% discount) =
value of a statistical life
(l)
remaining life expectancy
TDLYs remaining =
f—!—
Zrf (1+0.03)*-! '
(2)
and then compute the value of a QALY as:
$QALY (3% discount) =
value of a statistical life
(3)
total discounted life-years
7

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Using $5,000,000 as the value of a statistical life (Viscusi and Moore, 1988), the
estimated value of a QALY is $138,000 at a 0 percent discount rate, and $222,222 at a 3 percent
discount rate.
In computing the value of a QALY as described above, we used death as the index state.
Alternatively, the value of a QALY can be computed from estimates of the willingness-to-pay to
avoid other adverse health states, provided that the lost QALYs associated with these adverse
health effects are also estimated. For example, Rowe and Chestnut (1984) estimated the
willingness to pay to avoid a bad asthma day at $23.00. Using the Rosser and Kind scale, the
loss in QALYs associated with a day with asthma is estimated as 0.00008. Thus, using a day of
asthma as the index state will result in an estimate for a QALY of $287,500. This exercise can
be performed for a variety of different index states to generate a range of estimates for the value
of a QALY.
Estimate the Value of Avoiding Morbidity and Mortality
In the final step of the willingness-to-pay analysis, we compute the product of the QALYs
gained and the dollar value of a QALY to generate willingness to-pay estimates for the avoided
morbidity and mortality associated with foodborne illnesses. Estimated values for botulism,
salmonellosis, chronic hepatitis, and bladder cancer are presented in Table IX. The estimated
dollar value for avoiding foodborne illnesses associated with a high risk of death, such as severe
botulism or bladder cancer, is much higher than for avoiding nonfatal illnesses such as mild or
moderate cases of salmonellosis. Nevertheless, the estimated morbidity losses are not
insignificant.
Caution must be exercised when interpreting the implications of these estimates. Many
serious foodborne illnesses are rare, such as those presented as examples here. Since the
willingness-to-pay values are for statistical cases of each illness, the aggregate value of avoiding
all cases may be relatively small in comparison to a less severe illness with a much higher
prevalence. As an example, foodborne illnesses such as salmonellosis are usually not life
threatening, yet they are very common, especially in their milder forms. Consequently, the total
dollar losses associated with morbidity from this disease may be very high—in the billions of
dollars (Archer and Kvenberg 1985).
Estimate Morbidity and Mortality Losses Using the Cost-of-Illness Approach
An alternative approach to estimating the value of avoiding foodborne illnesses is to
estimate the direct and indirect costs avoided in terms of medical care and productivity losses.
8

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The cost-of-illness method advocates an accounting cost framework to estimate the observable
costs (medical care) and an opportunity cost framework to estimate the implicit costs
(productivity losses). Cost-of-illness estimates for botulism, salmonellosis, and bladder cancer
are presented in Table X.
Cost-of-illness methods have been applied in numerous studies for many different
illnesses and diseases. Despite its popularity, the cost-of-illness method tends to underestimate
the true value of the avoided illness because it does not address the value of avoiding certain cost
categories (e.g., pain and suffering). On the other hand, the cost-of-illness method may
overestimate the value of the avoided medical costs to the individual because these costs are
often shared via health insurance.
IV CONCLUSION
We described two methods that can be used to estimate the value of avoiding the
morbidity and mortality associated with foodborne illnesses: willingness-to-pay and cost-of-
illness. We demonstrated the use of these methods and estimated the value of avoiding statistical
cases of four foodborne illnesses: botulism, salmonellosis, chronic hepatitis, and bladder cancer.
At least three conclusions can be drawn as a result of this analysis. First, the fatality rate is the
key factor when determining the relative value of avoiding different levels of severity for acute
illnesses and cancers. Second the value of morbidity losses, both for those ultimately dying
from the illness and for those surviving, are significant. Finally, the estimated value of avoiding
chronic diseases is critically dependent on the degree of functional impairment associated with
the illness.
Although the cost-of-illness method is a convenient approach for estimating the tangible
costs of illness and disease, it is flawed because it does not consider disutility costs. Willingness-
to-pay methods are conceptually appealing because they are based on microeconomic utility
theory. Willingness-to-pay estimates include the disutility costs associated with illness and
disease such as physical and emotional pain and suffering.
Despite its theoretical strengths, the willingness-to-pay approach can be difficult to
implement due to data requirements. In addition, the estimates are highly sensitive to simplifying
assumptions and baseline parameter values (e.g., age at exposure, remaining life expectancy,
discount rate, health status index scale). Although these issues cannot be ignored, our
methodology is able to use secondary data to generate defensible estimates for the value of
avoiding a wide variety of morbidity states. More importantly, decisionmakers can use this
9

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methodology to include the value of reducing morbidity risks as well as the value of reducing
mortality risks in their benefits estimates. This is especially useful for FDA and other federal
agencies that regulate health risks.
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REFERENCES
Archer, D.L. and J. E. Kvenberg. 1985. "Incidence and Cost of Foodborne Diarrheal Disease in
the United States." Journal of Food Protection. 48:887-893.
Bush, J.W., R.M. Kaplan, and W.R. Blischke. October 31,. 1981. "Additive Utility
Independence in a Multiattribute Quality of Life Scale for the General Health Policy Model."
Paper presented at the Health Services Research Study Group on Utility Measurement and
Decision Theory, 109th Annual Meeting of the American Public Health Association, Los
Angeles,
Centers for Disease Control (CDC). 1980. "Botulism in the United States, 1979." The Journal
of Infectious Diseases. 142:302-305.
Cooper, B. S., and D.P. Rice. 1976. "The Economic Cost of Illness Revisited." Social Security
Bulletin 39(2):21-36.
Federation of American Societies for Experimental Biology (FASEB). September 1988.
"Identification of Foodborne Illnesses Associated with FD&C Act Violations." Appendix A
in Estimating the Value of Consumers' Loss from Foods Violating the FD&C Act. Research
Triangle Institute. Prepared for Center for Food Safety and Nutrition, Food and Drug
Administration, Contract No. 223-87-2097.
Hartunian, N. S., Smart, C.N., Thompson, M.S. 1981. The Incidence and Economic Costs of
Major Health Impairments. Washington, DC: National Academy Press.
Institute of Medicine. 1985. New Vaccine Development: Establishing Priorities. Volume I:
Diseases of Importance in the United States. Washington, DC: National Academy Press.
Lipscomb, J., J.T. Kolimaga, P.W. Sperduto, J.K Minnich, and K.J. Fontenot. 1983. Cost-
Benefit and Cost-Effectiveness Analyses of Screening for Neural Tube Defects in North
Carolina. Draft Report prepared for the State of North Carolina.
Mann, J.M., G.D. Lathrop, and J.A. Bannerman. 1983. "Economic Impact of a Botulism
Outbreak Importance of the Legal Component in Foodborne Disease." Journal of the
American Medical Association. 249:1299-1301.
Mauskopf, Dr. Josephine A., Dr. Michael T. French, A. Scott Ross, Dierdre M. Maguire, Craig R.
Hollingsworth, and Maria W. Bachteal . September 1988. "Estimating the Value of
Consumers' Loss from Foods Violating the FD&C Act." Prepared for Center for Food
Safety & Applied Nutrition, Food and Drug Administration.
Rice, D.P., T.A. Hodgson, and A.N. Kopstein. 1985. "The Economic Costs of Illness: A
Replication and Update." Health Care Financing Review 7:61-80.
Rosser, R. and P. Kind. 1978. "A Scale of Valuations of States of Illness: Is There a Social
Consensus." International Journal of Epidemiology. 7:347-358.
Rowe, R., and L. Chestnut (Energy and Research Consultants, Inc.). 1984. Oxidants and
Asthmatics in Los Angeles: A Benefit Analysis. EPA-230-0785-010. Washington, DC: U.S.
Environmental Protection Agency.
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Todd, E.C.D. 1985a. "Economic Loss from Foodborne Disease and Non-Illness Related Recalls
Because of Mishandling by Food Processors." Journal of Food Protection. 48:621-633.
Todd, E.C.D. 1985b. "Economic Loss from Foodborne Disease Outbreaks Associated with
Food Service Establishments." Journal of Food Protection. 48:169-180.
Viscusi, W. K., and M.J. Moore. 1987, "Worker's Compensation: Wage Effects, Benefit
Inadequacies, and the Value of Health Losses." The Review of Economics and Statistics
6912:249-261.
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Change in the
Probability
of a Violative
Product Reaching
Consumer
x
Probability that
the Violation
has an Adverse
Effect(s) on
Consumer
x
Value to
Consumer of
Avoiding Welfare
Loss from
Adverse Effect(s)
Figure 1. Benefits of Compliance Monitoring
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Data from human
and animal studies
Clinical and
survey data
Data from health
status index studies
Data from
economic studies
Estimate the gain in QALYs
Estimate the value of a QALY
Describe the health effects
on an individual consumer
Identify the foodbome
illness of concern
Compute the cost-of-illness
estimates for each
foodbome illness
Translate the health
effects into time spent
in specific health states
Compute the willingness-
to-pay estimates for avoiding
each foodbome illness
Figure 2. Flow Diagram of Estimation Model
14

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TABLE I. SAMPLE OF FOODBORNE ILLNESSES CAUSED BY VIOLATIONS
OF THE FD&C ACT
Violation
Acute Effects
Chronic Effects
Cancers
FD & C Red#10
Cat filth/damage
C. Botulinum
Human filth
Salmonella
Inadequate.
pasteurization,
LACF
Contact dermatitis
Toxoplasmosis
Botulism
Shigellosis, hepatitis,
listeriosis, colitis
Salmonellosis
Salmonellosis,
botulism
Bladder
Congenital
toxoplasmosis
Chronic hepatitis,
cirrhosis
Liver
Sulfite
Allergic response
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TABLE II. HEALTH EFFECTS OF BOTULISM, SALMONELLOSIS, AND CHRONIC
HEPATITIS
Illness	Symptoms Duration Treatment Functional Fatality
Status	Rate
Botulism
Mild
Malaise,
fatigue
weakness, 5 days
Antitoxin
5 house days
0%
Moderate Nausea/vomiting,
diarrhea,
abdominal pain,
fever, malaise,
weakness,
headache, dizziness
21 days
Antitoxin
7 hospital days
7 bed days
7 house days
0%
Severe Same as
moderate plus
respiratory
paralysis,
muscular paralysis,
pulmonary infection
180 days
Antitoxin,
respiratory
support
90 hospital days
30 bed days
60 house days
22.5%
Salmonellosis
Mild
Nausea/vomiting,
diarrhea
abdominal pain,
anorexia weakness
3 days
Oral fluids,
antispas-
modics
2 bed days
1 house day
0%
Moderate
Same as mild plus
fever, headache,
dehydration/
prostration
7 days
Oral fluids,
antispas-
modics
4 bed days
3 house days
0%
Severe Same as moderate
plus enteric
bacteremia
11-20 days
I.V. fluids,
antispas-
modics,
antibiotics
5-14 hospital days
3 bed days
3 house days
13%
Chronic Hepatitis
Malaise	1 year to None	Very minor	o%
lifetime	restrictions
Sources: FASEB (1988), Mann et. al., (1983), Todd (1985a), Todd (1985b), CDC (1980).
16

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TABLE III. HEALTH EFFECTS OF BLADDER CANCER
Estimated Duration

of Treatment,

Cured Patients =
< 2 years
Estimated Duration

of Treatment,

Uncured Patients =
1.97 years
Estimated

Fatality Rate =
51%
Associated Signs and Symptoms
Bloody urine
Pain on urinating
Abdominal pain
Further symptoms from metastasis
Frequently Used
Medical Treatments and
Associated Side Effects
Functional Status
During Treatment and Recovery
Surgery
Pain
Discomfort
Vomiting
Hair loss
Inflammation of mucous
membranes
Suppression of white cell
development
Cerebellar dysfunction at high
doses
Anorexia
Rashes
Inflammation of hair follicles
Hyperpigmentation
Fever/chills
Renal failure
Anemia
Cured Patients
First Second
Year Year

Hospital Days
10
7
Radiation Therapy
Days of Hospital Recovery
8
6
Diarrhea



Mucositis which can preclude
Chemotherapy Days

0
substantial oral intake and
Days of Chemotherapy Recovery
0
0
lead to malnutrition




Radiation Therapy Days
0
0
Chemotherapy
Days of Radiation Therapy Recovery
1

Nausea
Mild Distress Days
345
170
First Second
Uncured Patients
Year
Year
Hospital Days
18
35
Days of Hospital Recovery
14
28
Chemotherapy Days
3
24
Days of Chemotherapy Recovery
3
24
Radiation Therapy Days
7
14
Days of Radiation Therapy Recovery
3
7
Nursing Home Days
0
7
Partial Disability Days


Total Disability Days
0
41
Mild Distress Days
317
144
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TABLE IV. ROSSER AND KIND HEALTH STATES
Objective Disability	Distress
1.
None
1.
None
2.
Slight social disability
2.
Mild
3.
Severe social disability,
slight impairment at work
3.
Moderate
4.
Work severely limited
4.
Severe
5.
Unable to work


6.
Confined to chair


7.
Confined to bed


8.
Unconscious


Source: Rosser and Kind (1978)
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TABLE V. DISABILITY, DISTRESS, AND TIME IN SPECIFIC HEALTH STATES
FOR BOTULISM, SALMONELLOSIS, AND CHRONIC HEPATITIS
Illness
Disability
Distress
Duration

Index
Index

Botulism



Mild
4
2
5 days
Moderate
7
3
7 days

6
3
7 days

4
2
7 days
Severe
7
4
90 days

6
3
30 days

4
2
60 days
Salmonellosis



Mild
6
3
1 days

4
2
1 days
Moderate
6
3
4 days

4
2
3 days
Severe
7
3
10 days

6
3
3 days

4
2
3 days
Chronic Hepatitis
2
2
365 days/year
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TABLE VI. DISABILITY, DISTRESS, AND TIME IN SPECIFIC HEALTH STATES
FOR BLADDER CANCER
Duration
Functional Status During
Treatment and Recovery*
First Year
Second Year

Disability
Index
Distress
Index


Cured Patients


10
7
Hospital Days
7
3
8
6
Days of Hospital Recovery
6
3
0
0
Chemotherapy Days
5
3
0
0
Days of Chemotherapy Recovery
4
2
1
0
Radiation Days
5
3
1
0
Days of Radiation Recovery
4
2
o
345
170
Mild Distress Days
1
2


Uncured Patients


18
35
Hospital Days
7
3
14
28
Days of Hospital Recovery
6
3
3
24
Chemotherapy Days
6
3
3
24
Days of Chemotherapy Recovery
5
3
7
14
Radiation Days
6
3
3
7
Days of Radiation Recovery
5
3
0
7
Nursing Home Days
7
3
0
41
Partial Disability Days
4
2
0
41
Total Disability Days
6
3
317
144
Mild Distress Days
1
2
* Weighted average for cases
diagnosed in local, regional, and distant stages.

20

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TABLE VII. RELATIVE UTILITY WEIGHTS FOR THE ROSSER AND KIND
HEALTH STATUS INDEX
Distress Index
Disability		
Index	12	3	4
1
1.0
0.995
0.990
0.967
2
0.990
0.986
0.973
0.932
3
0.980
0.972
0.956
0.912
4
0.964
0.956
0.942
0.870
5
0.946
0.935
0.900
0.700
6
0.875
0.845
0.680
0.000
7
0.677
0.564
0.000
-1.486
8
-1.028
—
—
—
Source: Rosser and Kind (1978)
21

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TABLE VIII. LOSSES ON QUALITY-ADJUSTED LIFE-YEARS FROM BOTULISM,
SALMONELLOSIS, CHRONIC HEPATITIS, AND BLADDER CANCER
Illness
Fatality
Loss for
survivors
QALYs*
(QALDs)**
Weighted
Average Loss
QALYs*
(QALDs)**
Botulism



Mild
0%
0.00055
(0.2)
0.00055
(0.2)
Moderate
0%
0.0263
(9.6)
0.0263
(9.6)
Severe
22.5%
0.647
(236)
6.24
(2,279)
Salmonellosis



Mild
0%
0.001
(0.4)
0.001
(0.4)
Moderate
0%
0.004
(1.4)
0.004
(1.4)
Severe
13%
0.03
(H.l)
3.35
(1,221)
Chronic Hepatitis
0%
0.36
(130.4)
0.36
(130.4)
Bladder Cancer



Undiscounted
51%
0.068
(24.7)
12.9
(4,700)
Discounted
3% to Diagnosis
51%
0.067
(24.4)
9.57
(3,494)
Discounted
3% to Exposure
51%
0.037
(13.5)
5.30
(1,934)
* QALY = quality-adjusted life-year
** QALD = quality-adjusted life-day
22

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TABLE IX. WILLINGNESS-TO-PAY ESTIMATES FOR AVOIDING BOTULISM,
SALMONELLOSIS, CHRONIC HEPATITIS, AND BLADDER CANCER
Illness
Fatality
Rate
Survivors
Weighted
Average
Botulism



Mild
0%
$130
$130
Moderate
0%
$5,800
$5,800
Severe
22.5%
$143,750
$1,388,000
Salmonellosis



Mild
0%
$222
$222
Moderate
0%
$890
$890
Severe
13%
$6,700
$740,000
Chronic Hepatitis
0%
$79,400
$79,400
Bladder Cancer



Undiscounted
51%
$8,220
$1,178,000
Discounted
3% to Diagnosis
51%
$9,384
$1,780,000
Discounted
3% to Exposure
51%
$14,900
$2,127,000
23

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TABLE X. COST-OF-ILLNESS ESTIMATES FOR AVOIDING BOTULISM,
SALMONELLOSIS, AND BLADDER CANCER
Illness
Fatality
Survivors
Weighted

Rate

Average
Botulism



Mild
0%
$470
$470
Moderate
0%
$4,710
$4,710
Severe
22.5%
$68,500
$195,000
Salmonellosis



Mild
0%
$197
$197
Moderate
0%
$622
$622
Severe
13%
$65,556
$86,895
Bladder Cancer*
51%
$13,876
$215,000
* Lost earnings discounted at 3% to diagnosis.
24

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UTILITY IMPAIRMENT YEARS:
A LOW-COST APPROACH TO MORBIDITY VALUATION
by
Ted Miller3
Charles Calhoun13
W. Brian Arthurc
May 1989
This research was supported by Federal Highway Administration contract DTFH-
61-85-C-00107. The opinions expressed are strictly the authors'.
aSenior Research Associate, The Urban Institute
^Research Associate, The Urban Institute
cDean and Virginia Morrison Professor of Population Studies, Stanford
University

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2
Introduction
This article extends the Arthur (1981) social consumption equivalent (SCE)
value of life model to one that also accounts for health status and serious
injury. Death is only one possible outcome of risky activities, and by the
available evidence, not always the least desirable. Fates worse than death
are now recognized as important determinants of private decisions to avoid
risk and of the social value of public programs designed to reduce or
eliminate hazards to life and limb. Kind, Rosser, and Williams (1982)
examined the impacts of distress and disability on the joy of living and found
that permanent confinement to bed was considered as bad as death, and
permanent coma even worse. In a British study of injury severity by Green and
Brown (1978), university students ranked death third behind brain damage and
paralysis from the neck down. Jones-Lee, Hammerton, and Philips (1985) found
that in a probability sample of 1000 British residents, the median individual
considered lifetime confinement to a wheelchair as bad as death, and being
permanently bedridden was considered as bad or worse than death by 63 percent
of the respondents. Howard (1984) has examined the theoretical implications
of extreme disability for individual decisions regarding risk.
The impact of serious injury on individual and social welfare can be
substantial, as implied by the findings cited above. Implicit in these data
is the effect of injuries on the utility from additional years of life. A
person's health status is likely to have a direct effect on welfare—
particularly when pain and suffering are involved-as well as indirect effects
such as diminished utility from consuming other goods.
In addition to their effects on the utility associated with additional
years of life, permanent and temporary disabilities have important
implications for the age profile of consumption, production, and mortality.
Changes in the incidence of serious illness and injury also may have quite
different implications than changes in the death rate from the same cause.
The impact of a change in the incidence of serious injuries on labor market
productivity and consumption may include offsetting effects, for example,
depending on whether the change is associated with an increase or decrease in
death rates. Reductions in the injury rate that are not offset by an increase
in death rates should increase average labor productivity. The magnitude of
these effects will depend on the age of the individual, time to recovery, and
the extent to which it was already possible to switch to less physically
demanding activities following a serious injury. Consumption of costly
medical resources will decline with a reduction in the incidence of serious
injury, perhaps more than offsetting any increase in other types of
consumption.
The mortality implications of adding the seriously injured to the model
can be viewed in terms of resuscitated lives—saving those who would have died
as the result of a serious illness or injury through the application of
advanced medical technology or improved health and safety measures—and should
be contrasted with the elimination of a cause of death. The life-table
implications of lifesaving of this type have been worked out in detail by
Vaupel and Yashin (1985). Those who have been saved from death but not from
serious injury subsequently face a different regime of mortality risks than
those who have never been seriously injured. For example, the quadriplegic
must forgo risk-producing activities, such as driving, but faces increased
risks to life in other respects, for example, from infections.

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3
The social consumption equivalent (SCE) framework allows one to trace the
implication of changes in mortality across different ages on the various
components of the model. The following section briefly summarizes the main
points of the SCE model as it has been developed for death. Many of the more
technical details are included in a footnote. The discussion includes a
comparison of the SCE model with those based on willingness to pay and human
capital. This is followed by a formal presentation of the revised model that
includes health status as an additional argument of the utility function and a
determinant of the age patterns of productivity, consumption, and mortality.
Once health statuses are refined beyond the simple two-way classification
alive-dead, it is necessary to confront the problem of measuring the utilities
of alternative health states. The paper then reviews the utility measures
available and examines their consistency and capability through illustrative
valuations of selected illnesses and injuries.
The Social Consumption Equivalent Value of Life
The SCE method uses an age-specific, overlapping generation, economic
model to assess the cost of loss of life or the value of lives saved as the
result of a change in the pattern of mortality by age. The SCE method is: (1)
based on economic welfare theory, (2) gives values in dollar terms that are a
function of the age of the victim, (3) gives values that can be expressed in
terms of human capital and willingness to pay, and (4) is fully actuarial.
Under SCE, loss of life can be evaluated in three different ways: (1) by
changes in age-specific life-table survival risks (caused, say, by improved
highway design), (2) by "statistical" lives lost at a given age a, and (3)by
cause (cancer, airline accidents) where loss.of life occurs with a known age
incidence. SCE emphasizes that valuation must account for the additional
consumption of those whose lives are saved or lengthened. For example, when a
70 year-old's life is "saved," society gains that person's enjoyment or
utility of additional years that are otherwise lost. But the extra
consumption that supports utility in these additional years must be paid for-
-possibly by additional social security payments, by transfers from younger
relatives, or by additional saving earlier in life.
The SCE method can be viewed in terms of two key relationships. The first
of these is the social welfare function given by:
CO
W » / U(c(x) ,x]p(x)dx	(1)
0
where U[c,x] is the utility of being alive at age x, given consumption rate c;
P ( x) is the probability of surviving from birth to age x; and w is the maximum
age of surivorship. The second equation is given by the societal budget
constraint:
to	to
X e~9xp(x)c(x)dx - (f(k)-gk) J e~9xp(x)X(x)dx	(2)
0	0
where g is the constant rate of population growth; f(k)»F(K,L)/L is output per
worker at capital-labor ratio K/L for an economy with constant returns to
scale production function F; and X(x) is the age schedule of labor
participation.

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4
By considering the total differentials of equations (1) and (2) with
respect to an arbitrary pattern of changes in survival probabilities, Arthur
was able to show that the change in expected lifetime welfare is given by:
O)
5W « J U[c(x),x]Sp(x)dx
0

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5
SCE [ Sp ]
Social
Consumption
Equivalent
Value
(l/e)c6p
Average
Individual
Willingness
to Pay
wL6p c5p
Human Capital
Net of
Consumption
(P/AjnJvgp.
Value of
Additional
Children
Equation (7) shows that society's willingness to pay for mortality
improvements may be greater or less than individual willingness to pay for the
same change.
Adding Health Status to the Model
The SCE model can modified to include nonfatal risks by including a term
for health status in the welfare function. We assume that each person has a
utility function U[c(x),h(x),x], where h(x) is defined as the "state of
health" at age x. Health status is also assumed to have a direct impact on
health costs, consumption, fertility, mortality, and labor productivity.
Changes in fertility, mortality, and labor productivity will induce changes in
the equilibrium stable population growth rate and the equilibrium capital-
labor ratio. Suppose that some activity (e.g., less safe roads, changed
airline regulations) alters the health state by Sh(x) over the age dimension.
Suppose also that this change has associated with it direct health costs
ScH{ Sh], and alterations in consumption Sc( «hj, labor effectiveness «X[ Sh 1,
mortality &p[Sh], and fertility &n{5h]. The latter are all directly observed
changes for a specific category of injuries.
The social welfare function now takes the following form:
u
W- J U[c(x),h(x),x] -p(x)dx.	(8)
0
We can rewrite the societal budget constraint as:
CO	(l)	CO
J e"9*p(x)c(x)dx + J e~9*p(x)cH(x)dx * (f(k)-gk) I e"9xp(x)X(x)dx	(9)
o	0	0
breaking out health costs and consumption expenses separately. The change in
welfare caused by 5h is given by:

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6
0)	no
5W » 3U/3c(0) J" e~	(0
-	(f(k)-gk) { J e~^xX(x)6p[5h]dx + f e"9*p(x)5X[5h]dx }
0	0
0)
-	5k[Sh](f'-g) / e~9xX(x)p(x)dx - (S6g[5h].	(11)
0
Equation (11 ) is identical to equation (N. 6 ) in footnote 1 except for the
addition of the terms related to changes in medical costs (5ch[5h]) and
changes in labor productivity related to changes in health status (5X(6hl).
Also, the change in the population growth rate now includes the combined
effect of changes in fertility and mortality.
Using equation (11 ) to substitute for the first term in equation (10)
yields:

-------
0)	0}
SW => J U[c(x) ,h(x) ,x]Sp[ Sh]dx + / 3U/3h • 5h( x )p( x )dx
0	0
(0	CO
+ 3U/3c(0) { w-[ J e-9xX(x)Sp(x)c3x - f e^SXf 5h]p(x)dx ]
0	0
CO	03
-	J e'^ScuISh]p(x)dx - J e'^cufx)6p(x)dx
0	0
0)
-	J" e~<3xc(x)Sp(x)dx + 0Sg[Sh] }	(12)
0
This can be simplified to:
»	- «Sp	+ «5h
Life-Cycle	Utility of Utility"of
Welfare	Extra	Improved
Increase	Life Years Health Status
+ 3U/3c(0) { wLSp
- wL5h
Value of
Extra
Labor Years
Value of
Increased
Productivity
" cH,5h
" cH,5p
Social Cost of
Health Status
Improvements
" C«P
Social Cost of
Consumption
Upkeep
Social Cost of
Health Maintenance
Over Extra Years
+
^ V5p+V5m^/Am
Value of
Additional
Children
}
(13)
Where l5 ' c5 ' and CH 5 are expected extra person-years of production,
consumption, and health costs respectively, resulting from variation in
mortality; L§h» c$h» an^ CH 5 are the expected life-cycle increases in
productivity, consumption, and health costs directly associated with improved
health status; vg and vjjj are additional children per person due to variation
in mortality and health, respectively; and is the average age of
reproduction in the stable population.
A comparison of equation (13) with equation (3) indicates that improving
health status has benefits and cost above and beyond those associated with
improved longevity. There is a quality-of-life aspect to living longer, now

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8
captured by the second term in equation (13), that	was ignored in the original
model. A healthier population will also be a more	productive one, but at the
additional social cost of maintaining good health.	Finally, health status
changes may affect fertility rates, which in turn affect social welfare either
negatively or positively depending on the value of	additional children to the
society.
Empirical Estimation
This subsection describes methods for estimating each term in equation
(13). The remainder of this section, provides illustrative applications.
Since health status is accounted for explicitly in the model, the
utility per life year (the first term in the equation) should be uniform over
time . Its value can be estimated from a study of individual willingness to
pay for a statistical life by (a) selecting a discount rate, (b) computing the
present value (in years) of the remaining expected lifespan for someone at the
average age in the study population, and (c) dividing mean willingness to pay
by mean expected life span. Miller (1986) identifies 25 studies of individual
willingness to pay for a statistical life that are of reasonable quality.
After adjusting such parameters as the value of time to make the values in the
studies more comparable and adjusting for people's misperceptions of their
fatality risks using the procedure in Blomquist (1982), the mean value of a
statistical life across the studies was $1.95 million 1986 after-tax dollars
with a standard deviation of $.5 million.
Almost all of the 25 studies involved populations with mean ages around
38. According to the Statistical Abstract (1988), the average remaining
lifespan at age 38 is roughly 39 years. At a 6 percent discount rate, the
value per life year at age 38 is about $120,000 or $350 per day. At a 2
percent discount rate, it is about $70,000 per year or $200 per day. By way
of comparison, Moore and Viscusi (1988) estimates a statistical model of wage
premiums for risk that indicates the average individual is willing to pay
$90,000 for a life year and uses a 2 percent discount rate in safety
decisionmaking.
The utility per year of improved health status—the second term in
equation (13)--presents the greatest difficulty in valuation. Computation of
differences in welfare associated with changes in health status requires
knowing the utilities of alternative health states. Recent work on the
measurement of health status (reviewed in the next section) provides the
necessary data. This work produced scales indicating how utility loss varies
with the nature and extent of functional loss.
If the utility values on a scale are normalized so that death has a
value of zero and perfect health a value of one, the value associated with
unit utility loss for one year will be the value of a life year. The utility
in the second term is the product of the functional loss averted and the
utility of this loss. To get a dollar value, this product is multiplied times
the value of a 'functional life year.

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9
The third through seventh terms in equation (13) together constitute the
change in human capital net of consumption that results from the health status
change. This is a societal externality. The value of extra labor years and
increased productivity is measured by the gain in earnings attributable to
averting the illness or injury. The social costs related to health status
changes essentially we medical costs borne by third-party payers, charity, or
government. The seventh term is the impact of the health status change on
consumption, including consumption funded by transfer payments, insurance
payouts, and earnings. Under the assumption that all bequests stay within the
family, the change in the family's after-tax earnings that results from the
illness or injury should equal the change in the family's earnings-related
consumption—so they cancel out. Thus, the externalities resulting from
reduced illness or injury equal taxes gained plus transfer payments (including
medical care reimbursement) averted. The dollar value of the externalities
generally can be computed from the extensive literature on costs of morbid
conditions and data from the Health Interview Survey.
The explicit inclusion of transfer payments in the societal benefits is
consistent with the generally accepted principle that transfer payment
reductions are not benefits (see, for example, Klarman, 1965 or Hu and
Sandifer, 1981). Rational individuals will pay less to avoid disability if
transfer payments will cover some of the associated costs. Since transfer
payments were subtracted from individual willingness to pay, their explicit
addition yields zero net transfers in the societal benefit estimate.
The final term in equation (13) is the value of additional children born
due to the health status improvement. Arthur (1981) estimates the value of
this term as -$68,125 (in 1975 dollars), based strictly on the costs society
incurs per child. This approach ignores the noneconomic benefits that parents
derive from their children. Analyses of direct costs and opportunity costs of
children (Espenshade and Calhoun, 1986) suggest these benefits are at least as
large as the opportunity costs. In this article, therefore, the net value of
this term is assumed to be negligible and is ignored in the computations.
Consistency of Empirical Estimates across Scales
The operations research and medical decision-making literature contains
many scales that examine the multi-attribute utility loss associated with dif-
ferent health states. Some articles focus on individual diagnoses--for
example, the utility loss associated with blindness or kidney failure. Others
create functional ability scales and examine the utility associated with each
state on the scale. Torrance (1982, 1986) evaluates the different
methodological approaches used in this literature.
Tables 1 through 3 compare the utility loss that different scales
suggest is associated with selected diagnoses. The studies by Green and Brown
(1978), Card (1980), His et al. (1983), Miyamoto and Eraker (1985), Pliskin
Shepard, and Weinstein (1980), Sackett and Torrance (1978), and Viscusi et al.
(1989) directly estimate the utility loss associated with specific diagnoses.
The other loss estimates in this table were computed by developing descrip-
tions of the functional impairments associated with the diagnoses, then

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10
computing the utility losses that each scale suggests are associated with
these impairments. Impairments generally were evaluated on only a subset of
the utility scales because the other scales did not include appropriate
impairment categories.
This section first describes and evaluates the studies that provide
utility loss estimates for at least two diagnostic conditions. Next, for each
diagnosis, it compares the utility loss estimates across studies and sub-
stitutes the modal utility loss estimate into equation (13) to estimate an SCE
value. This analysis is the first systematic attempt to validate the utility
scales against one another or against utilities estimated from studies of
specific illnesses and injuries. To provide a fairer test of the scales, we
generally estimated the functional impairments on all scales first, then went
back and computed the associated utility losses.
Available Scales Showing Utilities
Torrance (1982) conducted a survey of 112 parents of school-age children
in Canada. The survey yielded utility loss estimates for scales that
evaluated four dimensions of functioning: impaired physical function, role
function (ability to work, play, etc.), social-emotional function, and health
function. Pain is incorporated, somewhat cursorily, in the last category.
Further analysis of the original ratings and supplemental interviews yielded a
multiplicative equation for combining the utility losses across dimensions of
impairment (Drummond et al., 1987). The utility losses have an uncertainty
range (two standard deviations) of ± 12 percent. The four impairment scales
are easy to use and applied to the widest range of diagnoses of any scale we
tested. The equation for combining ratings is simple and conceptually
appealing; it admits the possibility of fates worse than death and recognizes
that the utility loss associated with an impairment is lower if the individual
initially lacked full utility because of other impairments
Sintonen (1981) obtained ratings from 120 randomly selected Finns of the
relative utility of each point on 11 functional scales: raving, hearing,
speaking, seeing, working, breathing, incontinence, sleeping, eating, mental
functioning, and social participation. The respondents also provided guidance
on additive methods for computing a combined utility loss from the discrete
losses. The method allows the analyst to go into considerable detail, which
is helpful in evaluating a condition where a detailed medical description of
the typical course and consequences is available. The lack of a scale related
to pain detracts from rating quality, however, especially for conscious states
worse than death. The large number of factors and additive weights also mean
that impairments which are not systemically pervasive never are rated as very
severe, which is inconsistent with the information from other utility scales.
Kind, Rosser, and Williams (1982) developed a two-dimensional scale that
is particularly easy to use. One dimension measures disability, where 1 is
fully mobile and 8 is unconscious. The second dimension measures distress,
where 1 is none and 4 is severe. Median utility values were computed from the
non-economic component of British jury awards, which follow an informal
schedule. Interviews also were conducted with a non-random sample of 70

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11
subjects including healthy volunteers, doctors, nurses, and patients in
medical and mental hospitals. The survey has methodological problems,
however, in part because the 10 mental patients provided some extreme ratings
that were not censored. It also is inconsistent with both other survey-based
estimates of utility loss and the jury award scale. Even the jury award
scale's applicability is limited because it does not deal with sensory or
mental function. In addition, both the jury and survey data indicate
virtually all health states involve utility losses less than 20 percent or
more than 60 percent, which seems unlikely and disagrees with other studies.
Kaplan (1982) and Kaplan, Bush, and Berry (1976) provide a utility loss
estimates for a scale with simultaneous dimensions of mobility, physical
activity, and social activity, as well as linear score adjustments for 36
symptom-problem complexes. The scale, which was the first developed, was
calibrated through a population survey in San Diego. It has the major
limitation of excluding the possibility that impairments can be worse than or
even almost as bad as death. In addition, the symptom-problem complexes
sometimes are inconsistent; for example, why should a cough and fever add
.007 to utility while a cough alone subtracts .007? Also, more analytic
judgment is required to select an appropriate combination of complexes using
this scale than to rate diagnoses using any of the other scales.
His et al. (1983) enlisted four physicians—specialists in orthopedics,
neurology, plastic surgery, and general surgery— then divided 476 moderate
and severe injuries into their four specialty categories. The physicians
defined six functional scales, with impairment levels ranging from 0 to 4:
mobility, daily living (self care), cognitive/psychological sensory, cos-
metic, and pain. For each injury, the appropriate specialist rated the
probable number of weeks of impairment at each level during the first year,
and the probable impairment levels during the second through fifth years and
thereafter. Separate ratings were done for four age groups. The impact on
life expectancy and the need for corrective surgery also were estimated.
Using two physicians per injury, Carsten (1986) added physician ratings of
some additional injuries and redefined others, arriving at a final set of 432
injuries. Roughly 20 injury experts then used a structured computer exercise
to develop weights for combining the ratings on five of the impairment dimen-
sions (self care was omitted) into a total impairment score. Their weighting
was adjusted using ratings from an American Medical Association guidebook
(1984), which is discussed below. A decision by Carsten, without consulting
the physicians, established that no nonfatal injury was worse than death.
Luchter (1987) added the days of productivity loss as an impairment measure
for minor injuries. Miller, Brinkman, and Luchter (1988) converted the
workdays lost for minor injuries into utility loss estimates.
Three sources provide utility estimates for a range of diagnoses rather
than for points on functional scales.
The Guides to the Evaluation of Permanent Impairment (American Medical
Association, 1984) were developed by rare than 100 physicians. They are
intended primarily for assessing impairment through physical examination and
provide guidance at a micro level. For example, (a) the impairment associated

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12
with shoulder injuries is estimated separately for the more and less dominant
arms and varies with the percentage reduction in range of shoulder rotation,
and (b) nine levels of impairment are presented for lung cancer. The guides
also provide insight into typical impairment levels for some injuries and
illnesses. The guides are perfect. They assume nothing is worse than
death. Furthermore, no central control was exerted over the influence
specialists on a body system decided that system had overall functioning.
Therefore, the average impairment scores for some body systems seem high.
Green and Brown (1978) asked about 100 British university students to
rate the relative severity of death, selected injuries, and being unhurt in an
accident. Their results are interpreted in this article as indications of the
percentage utility loss during the period of disability for acute conditions
and of lifetime loss for chronic and irreversible conditions.
Finally, Sackett and Torrance (1978) asked a small random sample of
Canadians whether they would rather live their normal lifespan with selected
chronic illnesses or live a healthy life but die prematurely. The number of
years that people would trade to avoid the different impairments determined
the utility losses associated with them. The conditions examined included
tuberculosis, depression, renal failure, mastectomy, and an unnamed contagious
disease. An important lesson of this study is that the value of an impairments
rises with its permanence. More research is needed to determine (a) whether
the value of avoiding minor illnesses and injuries is significantly overes-
timated with the approach suggested in this article and (b) how to adjust the
values based on the duration of impairment.
Estimated Investment to Reduce Selected Injuries and Illnesses
Table 1 presents estimates of the utility loss and cost associated with
selected injuries. The values in the first column of data are for blindness.
The utility loss estimates from Torrance (1982) and Green and Brown (1978) can
be used to judge the quality of our estimates using other scales because these
studies asked people about the utility loss associated with blindness; the
estimates are 37 and 34 percent respectively. The 20 percent value in Card
(1980) also is a survey estimate, but may not be representative of the general
population because it was based on a small survey of medical personnel. We
estimated a 33 percent utility loss from Carsten (1986) by doubling the
estimate for losing one eye, so the estimate may be low. Our 39 percent
estimate from the Kaplan (1982) scale is for someone who did not drive, walked
without physical problems, was limited in choice of work, and wore glasses or
had trouble seeing. These two estimates agree with the survey data. The
lowest estimate, the 15 percent loss from the Kind, Rosser and Williams (1982)
scale, is for a severely limited work choice but no distress. Because this
description omits the sensory loss, the utility loss probably is underes-
timated. Sintonen (1981) provided an adjustment factor for blindness that we
used in conjunction with the rating of the impact on functioning to obtain an
estimated utility loss of 22 to 24 percent. This estimate may be low because
blindness only affects a few aspects of functioning, which means the Sintonen
scale unduly constrains the possible utility loss. Viewed from the

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13
perspective of the other estimates, the 85 percent utility loss estimate in
the American Medical Association guide is a severe overestimate.
We conclude that the utility loss associated with blindness is probably
between 33 and 39 percent. With the $1.95 million dollar value of a life,
this range implies typical individuals would be willing to pay between
$640,000 and $760,000 to prevent a statistical person among their group from
going blind. Data on the average foregone, taxes and transfer payments per
blind individual should be added to this value to estimate the SCE.
The second column of data shows the utility loss associated with severe
brain damage or lasting unconsciousness. Kind et al. (1982), Torrance (1984),
and Green and Brown (1978) measured the utility loss associated with this
injury directly and determined it was a fate 8 to 28 percent worse than death.
The physician ratings in Carsten (1986) and American Medical Association
(1984), which did not allow fates worse than death, rated the utility loss for
unconsciousness within 5 percent of the loss for death. Sintonen (1981) found
lasting unconsciousness was 3 percent worse than death. Torrance (1984) notes
that the visually based rating method used by Sintonen implicitly may have
indicated the survey designer expected people to consider death the worst
fate, so the 103 percent utility loss may be an underestimate. Kaplan's
(1982) scale does not provide good utility loss estimates for severely
disabling conditions; for unconsciousness, we estimated a utility loss of 71
percent.
The studies that allow fates worse than death provide the best estimates
of utility loss for lasting unconsciousness, with a 116 percent loss seeming
most probable. The last three rows of data in Table 1 indicate the medical
costs, lost earnings, and other public costs associated with unconsciousness
(and other injuries). The medical and earnings data are from Miller,
Brinkman, and Luchter (1988), while the public costs are from Miller (1986).
His et al. (1983) indicates that severe head injury causes roughly a 5-year
reduction in lifespan. If we use a Federal income tax rate of 23 percent
(Minarik, 1985) and a state rate of 5 percent (Feenberg and Rosen, 1986),
these data can be used with equation (13) to estimate the SCE for a severe
head injury at $3,100,000.
As the third column of utilities in Table 1 show, complete quadriplegia
is another fate worse than death, with a utility loss of 105 to 114 percent on
the three reliable scales, implying a best estimate of 109 percent. The
Sintonen scale did not work well here, yielding an estimated utility loss of
only 49 percent because its method for combining losses does not allow a large
total loss unless the sensory, mental, and rotor systems all are severely
affected. Kaplan's scale again worked poorly, while the physician's judged
this fate almost as bad as death. Both physician judgment (Carsten, 1986) and
interviews with quadriplegics who have adapted to their injuries (Torrance,
1988) indicate the utility loss may decrease over time, leveling out at about
65 percent. Complete quadriplegic reduces expected lifespan by 21.5 years
according to His et al, (1983) . The estimated SCE for a complete quadriplegic
injury is $2,600,000.

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14
Using the scales in Kind et al. (1982), Kaplan (1982), and Torrance
(1982),	we estimate the utility loss for paraplegia (data column 4) at 50 to
54 percent with incomplete paralysis and 62 to 65 percent with complete paral-
ysis. Paraplegics surveyed by Torrance (1988) and the physicians in Carsten
(1986) estimated a slightly smaller loss, around 45 percent. The students
surveyed by Green and Brown (1978) and the Sintonen (1981) scale (which did
not model paraplegia well) both gave estimates around 29 percent, which are
probably too low. As with blindness, the utility loss in the American Medical
Association (1984) guides seems much too high, 81 percent. Complete
paraplegia reduces expected lifespan by 15.3 years according to His et al.
(1983)	. The best estimate of the utility loss is 50 to 65 percent, with an
SCE of $1,300,000 to $1,600,000.
For older people, severe burns (data column 5) are the worst possible
fate. They typically spend the rest of their lives bedridden with sufficient
pain that they cannot do simple arithmetic. Using the utility scales in
Torrance (1982) and Kind et al. (1982), we estimate the utility loss at 137 to
139 percent. The physician ratings, which do not allow fates to be worse than
death, yield lower and less credible values. Severe burns shorten lifespan,
perhaps by about 5 years. The SCE is about $3.6 million to prevent a person
in late middle age from being severely burned.
A broken lower leg (data column 6) typically causes no permanent
impairment according to data from the Consumer Product Safety Commission's
injury cost model (which also provided the cost data for this injury) and the
physician ratings of impairment in Carsten (1986). Four of the five scales we
applied suggest a broken leg will reduce utility by 30 to 36 percent in the
year it occurs, while Kaplan (1982) yields an excessive estimate of 54
percent. The 34 percent estimate from Green and Brown (1978) was computed as
the loss for a broken arm times the ratio of losses for amputation of a leg
and an arm. With a one-year utility loss around 33 percent, the SCE for a
broken leg is about $40,000.
As the last column in Table 1 shows, our ratings with the Kind et al.
(1982), Torrance [1982), and Kaplan (1982) scales suggest typical minor
injuries reduce utility by 36 to 38 percent for a few days. These estimates
assume the number of lost work days (counting weekends as if they were
workdays) equals one half of the impairment days for an employed person who is
injured. The 36 to 38 percent range is consistent with survey estimates of 30
percent for a bruise and 40 percent for a sprain in Green and Brown (1978).
The Sintonen scale does not work well for minor injuries, yielding a low
utility loss estimate of 15 percent, because minor injuries only affect a few
aspects of functioning. Including the externality costs, the SCE for a minor
injury is about $1,500.
Table 2 shows estimates of the utility loss associated with selected
illnesses. The first two columns of data deal with mild and severe angina.
Hartunian, Smart, and Thompson (1981) provided the description of angina's
impairment impacts that we used and the data on economic costs.

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15
For mild angina, Pliskin, Shepard, and Weinstein (1980) conducted a
small survey that indicated the utility loss was 12 percent, in the mid-range
of the 10 to 15 percent loss estimate in the American Medical Association
(1984)	guides. Using the impairment scale in Kind et al. (1982), we estimated
the impairment at 0.7 to 16 percent. By assuming that mild angina reduced
physical and role function by half a level and also using half the pain score
(severe angina caused just one level of reduction on each dimension), we
estimated a 16 percent utility loss from the scale in Torrance (1982). This
scale, however, did not differentiate impairment as finely as was desirable to
analyze a largely asymptomatic condition. Using Kaplan's (1982) scale, we
estimated an 18 percent utility loss.
For severe angina, surveys by Miyamoto and Eraker (1985) and Pliskin et
al. (1980) yielded utility loss estimates of 30 to 31 percent, comparable to
the estimate of 25 to 32 percent we made from the Kind et al. (1982), Torrance
(1982), and Kaplan (1982) scales. The loss estimated by the American Medical
Association (1984) guides is slightly higher, 35 to 40 percent.
Utility losses of 12 percent for mild angina and 30 percent for severe
were used to compute SCEs of $220,000 to prevent a mild case of angina for
someone age 55 and $550,000 to prevent a severe case. These estimates seem
high, given the economic costs involved.
The third and fourth columns of data give estimates for food poisoning.
The estimates were based on the illness descriptions and cost data in Roberts
(1985).	They apply to cases of salmonella and Campylobacter.
Based on Roberts' description, we estimated half the severe cases
involve four days of severe discomfort and inability to leave home. We
estimated the other half would last six days, with three days of severe
discomfort and confinement to a hospital bed and three days of severe discom-
fort and an inability to leave home or moderate discomfort and extreme
weakness. Finally, we assumed all severe cases involve four days with no
discomfort, but somewhat reduced strength and resilience. The Kind et al.
(1982), Torrance (1982), and Kaplan (1982) utility scales provide consistent
estimates of utility loss: 39 to 45 percent over 10 days. During the first
three days, both scales indicate patients with severe cases will feel as if
they would rather be dead. The SCE estimate is $2,400 to $2,600 to prevent a
severe case of food poisoning.
To estimate the utility loss associated with a mild case, we made low
and high estimates of impact.
o Low estimate. Assume 30 percent of the cases involve two days of severe
discomfort and inability to leave home and the remaining 70 percent
involve just 1.5 days of mild discomfort that is not severe enough to
prevent the sufferer from going to work. Under this assumption, the
average case involves a utility loss (on the Kind et al. (1982) or
Kaplan (1982) scales) of 24 to 25 percent for an average of 1.65 days,
with an SCE of $140 to $150. The Kaplan (1982) scale suggests an

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16
uncomfortably high 41 percent utility loss for this mild case, ascribing
an overly high 33 percent utility loss to mild discomfort that does not
prevent someone from working.
O High estimate. Assume 75 percent of the cases involve just 1.5 days of
mild discomfort, 25 percent involve two days of severe discomfort, and 5
percent are as severe as the reportable cases. Under this assumption,
the utility loss is 25 to 26 percent for an average of 2.1 days, with an
SCE of roughly $200.
The SCE per day of mild food poisoning is $85 to $95. By comparison,
Berger et al. (1985) obtained a mean willingness to pay to avoid a day of
nausea of $91 from 18 respondents, while Gerking et al. (1986) obtained a mean
of $409 from five respondents. Gerking believes that his values, and possibly
even Berger's, may be higher than people actually are willing to pay.
Consistent with his belief, his values exceed the values derived from the
impairment scales, even though food poisoning probably is slightly worse than
just feeling nauseous.
The utility loss estimates for chronic bronchitis, given in the fifth
column of data, were based on a description of the course of illness developed
for EPA by Viscusi et al. (1989) and were generated before Viscusi fielded his
willingness-to-pay survey. Estimates we made using four scales suggest a
utility loss of 35 to 45 percent. The American Medical Association (1984)
guides, again high, suggest at least a 50 percent utility loss. Viscusi et
al. (1989), based on a survey, estimated the utility loss at 32 percent, close
to the range we predicted. Data on externality costs were not readily
available to compute the SCE for chronic bronchitis.
The sixth column provides estimates of the utility loss associated with
a day in the hospital. The survey by Kaplan (1982) provides a range of
utility losses from 41 to 60 percent for hospitalization, "depending on whether
the person can move around and perform self care. Sackett and Torrance (1978)
obtained an estimate of a 40 to 44 percent utility loss for hospitalization
with a contagious disease. The utility loss estimates we made with the Kind
et al. (1982) and Torrance (1982) scales were between 55 and 65 percent,
possibly a bit high, while the 47 percent loss we estimated with the Sintonen
(1981) scale was on the mark. Adding the $550 average charge for a hospital
day in 1985 (from the Statistical Abstract, 1988) to a utility loss of 40 to
60 percent, the SCE per hospital day avoided is roughly $700 to $750.
The last column in Table 2 provides estimates of the utility loss
associated with receiving regular dialysis for end stage renal disease.
Sackett and Torrance (1978) found the loss was viewed as 60 percent by the
general public and as 48 percent by those on dialysis. Again high, the
American Medical Association (1984) guide estimated a 90 percent utility loss.
Using the Kaplan (1982) scale, we estimated the loss at 48 percent. Using the
Torrance (1982) scale, we assumed mild physical limitation; some limitation of
work, with half the patients largely unable to work; frequent anxiety, but an
average number of friends; a disfiguring dialysis shunt; and some discomfort.
These assumptions imply a 62 percent utility loss. Without anxiety, the loss

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17
would be 50 percent. The Kind et al. (1982) scale was difficult to apply to
this impairment. It suggests a utility loss of 42 to 48 percent, depending on
whether the distress level is assumed to be mild or moderate. The costs
associated with end stage renal disease derive from unpublished analyses by
The Urban Institute, which also indicate that 10 percent of dialysis patients
die each year. With a 60 percent utility loss, the SCE is $1,500,000 per case
prevented.
Table 3 presents estimates of the utility loss associated with
retardation, by severity. No direct survey data are available on this
condition. We included it because so many public health problems, among them
lead poisoning, fetal alcohol syndrome, malnutrition, foodborne listeriosis,
and workplace chemical exposures, can cause children to be retarded. In the
future, someone is likely to estimate willingness to pay to avoid retardation,
and our estimates will be available for comparison; in the meantime, they may
be useful for policy analysis.
We estimated a range of retardation levels, with a utility loss of about
20 percent associated with the need for special education, a severely limited
ability to work associated with a utility loss around 50 percent, need for
help in self care raising the utility loss to 55 to 60 percent, and very
severe retardation raising the loss above 75 percent. The American Medical
Association (1984) guides performed well in evaluating retardation, agreeing
reasonably well with our ratings from the Torrance (1982) and Kaplan (1982)
scales.
A Further Comparison
The impairment estimates in the lineage from His et al. (1983) cover all
possible injuries in motor vehicle crashes. Miller, Brinkman, and Luchter
(1988) substitute the utility losses for fates worse than death shown here for
the physician ratings, then apply the data to estimate the utility loss and
associated willingness to pay to avoid a typical injury. For each diagnosis,
they compute the present value of future impairment years at a 6 percent
discount rate. They then estimate aggregate impairment by multiplying the
impairment by diagnosis times data on 1982-1984 injury incidence derived from
a sample, compiled by the National Highway Traffic Safety Administration in
its National Accident Sampling System. The sample includes all injuries in
roughly 30,000 crashes that were reported to the police. The aggregate
impairment years next are multiplied times the $120,000 willingness to pay to
save a life year. An estimated average willingness to pay to avoid injury of
$12,800 results.
Insight into the quality of this $12,800 estimate, and of the impairment
estimates, can be obtained from a comparison with estimates of willingness to
pay to avoid nonfatal injury in the workplace. Five estimates exist that
cover all reported injuries, as opposed to just lost workday injuries. All
five derive from hedonic regressions that examine pay differentials for risky
jobs. As Table 2 shows, four of the five estimates are between $10,500 and
$13,000, satisfyingly close to the estimate from physician ratings of
impairment.

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18
The comparison between the willingness to pay to avoid motor vehicle and
workplace injuries implicitly assumes that the distribution of injuries is
similar in these two settings. That assumption is questionable, because back
injuries occur more frequently in the workplace. A special analysis we ran of
National Council on Compensation Insurance detailed claims data shows back
injuries account for 30 percent of all on-the-job injuries that cause lost
workdays, while Luchter (1986) indicates they account for only 5 percent of
more-than-minor injuries in rotor vehicle crashes. Thus, the agreement in
willingness-to-pay values provides only molest confirmation of the utility
loss estimates.
Conclusion
Scales on the utility of functional impairment provide a quick,
inexpensive, reasonably consistent, and theoretically supportable way to
estimate SCEs for preventing a wide range of diagnoses. Using these methods
requires estimating the functional impairment and reduction in lifespan
associated with the health status changes. The impacts on transfer payments
(including health insurance payments), administrative costs, and taxes on
earnings also must be estimated.
The available utility scales yield reasonably consistent values, but
these values occasionally seem unreasonably high compared to the economic
costs involved (witness mild angina). Pre-planned research validating the
utility losses against willingness-to-pay estimates would make it easier to
use the scales with confidence.
Scales that do not allow the possibility of fates worse than death
should not be used to evaluate severely disabling conditions. Torrance (1982)
probably is the most reliable and flexible scale presently available, but
lacks utility loss estimates for some aspects of functioning (for example,
loss of reproductive capability, sustained pain) and very mild symptoms. The
simplistic approach taken by Green and Brown (1978) of asking people to score
relative severities of different diagnoses provided surprisingly reliable
results. The American Medical Association (1982) guides to permanent impair-
ment, which are based on physician judgment, generally overestimate utility
loss.

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Table 1
Percentage Utility Loss and Cost Associated With Selected Injuries
Study
Kind, Rosser,
& Williams
Kaplan
Torrance
rehabed patients
Green & Brown
Card
Sintonen
Carsten
Am Med Assoc
Blind
15
39
37*
34*
20*
22-24
33*
85*
Severe
Head
108
71
116
128*
103
93-100*
95*
Quad
114
66
105
65*
109^
49
Severe
Burn
Para (age 45+)
52-65
50-64
54-62
45*
29*
29
85-86* 42-45*
99	81
137
139
91*
95*
Broken
Lower
Leg
31
54
34
30
36
Minor
Injury@
38
36
37
30-40*
15-16
Medical Cost	DK	680,000
Productivity Loss	DK	400,000
Legal, Admin,
Transfer	DK	60,000
390,000 235,000 450,000 200 285
210,000 160,000 100,000 1,350 280
60,000 35,000 60,000 DK DK
@ Average daily utility loss until recovery, which occurs in less than 1 year.
* Direct measurement.

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Table 2
Percentage Utility Loss and Cost Associated With Selected Illnesses
Study
Kind et al.
Torrance
Kaplan
Sintonen
Sackett & Torrance
patients
Miyamoto & Eraker
Pliskin et al.
Viscusi et al.
Am Med Assoc
Angina
Mild Severe
.7-16
16
18
12'
25-31
32
32
30*
31*
Food Poisoning®
Severe Mild
45
39
45
24-25
25-26
41
Chronic
Bronchitis
23-37
34-45
45
30-36
10-15* 35-40*
32*
50+
Day in
HospitalB
61-62
55-65
41-60*
47
40-44*
ESRD
42-48
62
48
60*
90J
Medical Cost	2700
Productivity Loss	50
Transfer & Admin	o
60
30
1000
300
DK
DK
DK
DK
500
50
DK
250,000
90,000
10,000
0 Average daily utility loss until recovery, which occurs in less than 1 year.
* Direct measurement.

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Table 3
Utility Loss Associated with Retardation
Condition	Util Loss	Source
Very severely retarded	83	Torrance
75+	Am Med Assoc
Retarded needing help with care	57	Kaplan
55	Torrance
55-75	Am Med Assoc
Moderately retarded with self-care	42-51	Kaplan
52	Torrance
25-50	Am Med Assoc
Mildly retarded	33	Kaplan
20-32	Torrance
23	Sintonen
10-20	Am Med Assoc
Table 4
Willingness to Pay to Avoid Non-fatal Workplace Injuries
(1985 After-tax Dollars)
Study
Butler (1983)
Dillingham (1983)
Olson (1981)
Smith (1983)
Viscusi (1978)
Value
$10,500
$17,000-$26,000
$12,000-$13,000
$11,000
$12,000-$21,000
Note: Values were converted to after-tax dollars using the method described in
Miller (1986).

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NOTES
1. The societal budget constraint represents a synthesis of Lotka stable
population growth dynamics with the standard Solow steady-state growth
model. The equilibrium population growth rate is the solution to the
integral equation of stable population theory given by:
(a)
1 = 1 e~9xp(x)m(x)c3x
0
where m(x) is the female birth rate to women aged x years. The
equilibrium capital-labor ratio is the solution to:
k= sf(k)
gk
(N.2)
where k is rate of change in k and s is savings per worker. The
comparative-static change in expected lifetime welfare (5W) resulting from
a change in mortality rates across different ages (5p(x)) is found by
taking the differential across equation (1):
ft)	CO
5W = / U[c(x),x]5p(x)dx + J 3U/3c(x) '5c[Sp]p(x)dx.	(N 3)
0	0
Under the assumptions of utility maximization and perfect capital markets
the life-cycle consumption pattern is given by:
w/at(x) = SU/ScfOJe-^*	(N.4)
so that
(•>	<0
SW - J U[c(x),x]Sp(x)dx + 3U/3c(0) J e-9*Sc[Sp]p(x)dx	(N.5)
0	0
The two terms in equation (N.5) can be interpreted as the change in
expected lifetime welfare that come from extra years and the value of
changes in the consumption pattern needed to accomodate the additional
years of living. The change in consumption can be evaluated by taking
differentials across the societal budget constraint, yielding:

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00	0)	00
0 = J e-^ct x) £p(x )dx + J e~'?x6c[ Sp]p(x)dx - (f(k)-gk) J e~9x>,( x) 5p( x )dx
0	0	0
0)
- 5k[5p](f'-g) J e~9xX(x)p(x)dx - |3Sg[$p]	(N.6)
0
where
CO	CO	0)
0 = J xe~9xc(x)p(x)dx - (f(k)-gk) J xe~"9*X(x)p(x)dx - k J e-9XX(x)p(x)dx.
0	0	0
@ is the life-cycle value	of a marginal increase in the population growth
rate (Arthur and McNicoll,	1978) . Following Arthur (1981) this term can
be expressed as:
0 = (1/b) [CfAc-A^-kn]	(N.7)
where b is the crude birth rate in the stable population C is per capita
consumption, Pi^ and are the average ages of consumption and production,
respectively, and n is the labor/population ratio. Using equation (N.6)
to substitute for the second term in equation (N.5) results in the
expression for the change in lifetime welfare given by equation (3) in the
text.

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Statistical Abstract of the United States - 1988, Washington, DC, U.S.
Government Printing Office, 1988.
Torrance, George W., Personal Communication with Ted Miller, July 1988.
Torrance, George W., "Measurement of Health State Utilities for Economic
Appraisal," Journal of Health Economics, March 1986, 5(1), 1-30.
Torrance, George W., "Health States Worse Than Death," in Third International
Conference on Systems Science in Health Care, (cd.) W. von Eimeren, R.
Engelbrecht, and C.D. Flagle, Springer Verlag, Berlin, 1984.
Torrance, George W., "Multiattribute Utility Theory as a Method of Measuring
Social Preferences for Health States in Long Term Care," in Values and Long
Term Care," Robert L. Kane and Rosalie M. Kane, (d.), D.C. Heath,
Lexington, 1982, 127-156.
Vaupel, J.W., and A.I. Yashin, "Repeated Resuscitation: How Lifesaving Alters
Lifetables," Institute for Applied Systems Analysis, Vienna, December 1985,
WP-85-85.
Viscusi, W. Kip, Wesley A. Magat, and Joel Huber, "Pricing Health Risks:
Survey Assessments of Risk-Risk and Risk-Dollar Tradeoffs," AERE Workshop
on Estimating and Valuing Mobility in a Policy Context, June 1989.
Viscusi, W. Kip, "Labor Market Valuations of Life and Limb: Empirical Evidence
and Policy Implications," Public Policy, Summer 1978, 359-386.

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Valuing Nonmarket Goods:
A Household Production Approach*
Mark Dickie
School of Social Sciences
University of Texas at Dallas
Shelby Gerking
Department of Economics
University of Wyoming
June, 1988
This research was supported by the U.S. Environmental Protection Agency
under Cooperative Agreement #CR812054-01-2. It has not been subjected,
however, to the Agency's peer and administrative review and therefore it
does not necessarily reflect the views of the Agency, and no official
endorsement should be inferred. We thank Don Waldman for assistance and
advice concerning econometric procedures, Anne Coulson, Don Tashkin, and
John Demand for invaluable assistance in survey design and data
collection, Alan Krupnik, David Brookshire, Don Coursey, John Tschirhart
and seminar participants at Arizona State University for comments on an
earlier draft, and Alan Carlin for his patience and encouragement
throughout the project.

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ABSTRACT
This paper presents a unique application of the household production
approach to valuing public goods and nonmarket commodities. Technical
relationships are estimated between health attributes, private goods that
affect health, and air quality using panel data drawn from a special
survey. Statistical tests show that individuals equate marginal rates of
technical substitution in household production with relevant price ratios.
This result confirms theoretical implications in a particularly critical
context for estimating values of health attributes and air pollution.
Value estimates obtained also bear on current questions facing
environmental policymakers.

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I. Introduction
Individuals frequently apply a household technology to combine public
and private goods in the production of nonmarket commodities for final
consumption. Hori (1975) demonstrates that in these situations, market
prices of private goods together with production function parameters mav
encode enough information to value both public goods used as inputs and
nonmarket final consumption commodities. Although this valuation
methodology is objective and market based, it seldom has been applied for
three reasons. First, underlying technical relations either are unknown or
data needed to estimate them are unavailable. Second, even if relevant
technical information is at hand, the consumer's budget surface in
commodity space may not be differentiable when joint production and other
complicating factors are present. As a consequence, the commodity bundle
chosen is consistent with any number of marginal rates of substitution and
sought after values of public goods and nonmarket commodities remain
unknown. Third, joint production and nonconstant returns to scale also
pose serious difficulties when taking the closely related valuation
approach' of estimating the area behind demand curves for private goods
inputs and final consumption commodities Pollak and Wachter 1975;
Bockstael and McConnell 1983).
This paper presents a unique application of the household production
approach to valuing public goods and nonmarket commodities which allows for
certain types of joint production and addresses key problems identified by
previous authors. Technical relationships are estimated between health
attributes, private goods, and air quality. Data used in the analysis are
drawn from a special survey designed to implement the household production
approach. Econometric estimates allow for truncated dependent variables in

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2
panel data using tobit models with individual-specific variance components.
Key results are: (1) attempts to value detailed attributes of nonmarket
home produced commodities may be ill-advised; however, estimating a common
value for a broadly defined category of attributes may be possible, and (2)
statistical tests show that individuals equate marginal rates of technical
substitution in household production with relevant price ratios. This
latter result confirms behavioral implications of the theory in a
particularly critical context for estimating values of nonmarket
commodities and public goods. Also, value estimates obtained bear on
current questions concerning air pollution control policy. The Clean Air
Act of 1970 and its subsequent amendments focus exclusively on health to
justify regulation and requires air quality standards to protect even the
health of those most sensitive to pollution. The survey data are
sufficiently rich to allow separate value estimates for persons with normal
respiratory function and persons with chronic respiratory impairments.
The remainder of this paper is divided into four sections. Section II
describes a simple household production model in a health context and
reviews theoretical issues in obtaining value estimates. Section III
discusses the survey instrument and the data collected. Section IV
presents econometric estimates of production functions for health
attributes, as well as values of better air quality and improved health for
both the normal and respiratory impaired subsamples. Implications and
conclusions are drawn out in Section V.
II. PRELIMINARIES
The model specifies utility (U) as a function of market goods (Z) and
health attributes, called symptoms, (S) .

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3
U = U(Z, S)
(1)
For simplicity, Z is treated as a single composite good, but S denotes a
vector measuring intensity of n health symptoms such as shortness of
breath, throat irritation, sinus pain, headache, or cough. Intensity of
the symptom is reduced using a vector (V) of m additional private goods
that do not yield direct utility, a vector of ambient air pollution
concentrations (a) , and an endowment of health capital (ft) .
Elements of V represent goods an individual might purchase to reduce
intensity of particular symptoms, and ft represents genetic predisposition
to experience symptoms or presence of chronic health conditions that cause
symptoms. Notice that equation (2) allows for joint production in that
some or all elements of V may (but do not necessarily) enter some or all
1
symptom production functions. The budget constraint is
Aspects of this general approach to modeling health decisions have
been used in the health economics literature (e.g., Grossman 1972;
Rosenzweig and Schultz 1982, 1983), where medical care is an example of V
often considered. In these three papers, however, the stock of health
rather than symptoms is treated as the home produced good, and Grossman
treats decision making intertemporally in order to analyze changes in the
health stock over time. A multiperiod framework would permit a more
complete description of air pollution's cumulative physiological damage,
but the present model's focus on symptoms of short duration, suggests that
a one period model is appropriate. Moreover, long term panel data
S1 = SX(V, a; Q)
i=l, . . .,n
(2)
where P denotes the price of Z, P denotes the price of V , and I denotes
income

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4
containing both economic and health information necessary to assess
cumulative physiological damage are difficult to obtain.
Similar models also have been used in environmental economics to
derive theoretically correct methods for estimating values of air quality
and other environmental attributes (e.g., Courant and Porter 1981; Harford
1984; Harrington and Portney 1987) , These models, however, only consider
the case in which m = n = 1 and rule out the possibility of joint
production. In this situation, the marginal value of or willingness to pay
(WTP) for a reduction in air pollution can be derived by setting dU = 0 and
using first order conditions to obtain
wt:p« - - u^A - - p^J/s}	(4)
where denotes marginal disutility of the symptom, denotes the
marginal effect of air pollution on symptom intensity, sj denotes the
marginal product of in reducing symptom intensity, and A denotes
marginal utility of income. As shown, marginal willingness to pay to
reduce symptom intensity (- U^/A) equals the marginal cost of doing so
(- p^sJ).
Extensions to situations where m and n take on arbitrary values have
been considered in the theory of multi-ware production by Frisch (1965) as
well as in a public finance context by Hori (1975). Actually, Hori treats
four types of household production technology. His case (3) involving
joint production appears to best characterize the application discussed in
Section IV because a single V may simultaneously reduce more than one
symptom. In this situation, a key result is that marginal values of
symptom intensity (- U^/X) cannot be re-expressed in terms of market prices
(pJ and production function parameters (S*) unless the number of private
J	J
goods is at least as great as the number of symptoms (m >_ n)• Intuitively,

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5
if m < n, the individual does not have a choice among some alternative
combinations of symptom intensities because there are too few choice
variables
(v
and the budget surfaces on which each chosen value of g1 must
2
lie is not differentiable.
Another perspective on this result can be obtained from the m first
order equations for the V. shown in (5)
j
sn
•J ^ • • • o ^
. sl
®.

lyx
•

pi
•

•
-
•

•
. vx.

«
0
a
(5)
Each first order condition holds as an equality provided each private good
is purchased in positive quantities. If m < n the rank of the symptom
technology matrix S ¦	most m, the system of equations in (5) is
underdetermined, intensity of one symptom cannot be varied holding others
constant, and the marginal value of an individual symptom cannot be
determined. On the other hand, if m = n and the symptom technology matrix
is nonsingular, then the rank is n and unique solutions can be computed for
the U^/X. If m > n and the technology matrix has full rank, then the
system is overdetermined, and values for the U^/X can be computed from a
subset of the first order equations.
Solving (5) computes marginal values for the nonmarket commodities
produced by the individual. The value of the public good input, a, is the
weighted sum of the value of the commodities, where the weights are the
marginal products of o in reducing symptoms:	" - E^CU^/AJS^. If the

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6
marginal products of a are known or estimated, solving (5) provides the
information necessary to value nonmarket commodities and public goods.
This theoretical overview yields several ideas useful in empirical
application. First, if mi n and the household technology matrix has rank
n, then values of nonmarket commodities and public goods are calculated in
a relatively straightforward manner because utility terms can be
eliminated. Second, even in cases where m_> n, the household production
approach may fail if there is linear dependence among the rows of the
technology matrix. Thus, statistical tests of the rank of the matrix
should be performed to ensure differentiability of the budget surface.
Third, if m > n, first order conditions impose constraints on values that
can be taken by the S^; validity of these constraints can be tested.
Fourth, the possibility that m < n suggests that the household production
approach may be incapable of estimating separate values for a comparatively
large number of detailed commodities and that aggregation of commodities
3
may be necessary to ensure m > n.
Fifth, if m > n, values of and need not yield positive values
for -U^/X, the marginal willingness to pay to reduce intensity of the
symptom. Of course, in the simple case where m = n = 1, the only
requirement is that	>0. If m = n = 2, a case considered in the
empirical work presented in Section IV, values of -U^/x and -l^/X both will
be positive only if (sj/S^) %	> (S^/S^) • If VL and V2 are not
chosen such that their marginal rates of technical substitution bracket
their price ratio, then it is possible to reduce intensity of one symptom
without increasing intensity of the other and without spending more on
symptom reduction.

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Sixth, complications arise in expressing symptom and air pollution
values in situations where some or all of the are sources of direct
utility, a form of joint production. This problem is important (and it is
encountered in the empirical work presented in Section IV) because of the
difficulty in identifying private goods that are purchased but do not enter
the utility function. To illustrate, assume that m = 2, n = 1 and that
but not is a source of both direct positive utility and symptom relief.
WTP^ still would equal	and therefore could be calculated without
knowing values for marginal utility terms. If consumption of Vhowever,
was used as a basis for this calculation, the simple formula
would overestimate WTP by an amount equal to -(u,s;i/xs:b where U-, denotes
a	4- OL £.	£
marginal utility of (Uj > 0) . When m and n take arbitrary values, the
situation is more complex, but in general nonmarket commodity and public
good values can be determined only if the number of private goods which do
not enter the utility function is at least as great as the number of final
commodities. Even if this condition is not met, however, it is possible in
some cases to determine whether the value of nonmarket commodities and
A
public goods is over- or underestimated.
III. DATA
Data used to implement the household production approach were obtained
from a sample of 22 6 residents of two Los Angeles area communities. Each
respondent previously had participated in a study of chronic obstructive
respiratory disease (Detels et al. 1979, 1981). Key aspects of this sample
are: (1) persons with physician diagnosed chronic respiratory ailments
deliberately are overrepresented (76 respondents suffered from such
diseases), (2) 50 additional respondents with self-reported chronic

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8
cough or chronic shortness of breath are included, (3) 151 respondents
lived in Glendora, a community with high oxidant air pollution, and 75
respondents lived in Burbank, a community with oxidant pollution levels
more like other urbanized areas in the U.S. but with high levels of carbon
monoxide, (4) all respondents either were nonsmokers or former smokers who
had not smoked in at least two years, and (5) all respondents were
household heads with full-time jobs (defined as at least 1,600 hours of
work annually).
Professionally trained interviewers contacted respondents several
times over a 17 month period beginning in July 1985. The first contact
involved administration of an extensive baseline questionnaire in the
respondent's home. Subsequent interviews were conducted by telephone.^
Including the baseline interview, the number of contacts with each
respondent varied from three to six with an average number of contacts per
respondent of just over five. Of the 1147 total contacts (s 226 x 5), 644
were with respiratory impaired subjects (i.e., those either with
physician-diagnosed or self-reported chronic respiratory ailments) and 503
were with respondents having normal respiratory function.
Initial baseline interviews measured four groups of variables: (1)
long term health status, (2) recently experienced health symptoms, (3) use
of private goods and activities that might reduce symptom intensity, and
(4) socioeconomic/demographic and work environment characteristics.
Telephone follow-up interviews inquired further about health symptoms and
use of particular private goods. Long term health status was measured in
two ways. First, respondents indicated whether a physician ever had
diagnosed asthma (ASTHMA), chronic bronchitis (BRONCH), or other chronic
respiratory disease such as emphysema, tuberculosis, or lung cancer

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9
(OTHDIS). Second, they stated whether they experience chronic shortness of
breath or wheezing (SHRTWHZ) and/or regularly cough up phlegm, sputum, or
mucous (FLEMCO) . Respondents also indicated whether they suffer from hay
fever (HAYFEV); however, this condition was not treated as indicative of a
chronic respiratory impairment.
Both background and follow-up instruments also asked which, if any, of
26 health symptoms were experienced in the two days prior to the interview.
Symptoms initially were aggregated into two categories defined as: (1)
chest and throat symptoms and (2) all other symptoms.*' Aggregation to two
categories reduces the number of household produced final goods (n)
considered; however, assigning particular symptoms to these categories
admittedly is somewhat arbitrary. Yet, the classification scheme selected
permits focus on a group of symptoms in which there is current policy
interest. Chest and throat symptoms identified have been linked to ambient
ozone exposure (see Gerking et al. 1984, for a survey of the evidence) and
federal standards for this air pollutant currently are under review.
Moreover, multivariate tobit turns out to be a natural estimation method
and aggregating symptoms into two categories permits a reduction in
computation burden. Dickie et al. (1987(a)) report that respondents with
chronic respiratory impairments experienced each of the 26 individual
symptoms more often than respondents with normal respiratory function.
This outcome is reflected in Table 1 which tabulates frequency
distributions of the total number of chest and throat and other symptoms
reported by respondents in the two subsamples.''
In the empirical work reported in Section IV, data on the number of
symptoms reported are assumed to be built up from unobserved latent
variables measuring symptom intensity. As intensity of a particular

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10
symptom such as cough rises above a threshold, the individual reports
having experienced it; otherwise he does not. Thus, the frequency
distribution tabulated in Table 1 merely reflects the number of symptoms
that crossed the intensity threshold in the two days prior to the
interview.
Private goods which indicated steps taken in the past that might
reduce symptoms over a period of years, measured whether the respondent has
and uses: (1) central air conditioning in the home (ACCEN) , (2) an air
purifying system in the home, (3) air conditioning in the automobile
8
(ACCAR), and (4) a fuel other than natural gas for cooking (NOTGASCK) .
These variables represent goods that may provide direct sources of utility
to respondents. Air conditioners, for example, not only may provide relief
from minor health symptoms; but also provide cooling services that yield
direct satisfaction. This problem is discussed further in Section V.
Socioeconomic/demographic variables measured whether the respondent
lived in Burbank or Glendora (BURB) as well as years of age (AGE) , gender,
race (white or nonwhite), marital status, and household income. Also,
respondents were asked whether they were exposed to toxic fumes or dust
while at work (EXPWORK).
Finally, each contact with a respondent was matched to measures of
ambient air pollution concentrations, humidity, and temperature for that
day. Air monitoring stations used are those nearest to residences of
respondents in each of the two communities. Measures were obtained of the
six criteria pollutants for which national ambient air quality standards
have been established: carbon monoxide (CO), nitrogen dioxide (N02), ozone
(03), sulfur dioxide (S02), lead and total suspended particulate.
Readings for lead and particulate, however, only were available for about

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11
ten percent of the days during the study period, forcing exclusion of those
pollutants from empirical work. Each of the remaining four pollutants were
measured as maximum daily one-hour ambient concentrations. Maxima are used
because epidemiological and medical evidence suggests that acute symptoms
may be more closely related to peak than to average pollution
concentrations. The air pollution variables entered then, are averages of
one hour maxima on the two days prior to the interview so as to conform
9
with the measurement of symptoms. Temperature and relative humidity data
similarly were averaged across two day periods.
IV. ESTIMATES OF HOUSEHOLD SYMPTOM TECHNOLOGY
This section reports estimates of production functions for chest and
throat and other symptoms. Empirical estimates of household production
technology in a health context also have been obtained by Rosenzweig and
Schultz (1983); however, these investigators consider determinants of birth
weight rather than health symptoms and do not focus on valuing nonmarket
10
commodities and public goods. The symptom production functions reported
below are estimated in a bivariate tobit framework with variance
11
components.	Bivariate tobit estimation was performed because of the
probable correlation between disturbances across equations. Given that
symptoms often appear in clusters, individuals reporting symptoms in one
category may also report them in the other. Also, as noted in the
discussion of Table 1, the modal number of symptoms reported was zero.
Random disturbances follow an error components pattern, consisting of
the sum of a permanent and a transitory component.
£iht " wh + Uiht	1 * R' N	(6)
where i denotes type of symptom (chest and throat, other), h denotes

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12
respondent, and t denotes time. The transitory error component,
captures unmeasured effects that vary over individuals, symptoms, or time.
The permanent error component in contrast, varies only over
individuals; for a given individual it is constant over time and common to
production functions for both types of symptoms. The permanent error
component serves two purposes in the model. First, it captures persistent
unmeasured but individual specific factors that influence symptoms,
including unmeasured elements of ft and/or the threshold at which symptoms
are reported. Hence, exerts an independent influence by allowing
individuals with identical measured characteristics to have different
numbers of symptoms. Second, a given individual's permanent error
component captures contemporaneous correlation between the two symptom
classes.
The are assumed to be independent drawings from identical
distributions. Mundlak (1978) and others have argued that the are
likely to be correlated with values of the explanatory variables, and the
error components. For example, if an individual knows his own then
utility maximization would imply that his choice of private goods depends
on	A possible solution would be to replace the random effects with
fixed effects in which the are assumed to be constants that vary across
individuals. Mundlak notes, however, that the fixed effects model suffers
from a serious defect if is correlated with some or all covariaCes: It
is impossible to distinguish between the effects of time invariant
covariates and the fixed effects. This defect of the fixed effects model
is troublesome, because all covariates except the air pollution measures
are time invariant. Since the valuation procedure of Section 2 reguires
distinguishing marginal products of private goods from the individual's

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13
predisposition to illness, the fixed effects model was rejected in favor of
random effects.
Both transitory and permanent error components are assumed normally
distributed with E(p.) - 0, E(p^) - a2, and E(u,iO - 0 for h ^ h';
n	hp	n n
E(uiht) - 0, E(u^ht) - a2, and E(uihtui'h't') " 0 for 1 ^ i" or h f h' or
t 5* C. The permanent error component is distributed independently of the
transitory error component, so the distribution of the summed error
components is normal with E(e.. ) * 0, E(ef. ) « a* + and
ihty	v iht u v
E(eiht£iht-' - au~"~^cRhteNht^'
Given and the distributional assumptions about the error
components, the likelihood for the h^*1 individual is the product of
independent tobit likelihoods: one tobit for each symptom class in each
time period. The conditional likelihood for the h^ individual is
LjjfUjj) - It fCuRElu) 1 F(uRtlu) "	* r(UNt'u) (7>
SKt>0	SRt-°	SNt>0
where f(-) is the normal density and F(*) is the normal distribution.
Conditioning was removed by integrating over y. In order to address the
problem of an unequal number of interviews per respondent, log-likelihood
values first were computed for each respondent, and then summed to obtain
12
totals.
Tables 2 and 3 present illustrative symptom production function
estimates for the impaired and normal subsamples. Equations presented are
representative of a somewhat broader range of alternative specifications
that are available from the authors on request. Alternative specifications
included attempts to correct for simultaneity between symptoms and private
goods. Bartik (1988) calls attention to this problem in a related context
and Rosenzweig and Schultz treat it in their previously cited birthweight

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14
study. Procedures devised for the present study are analogous to two-stage
least squares. In the first stage, reduced form probit demand equations
for each of four private goods (ACHOME, ACCAR, APHOME, NOTGASCK)^ were
estimated. In the second stage, predicted probabilities from the reduced
form probits were to be used as instruments for private goods in the tobit
symptom production function models. However, explanatory power of the
reduced form probit equations was very poor. In half of the equations for
each subsample the null hypothesis that all slope coefficients jointly are
zero could not be rejected at the 5 percent level and in all equations key
variables such as household income had insignificant and often wrongly
signed coefficients. Another problem is the absence of private good price
data specific to each respondent. The original survey materials requested
these data but after pretesting, this series of questions was dropped
because many respondents often made purchases jointly with a house or car
and were unable to provide even an approximate answer. As a consequence,
simultaneous equation estimation was not pursued further with the likely
outcome that estimates of willingness to pay for nonmarket commodities and
14
public goods may have a downward bias.
In any case, one result of interest from the bivariate tobit estimates
in Tables 2 and 3 is the outcome of testing the null hypothesis that
estimated symptom production parameters jointly are zero. In the four
equations reported, a likelihood ratio test rejects this hypothesis at
significance levels less than 1 percent. Also, estimates of the. individual
specific error components, denoted a, have large asymptotic t-statistics
which confirms persistence of unobserved personal characteristics that
affect symptoms.

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15
Table 2 shows that chronic health ailments and hay fever are
positively related to symptom occurrence among members of the impaired
group. Coefficients of ASTHMA, BRONCH, SHRTWHZ, and HAYFEV are positive in
equations for both chest and throat and other symptoms and have associated
asymptotic t-statistics that range from 2.1 to 7.6. The coefficient of
FLEMCO is positive and significantly different from zero at conventional
levels in the chest and throat equation, but its asymptotic t-statistic is
less than unity in the equation for other symptoms. The coefficient of AGE
was not significantly different from zero in either equation and the
EXPWORK variable was excluded because of convergence problems with the
15
bivariate tobit algorithm. Variables measuring gender, race, and marital
status never were included in the analysis because 92 percent of the
impaired respondents were male, 100 percent were white, and 90 percent were
married. Residents of Burbank experience chest and throat symptoms with
less frequency than do residents of Glendora. Of course, many possible
factors could explain this outcome; however, Burbank has had a less severe
long term ambient ozone pollution problem than Glendora. For example, in
1986 average one day hourly maximum ozone readings in Burbank and Glendora
were 8.7 pphm and 10.2 pphm, respectively.
With respect to private and public inputs to the symptom production
functions, the coefficient of ACCAR is negative and significantly different
from zero at the 10 percent level using a one tail test in the other
symptoms equation, while the coefficient of ACCEN is negative and
significantly different from zero at the 5 percent level using a one tail
test in both equations. Results from estimated equations not presented
reveal that NOTGASCK and use of air purification at home never are
significant determinants of symptoms in the impaired subsample. Also, 03,

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16
CO, and N02 exert insignificant influences on occurrence of both types of
symptoms. When four air pollution variables were entered, collinearity
between them appeared to prevent the maximum likelihood algorithm from
converging. Consequently, S02 was arbitrarily excluded from the
specification presented and the three air pollution measures included as
covariates should be interpreted as broader indices of ambient pollutant
concentrations. Variables measuring temperature and humidity were excluded
from the Table 2 specification; but in equations not reported their
coefficients never were significantly different from zero.
Table 3 presents corresponding symptom production estimates for the
subsample with normal respiratory function. HAYFEV is the only health
status variable entered because ASTHMA, BRONCH, SHRTWZ, and FLEMCO were
used to define the impaired subsample. Coefficients of HAYFEV are positive
in equations for both chest and throat and other symptoms and have
t-statistics of 1.61 and 1.87, respectively. Coefficients of BURB are
negative; but in contrast to impaired subsample results, they are not
significantly different from zero at conventional levels. AGE and EXPWORK
enter positively and their coefficients differ significantly from zero at
25 percent in the other symptoms equation. Among private goods entering
the production functions, coefficients of APHOME and ACHOME never were
significantly different from zero at conventional levels, and these
variables are excluded from the specification in Table 3. Use of air
conditioning in an automobile reduced chest and throat symptom occurrences
and cooking with a fuel other than natural gas (marginally) reduces other
symptoms. Variables measuring gender, race, and marital status again were
not considered as the normal subsample was 94 percent male, 99 percent
white, and 88 percent married. In the normal subsample, collinearity and

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1
algorithm convergence problems again limited the number of air pollution
variables that could be entered in the same equation. As shown in Table 3,
when 03, CO, and N02, coefficients had associated t-statistics of 1.16 or
smaller. Temperature and humidity variables are excluded from the
specification shown in Table 3. In alternative specifications not
reported, coefficients of these variables never were significantly
different from zero in alternative equations not reported.
Three pieces of information are required to use the estimates in
Tables 2 and 3 in the calculation of values for nonmarket commodities (the
two types of symptoms) and public goods (air pollutants): (1) marginal
effects of air pollutants on symptoms, (2) marginal effects of private
goods on symptoms, and (3) prices of private goods. Marginal products were
defined as the effect of a small change in a good on the expected number of
symptoms. Computational formulae were developed extending results for the
tobit model (see McDonald and Moffit 1980) to the present context which
allows for variance components error structure. However, because private
goods are measured as dummy variables and, therefore, cannot be
continuously varied, incremental, rather than marginal, products are used.
The final elements needed to compute value estimates are the prices of
private goods. Dealers of these goods in the Burbank and Glendora areas
were contacted for estimates of initial investment required to purchase the
goods, average length of life, scrap value (if any), and fuel expense.
After deducting the present scrap value from the initial investment, the
net initial investment was amortized over the expected length of years of
life. Adding annual fuel expense yields an estimate (or range of
estimates) of annual user cost of the private good. The annual costs then
16
were converted to two-day costs to match the survey data. The dependent

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18
variables used in the estimated equations do not distinguish between one-
and two-day occurrences of symptoms, but approximately one-half of the
occurrences were reported as two day occurrences. As a consequence, the
value estimates obtained were divided by 1.5 to convert to daily values.
Two tests were performed prior to estimating values of symptom and air
pollution reduction. First, calculations were made for both normal and
impaired subsamples to ensure that relevant ratios of incremental products
of private goods in reducing symptoms bracketed the corresponding price
ratio. Recall from the discussion in Section 2 that this condition
guarantees that value estimates for reducing both types of symptoms are
positive. A problem in making this calculation is that estimates of
incremental rates of technical substitution vary across individuals
(incremental products are functions of individual characteristics), but no
respondent specific price information is available. As just indicated,
dealers in Glendora provided the basis for a plausible range of prices to
be constructed for each good. If midpoints of relevant price ranges are
used together with incremental rates of technical substitution taken from
Tables 2 and 3, the bracketing condition is met for all 100 respondents in
the normal subsample and 117 of 126 respondents in the impaired subsample.
Of course, alternative price ratios selected from this range meet the
bracketing condition for different numbers of respondents.
Second, possible singularity of the symptom technology matrix was
analyzed using a Wald test (see Judge et al. 1985, p. 215 for details).^
In the context of estimates in Tables 2 and 3, the distribution of the test
statistic (A) is difficult to evaluate because relevant derivatives are
functions of covariate values and specific to individual respondents.
However, if derivatives are evaluated in terms of the underlying latent

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19
variable model, they can be expressed in terms of only parameters and A is
2
distributed as x with 1 degree of freedom. Adopting this simpler
approach, p-values for the Wald test statistic are large: p = .742 for the
impaired subsample equations and p = .610 for the normal subsample
1 8
equations. As a consequence, the null hypothesis of singularity of the
symptom technology matrix is not rejected at conventional levels. This
result suggests that in both subsamples, there does not appear to be an
independent technology for reducing the two types of symptoms, budget
constraints are nondifferentiable, and separate value estimates for
chest and throat and ocher symptoms should not be calculated.
A common value for reducing chest and throat and other symptoms still
can be obtained by aggregating the two categories and re-estimating
production functions in a univariate tobit framework. Table 4 shows
results based on using the same covariates as those reported in Tables 2
and 3 and retaining the variance components error structure. The Table 4
equations also make use of a constraint requiring that if m > n = 1, values
of marginal willingness to pay to avoid a symptom must be identical no
matter which private good is used as the basis for the calculation. In the
case where m = 2 and n = 1, as discussed in Section II, this single value
is -Uj/A - -(PjVsJ) - -(P^S*). In the impaired subsample, the restriction
can be tested under the null hypothesis, Hq : &ACCAR *
where the B. are coefficients of ACCAR and ACHOME
AULA& ACHOME ACHUML	1
in the latent model and the are midpoints from the estimated range of
two day prices for the private goods. In corresponding notation, the null
hypothesis to test in the normal subsample is, H_ : 6Ar,rAP =
(PACCAR/PNOTGASCK)SNOTGASCK- Both hyPotheses are tested against the

-------
20
alternative that coefficients of private goods are unconstrained
parameters.
P-values for the parameter restrictions are comparatively large; P =
.623 in the impaired subsample and P = .562 in the normal subsample. Thus,
the above null hypotheses are not rejected at conventional significance
levels. Respondents appear to equate marginal rates of technical
substitution in production with relevant price ratios; a result that
supports a critical implication of the previously presented household
production model. Moreover, coefficients of private good variables defined
under the null hypotheses for the two subsamples have t-statistics
exceeding two in absolute value. Performance of remaining variables is
roughly comparable to the bivariate tobit estimates. A notable exception,
however, is that in the normal subsample univariate tobit estimates,
coefficients of 03 and N02 are positive with t-statistics exceeding 1.6.
This outcome suggests that persons with normal respiratory function tend to
experience more symptoms when air pollution levels are high, whereas those
with impaired respiratory function experience symptoms with such regularity
that there is no clear relationship to fluctuations in air quality.
Intensity of particular symptoms may be greater in both subsamples when
pollution levels are high, but this aspect is not directly measured.
Table 5 presents estimates of marginal willingness to pay to avoid
symptoms to reduce two air pollutants. Unconditional values of relieving
symptoms and reducing air pollution are calculated for each respondent from
observed univariate tobit models. Table 5 reports the mean, median, and
range of respondents' marginal willingness to pay to eliminate one health
symptom for one day as well as mean marginal willingness to pay to reduce
air pollutants by one unit for one day for the normal subsample. Symptom

-------
21
reduction values range from $0.81 to $1.90 in the impaired subsample and
from $0.49 to $1.22 in the normal subsample with means of $1.12 and $0.73
19
m the two subsamples, respectively. Also, values of willingness to pay
to reduce one hour daily maximum levels of 03 and N02 by one part per
million are $0.31 and $0.91 in the normal subsample. Corresponding
calculations are not reported for the impaired subsample because, as shown
in Table 4, coefficients of air pollution variables are not significant at
conventional levels.
V. CONCLUSION
Willingness to pay values of symptom reduction and air quality
improvement just presented should be viewed as illustrative approximations
for two reasons. First, private goods used in computing the estimates are
likely to be direct sources of utility. Second, symptom experience and
private good purchase decisions are likely to be jointly determined.
Nevertheless, these estimates still are of interest because aspects of
joint production are taken into account. A key finding is that independent
technologies for home producing symptoms are difficult to identify, thus
greatly limiting the number of individual symptoms for which values can be
computed. In fact, the 26 symptoms analyzed here had to be aggregated into
a single group before willingness to pay values could be computed.
This outcome appears to have implications for estimating willingness
to pay for nonmarket commodities in other contexts. An obvious example
concerns previous estimates of willingness to pay to avoid health symptoms.
Berger et al. (1987) report one day willingness to pay values for
eliminating each of seven minor health symptoms, such as stuffed up
sinuses, cough, headache and heavy drowsiness that range from $27 per day

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22
to $142 per day. Green et al. (1978) present estimates of willingness to
pay to avoid similarly defined symptoms ranging from $26 per day to $79 per
day. In both studies, however, willingness to pay estimates were obtained
symptom by symptom in a contingent valuation framework that ignores whether
independent technologies are available to produce each. Thus, respondents
simply may have lumped total willingness to pay for broader health concerns
onto particular symptoms. Some respondents may also have inadvertently
stated their willingness to pay to avoid symptoms for periods longer than
one day.
Another example relates to emerging research aimed at splitting
willingness to pay to reduce air pollution into health, visibility, and
possibly other components. From a policy standpoint, this line of inquiry
is important because the Clean Air Act and its subsequent amendments focus
exclusively on health and give little weight to other reasons why people
may want lower air pollution levels. Analyzing location choice within
metropolitan areas, for example, may not provide enough information to
decompose total willingness to pay into desired components. Instead,
survey procedures must be designed in which respondents are either reminded
of independent technologies that can be used to home produce air pollution
related goods or else confronted with believable hypothetical situations
that allow one good to vary while others are held constant.

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23
REFERENCES
Bartik, T. J. "Evaluating the Benefits of Non-marginal Reductions in
Pollution Using Information on Defensive Expenditures." Journal of
Environmental Economics and Management 15(1) (March 1988): 111-127.
Berger, M. C., Blomquist, G. C., Kenkel, D., and Tolley, G. S. "Valuing
Changes in Health Risks: A Comparison of Alternative Measures."
Southern Economic Journal 53(4) (April 1987): 967-984.
Berndt, E. R., Hall, B. H., Hall, R. E., and Hausman, J. A. "Estimation
and Inference in Nonlinear Structural Models." Annals of Economic and
Social Measurement 3(4) (October 1974): 653-665.
Bockstael, N., and McConnell, R. "Welfare Measurement in the Household
Production Framework." American Economic Review 73 (September 1983):
806-814.
Chamberlain, G. "Analysis of Covariance with Qualitative Data." Review of
Economic Studies 47 (1980): 225-238.
Chestnut, L., and Violette, D. Estimates of Willingness to Pay for
Pollution-Induced Changes in Morbidity: A Critique for Benefit Cost
Analysis of Pollution Regulation. EPA-68-01-6543 (1984).
Courant, P. N., and Porter, R. C. "Averting Expenditure and the Cost of
Pollution." Journal of Environmental Economics and Management 8
(December 1981): 321-329.

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24
Detels, R., Rokaw, S., Coulson, A., Tashkin, D., Sayre, J., and
Massey, F., Jr. "The UCLA Population Studies of Chronic Obstructive
Respiratory Disease I. Methodology." American Journal of
Epidemiology 109 (1979): 33-58.
Detels, R., Sayre, J., Coulson, A., et al. "The UCLA Population Studies of
Chronic Obstructive Respiratory Disease IV. Respiratory Effects of
Long Term Exposure to Photochemical Oxidants." American Review of
Respiratory Disease 124 (1981): 673-680.
Dickie, M., Gerking, S., McClelland, G., and Schulze, W. "Valuing
Morbidity: An Overview and State of the Art Assessment." Volume I of
Improving Accuracy and Reducing Costs of Environmental Benefit
Assessments, U.S. Environmental Protection Agency, Cooperative
Agreement #CR812054-01-2, December (1987(a)).
Dickie, M., Gerking, S., Schulze, W., Coulson, A., and Tashkin, D. "Value
of Symptoms of Ozone Exposure: An Application of the Averting
Behavior Method." Volume II of Improving Accuracy and Reducing Costs
of Environmental Benefit Assessments, U.S. Environmental Protection
Agency, Cooperative Agreement #CR812054-01-2, December (1987(b)).
Frisch, R., Theory of Production. Chicago: Rand McNally & Company, 1965.
Gerking, S., Coulson, A., Schulze, W., Tashkin, D., Anderson, D.,
Dickie, M., and Brookshire, D. "Estimating Benefits of Reducing
Community Low-Level Ozone Exposure: A Feasibility Study." Volume III
of Experimental Methods for Assessing Environmental Benefits, U.S.
Environmental Protection Agency, Cooperative Agreement
#CR-811077-01-0, September (1984).

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25
Green, A. E. S., Berg, S. V., Loehman, E. T., Shaw, M. E., Fahien, R. W.,
Hedinger, R. H., Arroyo, A. A., and De, V. H. An Interdisciplinary
Study of the Health, Social and Environmental Economics of Sulfur
Oxide Pollution in Florida. Interdisciplinary Center for Aeronomy and.
(other) Atmospheric Sciences, University of Florida, Gainesville,
Florida (1978).
Grossman, M. "On the Concept of Health Capital and the Demand for Health."
Journal of Political Economy 80 (March 1972): 223-255.
Harford, J. D. "Averting Behavior and the Benefits of Reduced Soiling."
Journal of Environmental Economics and Management 11 (September 1984):
296-302.
Barrington, W., and Portney, P. R. "Valuing the Benefits of Health and
Safety Regulation." Journal of Urban Economics 22(1) (July 1987):
101-112.
Hori, H. "Revealed Preference for Public Goods." American Economic Review
65 (December 1975): 947-954.
Judge, G. G., Griffiths, W. E., Hill, R. C., Lutkepohl, H., and Lee, T. C.
The Theory and Practice of Econometrics, 2nd Edition. New York: John
Wiley and Sons, 1985.
McDonald, J. F., and Moffit, R. A. "The Uses of Tobit Analysis." Review of
Economics and Statistics 62(1) (May 1980): 318-21.
Mundlak, Y. "On the Pooling of Time Series and Cross-Section Data."
Econometrics 46 (January 1978): 69-85.
Pollak, R. A., and Wachter, M. L. "The Relevance of the Household
Production Function Approach and Its Implications for the" Allocation
of Time." Journal of Political Economy 83 (April 1975): 255-277.

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Rosenzweig, M. R., and Schultz, T. P. "The Behavior of Mothers as Inputs
to Child Health: The Determinants of Birth Weight, Gestation, and
Rate of Fetal Growth." In Economic Aspects of Health, edited by
Victor R. Fuchs. Chicago: The University of Chicago Press, 1982.
Rosenzweig, M. R., and Schultz, T. P. "Estimating a Household Production
Function: Heterogeneity, the Demand for Health Inputs, and Their
Effects on Birth Weight." Journal of Political Economy 91 (October
1983); 723-746.
Samuelson, P. A. "The Pure Theory of Public Expenditures." Review of
Economics and Statistics 36 (November 1954): 387-389.

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ENDNOTES
1.	Another, possibly troublesome, aspect of joint production occurs if
some or all elements of V are arguments in the utility function. This
complication is discussed momentarily.
2.	Hori identifies three sources of nondifferentiability of the budget
surface under joint production. The first occurs if the number of
private goods is less than the number of commodities. The second
arises because of nonnegativity restrictions on the private goods.
This is not treated directly in the present paper, but if each private
good is purchased in positive quantities, the chosen commodity bundle
will not lie at the second type of kink. Hori's third cause of
nondifferentiability implies linear dependence among the rows of the
technology matrix.
3.	Notice that this point on aggregation may apply to other valuation
methods as well. Using contingent valuation surveys, for example,
Green et al. (1978) and Berger et al. (1987) obtained value estimates
of several specific symptoms; however, issues relating to existence of
independent symptom technologies never was faced. Future contingent
valuation surveys may do well to consider this point prior to
eliciting estimates of willingness to pay.
4.	For example, suppose m = n = 2 and both private goods are direct
sources of utility. If equation (6) is used to solve for the IK/A,
then: (1) if the two marginal rates of technical substitution (MRTS)
do not bracket the price ratio, then the value of the commodity whose

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28
MRTS is closer in magnitude to the price ratio will be overestimated,
while the value of the other commodity will be underestimated; (2) if
the two MRTS values do bracket the price ratio, then the value of
either one or both of the commodities will be overestimated; and (3)
in no case will the value of both commodities be underestimated.
5.	Both questionnaires are presented and extensively discussed in Volume
II of Dickie et al. (1987(b)).
6.	Chest and throat symptoms include (1) cough, (2) throat irritation,
(3) husky voice, (4) phlegm, sputum or mucous, (5) chest tightness,
(6) could not take a deep breath, (7) pain on deep respiration, (8)
out of breath easily, (9) breathing sounds wheezing or whistling.
Other symptoms are (1) eye irritation, (2) could not see as well as
usual, (3) eyes sensitive to bright light, (4) ringing in ears (5)
pain in ears, (6) sinus pain, (7) nosebleed, (8) dry and painful nose,
(9) runny nose, (10) fast heartbeat at rest, (11) tired easily, (12)
faintness or dizziness, (13) felt spaced out or disoriented, (14)
headache, (15) chills or fever, (16) nausea, and (17) swollen glands.
7.	An alternative to counting the number of different symptoms
experienced in the two days prior to the interview would be to
consider the number of symptom/days experienced. Both approaches were
used to construct empirical estimates; however, to save space, only
those based on counts of different symptoms are reported. Both
approaches yield virtually identical value estimates for symptom and
air pollution reduction.
8.	The first three private goods reduce exposure to air pollution by
purifying and conditioning the air. The fourth reduces exposure
because gas stoves emit nitrogen dioxide.

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9. The equations also were estimated after defining the pollution
variables as the largest of the one hour maxima on the two days;
similar results were obtained.
10.	Rosenzweig and Schultz also initially specify their production
functions in translog form and then test whether restrictions to CES
and Cobb-Douglas forms are justified. This type of analysis is not
pursued here as most of the covariates used are 0-1 dummy variables.
Squaring these variables does not alter their values. Interaction
variables of course, still could be computed.
11.	Although there is a linear relationship between the latent dependent
variables and the private goods in the tobit model, the relationship
between the observed dependent variables and the private goods has the
usual properties of a production function. The expected number of
symptoms is decreasing and convex (nonstrictly) in the private goods.
12.	The tobit coefficients and variances of the model are estimated by
maximizing the likelihood function using the method of Berndt, Hall,
Hall, and Hausman (1974). The score vectors are specified
analytically and the information matrix is approximated numerically
using the summed outer products of the score vectors. Starting values
for the coefficients and the standard deviations of the transitory
error components were obtained from two independent tobit regressions
with no permanent error component. In preliminary runs a starting
value of unity was used for the standard deviation of the permanent
error component, but the starting value was adjusted to 1.5 after the
initial estimate was consistently greater than one.

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30
13.	Covariates in the reduced form regressions are: ASTHMA, BRONCH,
FLEMCO, SHRTWZ, HAYFEV, BURB, AGE, EXPWORK, years of education, number
of dependents, household income, and an occupation dummy variable
measuring whether respondent is a blue collar worker.
14.	An alternative to the two-stage procedure was suggested by Chamberlain
(1980) for random effects probit models. Chamberlain's approach uses
information from temporal variation in choice variables to distinguish
between production function parameters and the parameters of an
assumed linear correlation between choice variables and the permanent
error component. The approach is not well-suited to the present study
because of the lack of temporal variation in the private goods.
15.	In the impaired subsample, inclusion of EXPWORK frequently caused the
bivariate tobit algorithm to fail to converge. This problem arose in
the specification presented in Table 2; consequently the EXPWORK
variable was excluded.
16.	The estimated two-day prices are: $2.34 for ACCEN, $1.00 for ACCAR,
$0.80 for NOTGASCK. The discount rate was assumed to be 5 percent.
For further details of the procedure used to estimate prices, see
Dickie et al. (1987(a)).
17.	The Wald test was chosen because its test statistic can be computed
using only the unconstrained estimates. Since the likelihood and
constraint functions both are nonlinear, reestimating the model with
the constraint imposed would be considerably more difficult than
computing the Wald test statistic.
18.	In other estimates of symptom production functions not reported here,
corresponding p-values also are large, almost always exceeding .25 and
sometimes the .80-.90 range.

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31
19. For comparison purposes, mean values also were estimated at subsample
means of all explanatory variables. Results differ little with means
computed over respondents. Evaluated at subsample means, willingness
to pay to eliminate one symptom for one day is $1.05 in the impaired
subsample and $0.70 in the normal subsample.

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0
1
2
3
4
5
6
8
9
10
11
12
13
14
15
16
17
e
TABLE 1
FREQUENCY DISTRIBUTIONS OF SYMPTOMS BY SUBSAMPLE
NUMBER OF CHEST AND
THROAT SYMPTOMS
EXPERIENCED IN PAST
TWO DAYS
Impaired	Normal
351
408
84
41
64
18
CO
15
37
9
26
4
16
6
8
0
2
n
0
2
u
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.348	0.453
NUMBER OF OTHER
SYMPTOMS EXPERIENCED
IN PAST TWO DAYS
Impaired	Normal
257
338
123
79
85
42
73
18
45
12
28
5
14
6
9
2
4
1
2
0
1
0
1
0
2
1
0
0
0
n
0
n
U
0
u
0
0	0
1.668	0.692

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TABLE 2
BIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES:
IMPAIRED SUBSAMPLE3

Chest and Throat
Symptoms
Other
Symptoms
CONSTANT
-3.085
-2.043

(-3.035)
(-2.125)
ASTHMA
0.8425
0.6724

(2.328)
(1.851)
SRONCH
3.774
2.936

(7.663)
(6.668)
SHRTWHZ
1 .494
1.235

(3.683)
(3.428)
FLEMCO
1.458
0.2526

(4.038)
(0.8558)
HAYFEV
1.110
0.6613

(3.509)
(2.365)
BURB
-1.431
-0.7330

(-2.728)
(-1.539)
ACE
0.2986
2.042

(0.1596)
(1.177)
EXPWORK
	b
	b
ACCAR
-0.3485
-0.4395

(-0.8885)
(-1.364)
ACCEN
-1.9961
-0.6291

(-2.834)
(-1.829)
03
-0.1672
0.1252

(-0.5638)
(-.4475)
CO
1.279
-0.06285

(1.259)
(-0.06356)
N02
0.5475
0.6384

(0.7744)
(0.9282)

2.617
2.454
V
(17.70)
(20.81)
a..
1.827


(21.17)

Chi-Square0
148.7

P-Value for


Wald Test
0.742

Number of ,


Iterations
21

at-statisties are in parentheses.
''Denotes omitted dummy variable. Also, long term health status covariates entering these
equations do not represent mutually exclusive categories.
°The chi-square test statistic is -21nX, where X is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
^The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.

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TABLE 3
BIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES:
NORMAL SUBSAMPLEa
CONSTANT
HAYFEV
BURB
ACE
EXPWORK
ACCAR
NOTCASCK
03
CO
NO 2
Chest and Throat
Other
Symptoms
Symptoms
-5.789
-5.479
(-2.157)
(-2.790)
2.316
1.461
(1.614)
(1.871)
-1.388
-0.6248
(-1.180)
(-0.8470)
4.143
7.075
(0.7873)
(2.091)
0.8707
1.329
(1.157)
(2.297)
-1.949
-0.6705
(-2.905)
(-1.057)
-0.4613
-0.856S
(-0.6312)
(-1.594)
0.2757
0.3592
(0.5867)
(0.9674)
0.1788
-0.07200
(0.07729)
(-0.05241)
1.841
1.069
(1.162)
(1.127)
3.204
2.435
(10.15)
(11.31)
a	1.828
W	(10.44)
Chi-Square''	69.81
P-Value for
Wald Test	0.610
Number of
Iterations	20
at-statisties in parentheses.
bThe chi-square test statistic is -21nA, where X is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
cThe convergence criterion is 0.5 for the gradient-weighted inverse Hessian.

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TABLE A
UNIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES3,

Impai red
Normal

Subsample
Subsample
CONSTANT
-2.253
-6.085

(-1.263)
(-2.329) "
ASTHMA
1.0333
(1.953)

BRONCH
*.649
(7.708)

SHRTWHZ
1.909
(3.242)

FLEMCO
1.769
(3.607)

HAYFEV
1.574
2.216

(3.137)
(2.378)
BURB
-1.830
-1.623

(-2.927)
(-1.126)
ACE
1.200
6.351

(0.40g4)
(1.165)
EXPWORK
1.725
(2.039)
ACCAR
-0.5900
-1.260

(-2.585)
(-2.425)
03
0.1629
0.5941

(0.4846)
(1.616)
CO
1.013
0.3722

(0.8041)
(0.2163)
N02
0.8930
1.726

(1.130)
(1.784)

3.884
3.790
V
(37.29)
(22.47)
CT-f
2.582
2.516
y
(15.84)
(8.822)
Chi-Square0
77.88
36.45
P-Value for


Parameter Restrictions
0.623
0.562
Number of .


Iterations
8
5
at-statisties in parentheses.
^Denotes omitted dummy variable. Also, long term health status covariates entering these
equations do not represent mutually exclusive categories.
cThe chi-square test statistic is -21nA, where X is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
^The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.

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TABLE 5
MARGINAL WILLINGNESS TO PAY TO RELIEVE SYMPTOMS AND AVOID AIR POLLUTION
IMPAIRED SUBSAMPLE
Symptoms
03
N02
CO
Mean
Median
Maximum
Minimum
$1.12
$1.09
$1.90
$0.81
Symptoms
NORMAL SUBSAMPLE
03
N02
CO
Mean
Median
Maximum
Minimum
$0.73
$0.70
$1.22
$0.49
$0.31b
$0.91b
denotes coefficient not significantly different from zero at 10 percent
level using one tail test in estimated equations presented in Table 4.
b
Estimates of willingness to pay for reduced air pollution do not vary
across sample members. In the computational ratio, respondent specific
information appears both in the numerator and denominator and therefore
cancels out.

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VALUATION OF MORBIDITY REDUCTION DUE TO AIR POLLUTION ABATEMENT
DIRECT AND INDIRECT MEASUREMENTS
Mordechal Shechter
Natural Resource and Environmental Research Center
University of Haifa, Haifa 31 999 Israel
Paper presented at the AERE Workshop
"Estimating and Valuing Morbidity in a Policy Context"
Research Triangle Park, NC, June 8-9, 1989
+
On leave, Dept. of Regional Science, University of Pennsylvania.

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ABSTRACT
The paper is a comparative study of alternative approaches to
the valuation of a public good - air quality, in terms of its
effect on morbidity levels. Three indirect approaches have been
employed in the study: (1) cost of illness, (2) household health
production, and (3) a market goods approach, involving the
derivation of willingness to pay for clean air by exploiting the
relationships among the public and market goods. The direct
valuation approach encompassed several contingent valuation
experiments: (1) open-ended, (2) probe biding, and (3) binary
choice. The estimates of welfare change valuations derived under
the various approaches are discussed and compared. The empirical
analysis is based on results from a household survey, consisting
of a stratified random sample of about 3,300 households from the
Haifa metropolitan area (in northern Israel). It was carried, out
over a period of 12 months during 1986-87.

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VALUATION OF MORBIDITY REDUCTION DUE TO AIR POLLUTION ABATEMENT
DIRECT AND INDIRECT MEASUREMENTS*
1. INTRODUCTION
The attributes of environmental quality, a public good,
require the adoption of different valuation approaches than those
customarily employed in studies of market goods. Basically, our
aim is to quantify the change in consumer welfare, or benefits,
measured in money units, associated with a change (an increase or
a reduction) in the quantity of the environmental good (and the
flow of services concurrent with this change). Willingness to pay
(WTP) is the term commonly used to denote this welfare change. The
monetary measures of welfare change are the compensating variation
and equivalent variation, or surplus in the case of nonmarket
goods where quantity, rather than price changes are involved. The
compensating surplus (CS) is defined as the income change which
offsets the change in utility induced by a change in the level of
the public good, y,holding utility constant at its original level.
In terms of the expenditure function, fi, it is given by:
cv = fi(y°; p£. v°) - jiCy1; p£. v°).	(y^y0)	(i)
where the superscripts indicate initial (0), or subsequent (1),
states, is the vector of market goods prices, V is the indirect
utility function, V(P^,M,y), M is the expenditure on the market
goods, and y is the public good. Analogously, the equivalent
Support for this research was provided by a grant from the
U.S.-Israel Binational Science Foundation. Several individuals
collaborated with me on different parts of the project, and I am
gratefully indebted to them for their contributions: L. Epstein of
Carmel Hospital, A. Cohen of the Faculty of Industrial &
Management Engineering at the Technion - Israel Institute of
Technology, M. Kim of the Department of Economics at the
University of Haifa. L. Golan, B. Miller, N. Azolai, and G.
Mehrez, all graduate students at the Department of Economics,
provided me with invaluable research assistantship. I wish also
to thanks D. Shefer, L. Lave, E. Mills, and E. Loehman for
beneficial discussions and advice. Needless to say, I remain
responsible for any remaining errors of omission or commission.
1

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surplus (ES) is the change in income equivalent to the utility
gain induced by a change in the level of the nonmarket good,
holding utility at its subsequent level:
ev = #x(y°;P£. v1) - iitySpJ. v1)	(2)
Two totally different approaches for the valuation of air
quality have been used. The first employs indirect methods, all
of which essentially attempt to infer the implicit value of the
public good from observable (and presumably accurately measured)
prices of private goods and services. For example, air quality
affects housing prices as well as expenditures on preventive and
medical care that are associated with the effect of pollution on
health. Changes in air quality levels would be expected to shift
the observed demand schedules for these market goods. From the
extent and direction of these shifts, implicit prices (or marginal
willingness to pay valuations) of the relevant public good might
be inferred. The use of market data in the valuation of
environmental goods has been expounded by M&ler (1974), Freeman
(1979], and more recently and exhaustively by Bockstael, et al.
(1984), and Johansson (1987). One of the indirect approaches used
in this study has to the best of our knowledge seldom been used in
the valuation of public goods in general, and environmental goods
in particular, and in this sense constitutes a novel contribution.
"Traditional" indirect approaches employed in valuing
environmental resources involved techniques such as the travel
cost method (TCM), characteristically used in recreation demand
studies, or the hedonic price method (HPM) , which has been used to
monetize urban public amenities through the analysis of housing
markets (e.g., Brookshire, et al., 1982, who studied air pollution
effects on property values in California). In TCM, for example,
researchers have attempted to value the benefits of a public good,
e.g. water quality, associated with the provision of outdoor
recreation services (the latter being, at least in principle, a
market good).
2

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Household health production is another indirect method. It
focuses on the consequences of health damages associated with an
inadequate supply of an environmental good, such as clean air and
water (e.g., Cropper, 1981, Gerking and Stanley, 1986, Berger, et
al, 1987) . Here one posits technical relationships between the
individual consumer's health attributes, exposure to environmental
pollution, and the consumption of private goods that affect health
(such as medical services, or goods which help protect against
exposure to health risks). The maximization of utility derived
from the consumption of goods and services and from being healthy,
given these relationships, yields an implicit value assigned by
the consumer to the environmental good under study.
Closely related to the health production approach, is the
"cost-of-illness" (COI) method, long used by economists and
medical researchers to value the damages inflicted by
environmental pollution, and hence the value attributable to
Improvements in the supply of environmental goods. Here one
estimates the expenditure on medical services and the value of
lost work and productivity associated with excess morbidity or
mortality. Although easiest to apply in terms of data
availability, it can be shown Harrington and Portney, 1987) that
this method yields an underestimate of the (theoretically correct)
value of the public good.
Alternatively, an altogether different approach, less and
less hesitantly used economists, especially in the valuation of
environmental and amenity resources, is a direct approach, in the
sense that it attempts to elicit consumers' valuations through
survey interview methods. This is the contingent valuation method
(CVM) - which elicits valuations within a framework of a
hypothetical, contingent market for the good or service in
question. The "state-of-the-art" of the contingent valuation
method has been summarized by Cummings, et al ( 1986) and, more
recently, by Mitchell and Carson (1989).
3

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The different approaches investigated in the present study
are described in Figure 1 (the residential property hedonic model
is not dealt with here, however) . In this paper we apply them to
the valuation of benefits derived from reducing air
1
pollution-induced morbidity. To the best of our knowledge, ours
is the first comprehensive study which has employed most of the
approaches currently used by economists to derive monetary values
of pollution-induced health damages, based on a single, large
primary micro-data base.
Figure 1
The data were collected through a household survey, carried
out the author in the city of Haifa in northern Israel, over a
12 month period in 1986-87. All the approaches employed in the
study (with the exception of the residential prices hedonic model)
are based on the same set of sample observations. This made it
possible to carry out a rather comprehensive empirical analysis of
the different approaches.
*
Section 2 of the paper describes the study area, the survey
design and the data collected, as well as presenting a number of
selected epidemiological results. Section 3 deals with the CVM
experimental design and valuations. Section 4 details the specific
indirect market goods model employed in this study. In section 5
we present a brief description of the household health production
mode 1, and in Section 6 the results from the COI analyses,
focusing on the estimation of due to production gains from
reducing work losses. A comparative analysis in Section 7 sums up
1
A survey of economic studies which have dealt with the valuation
of morbidity damages associated with environmental pollution has
just recently been published. See Cropper and Freeman (1988).
Berger, et al. (1987) have compared CVM with COI using a small
sample of Chicago and Denver residents.
4

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the alternative valuation approaches.
2. DATA AND STUDY DESIGN
2.1 Background
Haifa, is an industrial city in northern Israel, situated on
the slopes of Mt. Carmel and the adjoining Haifa Bay area. The
combination of the region's topography and meteorological
conditions, and a concentration of heavy industry in the lower Bay
area (a power plant, oil refineries, a petrochemical complex, and
others) create conditions conducive to high ambient concentrations
of pollutants, especially SOg and particulate, in parts of the
metropolitan region (depending on topography and wind direction)
during certain periods of the year.
Maximal mean 24-hour SOg concentrations of 197 and 28 6
were recorded in 1986 and 1987, respectively, with corresponding
2
maximal half-hour readings of 1,271 and 2,552. During the period
January 1986 - April 1987, 15 violations of the absolute SOg
standard were recorded in Haifa. An Intermittent Control System
(ICS) which directs the area's major polluters to switch to
low-sulfur fuels during environmental episodes, was activated on
23 days. In one single day, April 12, 1996, the monitoring
stations registered 12 violations of the 99% standard and 2 of
the 100% standard. It had been estimated that on that day alone
the ICS had prevented the occurrence of at least 6 additional
violation of the absolute standard! (Environmental Protection
Service, 1988). It has also been noted that during the same period
measurements of sulfates concentrations at certain neighborhoods
(these are not taken on a regular basis) have registered a
2
Currently there are two ambient standards for	A 99%
"statistical" standard of 780 fig/M^ (300 ppb), with a 1%
exceedance level (176 half-hours per year), and an absolute
standard of 1560	(600 ppb). An expert committee has recently
proposed converting the 99% standard into a single, 100% standard.
5

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three-fold increase over those measured in 1976. High values of CO
were also recorded in some areas of the city during the report
period.
Concomitantly, evidence has been accumulating indicating a
higher incidence and prevalence of respiratory illnesses in the
area. Expansion, actual or planned, of the power and
petrochemical industries has fostered the familiar Conflict
between economic development, regional employment and income, on
one hand, and the desire for a cleaner environment, on the other
hand. This, as expected, has stimulated a good deal of public
controversy and media involvement.
2.2 The Household Survey
A household survey, based on a stratified, cluster area
probability sample of about 3,600 households, in the metropolitan
area of Haifa was carried out from May 1986 through April 1987.
The sample was drawn from 137 Census Statistical Areas (CSA),
classified into four socioeconomic groups on the basis of the
latest (1983) Census. They were then further classified into three
levels of ambient pollution. 16 CSAs, each approximating a
different residential neighborhood, were selected to represent the
12 sampling strata. City blocks were randomly sampled within each
stratum. Heads (either spouse) of all the households within each
block were interviewed. The data were collected in the course of a
structured interview, lasting about 30-45 minutes. The overall
response rate was 81%; 9% refused to be interviewed, and another
10% could not be reached after a second visit.
Beside the usual socioeconomic and demographic data, and CVM
questions (discussed below), respondents were asked about
perceived air pollution levels in the neighborhood and the work
place, and attitudes towards air pollution. The questionnaire
included questions on self-assessed health status, present and
past smoking habits of household members, and respiratory
system-related symptoms and diseases of the respondent and
6

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household members. These included the following: Cough and phlegm;
coughing or phlegm production first thing in the morning in summer
ant/or winter, and at other times of the day; and wheezing and its
relationship to having a cold. Additional symptoms and diagnoses
were elucidated, in relation to the respondent or other household
members: Eye "infection", sinusitis, allergic irritation of nose
or eyes, eczema, headache, a running nose, dyspnoea (with or
without effort), pneumonia, bronchitis, and asthma (including
frequency of attacks over the preceding 12-month period for the
latter three). Use of medical services (primary clinic visits,
medications), bed days during a two-week recall period, and
hospitalization during the 12 months preceding the interview by
any member of the household were also recorded.
2.3 Some Epidemiological Findings
A dichotomous logit model served to characterize respiratory
system diseases and symptoms by fitting the model to a binary
(0-1) dependent variable, where 1 indicates a reported presence,
and 0 the absence of a given symptom or disease. The logit model
fits the data to an equation where the dependent variable is
specified as the natural logarithm of the odds, y = In p/(1—p), p
being the probability of observing the phenomenon (symptom or
disease) and 1-p the probability of not observing it, and y is
regressed against a set of explanatory variables. Separate
equations were estimated for respondent, his or her spouse, and
the family's children (the latter grouped as one observation).
Thus, the fitted equation is of the form:
y ¦ In p/(l-p) = a + bxPOL +	(3)
where POL is the variable indicating pollution level (perceived by
the respondent, or measured) In the relevant neighborhood, and the
's are other explanatory variables. For a dichotomous
classification of neighborhood pollution (used in this analysis) ,
an odds ratio, indicating the relative "riskiness" of a polluted
neighborhood with respect to the prevalence of a given symptom or
7

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disease, is denoted by p, whose pint estimate is given by
y(l) - y(0) = b = in p = In [

|roLll / (p/l-p) |row3] b ••• P - e (4) Thus it has been assumed that there is a constant ratio between the two odds ratios for given values of the other relevant variables, and that this ratio is independent of those variables when individuals with similar attributes, but residing in different neighborhoods, are compared. Table 1 and Figure 2 give the odd ratios (in Table 1 also the upper and lower confidence intervals) for various symptoms and diseases. It should be stressed that there relationships are also controlled for smoking habits (which tend to cause similar symptoms) . Only findings in which the lower 95% confidence interval is more than 1 are reported. There is a marked consistency of the findings and the significant relationship between exposure to air pollution and various measures of morbidity is clear. The analysis of data relating to the spouse of the respondent revealed similar findings. The findings in relation to the children in the households also reveal a relationship between morbidity measures and exposure to air pollution (where the smoking habits controlled for are those of the parents). Table 1 Figure 2 3. DIRECT VALUATIONS: CVM 3.1 Elicitation Technigue and Analysis of Responses Economists have long since shown that the correct measure of welfare changes due to pollution reduction, and the associated health improvements, should be based on people's willingness to pay (WTP) for pollution abatement (Schelling, 1968; Mishan, 1971). Conceptually, this measure should capture the four components 8


-------
which constitute morbidity damages, namely, (a) opportunity cost
of time sick, (b) out-of-pocket and indirect (public) outlays for
medical services, (c) defensive expenditure, and (d) psychological
losses associated with suffering, pain, hedonic damages, and other
direct utility losses not accounted by the first three categories.
A comprehensive approach to pollution-induced health damage
valuation should incorporate all four components. The money
equivalent of these damages is represented by WTP for enhancing
ambient air quality, through the implied reduction in exposure to
morbidity risks. Of course, other benefits associated with air
pollution abatement should be excluded in this case.
In the present study, pre-testing has shown that - at least
in the case of Israeli respondents - questions which attempted to
elicit monetary valuations for reduced morbidity (e.g., reduction
in a stated number of bed days, the number of days with
respiratory symptoms, or the number of acute situations during a
given period), were ill received by the respondents, or they had
difficulties relating to the situations described in such
questions. Hence, it was imperative to state WTP in terms of
reduction in pollution levels. The Israeli public in general, and
in Haifa in particular, is well aware of the connection between
air pollution and respiratory ailments, although of course not
necessarily of the true dose-response relationships.
Interviewees were queried about the perceived air pollution
levels in their own neighborhood. In order to provide a visual
stimulus, they were shown photographs of the city of Haifa on
q
visibly polluted and on relatively clean days. They were asked to
state their maximum willingness to pay for pollution abatement:
(a) In order to prevent a 50% reduction of present air quality
level of their neighborhood; (b) To achieve a 50% Improvement in
The pollution levels shown in the pictures did not necessarily
correspond to the indicated changes in pollution levels, and
mainly served to introduce a measure of realism to the
hypothetical nature of the CVM environment.
9

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4
present neighborhood levels. The first measure corresponds to ES
(and following Randall and Stoll, 1980, will be denoted by WTE^ ) ;
c
the second corresponds to CS (denoted by WTP ) . The notation
serves to emphasize that both are willingness to pay measures, not
willingness to accept (WTA) ones. Because of the inherent
difficulties in obtaining non-inflated WTA responses it was we
decided against employing them in the questionnaire, given the
5
possibility that this could have mired the WTP responses as well.
The payment vehicle was the municipal property tax, which is
the sole local tax. Respondents were asked to state their WTP in
terms of a percentage of the annual tax assessment (over and above
their present tax assessment) , by selecting the appropriate
percentage figure from a payment card. Respondents who were not
willing to pay any sum were asked about the reasons for the zero
valuation. It was thus possible to distinguish between "true" 0's,
i.e. people who did not place any positive value on the
improvement (or, alternatively, the prevention of deterioration) ,
and those who Implicitly registered a protest vote for a variety
of reasons (objecting to the payment vehicle, believing that the
polluter should pay, and so on) , but who did not necessarily view
Specifically, they were instructed to refer back to the
perceived level which they had previously indicated as the one
prevailing in their area.
5
On the use of WTA vs. WTP m CVM,	and the controversies
surrounding their derivation in empirical	studies,see Bishop and
Heberlein (1979); Knetsch and Sinden (1984); Gregory (1986);
Mitchell and Carson (1989).
6
Percentage categories (from 0% to 100%) were listed on the card
in either ascending or descending	order, vertically or
horizontally These options were randomly	assigned to households.
The upper 100% limit did not seem to constrain the range of WTP
responses. While 90% of the WTPe or WTP	values were below 100
NIS, only 0.4% of the households were in	the 100 NIS or less tax
bracket.
10

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air quality improvement as valueless .
The variables found to be significant in explaining the
variation in WTP Cand WTP 6 (exclusive of protest zero bids) are
presented in Table 2. Since the analyses of the CVM experiments
focused on the subset of positive bidders, it was necessary to
correct for a possible selection bias introduced by dropping the
zero responses. A procedure accounting for this bias is described
g
in Maddala (1983) . The analysis proceeded in two steps. First, a
probit model is used to analyze the determinants of zero bids,
where the dependent variable takes a value of 1 if WTP>0, and 0
otherwise. In the second step positive responses are analyzed
separately, with the probit model providing an estimator to
correct for the selectivity effects resulting from dropping the
observations with zero bids. The adjustment factor is given by the
ratio	where 0 and ~ are the normal probability density
function and cumulative density function, respectively, and
V=b'_x. The b's are maximum likelihood estimators from the probit
analysis, end x is a vector of explanatory variables belonging to
three categories: variables associated with the respondent's - or
other family members' - health status, demographic and
socioeconomic variables (age, sex, education, birth origin, work
status, family size), and attitude shaping variables, such as
perception of the authorities' involvement with pollution control,
the amount of annual taxes paid, and perceived exposure to air
Our interpretation of the data is that although some vehicle
bias exists, it has had only a limited impact upon the results.
Out of about 35% of respondents whose WTP=0, 21% (for WTE^ ) and
0
17% (for WTP ) gave reasons which could possibly imply an
objection to the payment vehicle itself ("I already pay too much
tax"; "I am not willing to pay any more taxes") . Namely,
altogether approximately not more than 7% of all respondents were
affected by the vehicle to such an extent that they refused to pay
any positive sum. Of course, the sums offered by other respondents
may have also been affected to some unknown degree.
g
It was applied by Kealy and Bishop (1986) in studying recreation
use behavior, and by Smith and Desvousges (1987) in a CVM study on
risks of exposure to hazardous wastes.
11

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pollution at home or at the work place. There has been an expected
2
marked improvement in R when the equations were estimated over the
set of nonzero bid observations.
Table 2
C	©
The estimated regressions of nonzero WTP and WTP bids, for
the subset of standard WTP responses (see the section below) are
reported in table 2 (n=2,230). Respondents who are younger,
female, and from a higher socioeconomic status tend to be willing
to pay more to improve air quality, or prevent its further
deterioration. Respondents who are more aware of pollution in
their neighborhoods or work place, who believe too little is spent
on pollution control, believe government Is not too effective in
controlling it, and are willing to devote of their time in public
activities to this end, are also willing to contribute more
towards this goal. And those who themselves, or their families,
suffer from the ill health effects of pollution, are also willing
to pay more to control it.
3.2 Contingent valuation experiments
The sampling design used in the study afforded the
possibility of experimenting with alternative CVM formats, used
for difference subsets of the sample, each of which could be
viewed as a separate random sample from the same population. The
only difference between these samples was that they were taken at
different points in time. Clearly, to the extent that time of year
affected the CVM responses, the statement above would have to be
qualified.
The first set of questionnaires (n af 2,300), the "standard"
CVM format was used, namely, an open-ended WTP question. The
respondent was asked to state his or her maximum WTP for the
proposed change.
12

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It has been suggested that a more "natural" way to conduct
CVM surveys, thereby adding realism and reducing the inherent
hypothetical element, is through the use of a "Buy - Not buy"
choice implied by the binary choice format (Cummings, et al,
1986). To this end, a second set of questionnaires (n * 450)
replaced the standard format with a binary choice format, in which
respondents were asked to state whether they would be willing to
pay a given percentage increase in the municipal tax for the same
±505i changes in pollution levels. The percentage categories were
drawn from the pay card table, and randomly assigned to
households.
To analyze these responses, behavior is usually modeled in a
stochastic fashion, often by positing a random utility model to
represent consumer behavior. While the binary choice format does
not provide the investigator with information regarding the sample
distribution of WTP valuations, it does nevertheless enable to
deduce its first moments - the mean and the median. These can be
compared with the corresponding statistics of the distributions
obtained from the other experiments. Our analysis followed the
work of Hanemann (1984) and Loehman and De (1982).
A third variant of the CVM format (n 91 490) was aimed at
attempting to elicit respondents' true maximum WTP statements, by
asking them whether they would have agreed to Increase - and then
by how much - their initial sums had they been informed that that
sum would not be sufficient to accomplish the indicated 50%
change.
In the course of the survey doubts were raised whether
respondents were indeed interpreting it to be a one-time payment,
instead of an annual contribution, in conjunction with the payment
of their annual municipal taxes. To this end, a fourth change,
involving a different subset of about 400 respondents, modified
the nature of the payment, from a one-time to an annual payment.
13

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Tables 3 and 4 display various statistics for the four
experiments, and for the overall sample: "Standard" maximum WTP,
repeat bidding, binary choice, and annual vs. one-payment, for
c 	e
WTP and WTP valuations, respectively, responses. We present here
the results for the analyses excluding "protest" zero-bidders
(identified through the follow-up question).
Table 3
Table 4
© c
In general, WTP >WTP , namely, on average respondents were
willing to pay more to prevent worsening of pollution than to
improve present levels. However, as noted above, unless we know
the shape of the indifference curves we cannot say a priori
whether this indeed should be the case.
Means of the binary choice format are surprisingly close to
those of the standard, and especially the repeat-bid, formats.
Though eliciting less information (WTP above or below a certain
value, but not actual WTP itself), the resulting welfare change
estimates do not very much from the standard format (particularly
6	C	0
WTP valuations), or from both WTP and WTP in the repeat bid
valuations. The results suggest that, given the simplicity of the
binary choice format, it should be considered first as the
preferred alternative, particularly where there would not be any
special interest in obtaining the sample distribution of the CVM
valuations.
Regarding the repeat bidding elicitation procedure, we found
t •r»T*C	. --.6
a significant increase in mean WTP and WTP , for those
respondents who were willing to increase their payments (who make
up only a subset of all respondents, as one would expect), and who
gave a consistent answer. We tend to interpret these results as
evidence of the efficacy of this approach in deriving better WTP
estimates, supporting Mitchell and Carson's (1986) advocacy of it.
14

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We did not find significant differences between the responses
of the annual and one-payment groups, supporting our suspicion
that respondents processed the WTP questions in the same way they
would relate to the annual municipal tax payment.
3.3 WTP° vs. WTPC responses
A different analysis of WTP responses is presented in Table
5, where a different grouping of mean sample values of WTP and WTP
for air quality changes is presented. The table is based on
responses from the subset of standard WTP questionnaires.
Neighborhoods (=CSA's) were divided into the three pollution
g
levels. With regard to WTP , it was assumed that a 50% improvement
roughly implies that a neighborhood with moderate air quality
would be upgraded into one with good air quality, i.e., a
(relatively) clean one, and that a "bad" neighborhood would move
0
into the "moderate" category. Similarly, with respect to WTP , a
50% deterioration In pollution levels would imply a downgrading of
a relatively clean neighborhood to one with moderate levels, and
9
so on. Thus, on average, an individual living m a moderately
polluted neighborhood (according to his or her perception) would
be willing to contribute NIS 37.9 annually towards improving air
quality, and NIS 40.0 In order to prevent a worsening of present
levels.
Table 5
The relationship between these two welfare change measures
for any given sub-sample of neighborhood households is ambiguous.
6	C
While WTP > WTP for moderately polluted neighborhoods, the
£
reverse holds for those badly polluted. However, both WTP and
g
WTP increase with pollution levels, and the between-group
9	...
The neighborhood marked "Very poor" in Table 5 is a fictitious
neighborhood, created by hypothetically downgrading the "poor"
neighborhood category.
15

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differences are significant (non-parametric median test) . The
C	0
two-sample mean tests indicate that although WTP and WTP differ
c	©
significantly, WTP > WTP in one case (respondents from
poor-quality neighborhoods), but the reverse holds for
moderate-quality neighborhoods.
3.4 Reliability of CVM valuations
Doubts about the truthful revelation of preferences obtained
through direct questioning procedures still dominate many
discussions involving the use of direct WTP valuations. Four
"Reference Operating Conditions" (ROC's) have been proposed by
Cummings, et al (1986), as criteria for evaluating CVM
applications in general, and for evaluating the accuracy of the
values obtained in particular. These conditions are (a)
familiarity with the commodity, (b) prior valuation and choice
experience with respect to consumption levels of the commodity,
(c) the presence of little uncertainty and, (d) the use of WTP,
rather than WTA (willingness to accept) valuations.
In examining these conditions In the context of the present
study, we note first that the city of Haifa and its environs
provide a suitable setting for obtaining WTP responses in a CVM
environment. Its topographical layout and the location of its
industry introduce inter-neighborhood variability in ambient air
quality, about which there is a fair level of public awareness. In
recent years, the local media have frequently addressed the issue
of air pollution-induced diseases. It is therefore likely that
respondents were not placed in a position of having to respond to
hypothetical CVM questions. Moreover, it has been surmised that a
willingness to pay for air pollution abatement would tend to
involve little or no strategic biases attributed to CVM surveys,
because relatively small sums of money (per household) are
typically involved. Thus, of the four conditions noted above, the
16

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first and the last have been satisfied in this study.
Regarding ROC #2, all that can be claimed is that subjects
were familiar with the vehicle (city property tax assessments),
although, naturally, they had had no prior experience with
valuing air quality in this particular manner. However, it is
doubtful whether ROC #3 was fulfilled in this study. First,
uncertainty is ingrained in dose-response relationships between
air pollution and health, especially when lay people are involved.
Secondly, an altogether different type of uncertainty may have
surrounded the stipulated change in the supply of the "paid-for"
commodity (the indicated level of air quality improvement) , had
the payment indeed been made. Although the phrasing of the
relevant question attempted to alleviate this source of
uncertainty, we have no way of ascertaining whether this had been
successfully achieved.
3.5 Population CVM Estimates
C	A
Population estimates of WTP and WTP for the entire Haifa
metropolitan region, were derived using the following entities:
= The number of households in the i-th CSA by employment
status (s) of the head of the household (employed, self-employed,
and unemployed].
I = Average net monthly income per household of households
whose heads were employed (Central Bureau of Statistics, 1985b).
Since income of self-employed by CSA is not available, it was
determined on the basis of sample means, after proper adjustments.
Income levels were converted to 1987 NIS using the Cost-of-Living
Index and the change in real income of salaried workers (Bank of
Israel, 1988) .
All census areas were classified by socioeconomic level (e)
Indeed, the survey indicates that subjects were highly familiar
with the various pollution levels in their respective
neighborhoods. As noted in an earlier footnote, a high partial
correlation between measured and perceived pollution levels is
evident.
17

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and pollution level (p), corresponding to those used in
c	©
delineating the sampling strata. Using these data, WTP and WTP
totals for each CSA, were derived by grouping all CSA's (sample
and non-sample) according to their respective socioeconomic level
(e) and pollution level (p) . Each CSA was further sub-divided by
employment status. The corresponding sample CSA mean WTP value was
used for calculating population totals for each sub-group within
each CSA. Regional totals were then obtained by aggregating
employment-group totals within each CSA, and then aggregating over
all CSA's. Total regional annual benefits of pollution reduction
(ZWTPC) and of prevention (ZWTP6) amounted to NIS 3.9 and 9.9
mil., respectively (at the then prevailing exchange rate of 1.5
NIS to $ 1 US, $2.6 and 6.6 mil.)
4. INDIRECT VALUATION: DERIVING EXACT WELFARE CHANGE MEASURES
4.1 Introduction
In calculating benefits associated with a larger supply of
the environmental public good through its relationship" with some
market good(s), one might begin with estimating a demand function
for the market good from observed price-quantity data. The
benefits from the public good would be derived by computing the
change in consumers' surplus associated with a corresponding shift
in the market demand schedule. This method would be expected to
yield an approximate value of the potential welfare change (Just,
et al, 1982). Alternatively, exact (in the theoretical, not
statistical, sense) measures of welfare change may be obtained by
evaluating an expenditure function underlying the ordinary
market-good demand system, using duality theory (Hausman, 1981;
Vartia, 1983; Loehman, 1986) . This approach is discussed in this
section.
In order to eventually "untangle" the demand valuations of
the public good from those observed for the market goods, the
posited demand system ought to satisfy two conditions. The market
and nonmarket goods must be non-separable, and a price vector
which would drive the marginal utility from the nonmarket goods to
18

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zero should exist (Maler, 1974). These conditions enable the
recovery of the preference ordering for this group of goods and,
subsequently, the compensated demand (or marginal willingness to
pay) schedule for the public good, from which valuations of
changes in the quantity of that good can be derived. The demand
system specified below satisfies the first condition; the second
condition is not testable, but assumed.
Specifically, in this study a twice differentiable indirect
utility function was assumed. Duality theory (Roy's identity) is
invoked in deriving the corresponding budget share equations. This
11
partial system encompasses two market goods, housing services and
medical services, denoted by the vector X in the formulation
below," and a public good, air quality, denoted by y. The
expenditure function, derived from the posited indirect utility
function, is then used to calculate the monetary value of welfare
changes associated with shifts in the level of air quality. By
Shephard's Lemma, the partial derivative of the expenditure
function with respect to price yields a Hicksian compensated
demand function (cf. Varian, 1984) ; the derivative with respect
to the public good yields the demand "price" function for the
public good.
We know of only one recent study which adopted a similar,
indirect market good approach to the empirical estimation of the
Partial demand system are frequently encountered in empirical
studies. This is characteristically due to data limitations which
preclude the estimation of all the unknown parameters in the
complete demand system. In order to recover the preferences for
the nonmarket good from the partial system it is necessary to
assume that the group of commodities which make up the partial
system is separable in consumption from all other commodities
(Hanemann and Morey, 1987) . These authors go on to show that the
compensating and equivalent measures calculated from a partial
demand system need not be identical with those calculated from a
full system. CV would be a lower bound on the conventional
compensating measure, while EV might be greater than, less than,
or equal to the full system measure.
19

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benefits associated with an environmental good (Shapiro and Smith,
1981). Our paper differs in its use of individual, micro data, as
compared to their use of aggregate data, and in deriving exact
welfare measures (which was not the focus of that paper) . In
connection with measuring cost of living changes, Cobb (1987) has
used a "translating variables" specification in incorporating
nonmarket goods in budget share equation systems.
4.2 Model specification and estimation
The specification chosen for the indirect utility function is
the translog function (Christensen et.al., 1975), defined in terms
of normalized prices of the two market goods, P =P^/M, the
nonmarket good - air quality - y, and household characteristics:
• •
InV » aQ + (1 + lny) + (o^ + Tjlny) In Pj + (a2 + r2lny) In P2 +
+ | [(^n + 5n lny)tin P*]2+(012 + 512 lny)lnP* InP*
(5)
+ (*21 + 521 lny)lnP! lnP2 + (*22 + *22 ^HlnP*]2]
+ In P1 l^11h1 ~ *i2h2 - ^ghg + ^uh4 -
+ ln P2 [*21hl + *22*2 + *23*3 + *24h4 + ^sV + Z *ihi
• •
where P^ is the (normalized) price of housing services, and P2 is
the (normalized) price of medical services. The	are
dichotomous variables which represent family or head of household
health characteristics: hj - smoking habits, hg - respiratory
illness symptoms (head of household) ,	- respiratory illness
symptoms (all other household members), - respiratory diseases
(head of household) , and hg - respiratory diseases (all other
household members).
By Applying Roy's identity to eq. (5) the following share
equations are derived:
py
a InV / aire/ _ o _ 1
~ 8lhPi / dtnM i M
20

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= ^(aj+rjlny) + Oil+5illny)lnP1 + |oi J+51 jlny) lnP^
* I' W1*' lnpj*1 *iA } /D 1"1-2 (6)
where
• •
D * (a^TjlnyJ + Caj+rjlny) + (0^+S^lny) InPj + (0jj+5jjlny)InPj
* 2 (3l/aijlnyHlnPI *lnPj>4(
-------
those of the first system; hence, only one equation needs to be
estimated. We may note that the present data base has made it
possible to incorporate individual health characteristics, related
to respiratory illnesses and symptoms, into the posited preference
13
function. In this sense, the present indirect valuation can also
be likened to the household health production approach used to
evaluate morbidity and mortality benefits (see below).
Annual municipal tax assessments were used as proxies for
housing prices in the estimation of the budget share (eq. 6) . Its
rates generally reflect dwelling quality and the socioeconomic
status of the neighborhood. This variable was used instead of
imputed rental value because there are no reliable, published
statistics on housing prices by neighborhood and housing quality.
Consumption of housing services has been assumed to be given by
dwelling size.
The price of medical services was calculated as a weighted
index of national, average estimates of primary clinic cost per
patient visit and hospitalization costs for all illnesses.
Consumption of medical visits was given by a predicted number of
clinic visits, derived from a logit regression analysis of the
14
survey data. Hospitalization data were taken directly from the
For the inclusion of characteristics in an indirect translog
utility function, see Woodbury (1983), in connection with a model
describing labor compensation. The characteristics there are
parameters which describe the worker or the work place. In a
similar vain, Morey (1985) incorporated personal and site
attributes in estimating a demand system for ski resorts (see also
Jorgenson and Slesnick, 1987).
14
Respondents were asked whether they visited a clinic during a
two week recall period prior to the date of the interview. The
logit regressions yielded predicted probabilities of at least one
visit during the two week period as a function of socioeconomic
and health characteristics, and a seasonal variable. These
probabilities were then converted into an expected annual number
of visits for each household.
22

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questionnaire, where respondents were asked to indicate whether
they had been hospitalized for respiratory system-related
15
illnesses during the 12-month period preceding the interview. The
hh^s are health attributes of the respondent (head of household)
or other household members, that are presumed to be associated
with, or induced by, air pollution (with the exception of smoking
which itself induces similar symptoms). The health variables
include coughing, wheezing, sputum emission and shortness of
breath; diseases refer to asthma, bronchitis, pneumonia, and other
lower respiratory tract diseases. As already indicated, y stands
for the perceived level of neighborhood pollution. Respondents
16
were requested to indicate this on a severity scale of 1 to 6.
To estimate the share equation (6) we employed a procedure
that combines iterative minimization methods for non-linear
regression with OLS estimation, imposing the symmetry and
adding-up restrictions. All variables were normalized through
division by their respective sample mean. Table 6 displays the
parameter estimates. Inserting the parameter estimates from the
budget share (5) into the indirect utility function (4), and
It should be noted that the majority of families belong to one
of several quasi-public health insurance schemes, and do not pay
directly for medical services. However, paying for private medical
visits and medications in order to obtain faster, and often better
quality treatment is quite common, especially with sick children.
Information on these extra costs, available from the survey, was
also used in deriving expenditure levels. It can therefore be
surmised that the number of clinic visits, in and by itself,
reflects an opportunity cost of time in obtaining medical
treatment, even though no immediate payment is necessarily
associated with it.
16
While the perceived level of pollution may directly affect the
demand for housing and hence values, its impact upon medical
expenditure is indirect; the latter, are affected by actual
pollution levels. However, there is a rather high partial
correlation between these two measures (r=0.77). On the
appropriateness of using perceived rather than actual measures of
pollution levels from a psychological perspective, see Zeidner and
Shechter (1988) . It may be noted that had it been possible to
elicit quantitative responses for perceived air quality, it
probably would have been possible to use the restricted indirect
utility function as suggested by Diewert (1978).
23

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evaluating its partial derivatives with respect to prices, income,
and the public good, at the point of means, it can be shown that
3V/3Pj<0 (i=l,2), 3V/3M>0, and 3V/3y>0, as expected. utility
decreases with a rise in the (normalized) prices of housing and
medical services, and rises with the level of money expenditure on
the two market goods and with the level of air quality. It can
also be shown that the function possesses the correct signs for
the second derivatives.
Table 6
4.3 Welfare change measures
The expenditure function takes on the form:
t [[a1+V(lnP1)(b1rt2)MlnP2)(b2*b3)]2
- (2^+4^+2^) ^a+anPjHaj+djHUnPgHa^+d^+ib^ lnPj)2*
1
* b2lnPllnP2 * 2*3(lnP2)2 " lnVF ' [v2Vbj	(7)
J
where n=lnM, a - aQ+l+lny, ^ ¦ aj+rjlny,	- a2+r2lny,
V *11+ 5lllny' b2 = P12+S12lny' b3 = *22 +522lny*
S	3
dl " WZ 'lk "k • ^ d2 - 1
k=1	k=l
Given the parameter estimates from eq. (6), CS and ES values
(eqs. 1 and 2) - associated with a ±50% shift from the baseline
air quality levels - can be calculated using eq. (7). These
calculations yielded annual payments of 2.33 end 105.10 NIS,
respectively, per household. Because the expenditure function is
nonlinear, the values which have Just been calculated are
equivalent to evaluating a function of the form f(x), which
generally would not yield the same values obtained from evaluating
f(x) instead. Thus, we have also computed the means of individual
24

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valuations by calculating the two welfare measures for each
household, using the relevant attributes for that household. These
calculations yielded the following mean valuations for the sample
of households: WTPC= 9.81 NIS (S = 38.3), and WTP6 = 73.25 (s =
106.2). As noted above, and shown by Loehman (1986), there is no a
priori theoretical Justification for expecting either EV>CV or the
reverse; both cases are consistent with theory, and the direction
of the inequality sign depends on the shape of the indifference
curves.
The expenditure function for utility kept at a level
associated with the initial (sample mean) air quality is shown in
Figure 3 (on a logarithmic scale). The corresponding Bradford-type
bid curves, showing WTP as a function of y for utility held at the
initial level (CS), and at the final level (ES), are drawn in
A
Figure 4 (marked WTP and WTP , respectively). It can be seen from
Figure 3 that the marginal bid function, or the compensated demand
for the public good (the partial derivative of the expenditure
function with respect to the public good, for given market good
prices and utility level), would be negatively sloped.
Figure 3
Figure 4
5. INDIRECT VALUATION: HEALTH PRODUCTION APPROACH
5.1 Introduction
The household health production is the basis of a valuation
approach in which the benefits from a public good, viz.,
environmental quality, are assessed indirectly through household
optimizing behavior with respect to the production (and
consumption) of good health. This health "capital" is an argument
in the utility function, along with other goods and services. The
production of health contributes to utility on two counts: (1)
Reducing expenditures on health care services, which otherwise
would have decreased the amount of income available for spending
25

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on utility-enhancing goods and services ; (2) Diminishing the
impact on utility through income reduction caused by work-loss
days, or increasing income through productivity gains. In this
framework, one would also have to consider decisions concerning the
money time spent on preventive or averting activities. These
contribute directly to the production of health stock (but also
reduce the budget available for goods and services). Of course,
the total effect on utility amounts to a WTP valuation of the
welfare changes attributable to changes in the quantity of the
environmental good.
Several studies have used the health production approach to
estimate the value of reducing health risk resulting from air
pollution abatement (e.g., Cropper, 1981; Gerking and Stanley,
1986; Harrington and Portney, 1987; Berger, et al., 1987; Dickie
and Gerking, 1988). The emphasis has been on the inclusion of
preventive expenditure in a utility maximizing framework, and
demonstrating the theoretical superiority of this approach
compared to the COI approach. The latter overlooks preventive
expenditure, namely, the possibility that individuals yield a
measure of control over the state of their health, any direct
utility losses associated with illness, and the value of bed-day
losses of the non-working population (cf., e.g., Cooper and Rice,
197 6). It should be noted, however, that in the various empirical
applications of the health production approach,	the
budget-reducing or income-enhancing effects have generally been
not explicitly considered, and a fixed budget is assumed. What one
is left with is usually a utility maximizing framework where only
preventive activities (in addition to medical care and other
consumption expenditure) are taken into account (see the empirical
sections of the above cited studies).
In this section we outline a model which attempts to provide
17
To the extent that the utility derived from consumption of goods
and services is in turn affected by health conditions, then
reduction of bed days would also be taken into account.
26

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a comprehensive framework for dealing with uncertainty and the
dynamic aspects of the health production process. Since we too
assume a fixed budget, our approach yields Valuations of the
environmental good which do not take into consideration the labor
savings component. We only outline the model here (for a full
description see Shechter, 1988), and then provide some tentative
WTP estimates.
5.2 The model
Assume an individual producing different levels of health
depending upon initial health stock, the amount of medical or
preventive care consumed, the level of the environmental public
good, and socioeconomic attributes. Uncertainty is represented by
probabilities of being in an ill or a healthy state, following a
first-order Markovian process (Hey and Patel, 1983) . Several
simplifying assumptions, some quite strong, have been made: (1)
The probabilities are a function of the individual's current
health state and not affected by age or by past medical history.
(2) Two types of health stock related expenditure exist:
Preventive care and medical care, where the former is exercised
only when the individual is healthy, while the latter is consumed
only when he or she is ill.
The health production process is given by:
H^m^, y, 0 ; -a—S>0 ; >0 and §5 >0 (for h and s); 		 <0; 		 <0
3mh Sms 8y	d
-------
where
H- the individual's health level,
"fa- amount of preventive care consumed,
m - amount of medical care consumed,
s	'
y - the level of the environmental good,
WC•), and that the
individual is risk averse: V'>0, V"<0, W'>0, and W"<0.
For the Markovian process of transition between health states
28

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over time the following probabilities have been defined:
P - The probability that an individual who is healthy
today will also be healthy in the next period, where
P' (h) > 0;
1-p - The probability that an individual who is healthy
today will be ill in the next period;
q - The probability that an Individual who is ill today
will be healthy in the next period, Q'(h) >0;
1-Q - The probability that an individual who is ill today
will also be ill in the next period.
5.3 Optimization
The individual is assumed to maximizes lifetime expected
utility, allocating the budget among x, "k. and m , given the
"	s
health production function and the budget constraint. Expected
lifetime utility from T onward is given by
I pt_T U. (X;H)	(11)
t=T
where p is the rate of time preference.
One first solves for the optimal values of X, °h and nig,
subject to the constrains. As noted, these optimal values are
time-invariant, implying that all time periods are identical,
given the state of the individual' health. Upon totally
differentiating the first order condition, it is possible to
obtain an expression for the individual's willingness to pay for a
change in the level of ¦ the environmental good, , measuring the
value at the margin of the public good after all
utility-maximizing, consumption adjustments have been made. We
omit the details of the derivation (see Shechter, 1988), and give
the final expression:
29

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dl
dy
p.f5i
3y
"ins-
ch 5mh
5H
'V
C dm
s s
(12)
Note that expressions involving utility terms have been factored
out, facilitating in principle empirical applications (cf.
Gerkings and Stanley, 1986; Berger, et al., 1987).
We would generally expect	to be negative, because a
decrease in air quality would require some compensation for
utility (at the optimal level) to remain unchanged. The change
would increase health risks and welfare losses, even after the
individual makes an attempt to offset this increase, at least
partially (depending on one's preferences), through some budget
reallocations entailing, among others, more spending on preventive
or medical care. For	the following conditions, - which seem
reasonable - should simultaneously be satisfied:
(a)	W'>V' -- the marginal utility of income of a non-healthy
Individual is higher than that of a healthy individual.
3H. SH
(b)	P Sy < QV
That is, the change in the probability of being healthy in the
next period due to a change in air quality is higher for an ill
person than for a healthy one.
In order to apply the model to available data, an additional
simplifying assumption was made, namely that there is no
distinction between medical and preventive activities, and both
having the same unit price. Thus:
3Hh
a h
m _ m fdH _ SH _ 3H . _ __	n_ s
n s' ^ms~ ~ 3m J' h~ s~ * dy dy
From this it follow that
30

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dl
dy
r 5H 1
3y
(P'-Q*)
ei 
-------
with no alternative but to assume that only medical care budget
reallocations matter in households' health production decisions.
19
Rewriting eg. (13) as (5m/3H) C (3H/3y), we estimated the
first term using conditional probabilities. First, specifying a
logit model, we estimated the probability of at least one doctor
visit during a two-week recall period prior to the interview, for
each of three health states: h=0, healthy; h=l, having symptoms;
h=2, having symptoms and respiratory diseases. All the other
explanatory variables (except AV14, see below) are dichotomous.
Medical services covered here include doctor visits (mostly at
primary health clinics belonging to one of the health maintenance
organizations, the so-called "sick funds") of the interviewee,
spouse, and children.Logit regressions were estimated for doctor
visits, including private consultations (separately for
respondents, spouses, and children).
Table 7
The variable representing pollution, AV14, Indicates measured
Assuming the health production function enables us to write
express it in terms of its inverse, m(H,y), namely, that the
conditions of the implicit function theorem hold.
20
In Israel almost all medical services are publicly provided,
then, unless they actually sought private medical services, people
are usually not fully informed of the out-of-pocket expanses.
However, it is reasonable to expect that they would take
cognizance of the time and psychological costs involved in a
clinic visit or a hospital stay. These may bear some relationship
to the real economic costs of providing the service. Children
visits to a physician refer to at least one visit by at least one
child from the respondent's family, since children were not
individually identified in the questions relating to health
conditions. See also footnote 15 above.
32

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21
(actual or extrapolated) SO_ concentrate ions (in ppb).	The
22
variable AV14 is significant in every regression. Respondents
with respiratory system problems are more inclined to seek medical
help, and so are females, respondents with no children in the 0-18
age group (probably a proxy for older respondents) , and those of
Asian-North African origin (may also be related to belonging to a
lower income group) . The results for spouses and children were
similar, with AV14 figuring in all of them, but they have not
been used here.
Next, we specified a multinomial logit model to describe the
relationship between health state and pollution levels, where
Pj = prob(h£l), and = prob(h=2). The results are given in Table
8. Again, as expected from the discussion in Section 2 above, AV14
is highly significant. The coefficients of the socioeconomic
variables have also the expected sign.
Table 8
Viewing the medical care use probabilities as conditional
probabilities given one's health state, we have calculated the
change - at mean values of the other explanatory variables - of
reducing mean AV14 by 50% (going from Yg to y^. Viz.,
p(doctor visit in past 2 weeks / h^) x p(hj/y=yg)
21
Since pollution data is measured only at a few points m the
Haifa metropolitan region (and only SC>2 on a continuous basis) , it
was necessary to extrapolate ambient concentrations for the rest
of the survey neighborhoods using an ad hoc dispersion model.
Average concentrations were computed for two-week periods
preceding the date of any given interview. The two-week averages
are based on half-hour concentration readings.
22
An alternative set of regressions was run with the variable
MAX14, representing maximum daily concentration for the preceding
two-week period, but AV14 turned out to be a better predictor.
33

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- p (doctor visit in past 2 weeks / h^) x p(h^/y=y^), i=0,l,2
The decrease amounted to 2.26% percentage points, or about 8% from
present usage levels. Converting this result to expected number of
annual visits, and multiplying by C, the cost per visit of NIS
30,23 yields a rough approximation of WTP of NIS 32.43.
Of course, this figure is an underestimate: (a) It does not
include visits of spouse and children; (b) it is based on a
question which asked whether there was at least one visit during
the preceding two-week recall period, but did not ask for the
actual number of visits; (c) it does not include hospitalization
24	25
cost or medication costs ; (d) finally, as explained above, it
overlooks the labor cost savings.
An altogether different question is associated with the
nature of medical care services in a country like Israel, where
most of the population Is covered by one form or another of a
subsidized quasi-public health insurance scheme. In this sense
individuals do not have to make budget reallocation adjustment in
the way assumed in the model. However, as remarked above, time and
Inconvenience associated with a visit to a primary health clinic
might nevertheless be playing a major role, not much different
from that of money expenditures. This of course is another major
drawback of the empirical results, but we surmise that CVM
valuations may have well been similarly affected.
Although no statistics are available, we believe this figure to
be close, though somewhat lower than the corresponding cost of a
private consultation visit to a general practitioner.
24
Respondents were also asked about hospitalization during the 12
month period preceding the interview for illnesses connected with
the respiratory system, but the number of responses was too small
for any meaningful analysis.
25
The expected decrease in the probability of obtaining medication
resulting from pollution reduction, has been calculated to reach
17% approximately (a decrease from p=0.113 to 0.094).
34

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6. COST OF ILLNESS (COI) VALUATIONS
6.1 Consumption of Medical Services and Bed Day Losses
The COI approach normally covers direct (expenditures on
medical services) and indirect (income reduction due to work day
and productivity losses). As observed above, given that work loss
has been neglected in the household production model, we have made
an attempt to estimate these losses. Since individuals would not
directly suffer the consequences of work loss days because of the
almost universal coverage by employer-paid sick-day leave, this
cost is distinctly a social cost. We would not expect it to be
expressed through individual WTP valuations.
A binary response model was used to analyze bed days during
the two week recall period. The response variable, STY, was
defined as follows:
2TY_	1 if respondent missed one or more days
0 otherwise.
Although our sample was large (n=954), the results are
nevertheless based on a relatively small number of observations,
since only 65 cases were respondents who reported that they were
absent from work for at least one day during the fortnight. A model
was fitted with both socioeconomic and health attributes, using
backwards elimination to fit the logistic regression. The
estimated equation is given in Table 9.
Table 9
When AV14 is reduced by 50%, the probability of at least one
bed day decreases from p=0.051 to 0.041, a drop of 18 percent.
Work loss days at present pollution levels constitute about 1.85%
of all work days. The total expected annual savings in number of
work loss days due to pollution abatement, AL (assuming 300
working days per year), is given by AL = E x 300 x 1.85 x Ap,
35

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where E is the number of employed persons (above age 15) in the
metropolitan region, and Ap = 0.18. A similar calculation was
performed for the non-working persons in the sample. The weighted
mean sample percentage of bed days (corresponding to the working
group's work loss days) is 3.57.
Assigning a money value to these savings, would of course
vary with the specific assumptions relevant in each case. The
present calculations were based on 1987 gross wages per salaried
employee, including social benefits, of NIS 1,832 per month, or
$1,221 (Central Bureau of Statistics, Statistical Monthly, April,
1988)	. At this wage rate, the money value of the savings would
total NIS 10 million per year for the working group. For
illustrative purposes, if we also value a day of a non-working
person at 1/2 that of a working person, an additional savings of
almost NIS 8.5 million would be achieved, for a total of NIS 18.5
million. On a per household level, the expected savings would
amount to about NIS 185.0
7. COMPARATIVE EVALUATIONS
7.1 CVM vs. Indirect Approaches
Several writers (e.g., Randall, 1987; Mitchell and Carson,
1989)	have noted that the CVM approach deals with ex ante
valuations, while the indirect approaches are usually associated
with ex post valuations. This implies that one therefore should
not expect to necessarily obtain close estimates in the two
approaches; but the opposite is not necessarily true, either.
Reliability of either approach (which one would supposedly be an
empirical question) might be questioned, however, if results
derived from the same set of observations turn out to be vastly
different. Hence, a comparison of the results from the various
approaches should be illuminating. Table 10 summarizes the values
obtained under the different approaches.
Table 10
36

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The closeness of the valuations is quite encouraging.
Although the indirect approaches cover all respondents, including
zero bidders, it is assumed that the this approach yields true
valuations of protest bidders as well, and hence, the comparison
should be made with the true bidders (non zero and true zero) of
the corresponding CVM experiments (Tables 3 and 4) . It should be
noted especially that the mean values of individual household
valuations in the two approaches are within the same order of
magnitude (NIS 9.8 vs. 34.5 for WTPC, and 73.3 vs. 68.6 for WTP ).
7.2 Health Production, COI and CVM valuations
Although very tenuous assumptions were made in applying the
household health production approach, one observes the closeness
of the results to the CVM valuations. Since the model measures
responses to reduction in pollution, the appropriate comparison is
c
with the WTP valuations. Indeed, if other health and preventive
Q
care components were added, the results of the WTP comparisons
could have turned out to be even closer.
Theoretically, the cost of illness estimates should have at
best provided a lower bound on WTP valuations. But this should not
have been the case in the present study, given that COI estimates
refer to social rather than individual WTP, and include components
which do not figure directly in the individual's decision making
process. Thus, households do not directly bear all the cost of air
pollution damages. They are covered by medical insurance, and do
not bear the full cost of medical services. Part of the premium is
paid by employers and, furthermore, medical services are
subsidized by the government. In addition, paid sick-leave is
almost universal for salaried workers. But, moreover, people
clearly do not possess the kind of dose-response information which
would have enabled them to fully assess the economic impact of
exposure and disease. These facts would necessarily be reflected
in WTP valuations. One should also note that cost of illness
estimates are probably more susceptible that the others to data
"manipulation". The results are sensitive to what we assume about
37

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the appropriate values for work loss of employed and unemployed
individuals, the ratio between privately purchased and publicly
provided prescriptions, and the cost of physician visits, etc.
In a certain sense, one might speculate that CVM responses
represent willingness to pay to reduce the direct disutility
associated with morbidity, plus maybe the aesthetic disutility of
air pollution. Namely, CVM valuations are essentially the
psychological costs associated with pollution. Indeed, results
presented elsewhere (Zeidner and Shechter, 1988) indicate that WTP
is sensitive to anger and anxiety caused by perceived exposure to
air pollution. If this were indeed the case, then the CVM
valuations, or at least part of them, should be added to cost of
illness valuations!
7.3 Some concluding comments
Within the framework of a study dealing with the valuation of
benefits from pollution abatement, several approaches were
investigated. A notable feature of the present study has been the
use of the an identical data base - households, their attributes
and responses - in all three approaches. While contingent
valuation relies exclusively on direct question techniques, so
that survey data are a sine qua non, market demand systems are
normally estimated from aggregate, secondary market data. In this
study, however, the same primary data base was used. Valid
comparable valuations pertaining to the same set of households
were thus obtained. Since all approaches are presumed to measure
the same thing(s), one should a priori expect the results to be
close.
In this vein, we view the results as rather encouraging and
believe that they provide further impetus for the use of CVM. Of
course, improved statistics on health and preventive care should
offer an improved basis for alternative, indirect appaoraches.
38

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Dickie, M. and Gerking, S. 1988. "Valuing Nonmarket Goods: A
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40

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Loehman E. 1987. Measures of Welfare for Nonmarket Goods: Some
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Journal of Environmental Psychology. 8, 191-208.
41

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Table 1 Exposure to air pollution and morbidity in adults and
children: Odds ratios and 95% confidence intervals
Symptom or disease
Odds
Ratio
Lower	Upper
Confidence limit
A. Respondents
Winter cough & cold	1.432202	0.973711	-	2.106581
Permanent cough without cold	1.718250	1.267392	-	2.329494
Winter cough without cold	1.434010	1.151725	-	1.785482
Permanent phlegm & cold	1.572290	0.979119	-	2.524816
Winter phlegm & cold	1.400047	0.977708	-	2.004823
Permanent phlegm without cold 1.347164	1.024256	-	1.771871
Winter phlegm without cold	1.282863	1.040762	-	1.581281
Cough & phlegm	1.566648	1.247142	-	1.968010
Winter phlegm & cold	1.574363	1.252040	-	1.979665
Wheezing & cold	1.358134	1.052843	-	1.751950
Wheezing while breathing	1.352105	1.065619	-	1.715611
Dyspnoea	1.802163	1.530547	-	2.121982
Rhinitis	1.305185	1.043520	-	1.632463
Eye "infection"	1.302482	1.030010	-	1.647031
Headache	1.595975	1.356035	-	1.878371
B. Ch i1dren
Cough or phlegm & cold	1.695780	1.209402	-	2.377761
Cough or phlegm without cold 1.922437	1.365540	-	2.706449
Cough or phlegm	1.969765	1.528539	-	2.538353
Wheezing with cold	1.694218	1.150931	-	2.493961
Wheezing	1.466871	1.130402	-	1.903492
Asthma or bronchitis	1.487382	1.139776	-	1.940998
Pneumonia	1.269068	1.008890	-	1.596343
Rhinitis	1.271813	1.013503	-	1.595958
Eye "infection"	1.495645	1.109688	-	2.015841

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Table 2. Willingness to pay equations - nonzero bids only
Regression coefficients
c	©
Explanatory variable	VJTP WTP
Demographic and socioeconomic variables:
Age (years)	-7.86 (0.29) -0.73 (0.073)
Sex (l=female)	55.28 (4.76)
Education (years)	12.18 (0.71)
Blue collar worker (l=blue collar)	-53.33 (6.80)
Number of children ages 0-18	-24.64 (2.19) -6.93 (1.56)
Ethnic origin I (l=born in Africa/Asia)	-26.93 (6.20)
Ethnic origin II (l=born in Europe)	109.38 (6.38)
Annual municipal taxes	0.22 (0.006)
Attitudinal variables:
Perceived exposure to pollution at work
(l = yes)	81.29 (5.29) 14.42 (4.31)
Perceived neighborhood air quality (1-6)	-21.14 (1.51)
Believes budget share allocated to pollution
abatment too high	-382.22 (57.85) 101.72 (38.87)
Believes budget share allocated to pollution
abatment too low	163.85 (5.90)
Ready to devote time to public activities
concerned with pollution abatement (l=yes) 39.62 (1.64)	5.54 (1.30)
Perception of government influence on
pollution abatement (l=yes)	-26.99 (5.90)
Pollution induces defensive actions by
respondent (l=yes)	8.63 (4.48
Health status
Perceived health status (l=not healthy)	-67.55 (5.46)
Family history (exc. respondent) of asthma,
pnuemonia, or bronchitis (l=yes)	24.60 (4.78)	8.81 (4.29)
Family history exc. respondent) of respi-
¦k -k
ratory system symptoms (l=yes)	55.91 (4.58)
Adjustment factor	-952.98 (23.63)
Intercept	7708.53
	 Adj. R2	0.54 0.64
Not significant.
Cough, sputum, wheezing, dyspnoea

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Table 3. CVM Experiments: WTPC (in NIS, per household,
excluding protest zero bids, except in binary choice)
Elicitation	N	Mean	Median
method
Sample	2,518	34.5
Standard max. WTP	1,855	37.7
Repeat bids: One-time payment
1st bids 343	26.4
2nd bids 195	67.8 (+22.2)
Annual payment
1st bids 343	26.4
2nd bids 195	67.8 (+22.2)
Binary choice	360	66.2	65.0

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Table 4. CVM Experiments: WTP6 (in NIS, per household,
excluding protest zero bids except in binary choice)
Elicitation	N	Mean	Median
method
Sample	1,704	68.6
Standard max. WTP	1,348	70.9
Repeat bids: One-time	payment
1st bids	199	64.2
2nd bids	195	89.0 (+24.8)
Annual payment
1st bids	157	54.5
2nd bids	163	77.9 (+23.4)
Binary choice	360	69.1	67.2

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Table 5. Direct (CVM) valuations of perceived air quality changes
(Includes zero bids)
Present	Pollution level after change
pollution 	
level	Good	Moderate	Poor	Very poor
(a) WTP6
Mean = 2 6
Good	Median= 15
N = 847

(b) WTP°

(c) WTP®


Mean =37 .9

Mean = 4 0

Moderate
Median= 28

Median= 28


N =750

N =749



(d) WTPC

(e) WTPe


Mean =47 .2

Mean =42 .7
Poor

Median= 40

Median= 32


N = 192

N =192
Values in table refer to means and medians of the indicated
sample air quality stratum, and stated in NIS per household
per year.
Significance Levels:
Nonparametric median test for 2 samples:
Hq: WTPC (cell b) « WTP° (cell d)	 0.015
H^: WTP6 (cell a) = WTP® (cell c) WTP (cell e) . . 0.001
Paired t-test for means (2 tailed):
Hq: WTPC (cell b) = WTP6 (cell c)
Hq: WTP° (cell d) = WTP® (cell e)
0.001
0.049

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Table 6. Parameter Estimates of the Budget Share Equation
Parameter
Estimate
Parameter
Estimate
0
11
3
12

'22
11
'12
22
-0.348
(-110.38)
-0.721
(-15.74)
-1.404
(-16.42)
-0.181
(-21.06)
0.039
(2.49)
-0.159
(-4.90)
-0.417
(-12.16)
0.001
(0.06)
-0.527
(-8.77)
*
11
*
12
*
13

14
*
15
R = 0.27
N = 2,239
0.0006
(1.11)
-0.0009
(-0.73)
0.004
(3.27)
0.00002
(0.04)
0.0024
(2.12)
Asymptotic t statistics in parentheses.

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Table 7. Estimated Logit Regression: Consumption of Medical Care
Services (Physician Visits) - Respondents
Explanatory Variable	Regression	Standard
coefficient	error
Intercept

-4.397
0.217
Health status

0.715
0. 097
AVI 4

0. 018
0. 005
Sex (l=female)

0.405
0.134
No children 0-18 yrs.
(l=none)
0.588
0.134
Birth origin Asia-Africa (l=yes)
0.346
0.154
n = 3,612
X = 125.5 (5 df) .
Dependent variable: 1 = visited a physician in past 2 weeks
Health status 0
1
2
= healthy
= suffers from at least one of symptom
= suffers from at least 1 disease

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Table 8. Estimated Logit Regression: Health Risks and Exposure to
Pollution - Respondents
Explanatory Variable	Regression	Standard
coefficient	error
Intercept (h^)
0.880
0.134
Intercept (h^)
-0.732
0.134
AVI 4
0.011
0.002
Education (l=low level, 0-8 yrs.)
0.248
0.078
Birth origin (l=Europe or America)
0.285
0.072
Sex (l=female)
0.289
0.064
No children 0-18 yrs. (l=none)
0.254
0.088
Age of respondent (<40)
-0.845
0.120
Age of respondent (41-50)
-0.481
0.123
Age of respondent (51-60)
-0.372
0.102
n = 3,612
X = 316.5 (8 df) .
Dependent variable:
= suffers from at least 1 symptom or disease
hg = suffers from at least 1 disease

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Table 9. Restricted activity or bed days
Explanatory Variable Regression
	coefficient
AVI4	0.028
(0.012)
Income (1= "low" income-below NIS 1,300/mo.) 0.80
(0.295)
Intercept	-3.79
X =24.2 (18 df) .
Dependent variable: 1 = Stayed home at least 1 day during
the past two weeks.

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Table 10. Comparisons Between Direct & Indirect Valuations
(Including zero bids. Mean household values in NIS)
WTPC	WTP6
zm.
Standard bids
Repeat bids
Binary choice
Indirect
Expenditure function
Health production
Cost of illness (bed days)
37.70
67.80
66.20
9.81
32.43
185.0
70. .90
89.00
69.10
73.25
Corresponding to changes in perceived pollution levels.

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VALUATION of an ENVIRONEMNTAL GOOD
DIRECT vs. INDIRECT APPROACHES
direct approach
contingent
valuation
(CVM)
*
wtp
r
cost
of
illness
indirect (market)
approach
observed demand for
related market good(s)
~
house-
hold
production
function
t
wtp
~
hedonic
models
f
wtp
T
preferences
system
*
"exact"
welfare
measures
4
wtp
FIGURE 1

-------
2
2
a
6
4
2
1
8
6
4
2
0
ATIOS FOR SYMPTOMS & DISEASES
( interviewee, children )
/
./

r /
/ /
.z
"X
N
\
\
1\x
\
\
, \
\

~
/ ,

V
.Z'
X
k\
\ 1
/K x
\
\
\
iv-
< \
X

v


/ /
_z_

\
\
/\
V.
ZN
LZ
\
\
\
\
'N
\
N
\:

x:
i
[7"
id
/*
WINTERM COUGH
COUGH AND PHLEGM
WHEEZING
DYSPNOEA
COLDS
EYE "INFECTION"
HEADACHES
ASTHMA or BRONCHITIS 8
PNEUMONIA	g
-^q—
1
2
3
4
5
6
7
VTT71
/
v
/
/
/
/
/
/
/
j
/
/
Y /
/
5
'TGURE 2
8
9

-------
THE EXPENDITURE FUNCTION
I
I
T
T
T
T
AIR QUALITY
FIGURE 3

-------
BID CURVES FOR AIR QUALITY
6
WTP
3
4
C
2
1
WTPC
0
y
3
S
6
2
4
1
AIR QUALITY
FIGURE 4

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Risk,
Self-Protection
and
Ex Ante Economic Value*
by
Jason F. Shogren	and Thomas D. Crocker
Department of Economic	Department of Economics
Appalachian State University	University of Wyoming
Boone, NC 28608	Laramie, WY 82071
January 1989
*This research was partly supported by the Wyoming Water Research Center.
Perri and Fred Sterbenz have made helpful comments.

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Abstract
We examine the impact of self-protection on the ex ante value of reduced
human exposure to an environmental hazard. Assuming a continuous distribution
of health outcomes and self-protection that influences both the probability and
the severity of an undesired outcome, we develop three propositions:
1)	If risk is endogenous such that self-protection influences the
probability or the severity of an undesirable outcome, then unobservable
utility terms cannot be eliminated from the individual's ex ante valuation
expression.
2)	If risk is endogenous, knowledge of the convexity or the nonconvexity
of physical dose-response relations is insufficient to sign unambiguously
the change in an individual's ex ante marginal valuation of risk, even
when consumer cognition is perfect.
3)	If risk is endogenous, self-protection expenditures will not be a
consistent lower bound of the ex ante value that a risk-averse individual
attaches to a reduction in risk.
These three statements imply that several propositions originally
developed for cases of exogenous risk and which form the analytical basis for
most recent empirical work on the value of health risk changes are not
immediately transferable to settings where endogenous risks prevail.

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I. INTRODUCTION
Any person who might suffer harm from exposure to an undesirable state of
nature can reduce expected ex post costs by purchasing market insurance. Moral
hazard, however, compels insurers to defray only a fraction of these costs
[Arrow (1963), Shaven (1979)]. XL Consequently, individuals use self-
protection to reduce both the ex ante probability and expected costs of the
uninsured event [Ehrlich and Becker (1972)].2— We consider the implications of
this for models used to value risks to human health.
In particular, we find that:
1)	Given moral hazard, when self-protection influences the
probability, the severity, or both of an undesirable state,
unobservable utility terms cannot be eliminated from the individual's
ex ante valuation expression. Consequently, empirical studies that
attribute differences across groups in ex ante value estimates solely
to unobserved differences in household health production technologies
are misplaced.
2)	with moral hazard and self-protection, knowledge of the
convexity or nonconvexity of physical dose-response relations is
insufficient to sign unambiguously the change in an individual's ex
ante marginal valuation for a reduction in the level of the hazard,
even when consumer cognition is perfect. Therefore, we do not
support the traditional argument that those individuals exposed to
greater risk with greater income must place a higher value on a given
risk reduction.
3)	with moral hazard, an increase in the level of the environmental
hazard does not necessarily lead to an increase in the level of self-
protection. Therefore, self-protection expenditures are not a

-------
consistent lower bound of the ex ante value a risk averse individual
attaches to a reduction in risk.
These three statements imply that several propositions originally
developed for cases of exogenous risk and which form the analytical basis for
most recent empirical work on the value of health risk changes are not
immediately transferable to settings where endogenous risks prevail. 3—
Berger, et al. (1987) appear to be among the first to consider endogenous
risks in the context of human health.4— Our treatment differs from their
seminal effort in two significant ways. First, though they state the general
continuous distribution case of risks to human health, they examine ex ante
value only in a world of two mutually exclusive and independent states of
nature: survival or death. We extend the ex ante value concept to the general
continuous case. By maintaining continuity throughout, we allow the individual
to choose between contractually defining states of nature or making an effort
to alter states of nature. Spence and Zeckhauser (1972) demonstrate that the
ability to influence states of nature enhances both the ex ante and the ex post
gains from adaptation. In particular, we assume that individuals recognize
that outcomes are stochastically related to actions, implying that predictions
of behavior and the relative values that motivate it depend not only on
preference orderings over outcomes, but also on preference orderings of
lotteries over outcomes.
Second, Berger, et al. (1987) model only probability-influencing self-
protection. They disregard the severity of the health outcome being risked,
even though they concede that prior self-protection can influence both
probability and severity. As pointed out by Ehrlich and Becker (1972) the
distinction between self-protection that influences probability and self-
2

-------
protection that influences severity is somewhat artificial. The distinction is
often said to be made for theoretical convenience [see for example Hiebert
(1983)]. In contrast, we model the effects of self-protection that influences
both the probability and the severity of the undesired state, and consider the
effects on the ex ante value of reduced risk.
2. THE MODEL
Consider an individual who is involuntarily exposed to a health risk under
a particular liability regime. Assume the risk is created by exposure to an
ambient concentration of an environmental hazard, r, taken from the real
interval, R:
R - It, r]	(1)
Because of moral hazard, the individual cannot acquire enough market insurance
to avoid the risk completely. The individual must decide from a real interval,
S how much self-protection, s, to undertake:
S - [s, s]	(2)
Given exposure to the. hazard, the individual is uncertain as to which, i,
of N alternative health outcomes will occur. Let
H - {hj, h2» . • • , hN}	(3)
denote the outcome space where outcomes are the individual's human health
capital returns ordered from smallest to largest, given the individual's
genetic and development history.
Let f(h^; s, r) denote the probability of outcome i occurring given that
self-protection, s, is undertaken and that the exposure level to the
environmental hazard is r. Assume the following about f(*):
3

-------
Assumption 1: f(hi; s, r) > 0 for every i e [1, . . . . N] and every s e S and
r c R.
Let F(h^; s, r) denote the corresponding distribution function defined
over the support [a, b]
FCh^, s, r) - [ f; s, r)dh	(4)
J a
where a and b are the minimum and maximum health outcomes. s— We assume the
following about F(«):
Assumption 2: F(h^; s, r) is twice continuously differentiable in s e S and
r e R for every i c [1, . . . . N].
Assumption 3: Fs(hi5 s, r) < o for every s e S and r c R and every i c [1,
. . . . N] in the sense of first-order stochastic dominance.
Assumption 4: Fr(h^; s, r) ^ 0 for every s c S and r c R and every i e [1,
. . . . N] in the sense of first-order stochastic dominance.
Assumption 5: No restrictions are placed on the convexity of the distribution
function in the immediate neighborhood of an optimal level of self-
protection, s*, for all s c Sand r c R and for every i c [1, . . . . N] .
The individual is risk averse with a von Neumann-Morgenstern utility index
over wealth W, U(W). The following assumptions are made about U (W) :
Assumption 6: U is defined over the real interval (W,»] where W is 0.
Assumption 7: Lim U (W) = -ED.
W-»W
Assumption 8: U is strictly increasing, concave, and thrice continuously
differentiable.
For each health outcome the individual might realize, he selects a minimum
cost combination of medical care and foregone work and consumption. Let
C - CChi; s, r)	(5)
4

-------
be his ex ante expectation of realized costs which depend on the uncertain
health outcome, self-protection, and the exposure level to the hazard. Assume
the following about C(«):
Assumption 9: C is strictly decreasing, convex, and thrice continuously
differentiable in s c S for every i c [1, . . . . N] such that Cs < 0 and
css > 0 for all h c H.
Assumption 10: C is strictly increasing and thrice continuously differentiable
in r c R for every i c [1, . . . , N] such that Cr > 0. No restrictions,
however, are placed on Crr and Csr for all h c H.
Given incomplete insurance purchases, intertemporally separable utility,
and constant expected prices for medical care, the individual's choice problem
is then
rb
Max [ U(W - C(h; s, r) - s)dF(h; s, r)].	(6)
S J a
Note that the price of self-protection has been normalized to unity. The
subscript i is suppressed to maintain notational simplicity.
Given the model, we are now able to develop the propositions stated in the
introduction.
3. EX ANTE VALUE AND WILLINGNESS-TO-PAY
3.1 Endogenous Risk. A few recent refinements to the willingness-to-pay
approach to valuing environmental hazards have acknowledged the frequently
endogenous form of the problem. For example, Rosen (1981), Berger, et al.
(1987), and Viscusi, et al. (1987) note that self-protection affects survival
or injury probabilities, while Shibata and Winrich (1983) and Gerking and
Stanley (1986) allow self-protection to influence the severity of ex post
damages. In a nonstochastic world or in an uncertain world with only two
5

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feasible states, these studies demonstrate that marginal willingness-to-pay can
be expressed solely in terms of the marginal rate of technical substitution
between hazard concentrations and self-protection. This result cannot be
generalized to a continuous world with endogenous risk.
Proposition 1: Given the model assumptions, when self-protection
influences either the probability or the severity of health outcomes
or both, the individual's marginal willingness-to-pay for reduced
risk cannot be expressed solely in terms of the marginal rate of
technical substitution between ambient hazard concentrations and
self-protection. In particular, unobservable utility terms cannot be
eliminated from expressions for the ex ante value of reduced risk. 7—
Proof: To show that for a continuous distribution the individual's
compensating variation statement of willingness to pay for reduced risk
includes the unobservable utility terms, we examine self-protection that
influences either the distribution or the severity (costs) of the health
outcomes or both.
First, maximize the expected utility index (6) by selecting an optimal
level of self-protection s c S yielding the following first-order condition for
an interior solution
fb
EU - -E[U C ] + U C.F dh.	(7)
w	1 w s J a w h s
The left-hand side of (7) represents the marginal cost of increased self-
protection in terms of the utility of foregone wealth. The right-hand side
reflects two types of marginal self-protection benefits: the first term is the
direct utility effect of enhanced wealth resulting from reduced expected ex
post costs; the second term is the indirect utility effect of a stochastically
dominating change in the distribution of health outcomes.
6

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The indirect effect was derived by integrating by parts the effect of
self-protection on the distribution
b	b
U(*)dF (•) » UF I +
s 'a
U C, F dh
.whs.
¦i:
U C.F dh,
whs
since Fs (a;-) = Fs(b;-) = 0. Assume that improved health outcomes will
decrease the ex post costs, < 0.
Solve for the compensating variation statement of the willingness-to-pay
for reduced risk by totally differentiating the expected utility index (6), and
then applying the first-order condition (7). When self-protection influences
both the probability and severity of health outcomes such that Fs < 0 and Cs <
0, the willingness to pay expression is:
dW
dr
~JU C,F dh - JU C dF-
v h r	 v r
JU C.F dh - JU C dF
whs	w s
> 0,
where all integrals are evaluated over the support [a, b] . Obviously, the
unobservable utility indexes cannot be removed from the individual's
willingness to pay expression (8).
Even the assumption of a simple two state world fails to remove the
utility terms from (8). For example, let tt(s, r) and (1 - t:(s, r) )
respectively represent the subjective probabilities of healthy and of sick
states. Let Uq (W - s) and Uj (W - s - C (s, r) ) be the expected utility of being
healthy or sick, where Uq > U^. The individual thus chooses s c S to maximize
EU - n(s, r)U0(W - s) + (1 - tt(s,	- s - C(s, r)).	(9)
Following the same steps as before, the willingness to pay expression is
dW
dr
V"o - V -
"s[°0 - V - (1 - ",U0CS
> 0.
(10)

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where TTr < 0, tts > 0, = 9U1/3W, and Ug - auQ/8W. Again, utility terms
cannot be removed.
Next allow, as do Gerking and Stanley (1986), self-protection to influence
the severity, Cs < 0, but not the probability, Fs - o, of health outcomes.
Further assume that Fr - 0 which, with Fs = 0, implies that neither collective
nor individual actions will influence the probability of a particular health
outcome, i.e., hazard concentrations resemble sunspots or the phases of the
moon. With these assumptions, expression (8) reduces to:
E(u c 1
dW	w r
dr " E[UC ]
w s
EU EC - cov(U ,	C )
v r	w r
EU EC - cov(U ,	C )
v s w s
> 0.	(11)
For the unobservable utility terms to be absent from (11), the two covariance
expressions must be zero; however, our model assumptions do not allow them to
be zero. Therefore the two utility terms cannot be removed.
Finally, assume, as does Rosen (1981), that self-protection affects
probability, Fs < 0, but not severity, Cs - 0. In Rosen's (1981) terms, one
cannot be more severely dead. For similar reasons, Cr = 0. Under these
conditions, expression (8) reduces to:
/U C.F dh
dW	v h r
dr JU CF dh '	UZJ
whs
and again the willingness-to-pay expression cannot be rid of the unobservable
utility terms, which concludes the proof.•—
We could examine additional cases. For example, self-protection might
influence only the probability of a health outcome, but hazard concentrations
could affect probability and severity, or vice versa. The results would not
change: utility terms would loom up in the willingness-to-pay expressions,
implying that policy efforts to aggregate across individuals and to account

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simultaneously for the reality of probability and severity unavoidably involve
interpersonal utility comparisons.
3.2 Nonconvex Dose-Response Relations. Proposition 1 poses hurdles to
procedures which would establish a social risk-benefit test by summing
unweighted compensating or equivalent variations across individuals. Yet
another problem for consistent aggregation is the ambiguous effect that a
change in hazard concentrations has on the sign of compensating variation. In
a contingent valuation study of the risk valuations attached to hazardous waste
exposures, Smith and Desvousges (1986, 1987) report increasing marginal
valuations with decreasing risk. This finding is but the latest in a 15-year
long series of analytical [Starett (1972), Winrich (1981)] and empirical
[Crocker (1985), Repetto (1987)] papers which use prior information on physical
dose-response relations, individual abilities to process information about
these relations, or individual perceptions of the relations to produce a
declining marginal valuation result for more of a desirable commodity.
However, when risk is endogenous, no one has yet asked whether convexity of the
marginal value of risk follows when cognition is not an issue.
An individual's compensating variation can be shown to be ambiguous in
sign even if the strongest possible case for negative effects of increased
hazard exposure is imposed. To illustrate, define strong convexity as follows.
Definition 1: Strong convexity of risk is defined as: convex ex post cost,
C rr > 0; convexity of the distribution function, Frr > 0; and declining
marginal productivity of self-protection, Csr > 0, C^r > 0, Csjj > 0 and
Fsr > 0. Strong nonconvexity describes the conditions most favorable for the
traditional argument that increased risk requires progressively increasing
compensation to maintain a constant level of expected utility. Increased
9

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exposure increases the probability and the expected ex post costs of
undesirable health outcomes to the hazard at an increasing rate; moreover, the
marginal productivity of self-protection is decreasing across the board.
The opposite case is strong nonconvexity. Strong nonconvexity defines the
weakest case for negative effects of increased exposure to the hazard.
Definition 2: Strong nonconvexity of risk is defined as: nonconvex ex post
cost, Crr < 0; concavity of the distribution function, Frr < 0; and increasing
marginal productivity of self-protection, Csr < 0, C^r < 0, ^sh < 0 and
Fsr < o."L
The following proposition states the result:
Proposition 2: Even in the absence of cognitive illusions or failure to
consider all scarcity dimensions of the risk-taking problem, a maintained
hypothesis of strong convexity of risk is insufficient to guarantee that
increased exposure to a hazard requires progressively increasing
compensation to maintain a constant level of expected-utility. Similarly,
strong nonconvexity is insufficient to guarantee progressively decreasing
compensation.
The proposition is supported by Dehez and Dreze (1984, p. 98) who show
that the sign of the marginal willingness-to-pay for safety given an increase
in the probability of death is generally ambiguous. Dreze (1987, p. 172)
concludes that any assertions about this sign given a change in safety "...must
be carefully justified in terms of underlying assumptions".
Proposition 2 contradicts the argument of Weinstein, et al. (1980) and
others that individuals at greater risk must have a greater demand for safety.
Consequently, contrary to Rosen (1981), individuals at greater risk with
greater wealth cannot necessarily be weighted more heavily when risk reductions
10

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A
are valued. Similarly, the assertions by Kahneman and Tversky (1979) and Smith
and Desvousges (1987) that increasing marginal willingness-to-pay for reduced
risk constitutes a lapse from rational economic behavior are not supported. 11 —
Proof: To demonstrate that an increase in hazard concentration has an
ambiguous effect on an individual's compensating variation, differentiate the
compensating variation in expression (8) with respect to the hazard exposure:
d(dW/dr) . _ I C2 - U C ] -2j[U C C. - U C. ]F dh
dr	Q I	 ww r w rr	ww r h w hr r
+ Ju C F dh
w h rr 	I
-	(13)
E[U C C - U C ] + J[U C. - U CkC ]F dh
ww s r w sr	whr wwhr s
+ J[U C C - U C ]F dh + /U C.F dhl,
ww s r w sr r	w h sr J
where	0 - Ju CWF dh - Ju C dF > 0,
whs	w s
A - /U C.F dh - /U C dF < 0,
whr	w r
and all integrals are evaluated over the support [a, b].
The terms on the right-hand side of (13) can be defined in terms of direct
and indirect utility effects given an increase in exposure to a hazard. Q > 0
and A < 0 represent the combined first-order direct and indirect utility
effects of s and r. The first and fourth terms in (13) represent second-order
direct utility effects on expected costs with an increase in exposure. Given
strong convexity, the sign of the first term is negative. The sign of the
fourth term is ambiguous in the sense that alternative parameterizations are
conceivable in which either U^CjCj or UwCsr dominates in absolute magnitude.
The second, fifth, and sixth terms are second-order direct and indirect utility
effects weighted by the marginal effect on the distribution of either s or r.
Given strong convexity, the signs of all three terms are ambiguous in the above
11

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sense. Without prior information on the magnitude of the marginal effects on
the expected cost function, there is no reason to expect one term to dominate.
The third and seventh terms represent the second-order indirect and cross-
indirect utility effects of increased exposure. By the definition of strong
convexity, the sign on both terms is negative. Without knowing the relative
magnitude of all the direct and indirect utility effects, however, strong
convexity is insufficient to sign (13) unambiguously. Likewise, the assumption
of strong nonconvexity is also insufficient to sign (13). Whether one imposes
strong convexity or strong nonconvexity the sign of (13) is ambiguous.
Although sufficient conditions for increasing or decreasing marginal
willingness-to-pay can be determined, there is, in the absence of prior
information or simple ad hoc assumptions, no reason to expect that one or two
terms will dominate expression (13). This concludes the proof.
3.3 Self-Protection Expenditures as a Lower Bound. Consideration of self-
protection has not been limited to problems of ex ante valuation under
uncertainty. A substantial literature has emerged, e.g., Courant and Porter
(1981), and Harrington and Portney (1987), which demonstrates that under
perfect certainty the marginal benefit of a reduction in a health threat is
equal to the savings in self-protection expenditures necessary to maintain the
initial health state. This result cannot be extended to the uncertainty case
when self-protection influences both ex ante probability and ex post severity.
Proposition 3: Neither strong convexity nor strong nonconvexity of risk is
sufficient to sign the effect of a risk change upon self-protection
expenditures. Therefore these expenditures cannot be used to determine
the welfare effect of a risk change.
Proposition 3 contradicts Berger et al.'s (1987) argument that if
increased exposure increases the marginal productivity of self-protection,
12

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Fsr < 0} then self-protection will increase with exposure. Consequently,
Berger, et al.'s (1987 p. 975) sufficient conditions for "plausible" results do
not hold when self-protection influences both probability and severity.
Proof: To demonstrate that strong convexity is insufficient to determine
the effect increased hazard exposure has on self-protection, take the first-
order condition in equation (7) and apply the implicit function theorem. The
effect of increased exposure on self-protection is
where
71 - - ¥[U C(1+C)-UC ] + J[U C . - U C, (1 + C )]F dh
dr	ww r	s w rs	w sh ww h	s r
+ J[U CL - U C CjF dh + Ju C F dhl/D
whr wwrh s	whsr 	|
D a E[U C (1 + C ) - U C ] + 2/[U C . - U C.C ]F dh
ww s	s w ss	w sh ww h s s
(14)
: 15)
-Ju CJ dh + Ju C.F dh < 0
ww h s	w h ss
and all integrals are evaluated over
sufficient condition of the maximization problem (6), and is assumed to hold
whenever (7) holds.
Given D < 0, the sign of (14) depends on the sign of its right-hand-side
numerator. The first term in the numerator of (14) is the direct utility
effect of increased exposure on expected costs. Given strong convexity of risk
and (1 + Cs) > 0 from the first-order condition, the sign of the first term is
negative. The second term reflects the indirect utility effect of increased
exposure on the distribution. Given strong convexity, its sign is ambiguous in
the earlier defined parameterization sense. The third term is a direct utility
effect weighted by the marginal effect of self-protection on the distribution
(Fs < 0), and its sign is also ambiguous. The signs for the second and third
effect are ambiguous since there is no a priori reason to believe that any one
set of terms dominates the others. The fourth term in the numerator is the
13

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cross-indirect utility effect of increased exposure. Given strong convexity,
its sign is negative. Therefore, without prior information on the relative
magnitudes of the four direct and indirect utility effects, strong convexity is
insufficient to sign (14) unambiguously. Given the conditions most favorable
to the traditional argument that increased risk will increase self-protection,
we still require prior information on the impact that increased exposure has on
the marginal productivity of self-protection to support the argument.
Following the logic above, an assumption of strong nonconvexity of risk
leads to a similar conclusion of an ambiguous effect of increased exposure on
self-protection. Consequently, since self-protection may decrease as exposure
to a hazard increases, self-protection cannot be considered a consistent lower
bound on the ex ante value a risk averse individual attaches to a reduction in
risk. This concludes the proof.
4. CONCLUSIONS AND IMPLICATIONS
Individuals and policymakers use self-protection activities to influence
both their ex ante risks and their expected ex post consequences The
implications of this for models used to value risks to human health are
unequivocally negative. We show that unobservable utility terms cannot be
eliminated from marginal willingness-to-pay expressions, implying that
empirical efforts which identify marginal rates of substitution with
willingness-to-pay are misdirected. We also show that even under the most
favorable restrictions increased risk need not imply progressively increasing
levels of compensation in order to restore initial utility levels.
Consequently the traditional argument that those who are exposed to greater
risk and have greater wealth must value a given risk reduction more highly does
not follow. Finally, we demonstrate that increased risk need not imply
14

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increased self-protection expenditures; thus changes in these expenditures may
not bound the value of a risk change.
Some succor for health risk valuation efforts could be obtained by
stepping outside professional boundaries to draw upon prior information from
psychology, biomedicine, and other disciplines. Insight might therefore be
gained into the signs and the relative magnitudes of many terms in expressions
(13) and (14) . It is odd that the field of economics which explicitly
recognizes the policy relevance of incomplete markets has historically been
reluctant to use information from other disciplines in order to simulate the
valuation results of a complete market. We recognize that there is a growing
trend to incorporate restrictions drawn from other disciplines into the
behavioral postulates of economic models. 1The results of this paper suggest
that the incorporation process should be accelerated.
Incorporation will not overcome, however, the aggregation problems posed
by the presence of utility terms in individuals' willingness-to-pay
expressions. Approaches to aggregate risk-benefit analysis do exist other than
the mechanical summation of consumer surpluses calculated from the singular
value judgement that social welfare and aggregate total income are synonymous.
Given that individual consumer surpluses can be estimated, one possibility is
to draw upon the extensive equivalence scale literature, e.g., Deaton and
Muellbauer (1986), in order to weight each individual or household. Tradeoffs
can then be evaluated using an explicit social welfare function which
recognizes that personal health is in part self-produced and inalienable.
Alternatively, utilities might be calculated directly.
15

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FOOTNOTES
1.	Moral hazard refers to the tendency of insurance to influence an
individual's incentive to prevent loss.
2.	Self-protection includes everything from installing home water filters in
order to reduce pollutant concentrations in drinking water to medical care
and the use of tort law. [See Laffont (1980), Crocker (1984)].
3.	The empirical human health valuation literature typically assumes that
health risks are: (i) independent of individual actions; and (ii) usually
for the sake of analytical and empirical tractability, individuals require
progressively increasing levels of compensation to maintain constant
expected utility when confronted by increasing risk. Jones-Lee, et al.
(1985), for example, embodies both conditions. We argue these assumptions
are unnecessarily restrictive in the sense that they stretch the ability
of economic analysis to cover the domain of risky phenomena.
4.	Psychologists agree that individuals perceive that they have substantial
control over uncertain events [Perlmuter and Monty (1979)]. Stallen and
Tomas (1984) conclude that "... the individual is not so much concerned
with estimating uncertain parameters of a physical or material system as
he is with estimating the uncertainty involved in his exposure to the
threatening event and in opportunities to influence or control his
exposure" [emphasis added].
5.	The [a, b] interval could also be influenced in subsequent periods by
self-protection. We disregard this issue.
6.	Subscripts represent partial derivatives.
Assumptions of a risk-neutral individual with an identity map of ex post
costs would eliminate the unobservable utility expressions. These
assumptions seem excessively restrictive.
8.	One might eliminate the utility terms by using the pointwise optimization
technique that Mirrlees (1974) and Holmstro'm (1979) employ. However,
pointwise optimization evaluates self-protecting choices individually at
each and every health state rather than in terms of lotteries over health
states. It thus adopts an ex post rather than an ex ante perspective.
9.	See Polemarchakis, et al. (1986) for thinking on aggregation under
exogenous risk.
10.	Rogerson (1985) assumes that the distribution function must generally
satisfy the convexity of the distribution function condition (CDFC).
Therefore, the assumption of a concave distribution in r and s is perhaps
restrictive. As shown by Jewitt (1988), however, the CDFC assumption is
not universally required in that it satisfies very few of the standard
distributions set forth in statistics textbooks.
11.	Close inspection of the questionnaire formats upon which these assertions
are based reveals that respondent opportunities to influence risk and/or
severity were not fully controlled.
12.	See Warneryd (1986), Weinstein and Quinn (1983) and Smith and Johnson
(1988), for example.

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Kahneman, D. , and Tversky, A. (1979). Prospect Theory: An Analysis of
Decision Under Risk. Econometrica 47: 263-91.
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Spence, A.M., and Zeckhauser, R. (1972). The Effect of the Timing of
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THE ECONOMICS OF QUARANTINES: AN APPLICATION TO PESTICIDE REGULATION
Erik Lichtenberg
Department of Agricultural and Resource Economics
University of Maryland
College Park, MD
Robert C. Spear
School of Public Health
University of California
Berkeley, CA
David Zilberman
Department of Agricultural and Resource Economics
University of California
Berkeley, CA
This research was supported in part by the U.S. Environmental Protection Agency
under Cooperative Agreement CR811200-01 to the Western Consortium for Public
Health. The views expressed are those of the authors, not the agency.
Working Paper No. 88-38
December 1988

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THE ECONOMICS OF QUARANTINES: AN APPLICATION TO PESTICIDE REGULATION
One of the most common practices for dealing with hazardous situations is
simply to remove the hazard from human proximity, either spatially or temporally.
Such policies can be termed quarantines. The classic case is that of contagious
disease control, where infected individuals are kept apart from vulnerable
individuals until the threat of contagion has passed. Other examples include
imprisoning dangerous criminals; locating hazardous industries (e.g., military
testing grounds, nuclear power plants and other hazardous activities) in remote
areas; keeping dangerous chemicals, high voltage equipment, etc. in locked or
otherwise inaccessible locations; and keeping workers out of areas recently
treated with pesticides.
Any quarantine involves tradeoffs that must be evaluated whether the
decision maker is a government agency or an individual concerned with self-
protection from self-generated hazards. The benefits of quarantines obviously
consist of reductions in hazard. But quarantines typically have costs as well,
such as additional discomforts and lost wages of contagious patients or
productivity losses from suboptimal siting or scheduling. These tradeoffs must
be evaluated in determining the appropriate parameters of a quarantine, that is,
the length of time and/or location restriction. This paper develops a framework
for optimal quarantine determination and applies it to a widespread form of
quarantine, re-entry regulation of pesticide-treated fields. Section I contains
a model of optimal quarantine determination. Section II models optimal timing
of pesticide application under re-entry regulation. Interestingly, the
imposition of re-entry regulation may make it optimal for farmers to switch to
1

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prophylactic treatment of pests, a practice which has been widely criticized as
inefficient in the literature on pesticide use. Section III applies this model
to the case of pre-harvest intervals in apple production in three major producing
states. Section IV develops a model of acute poisoning from exposure to
pesticide residues under different re-entry intervals. Section V combines the
production and health models into a tradeoff model which is then used to obtain
a rough evaluation of current policy.
I. Optimal Quarantine Determination
Generally speaking, quarantine have both a spatial and a temporal
dimension: how far away the hazard is sited and how long the quarantine lasts.
Contagious disease quarantines have both: one must decide where to locate
infectious patients relative to other patients and the general populations well
as how long to continue isolation. Penal policy also does: prison location and
length of sentence will both depend on how dangerous a criminal is. In other
cases, one of these dimensions may be irrelevant. In pesticide regulation, for
example, only the temporal dimension may matter: many pesticide residues are
absorbed by touch and therefore the hazard affects only those entering a treated
field. In siting of military testing grounds, nuclear power plants or other
hazardous facilities, on the other hand, only location matters.
Let D represent the spatial dimension of the quarantine and T the temporal
dimension. Let Z represent a consumption or production activity affectedly the
quarantine. The benefits of consumption or production, B(Z,D,T), depend on Z
and on the quarantine parameters D and T, as does the level of hazard, H(Z,D,T).
Let W[B(Z,D,T), H(Z,D,T)] denote the utility function of an individual facing
a hazardous situation or a social welfare function. The relevant decision
2

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problem is to choose Z, D and T to maximize utility or social welfare. This is
typically accomplished in two stages. First, microeconomic theory is used to
derive a model of optimal consumptive or productive behavior conditional on the
quarantine parameters D and T. The resulting behavioral model is subsequently
used to derive the optimal policy parameters.
Formally, letting subscripts denote derivatives, the necessary conditions
are
(la) WbB2 + WaHz - 0
(lb) WbBd + WhHd - 0
(lc) WbBt + WhHt - 0.
The two-stage procedure described above consists of first solving equation (la)
to get the optimal level of consumption/production activity contingent on the
quarantine, Z*(D,T), and then choosing D and T to maximize W[B(Z*(D,T),D,T),
H (Z*(D,T,),D,T)] according to the necessary conditions
(2a) Vb(BzZd + B„) + Wh(H2Zd + H„) - 0
(2b) Wb(BzZt + Bt) + Wh(HzZt + Ht) - 0.
The case of pesticide regulation considered below is investigated by first
deriving profit-maximizing pesticide use patterns conditional on temporal
quarantine restrictions, Z* (T), and farm profits, B(Z*(T)). The risk of acute
organophosphate poisoning of farm workers is modeled as a function of pesticide
use, H(Z*(T)). These two components are combined into a tradeoff curve under
an assumption of equal welfare weights on farm income, B(Z*(T)) , and worker
safety, H(Z*(T)), that is WB - WH. Finally, this tradeoff curve is used to
derive the optimal length of the quarantine T* under different environmental
conditions.
One can conceptualize distance-related quarantine problems in the same way.
3

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For example, the size, operating procedures and transmission line requirements
of a nuclear power plant may depend on the distance between it and the population
and industrial centers it serves, so that one would begin with a relationship
between these factors and quarantine distance, Z*(D) : The risks posed by the
plant, H(Z*(D),D) depend on the quarantine distance D and the operating
characteristics of the plant, Z*(D). These two can be combined using the
appropriate welfare weights WB and WH to obtain a tradeoff relation that can then
be used to determine the optimal distance D*.
In sum, even in regulatory contexts it is typically necessary to solve
private optimization problems prior to considering the social decision problem,
since the private optimization problems are crucial elements of the tradeoff
relations needed. Moreover, close interdisciplinary, cooperation is often
required to specify the hazard functions H, since they depend in complex ways
on combined economic, environmental and biomedical factors.
II. Crop Production Under Re-Entry Regulation
One of the most common measures used to protect farm workers and other
rural inhabitants from the health hazards posed by applied pesticides is to
forbid entry into treated fields for a specified period of time during which
pesticide residue levels (and hence health risks) are thought to be excessive.
Similar regulations aim to protect consumers as well by forbidding harvest for
a specified interval after application of pesticides. Often, these re-entry
regulations lead to reductions in growers' incomes by preventing optimal
scheduling of harvest or intraseasonal activities like pruning or irrigation,
causing decreases in yield, quality or price received for the crop. Thus ,
whether the decision maker is a government agency charged with protecting farm
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workers or a farmer deciding whether to work in his/her own field, the
determination of an appropriate re-entry interval hinges on the choice of a
tradeoff between risks to human health and safety, on the one hand, and the
economic losses induced by regulation on the other.
For the sake of simplicity, we concentrate on the problem of re-entry
regulations affecting an individual farmer's harvest of a perishable crop
(fruits, vegetables), the kind of crop to which this form of regulation is
applied most often. We assume that benefits B are restricted to farm profits,
which are a function of pesticide use Z, itself a function of the re-entry
interval T. We assume also that the farmer applies the pesticide at a standard
application rate and focus on the determination of the timing of the application.
Assume that there is a time t0 representing the earliest date at which the
crop can be harvested; prior to t0, the crop will be immature and hence not
harvestable. Assume also that after to, the value of the crop declines because
of decreased quality or because of price decreases due to seasonal increases in
aggregate production, so that the farmer's revenue is maximized by harvesting
at to. Formally, this implies a revenue function R(t) such that R(t0) - max
(R(t)) - R*, and, letting subscripts denote derivatives, < 0 and R^ < 0 for
t > t0. Production costs, including pesticide materials and application costs,
will be assumed to be constant and will thus be ignored.
Now assume that a pest appears at a time ta shortly prior to the optimal
harvest time to. If left untreated, the pest will damage a proportion of the
crop which will then be unsalable. The larger the pest population is, the
greater the level of damage will be. This damage can be avoided by treating the
crop with a pesticide. To simplify matters, assume that only a single standard
treatment is available at a negligible cost. If the farmer treats the crop
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immediately upon arrival of the pest, i.e. , chooses a treatment time ts - ta, the
pest will be effectively eradicated and damage will be essentially reduced to
zero. If, on the other hand, the farmer treats the crop before the pest arrives
(t„ < ta), the pesticide will decay; its effectiveness will be reduced by the
time the pest arrives and the farmer will sustain some crop losses. The longer
is the interval between treatment and the arrival of the pest, the greater will
be the decay of the pesticide and the damage caused by the pest.
These characteristics can be represented formally by letting the proportion
of the crop damaged by a pest population of size k be a function g(k,ta - ts),
where ta - ts represents the time elapsed between treatment and the arrival of
the pest. The preceding discussion suggests that g* > 0, gt > 0 and g(k,0) ~ 0.
Pesticide decay curves are typically convex, so that one would expect get ^ 0 as
well.
There are two types of treatment strategies available to fartiters: a
reactive strategy of applying pesticides upon the arrival of the pest, and a
prophylactic or preventive strategy of applying pesticides in anticipation of
a pest problem. The reactive pest management strategy will maximize profits
whenever it is feasible, which implies an optimal choice of ta - ta whenever T
< t0 - ta. If the re-entry period T is sufficiently long, however (specifically
T > t0 - ta), following the reactive treatment plan may force the farmer to delay
the harvest and thereby lose revenue. In this case the farmer faces a tradeoff
between losing revenue from crop damage and losing revenue from harvesting
delays. Under some conditions, it may become optimal for the farmer to adopt
a prophylactic treatment strategy. While this practice has been much maligned
in the pest management literature, rigidities is scheduling such as those imposed
by re-entry regulation may make it desirable for farmers.
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Some casual empirical evidence supports the notion that re-entry intervals
actually provide a motivation for prophylactic treatment strategies. In Oregon,
plum growers expecting to need to use parathion for end-of-season codling moth
control typically apply the chemical 14 days — the length of the pre-harvest
interval — prior to the projected harvest date, regardless of whether the pest
is in evidence.
It should be clear that the farmer will never treat any earlier than needed
to be able to harvest at time t0, i.e. , that ts > t0 - T; treating any earlier
than C0 - T would imply accepting greater damage in return for no gain in revenue
and is thus less profitable than treating at t0 - T. It should also be evident
that the farmer will always harvest the crop as soon as possible, that is, at
least as soon as the re-entry period has ended. If the re-entry constraint is
non-binding, then the harvest time will be t0. if the re-entry constraint is
binding, then the harvest will occur T periods after the treatment time;
normalized (without loss of generality) to fit the revenue curve R. This can
be written ts + T - t0.
The pesticide use patterns adopted and revenues earned by the farmer thus
depend critically on whether or not the re-entry interval constitutes a binding
constraint. If it does not, then a reactive treatment strategy is always
optimal, ts - ta, the crop will be harvested at t0 and revenue will be R*. If
it does, the farmer will face a tradeoff between crop damage and decreased
revenue. The optimal pest management strategy will be determined by the choice
of a treatment time ts which maximizes realized revenue, given by:
(3) [1 - g(k, ta - t,)]R(ts + T - t0)
subject to the constraint:
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(4)	t0 - T < ts < ta.
Because the convexity of the pesticide decay function makes the damage
function g(k,ta - ts) convex, the realized revenue function (3) will be convex
unless R is quite strongly concave. Thus , the optimal treatment plan must be
analyzed according to two cases.
Case 1: The most likely case is that realized revenue (3) will be convex,
so that the optimal treatment time will be either the maximum or minimum possible
time, that is, either ta or t0 -T. jn essence? 0r course, this constitutes a
choice between reactive (ts - ta)	ancj pr0phylactic (ts - t0 - T) treatments. The
farmer will choose the one which	gives the greatest profit. If ta - t„ there
will be no damage (g - 0) but the farmer will have to wait until ts + T - t0 to
harvest and will thus realize a revenue of R(ta + T - t0). If t, - t0 - T, there
will be damage g(k,ta + T - t0); the farmer will harvest at t0 and thus realize
a revenue [1 - g(k, ta + T - C0)]R*. If the difference between these two realized
revenues,
(5)	V - R(ta + T - t0) - [i - g(k, ta + T - t0)]R*
is positive, the farmer will adopt the reactive strategy and treat at ta. If it
is negative, the farmer will adopt the prophylactic strategy and treat at t0 -
T. An increase in the size of the pest population k will increase V and thereby
make the farmer more likely to adopt a reactive strategy. An increase in the
re-entry interval T, though, will increase V only if the marginal increase in
the proportion of the crop damaged by treating earlier (gt) is less than the
marginal increase in the proportion of revenue lost by treating later (Rt/R*).
Thus , if gt > Rt/R*, an increase in T will make the farmer more likely to adopt

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a prophylactic strategy. An increase in the internal between the arrival of the
pest and the optimal harvest data, that is, in t0 - ta, will, of course, have
precisely the opposite effect of an increase in the re-entry interval T.
Case 2: If the revenue function R( ) is sufficiently concave to make
realized revenue (3) concave, the profit-maximization problem will have an
interior solution defined by:
(6)	gt R + (1 - g)Rt - 0
with sufficiency assured by:
(7)	Q - gtt R + (1 - g)Rtt < 0
which holds by assumption. It is readily apparent that an increase in the re-
entry interval will lead the farmer to treat earlier (dts/dT - -[Rt gt +
(l - g)Rttl/Q c 0), thereby accentuating the tendency toward prophylactic
treatment. If, as one would expect, the increase in damage from treating earlier
is greater for larger pest populations than for smaller ones (i.e. , g,^ SO), an
increase in the pest population size will induce the farmer to treat later
(dts/dk - - [ g^ R - gk Rt ] /Q > 0), thereby reducing the tendency toward
prophylactic treatment. As before, an increase in t0 - ta will have the opposite
effect of a increase in T.
III. Pesticide Use in Apple Production
Consider the case of re-entry regulation of organophosphate insecticides
used to protect apple crops from infestations of codling moth larvae from moth
flights shortly prior to harvest. The yield and quality of the apples is assumed
to increase up until the maturity date t0, which is the earliest date at which
9

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the crops may be harvested. After t0, yield and quality will remain constant
for a considerable length of time. However, the price the farmer receives for
the crop will decline as time passes because the aggregate supply of apples will
increase as producers in other regions harvest and market their crops. This
price decline will continue until the price of apples for fresh consumption
equals the price for processing uses, at which point the price will remain
constant. An analysis of the intraseasonal trends in farm-level apple prices
in three major producing states (Washington, Michigan, California) indicated that
this price decline is convex and could be represented well by an exponential
tune. Thus , the price received by a grower harvesting a full crop at time t
> t0 is R*exp(-a(t - t0)} .
The threat posed by a late-season flight of codling moths consists of an
infestation of larvae in the fruit, i.e., of wormy apples. This threat can be
alleviated by using organophosphates to kill the moths before they lay eggs.
"Standard doses of these pesticides are typically applied; without loss of
generality, normalize this standard dose to unity. Pesticide decay rates are
typically modeled as exponential curves, so that the proportion of the pest
population killed by a treatment applied at ts is exp{-b(ta - ts) and the
proportion surviving is 1 - exp{-b(ta - ts)). Assume that all infested fruit is
unsalable and that the proportion of the crop damaged is proportional to
survivorship. Letting k represent the proportion of the crop damaged by a moth
population of standard size, the damage function g(k,ta - ts) will be in this
case k[l - e{-b(ta - ts)}].
The realized revenue function (3) in this case will thus be:
(8) R - R* exp{-a(ts + T - t0)} (1 - k[l - exp(-b(ta - ts)})
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which is obviously convex. The difference in profit between treating at ta
and treating at t0 is thus
(7) V - R*exp(-a(ta + T- t0)} - R*(l - k[l-exp{-(ta + T - t0)}]).
which will be positive whenever
k > [1 - exp{-a(ta + T - t0)j]/[l - exp{-b(ta + T - t0))] - kc
and negative whenever k < kc. The optimal treatment strategy is thus:
(9) c -
s
t ,	k > k
a	c
t -	t, k < k
0	c
In addition to the comparative static results from the general case it is
straightforward to show that the faster the price declines over the season, the
more likely the farmer is to adopt a prophylactic strategy (dV/da < 0) and that
the faster the pesticide decays, the more likely the farmer is to adopt a
reactive strategy (dV/db > 0).
To provide a empirical mechanism for evaluating the impact of re-entry
regulation of pre-harvest use of parathion on apples in three main U.S. producing
states (Washington, California, Michigan) , the model was parameterized as
follows. A regression of weekly data on farm-level prices received in
Washington, California and Michigan over the period 1971-1980 on a time trend
and dummies to control for differences among years and states yielded an estimate
of the revenue decay parameter a - 0.0024. According to Johannes Joost,
California extension specialist on apples, the maximum price received in 1984
was about $300/ton, which, at a yield of 10 tons/acre, suggests a maximum revenue
of $150,000 for a 50-acre block. The regression analysis suggested that price
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levels in Michigan and Washington were about 17 percent and 32 percent above that
of California; however, because Michigan harvests about 4 weeks after California
and Washington, 2 weeks, the maximum price in these states should be 9.8 percent
and 28.2 percent higher than California, respectively, giving estimates of about
$165,000 per 50-acre block in Michigan and $192,000 per 50-acre block in
Washington. An estimate of the parathion decay parameter b = 0.8 was taken from
Spear et al. As (1975a) study, of parathion decay in California citrus orchards;
examination of parathion decay data on Washington apples (Staiff et al. (1975))
indicated that the decay patterns in the two cases were essentially identical.
Conversations with farm advisors indicated that, if left untreated, a codling
moth infestation caused by a population of normal size would damage about 10
percent of the crop; thus, k was given a value of 0.10. Calculation of the
damage threshold for prophylactic spraying over the range of reasonable re-entry
periods, kc, resulted in values ranging from .009 to .065, all well below k;
thus, it appears that reactive treatment will always be optimal. in fact, apple
prices would have to fall 2-10 times more rapidly before prophylactic treatment
would become desirable.
IV. Residue Poisoning From Parathion Exposure Among Apple Harvesters
The risk of clinical illness in workers as a result of exposure to residues
of parathion applied to apples at various locations was modelled according to
the overall scheme laid out by Popendorf and Leffingwell (1982). in essence,
the pesticide is applied, a decay process takes place in which some of the
parathion is converted to the oxygen analog, paraoxon, and exposure takes place
days or weeks later when crews enter the field to harvest the crop. If clinical
illness results, it is usually due to a dermally absorbed dose of paraoxon.
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There is considerable information available to quantify the various steps in this
process but very limited data on climatological effects on the decay process
itself.
The characterization of the residue decay process follows that of Spear
et al. (1975a) and Popendorf and Leffingwell (1978). In both cases, the
dislodgeable foliar residues of parathion and paraoxon are described by linear
ordinary differential equations. The parameterization of these models utilized
data obtained from citrus crops, but limited data on apples suggests a similar
decay pattern (Staiff et al. (1975)). The simplified form of the model used here
describes the residue relevant to worker hazard from day three post-application
onwards. After day three the parathion residue has decayed to the point where
the hazard to workers depends almost entirely on the paraoxon residue (Spear
(1975b)).
The form of the model is:
(10a) dx/dt - -bx
(10b) dr/dt - cx - qr
where parathion residue is denoted by x and the paraoxon residue by r. The units
are in ng/cm2. The solution to this set of equations is:
(11a) x(t) - x0 exp{-bt)
(lib) r(t) - (cx0/b + q) [exp(-qt) - exp(-bt)]
where t is the time post-application in days.
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There are, then, four parameters required to solve for r(t), the paraoxon
residue, b, c, q, and the initial condition xo • The first three parameters are
weather dependent whereas the last depends on the application rates and pre-
existing levels of foliar dust on the trees. Nigg et al. (1978) have studied
the effect of weather variables on the parathion decay process and have concluded
that rainfall and leaf wetness from other sources are the primary determinants
of the rate of residue disappearance after the period immediately post
application. Hence, climatological variability was modeled by assuming that
the decay parameters, b, c, and q, are the same for all three regions but that
the paraoxon residue is diminished as an exponential function of the cumulative
rainfall during the decay period. Under these assumptions the rainfall-modified
paraoxon residue at entry time T is given by:
(12)	r'(T) - r(T) exp(-.291CR)
where CR is the cumulative rainfall during the period (0,T). A one inch rainfall
leads to a diminution of the residue by 25 percent and a two inch rainfall a 44
percent decline. These predictions are more or less consistent with the data
presented by Gunther et al. (1977).
Estimates of the parameters b, c and d are available from Popendorf and
Leffingwell (1978) . Also, the initial condition, x0 was estimated from their
data by regressing their parameter a0 against the applied amount in pounds of
active ingredient per acre (AIA). The resulting expression is:
(13)	x0 - 1690(AIA) -3067 ng/cm2
The values used for the other parameters are b - 0.8, c - 0.08 and q - 0.05.
Following the procedure detailed by Popendorf and Leffingwell (1982) the
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dermal dose in mg/kg is related to the paraoxon residue by the expression
kdr'(t)ta where te is the exposure time in hours and kd a constant determined
empirically and set equal to 9.0 as observed in citrus crops. The exposure time
is taken to be an eight hour shift. For a single organophosphate the relation
between dermal dose and fractional inhibition of red blood cell cholinesterase
(RBCD) is given by:
(14)	RBCD - 1 - exp{-w,D/LD50)
where, for paraoxon, the dermal LD50 is 1.0 and we equals to 6.0, midway in the
reported range of 4.7 to 7.3. All members of a work crew are assumed to be
exposed to the same residue environment which is further assumed to result in
the same cholinesterase depression. Individual variability is modeled only in
the relationship between cholinesterase depression and clinical illness.
The relationship between cholinesterase depression and clinical signs and
symptoms of poisoning was modeled by assuming the probability of illness depended
on the degree of cholinesterase depression according to the expression:
(15)	P - 1/[ 1 + exptWi + w2RBCD}]
where and w2 were based on clinical experience and values reported in the
medical literature (Midtling et al. (1985), Milby (1988)). Two sets of
parameters were used, one relating to mild illness and the other to severe
illness. The probability of illness relates to each member of the crew at the
end of one eight-hour day and not to exposures cumulated over several days.
V. Profit-Health Tradeoffs in Re-Entry Regulation
The models presented in the two preceding sections can be used to evaluate
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the impact of re-entry regulations on apple growers' revenues and apple
harvesters' safety. The analysis was conducted under the assumptions that a
flight of coddling moths arrives four days before the optimal harvest date t0
(i.e., t0 - ta - 4), that parathion is applied at a rate of 2.0 pounds of active
ingredient per acre, and that, as is typical, the crop produced on a 50-acre
block will be harvested in one day by a crew of 500 (10 workers per acre).
Losses in growers' revenues were compared to the risk of severe and mild
poisoning to each individual worker. Rainfall levels of 0, 0.5, 1, 1.5, and 2
inches during the re-entry period were used to take into account the differences
in weather conditions encountered in the different regions under investigation:
California receives virtually no rainfall during the harvest period, Washington
receives an average of 0.5 inches and Michigan receives an average of 1.5 inches
under normal conditions.
Table 1 shows the expected numbers of severe and mild parathion poisoning
cases under California, Washington and Michigan conditions, plus the fraction
of revenue lost due to harvest delays. The risk of poisoning is clearly non-
negligible: With a pre-harvest interval of four days or less, there will be an
average of 2.5 severe cases and 43 mild cases under California conditions, 1.6
severe and 29 mild cases under Washington conditions and 0.8 severe and 15 mild
cases under Michigan conditions. (At any given time, there will be almost 19
times as many mild as severe cases.) Each additional day entry is prohibited
reduces the number of mild and severe cases by about 13 percent, while each
additional inch of rainfall reduces them by about 75 percent. Even so, the risk
of poisoning remains non-negligible for a relatively lengthy period of time:
If re-entry is prohibited for as much as 2 weeks, there will still be an average
of one severe poisoning incident for roughly every 2 50-acre blocks harvested
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in California, one severe incident for every 3 50-acre blocks harvested in
Washington and one severe incident for every 4 50-acre blocks harvested in
Michigan.
At the same time, the losses imposed by re-entry regulation can be
considerable. Each additional day's delay in harvesting reduces total revenue
by about 0.24 percent, corresponding to $360 per 50-acre block in California,
$460 per 50-acre block in Washington and $395 per 50-acre block in Michigan.
By way of contrast, total harvesting labor costs amount to about $425 per 50-
acre. block in Washington (Hinman, Tukey and Hunter). A pre-harvest internal of
2 weeks would result in a revenue loss on the order of 2.5 percent; since profit
margins in Washington apple production range from 3 to 10 percent (Hinman, Tukey
and Hunter), such a loss would represent a sizable fraction of net income.
The optimal pre-harvest interval in each state (assuming equal social
welfare weights on farmers' incomes and workers' health) is determined by
equating the marginal cost of additional harvest delays in terms of revenue lost
with the marginal benefits associated with reductions in the number of poisoning
incidents. For illustrative purposes, we calculated these optimal pre-harvest
intervals under the conservative assumptions that benefits were restricted to
average avoided costs , that is, to the average costs of hospitalization plus
average lost wages. This ignores long-term losses due to chronic neurotoxic
effects, the value of the disutility of suffering poisoning, losses caused by
additional risks to consumers from residues remaining at the time of ingestion
and so on.
A typical severe parathion poisoning case typically requires 3 days of
hospitalization, with the first day spent in intensive care, followed by two
weeks of recovery, i.e., lost work time. Assuming average costs of $1200 per
17

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day for intensive care and $500 per day for a standard hospital bed implies total
hospitalization costs of $2200. Assuming an average wage of $10 per hour for
an 8-hour day implies total lost wages of $800, for a total cost of $3000 per
severe case (Becker (1988)).
A typical mild case requires no hospitalization; medical care will
typically cost about $40 per case and there will generally be 2 days of lost work
time, for a total cost of $200 per case (Becker (1988)).
Figures 1, 2 and 3 show the respective marginal costs and marginal benefits
from severe and all poisoning cases associated with different pre-harvest
intervals in California, Washington and Michigan. The optimal pre-harvest
intervals are 15 days in California, 12 days in Washington and 9 days in
Michigan. Current EPA regulations require 14 days regardless of rainfall
conditions for applications of parathion on apples such as the one considered
here. Interestingly, the current pre-harvest interval is quite close to the
optimal levels calculated here, although our calculations suggest the
desirability of greater conservatism under California conditions and less
conservatism under Michigan conditions. They also suggest that, as long as local
rainfall can be monitored effectively, the same levels of safety implicit in the
14-day pre-harvest interval can be achieved at lower cost by making the pre-
harvest interval dependent on rainfall. For example, lowering the pre-harvest
interval from 14 to 9 days when there have been 2 inches of rain would cut the
losses suffered by Michigan apple growers by $1944 per 50-acre block, almost 50
percent, while lowering it from 14 days to 12 days when there have been 0.5
inches of rain would cut the losses suffered by Washington growers by $904 per
50-acre block, almost 20 percent.
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VI. Conclusions
Public authorities frequently use quarantines to ensure public safety by
removing people from hazardous situations either in time or space. Individuals
may pursue similar strategies to enhance their own safety in dealing with
hazards. This paper develops a methodology for assessing the tradeoffs between
productivity or utility losses from this type of regulation and reductions in
risk of disease, accident or illness and applies it to the case of re-entry
regulation in pesticides. We show that this form of regulation provides a
rational incentive for prophylactic applications of pesticides, a practice that
has been much maligned in the pesticide literature. In an empirical evaluation
of pre-harvest intervals for parathion used on apples, we demonstrate that the
tradeoffs involved are quite substantial, that the optimal pre-harvest intervals
implied by rather conservative benefits estimates are quite close to those
actually set by the Environmental Protection Agency, and that the same level of
worker safety as that implicitly targeted by EPA can be achieved at lower cost
by making pre-harvest intervals dependent on rainfall.
In order to focus on the main issues in deriving tradeoffs from quarantine
parameter choices, the model used here is partial and rather stylized. Obvious
improvements include incorporating considerations such as: pest population
dynamics and intraseasonal effects; general equilibrium effects of re-entry
regulation on prices and the distribution of production; choice of amounts of
pesticides and harvest crew size as well as time of application; the influence
of stochastic factors such as weather and size and time of arrival of pest
populations; and uncertainties about residue decay, dermal absorption,
cholinesterase depression and clinical response. The results we obtain, however,
strongly suggest that more elaborate modeling of re-entry regulation and other
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forms of quarantine is well worthwhile.
Further research along these lines is especially necessary because
environmental and occupational health problems such as the one addressed here
are a growing policy concern. While policy advice has been monopolized by
natural scientists until recently, recognition of the fact that absolute safety
is often unattainable has led to an appreciation of the importance of evaluating
tradeoffs between'enhanced safety and other social goals. A key problem is that
thorough tradeoff assessments require close interdisciplinary cooperation in
modeling a full spectrum of economic, physical and biological processes beginning
with production and terminating in risks to health.1 While the difficulties of
organizing such interdisciplinary cooperation have meant that this sort of
modeling has been performed only seldom in the past, hopefully the work reported
here will demonstrate the feasibility and importance of pursuing it.
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VII . Footnotes
1 While economists have studied the links between pollution and health (as in
the voluminous literature on air pollution and health initiated by Lave and
Seskin) and between production and pollution (see for example, Anderson,
Opaluch and Sullivan), to our knowledge none have modeled the entire path from
production to pollution to health.
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VIII. References
Glen D. Anderson, James J. Opaluch and W. Michael Sullivan, "Nonpoint
Agricultural Pollution: Pesticide Contamination of Groundwater Supplies",
American Journal of Agricultural Economics 67:1238-1243, 1985.
Charles Becker, MD, Chief of Occupational Medicine, San Francisco General
Hospital, personal Communication, September 1988.
F.A. Gunther, Y. Iwata, G.E Carman and C.A. Smith, "The Citrus Reentry Problem:
Research on Its Causes and Effects, and Approaches to Its Minimization", Residue
Revi ew 67(1977) :1.
H.R. Hinman, R.B. Tukey and R.E. Hunter, "Estimated Cost of Production for a Red
Delicious Apple Orchard in Central Washington", Extension Bulletin 1159,
Washington State University, Pullman, WA, June 1982.
L. B. Lave and E. P. Seskin, Air Pollution and Human Health. Baltimore: Johns
Hopkins, 1977.
J.E. Midtling, P. Barnett, M. Coye et al. , "Clinical Management of Field Worker
Organophosphate Poisoning," Western J. of Medicine 142(1985), 514-518.
Thomas H. Milby, MD, formerly Chief, Bureau of Occupational Health, California
Department of Health Services and Adjunct Professor, School of Public Health,
University of California at Berkeley. Personal Communication, September 1988.
H.N Nigg, J.C. Allen, R.W. King, N.P. Thompson, G.J. Edwards and R.F. Brooks,
"Dislodgeable Residues of Parathion and Carbophenothion in Florida Citrus: A
Weather Model", Bulletin of Environmental Contamination and Toxicology 1 9 (1 978) :
578-588.
W.J. Popendorf and J.T. Leffingwell, "Natural Variations in the Decay and
Oxidation of Parathion Foliar Residues", Journal of Agricultural and Food
Chemistry, 26(1978): 437-441.
W.J. Popendorf and J.T. Leffingwell, "Regulating OP Pesticide Residues for
Farmworker Protection," Residue Reviews, 82(1982), 125-200.
R.C. Spear, W.J. Popendorf, J.T. Leffingwell et al., "Fieldworkers Response to
Weathered Residues of Parathion," Journal of Occupationa1 Medicine. 19(1977),
406-410.
R.C. Spear, W.J. Popendorf, J.T. Leffingwell and D. Jenkins, "Parathion Residues
on Citrus Foliage. Decay and Composition as Related to Worker Hazard",
Agricultural and Food Chemistry 23(1975): 808-810.
D.C. Staiff, S.W. Comer and R.J. Foster, "Residues of Parathion and conversion
Products on Apple and Peach Foliage Resulting from Repeated Spray Applications",
Bulletin of Environmental Contamination and Toxicology 14(1975): 135-139.
22

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TABLE 1
HEALTH RISKS AND REVENUE LOSSES UNDER ALTERNATIVE RE-ENTRY INTERVALS
Expected number of	Expected number of	Fraction of
Re-entry 	severe poisoninps			mild poisonings	revenue lost
interval
(days) California Washington Michigan	California Washington Michigan
0-4
2.46050
1.63800
0.81650
42.6950 .
29.2650
15.0000
0
5
1.95600
1.33250
0.69i00
34.5800
24.0600
12.7600
0.002397
6
1.57650
1.09650
0.59100
28.2250
19.9600
10.9500
0.004788
7
1.28550
0.91250
0.51050
23.2450
16.7150
9.4850
0.007174
8
1.06000
0.76750
0.44520
19.3150
14.1300
8.2900
0.009554
9
0.88350
0.65250
0.39155
16.2050
12.0600
7.3050
0.011928
10
0.74500
0.56000
0.34725
•13.7200
10.3850
6.4900
0.014296
11
' 0.63400
0.48540
0.31045
11.7300
9.0250
5.8100
0.016659
12
0.54550
0.42450
0.27965
10.1200
7.9100
5.2350
0.019016
13
0.47340
0.37450
0.25370
8.8050
6.9900
4.7555
0.021368
14
0.41470
0.33315
0.23165
7.7300
6.2250
4.3460
0.023714
15
0.36960
0.29865
0.21290
6.8400
5.5900
3.9965
0.026054
16
0.32645
0.26970
0.19680
6.1050
5.0550
3.6965
0.028389
17
0.29305
0.24530
0.18295
5.4850
4.5995
3.4380
0.030718
18
0.26500
0.22450
0.17095
4.9515
4.2130
3.2135
0.033041
19
0.24125
0.20680
0.16000
4.5245
3.8825
3.0185
0.035359
20
0.22110
0.19155
0.15135
4.1495
3.5985
2.8480
0.037672
21
0.20385 •
0.17840
0.14335
3.8280
3.3530
2.6980
0.039978
22
0.18900
0.16700
0.13635
3.5515
3.1400
2.5660
0.042280
23
0.17620
0.15705
0.13010
3.3120
2.9540
2.4495
0.044575
24
0.16510
0.14835
0.12460
3.1040
2.7915
2.3465
0.046866
25
0.15540
0.14070
0.11970
2.9230
2.6485
2.2545
0.049150
26
0.14690
0.13400
0.11535
2.7640
2.5225
2.1725
0.051430
27
0.13945
0.12805
0.11145
2.6245
2.4110
2.0995
0.053704
28
0.12835
0.12275
0.10795
2.5010
2.3120
2.0340
0.055972
qt-tab.wp/dlw/12/23/88

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Figure 1
Optimal Re-Entry Interval in California
Marginal Benefits, Costs (Dollars)
3500
3000
2500
2000
1500
1000
500
I I I I I I i i i ? ?	A-.
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Re-Entry Interval (Days)
Revenue Loss In OA -B-Severe Cases (CA) —All Cases (CA)

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Figure 2
Optimal Re-Entry Interval in Washington
Marginal Benefits.-Costs (Dollars)
2500
2000
1500
1000
500
Re-Entry Interval (Days)
+—Revenue Loss In WA	Severe Cases (WA) -s-All Cases (WA)

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Figure 3
Optimal Re-Entry Interval In Michigan
Marginal Benefits, Costs (Dollars)
1000
800
600
200
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Re-Entry Interval (Days)
^-Revenue Loss in Ml -^-Severe Cases (Ml) —^— All Cases (Ml)

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VALUING REDUCED MORBIDITY:
A HOUSEHOLD PRODUCTION APPROACH*
Mark Dickie
Department of Economics
University of Georgia
Shelby Gerking
Department of Economics
University of Wyoming
May, 1989
This research was supported by the U.S. Environmental Protection Agency
under Cooperative Agreement #CR812054-01-2. It has not been subjected,
however, to the Agency's peer and administrative review and therefore it
does not necessarily reflect the views of the Agency, and no official
endorsement should be inferred. We thank Don Waldman for assistance and
advice concerning econometric procedures, Anne Coulson, Don Tashkin, and
John Demand for invaluable assistance in survey design and data
collection, Alan Krupnik, David Brookshire, Don Coursey, Don Kenkel, John
Tschirhart and seminar participants at Arizona State University for
comments on an earlier draft, and Alan Carlin for his patience and
encouragement throughout the project.

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ABSTRACT
This paper presents a unique application of the household production
approach to valuing public goods and nonmarket commodities. Technical
relationships are estimated between health attributes, private goods that
affect health, and air quality using panel data drawn from a special
survey. Statistical tests suggest that individuals equate marginal rates
of technical substitution in household production with relevant price
ratios. This result confirms that input choices are rational and is
critical for estimating values of health attributes and air pollution.
Value estimates obtained also bear on current questions facing
environmental policymakers.

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I. Introduction
Individuals frequently apply a household technology to combine public
and private goods in the production of nonmarket commodities for final
consumption. Hori (1975) demonstrates that in these situations, market
prices of private goods together with production function parameters may
encode enough information to value both public goods used as inputs and
nonmarket final consumption commodities. Although this valuation
methodology is objective and market based, it seldom has been applied for
three reasons. First, underlying technical relations either are unknown or
data needed to estimate them are unavailable. Second, even if relevant
technical information is at hand, the consumer's budget surface in
commodity space may not be differentiable when joint production and other
complicating factors are present. As a consequence, the commodity bundle
chosen is consistent with any number of marginal rates of substitution
between commodities and values of public goods and nonmarket commodities
remain unknown. Third, joint production and nonconstant returns to scale
also pose serious difficulties when taking the closely related valuation
approach of estimating the area behind demand curves for private goods
inputs and final consumption commodities (Bockstael and McConnell 1983) .
The problems posed by joint production are, troublesome because Pollak and
Wachter (1975) have argued that jointness is pervasive in home production,
and Graham and Green (1985) found empirical evidence of substantial
jointness in their estimation of a household technology.
This paper presents a unique application of the household production
approach to valuing public goods and nonmarket commodities which allows for
certain types of joint production and addresses key problems identified by
previous authors. Technical relationships are estimated between health

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attributes, private goods, and air quality. Data used in the analysis are
drawn from a special survey designed to implement the household production
approach. Econometric estimates allow for censored dependent variables and
cross-equation error correlations in panel data using tobit models with
individual-specific variance components. Wilcox-Gok (1983, 1985)
previously applied variance components estimation in a health context but
did not examine censoring and cross-equation correlation. Key results of
the present paper are: (1) attempts to value detailed attributes of
nonmarket home produced commodities may be ill-advised; however, estimating
a common value for a broadly defined category of attributes may be
possible, and (2) statistical tests support the hypothesis that individuals
equate marginal rates of technical substitution in household production
with relevant price ratios. The latter result confirms that input choices
are rational in the sense of Russell and Thaler (1985): choices are
consistent with utility maximization subject to a correct understanding of
the home technology. Also, value estimates obtained bear on current
questions concerning air pollution control policy. The Clean Air Act of.
1970 and its subsequent amendments focus primarily on health to justify
regulation and require air quality standards to protect even the health of
those most sensitive to pollution. The survey data are sufficiently rich
to allow separate value estimates for persons with normal respiratory
function and persons with chronic respiratory impairments.
The remainder of this paper is divided into four sections. Section II
describes a simple household production model in a health context and
reviews theoretical issues in obtaining value estimates. Section III
discusses the survey instrument and the data collected. Section IV
presents econometric estimates of production functions for health

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3
attributes, as well as values of better air quality and improved health for
both the normal and respiratory impaired subsamples. Implications and
conclusions are drawn out in Section V.
II. Preliminaries
The model specifies utility (U) as a function of market goods (Z) and
health attributes, called symptoms, (S) .
U = U(Z, S)	(1)
For simplicity, Z is treated as a single composite good, but S denotes a
vector measuring intensity of n health symptoms such shortness of
breath, throat irritation, sinus pain, headache, or cough. Intensity of
th
the i symptom is reduced using a vector (V) of m additional private goods
that do not yield direct utility, a vector of ambient air pollution
concentrations (a), and an. endowment of health capital (f2).
S1 => sx(vf o; fl)	i - 1, ... ,n	(2)
Elements of V represent goods an individual might purchase to reduce
intensity of particular symptoms, and ft represents genetic predisposition
to experience symptoms or presence of chronic health conditions that cause
symptoms. Notice that equation (2) allows for joint production in that
some or all elements of V may (but do not necessarily) enter some or all
1
symptom production functions. The budget constraint is
I = P_Z + Z.P.V.	(3)
2 J J J	1 J
where P^ denotes the price of Z, P^ denotes the price of V^., and I denotes
income.
Aspects of this general approach to modeling health decisions have
been used in the health economics literature (e.g., Grossman 1972;
Rosenzweig and Schultz 1982, 1983), where medical care is an example of V

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4
often considered. In these three papers, however, the stock of health
rather than symptoms is treated as the home produced good, and Grossman
treats decisionmaking intertemporally in order to analyze changes in the
health stock over time. A multiperiod framework would permit a more
complete description of air pollution's cumulative physiological damage,
but the present model's focus on symptoms of short duration suggests that a
one period model is appropriate. Moreover, long term panel data containing
both economic and health information necessary to assess cumulative
physiological damage are difficult to obtain.
Similar models also have been used in environmental economics to
derive theoretically correct methods for estimating values of air quality
and other environmental attributes (e.g., Berger et al. 1987, Courant and
Porter 1981; Harford 1984; Harrington and Portney 1987). These models,
however, only consider the case in which m = n = 1 and rule out the
possibility of joint production. In this situation, the marginal value of
or willingness to pay (WTP) for a reduction in air pollution can be derived
by setting dU = 0 and using first order conditions to obtain
= " UlSa/A = " PlSa/Sl	(4)
where denotes marginal disutility of the symptom, S* denotes the
marginal effect of air pollution on symptom intensity, sj denotes the
marginal product of in reducing symptom intensity, and X denotes
marginal utility of income. As shown, marginal willingness to pay to
reduce symptom intensity (- U^/x) equals the marginal cost of doing so
(- Vs}).
Extensions to situations where m and n take on arbitrary values have
been considered in the theory of multi-ware production by Frisch (1965) as
well as in a public finance context by Hori (1975). Actually, Hori treats

-------
four types of household production technology. His case (3) involving
joint production appears to best characterize the application discussed in
Section IV because a single V may simultaneously reduce more than one
symptom. In this situation, a key result is that marginal values of
home produced commodities cannot be re-expressed in terms of market prices
and production function parameters unless the number of private goods is at
least as great as the number of commodities (m > n). Intuitively, if
m < n, the individual does not have a choice among some alternative
combinations of symptom intensities because there are too few choice
variables (V ) and the budget surface on which each chosen value of S~ must
2
lie is not dirferentiable.
Another perspective on this result can be obtained from the first
order conditions of the individual's utility maximization problem. After
substituting, the symptom production functions into the utility function,
the first order conditions include the budget constraint and
U - XP = o
z z
EiUiSj " APj = °' j - 1. .... n.	(5)
The marginal value of a reduction in air pollution is a weighted sum of the
values of the individual symptom intensities (U^/A), where the weights are
the marginal products of pollution (S*): WTTq = - E^(U^/X)S^). Estimating
values for reductions in symptoms or pollutants on the basis of observable
behavior requires solving for the (U^/x) as functions of market prices of
private goods and production function parameters. Rearranging the m first
order conditions for the V gives

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6
i
u. A
p
l

6
m "
m
If m < n, the rank of the symptom technology matrix S
{S.} is at most m
and the system of equations in (6) is underdetermined. Intensity of one
symptom cannot be varied holding others constant, and the marginal value of
an individual symptom cannot be determined. On the other hand, if m = n
and the symptom technology matrix is nonsingular, then the rank is n and
unique solutions can be computed for the U A. If m > n and the technology
matrix has full rank, then the system is overdetermined, and values for the
ui/x can be computed from a subset of the first order equations.
This theoretical overview yields several ideas useful in empirical
application. First, if m > n and the household technology matrix has rank
n, then values of nonmarket commodities and public goods are calculated in
a relatively straightforward manner because utility terms can be
eliminated. Second, the possibility that men suggests that the household
production approach may be incapable of estimating separate values for a
comparatively large number of detailed commodities and that aggregation of
3
commodities may be necessary to ensure m > n. Third, even if m > n, the
household production approach may fail if there is linear dependence among
the rows of the technology matrix. Thus , statistical tests of the rank of
the matrix should be performed to ensure differentiability of the budget
surface. Fourth, if m > n, first order conditions impose constraints on
rejection of these constraints would
values that can be taken by the S

-------
7
imply that the outcome of the choice process is inconsistent with
utility-maximization subject to a known technology.
Fifth, if m > n, values of and P. need not yield positive values
J	3
for -U^/x, the marginal willingness to pay to reduce intensity of the
symptom. Of course, in the simple case where m = n = 1, the only
requirement is that	>o. I f m = n = 2, a case considered in the
empirical work presented in Section IV, values of -U./A and -U0/.\ both will
1	/L
be positive only if (sj/s*) > (Pj/Pj) > (S^/S*). If Vj and V, are not
chosen such that their marginal rates of technical substitution bracket
their price ratio, then it is possible to reduce intensity of one symptom
without increasing intensity of the other and without spending more on
symptom reduction.
Sixth, complications arise in expressing symptom and air pollution
values in situations where some or all of the V, are sources of direct
]
utility, another form of joint production. This problem is important (and
it is encountered in the empirical work presented in Section IV) because of
the difficulty in identifying private goods that are purchased but do not
enter the utility function. To illustrate, assume that m = 2, n = 1 and
that V2 -but not is a source of both direct positive utility and symptom
relief.	still would equal -(P^S^/sJ) and therefore could be
calculated without knowing values for marginal utility terms. If
consumption of Vhowever, was used as a basis for this calculation, the
simple formula	would overestimate WTPC, by an amount equal to
"(^S^/ASo) where denotes marginal utility of V2 (U2 > 0) . When m and n
take arbitrary values the situation is more complex, but in general
nonmarket commodity and public good values can be determined only if the
number of private goods which do not enter the utility function is at least

-------
8
as great as the number of final commodities. Even if this condition is not
met, however, it is possible in some cases to determine whether the value
4
of nonmarket commodities and public goods is over- or underestimated.
Each of these six issues is treated in the empirical work reported in
Section IV. Although m = n = 2 and relevant marginal rates of technical
substitution generally bracket input price ratios, statistical tests cannot
reject the hypothesis that the technology matrix has rank one. After
aggregating symptoms into one broad category, m > n (2 > 1), and first
order conditions constrain the marginal rate of technical substitution to
equal the price ratio. Failure to reject the constraint confirms that
behavior is consistent with the model's predictions; nevertheless the
likely possibility that both private good inputs are direct sources of
utility suggests that the model's value estimates should be interpreted as
lower bounds.
Ill . Data
Data used to implement the household production approach were obtained
from a sample of 226 residents of two Los Angeles area communities. Each
respondent previously had participated in a study of chronic obstructive
respiratory disease (Detels et al. 1979, 1981). Key aspects of this sample
are: (1) persons with physician diagnosed chronic respiratory ailments
deliberately are overrepresented (76 respondents suffered from- such
diseases), (2) 50 additional respondents with self-reported chronic
cough or chronic shortness of breath are included, (3) 151 respondents
lived in Glendora, a community with high oxidant air Pollution and 75
respondents lived in Burbank, a community with oxidant pollution levels
more like other urbanized areas in the U.S. but with high levels of carbon

-------
9
monoxide, (4) all respondents either were nonsmokers or former smokers who
had not smoked in at least two years, and (5) all respondents were
household heads with full-time jobs (defined as at least 1,600 hours of
work annually).
professionally trained interviewers contacted respondents several
times over a 17 month period beginning in July 1985. The first contact
involved administration of an extensive baseline questionnaire in the
respondent's home. Subsequent interviews were conducted by telephone. "
Including the baseline interview, the number of contacts with each
respondent varied from three to six with an average number of contacts per
respondent of just over five. Of the 1147 total contacts (= 226 x 5), 644
were with respiratory impaired subjects (i.e., those either with
physician-diagnosed or self-reported chronic respiratory ailments) and 503
were with respondents having normal respiratory function.
Initial baseline Interviews measured four groups of variables: (1)
long term health status, (2) recently experienced health symptoms, (3) use
of private goods and activities that might reduce symptom intensity, and
(4) socioeconomic/demographic and work environment characteristics.
Telephone follow-up interviews inquired further about health symptoms and
use of particular private goods. Long term health status was measured in
two ways. First, respondents indicated whether a physician ever had
diagnosed asthma (ASTHMA) , chronic bronchitis (BRONCH), or other chronic
respiratory disease such as emphysema, tuberculosis, or lung cancer.
Second, they stated whether they experience chronic shortness of breath or
wheezing (SHRTWHZ) and/or regularly cough up phlegm, sputum, or mucous
(FLEMCO) . Respondents also indicated whether a physician ever had

-------
10
diagnosed hay fever (HAYFEV); however, this condition was not treated as
indicative of a chronic respiratory impairment.
Both background and follow-up instruments also asked which, if any, of
26 health symptoms were experienced in the two days prior to the interview.
Symptoms initially were aggregated into two categories defined as: (1)
6
chest and throat symptoms and (2) all other symptoms. Aggregation to two
categories reduces the number of household produced final goods (n)
considered; however, assigning particular symptoms to these categories
admittedly is somewhat arbitrary. Yet, the classification scheme selected
permits focus on a group of symptoms in which there is current policy
interest. Chest and throat symptoms identified have been linked to ambient
ozone exposure (see Gerking et al. 1984, for a survey of the evidence) and
federal standards for this air pollutant currently are under review.
Moreover, multivariate tobit turns out to be a natural estimation method
and aggregating symptoms into two categories permits a reduction in
computation burden. Dickie et al. (1987(a)) report that respondents with
chronic respiratory impairments experienced each of the 2 6 individual
symptoms more often than respondents with normal respiratory function.
This outcome is reflected in Table 1 which tabulates frequency
distributions of the total number of chest and throat and other symptoms
reported by respondents in the two subsamples.
In the empirical work reported in Section IV, data on the number of
symptoms reported are assumed to be built up from unobserved latent
variables measuring symptom intensity. As intensity of a particular
symptom such as cough rises above a threshold, the individual reports
having experienced it; otherwise he does not. Thus , the frequency
distribution tabulated in Table 1 merely reflects the number of symptoms

-------
11
that crossed the intensity threshold in the two days prior to the
interview.
Private goods used to estimate symptom production functions include
durable goods which may relieve symptoms by reducing exposure to air
pollution. When asked during the baseline interview whether they changed
their activities at all when the air was smoggy, half the respondents in
the impaired group and 42 percent of the respondents in the normal group
reported that they tried to stay indoors and/or run their air conditioners
more in an attempt to avoid the pollution. The effectiveness of such a
strategy depends on the quality of the indoor air, which in turn depends
partly on whether the respondent has and uses the following private goods:
(1) central air conditioning in the home (ACCEN) , (2) an air purifying
system in the home, and (3) a fuel other than natural gas for cooking
g
(NOTGASCK) . Similarly, a respondent who has and used air conditioning in
the automobile (ACCAR) might reduce exposure to pollution, particularly
when driving or idling in traffic. Each of these private goods may provide
direct utility in addition to reducing exposure to pollution. Air
conditioners, for example, may provide not only relief from symptoms but
also cooling services that yield direct satisfaction. This problem is
discussed further in Section V.
Socioeconomic/demographic variables measured whether the respondent
lived in Burbank or Glendora (BURB) as well as years of age (AGE), gender,
race (white or nonwhite), marital status, and household income. Also,
respondents were asked whether they were exposed to toxic fumes or dust
while at work (EXPWORK).
Finally, each contact with a respondent was matched to measures of
ambient air pollution concentrations, humidity, and temperature for that

-------
12
day. Air monitoring stations used are those nearest to residences of
respondents in each of the two communities. Measures were obtained of the
six criteria pollutants for which national ambient air quality standards
have been established: carbon monoxide (CO), nitrogen dioxide (N02), ozone
(03), sulfur dioxide (S02), lead and total suspended particulate.
Readings for lead and particulate, however, only were available for about
ten percent of the days during the study period, forcing exclusion of those
pollutants from empirical work. Each of the remaining four pollutants were
measured as maximum daily one-hour ambient concentrations. Maxima are used
because epidemiological and medical evidence suggests that acute symptoms
may be more closely related to peak than to average pollution
concentrations. The air pollution variables entered then, are averages of
one hour maxima on the two days prior to the interview so as to conform
Q
with the measurement of symptoms. " Temperature and relative humidity data
similarly were averaged across two day periods.
IV. Estimates of Household Symptom Technology
This section reports estimated production functions, hypothesis tests,
and estimated values of public goods and nonmarket commodities. A
bivariate tobit model with variance components was developed to account
for: (1) probable correlation of disturbances across production functions,
(2) censoring of reported symptoms at zero, and (3) repeated observations
10
of the same individuals at different times. Both tobit and variance
components models frequently are applied; however, as discussed by Maddala
(1987), there have been few applications of tobit with variance components
to panel data.

-------
Empirical estimates of household production functions for health also
have been obtained by Rosenzweig and Schultz (1983)^ and variance
components models have been applied to health production by Wilcox-Gok
12
(1983, 1S85) ; however, neither of these investigators focus on valuing
nonmarket commodities and public goods. Rosenzweig and Schultz consider
birthweight rather than symptoms and Wilcox-Gok examines days missed from
usual activities due to illness or injury and visits to certain health care
facilities. Although the dependent variables used by Wilcox-Gok would
appear to be correlated and censored at zero, the estimation procedures
employed by Wilcox-Gok did not correct for either problem. In contrast,
the bivariate tobit model presented below allows for both censoring and
cross-equation error correlation.
The symptom production functions are specified as
'SA + *iht « v. + c.ht > 0	^
0	otherwise
1	- 1, 2.
In equation (7) , i denotes type of symptom (chest and throat = 1, other
2), h denotes respondent, and t denotes time; S^t represents the number of
symptoms reported and is a vector including explanatory variables such
as measures of health capital, private goods, and air pollutants.
Random disturbances consist of the sum of a transitory component and a
permanent component common to both production functions
eiht " "h + ''iht	i - 1. 2	(8)
The transitory error components,	capture unmeasured influences that
vary over individuals, symptoms, or time. The permanent error component,
uh, varies only over individuals, capturing unmeasured individual specific
influences that persist over time. The assumption that the same permanent


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14
component enters both production functions results in computational savings
and is at least plausible, since the same individual produces both
categories of symptoms.
Permanent components are assumed normally and independently
n
distributed with mean zero and variance cr~. Transitory components are
assumed normally and independently distributed, conditional on the
2
permanent component, with mean zero and variance ct_. , 1 = 1, 2. Despite the
common permanent component, the correlation coefficient between the two
2 , 2 f l 9	*> 1
symptom classes in the same time period,	+cp (a + , is
distinct from the correlation coefficient between the same symptom class at
2 2 2
different times, cr^/+ o^), i = 1, 2.
Let Fiht and f iht rePresent' respectively, the normal distribution and
density functions evaluated at (S^t -	conditional on
The log-likelihood function is
L - Ehln / M	• i *0 «iht1S(l,)du	i«S
ht	ht
13
where g(0 is the normal density.
An alternative to the variance components or random effects model is
the fixed effects model in which the are treated as fixed constants
rather than as random variables. Two arguments can be made in favor of the
14
random effects specification of the symptom production model.
First, treating the as constants subsumes the effects of all
individual specific, time invariant variables into the fixed effects.
Since the private goods measured in the data are fixed during the sampling
period, using the fixed effects model would make it impossible to identify
the production function parameters (S^) necessary to estimate values for
reductions in symptoms and air pollutants. Similarly, estimating the

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15
separate effects for the various chronic health impairment variables is of
some interest, but these effects could not be distinguished from the y^ in
the fixed effects specification.
The second argument in favor of random effects rests on the
inconsistency of the fixed effects tobit estimator. The individual effects
cannot be estimated consistently for a small number of time periods even
as the number of individuals increases without bound. Intuitively, each
individual brings to the sample a distinct y^> with the result that
increasing the number of individuals fails to increase the information
available to estimate the y^. In many nonlinear models, including tobit,
fixed effects estimators for the remaining parameters cannot be derived
independently of the y^, so that the entire set of parameters is estimated
inconsistently. By contrast, the random effects model attempts to estimate
only the mean and variance of the y^ rather than the individual effects
themselves and thus can estimate the slope coefficients of the model
consistently.
While these arguments present a compelling case for the random effects
model, biased estimation can result because the model ignores the
correlation that may exist between the explanatory variables and the
permanent error component (see, e.g., Mundlak 1978). For example, if an
individual knows his own y^> utility maximization would imply that his
choice of private goods depends on	A solution to this problem proposed
for probit models by Chamberlain (1980) is to specify y^ as a linear
function of the individual's explanatory variables plus an orthogonal
residual:	+ nh> where includes the individual's entire time
series of observations on explanatory variables. This auxiliary regression
then could be substituted for y^ in the specification of the symptom

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16
production functions, and the likelihood derived by integrating over the
density of n rather than the density of p. But owing to the lack of
temporal variation in all explanatory variables except the measures of
pollution and weather, the substitution would produce collinearity in the
matrix of explanatory variables as each time-invariant variable in the
auxiliary regression above would be perfectly collinear with its
counterpart already included in the model specification. As a consequence,
Chamberlain's approach was not pursued.
An alternative approach to correct for correlation between covariates
and errors is analogous to the two stage least squares procedure employed
by Rosenzweig and Schultz in their previously cited birthweight study. In
the first stage, reduced form probit demand equations for each of four
private goods (ACHOME, ACCAR, APHOME, NOTGASCK) are estimated.15 In the
second stage, predicted probabilities from the reduced form probits were to
be used as instruments for private goods in the tobit symptom production
function models, but explanatory power of the reduced form probit equations
was very poor. In half of the equations for each subsample the null
hypothesis that all slope coefficients jointly are zero could not be
rejected at the 5 percent level and in all equations key variables such as
household income had insignificant and often wrongly signed coefficients.
Another problem is the absence of private good price data specific to each
respondent. The original survey materials requested these data but after
pretesting, this series of questions was dropped because many respondents
often made purchases jointly with 3 house or car and were unable to provide
even an approximate answer. As a consequence, two-stage estimation was not

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17
pursued further with the likely outcome that estimates of willingness to
pay for nonmarket commodities and public goods may have a downward bias.
Tables 2 and 3 present illustrative symptom production function
estimates for impaired and normal subsamples. Equations presented are
representative of a somewhat broader range of alternative specifications
available from the authors on request. The overall explanatory power of
the model was evaluated by testing the null hypothesis that all estimated
coefficients (excepting the constant terms) jointly are zero. A Likelihood
ratio tests rejects this hypothesis for both subsamples at significance
levels less than one percent. Also, estimates of the individual specific
error components, denoted a , have large asymptotic t-statistics which
confirms persistence of unobserved personal characteristics that affect
symptoms.
Table 2 shows that chronic health ailments and hay fever are
positively related to symptom occurrence among members of the impaired
group. Coefficients of ASTHMA, BRONCH, SHRTWHZ, and HAYFEV are positive in
equations for both chest and throat and other symptoms and have associated
asymptotic t-statistics that range from 2.1 to 7.6. The coefficient of
FLEMCO is positive and significantly different from zero at conventional
levels in the chest and throat equation, but its asymptotic t-statistic is
less than unity in the equation for other symptoms. The coefficient of AGE
was not significantly different from zero in either equation and the
EXPWORK variable was excluded because of convergence problems with the
16
bivariate tobit algorithm. Variables measuring gender, race, and marital
status never were included in the analysis because 92 percent of the
impaired respondents were male, 100 percent were white, and 90 percent were
married. Residents of Burbank experience chest and throat symptoms with

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18
less frequency than do residents of Glendora. Of course, many possible
factors could explain this outcome; however, Burbank has had a less severe
long term ambient ozone pollution problem than Glendora. For example, in
1986 average one day hourly maximum ozone readings in Burbank and Glendora
were 8.7 pphm and 10.2 pphm, respectively, and a similar difference in
ozone readings has persisted at least since 1983.
With respect to private and public inputs to the symptom production
functions, the coefficient of ACCAR is negative and significantly different
from zero at the 10 percent level using a one tail test in the other
symptoms equation, while the coefficient of ACCEN is negative and
significantly different from zero at the 5 percent level using a one tail
test in both equations. Results from estimated equations not presented
reveal that NOTGASCK and use of air purification at home never are
significant determinants of symptoms in the impaired subsample. Also, 03,
CO, and N02 exert insignificant influences on occurrence of both types of
symptoms. When four air pollution variables were entered, collinearity
between them appeared to prevent the maximum likelihood algorithm from
converging. Consequently, S02 was arbitrarily excluded from the
specification presented and the three air pollution measures included as
covariates should be interpreted as broader indices of ambient pollutant
concentrations. Variables measuring temperature and humidity were excluded
from the Table 2 specification; but in equations not reported their
coefficients never were significantly different from zero.
Table 3 presents corresponding symptom production estimates for the
subsample with normal respiratory function. HAYFEV is the only health
status variable entered because ASTHMA, BRONCH, SHRTWZ, and FLEMCO were
used to define the impaired subsample. Coefficients of HAYFEV are positive

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19
in equations for both chest and throat and other symptoms and have
t-statistics of 1.61 and 1.87, respectively. Coefficients of BURB are
negative; but in contrast to impaired subsample results, they are not
significantly different from zero at conventional levels. AGE and EXPWORK
enter positively and their coefficients differ significantly from zero at
2\ percent in the other symptoms equation. Among private goods entering
the production functions, coefficients of APHOME and ACHOME never were
significantly different from zero at conventional levels, and these
variables are excluded from the specification in Table 3. Use of air
conditioning in an automobile reduced chest and throat symptom occurrences
and cooking with a fuel other than natural gas (marginally) reduces other
symptoms. Variables measuring gender, race, and marital status again were
not considered as the normal subsample was 94 percent male, 99 percent
white, and 88 percent married. In the normal subsample, collinearity and
algorithm convergence problems again limited the number of air pollution
variables that could be entered in the same equation. As shown in Table 3,
03, CO and N02 coefficients had associated t-statistics of 1.16 or
smaller. Temperature and humidity variables are excluded from the
specification shown in Table 3. In alternative specifications not
reported, coefficients of these variables never were significantly
different from zero in alternative equations not reported.
Three pieces of information are required to use the estimates in
Tables 2 and 3 in the calculation of values for reductions in symptoms and
air pollutants: (1) marginal effects of air pollutants on symptoms, (2)
marginal effects of private goods on symptoms, and (3) prices of private
goods . Marginal products were defined as the effect of a small change in a
good on the expected number of symptoms. Computational formulae were

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20
developed extending results for the tobit model (see McDonald and Moffit
1980) to the present context which allows for variance components error
structure. However, because private goods are measured as dummy variables
and, therefore, cannot be continuously varied, incremental, rather than
marginal, products are used.
The final elements needed to compute value estimates are the prices of
private goods. Dealers of these goods in the Burbank and Glendora areas
were contacted for estimates of initial investment required to purchase the
goods , average length of life, scrap value (if any), and fuel expense.
After deducting the present scrap value from the initial investment, the
net initial investment was amortized over the expected length of years of
life. Adding annual fuel expense yields an estimate (or range of
estimates) of annual user cost of the private good. The annual costs then
17
were converted to two-day costs to match the survey data. The dependent
variables used in the estimated equations do not distinguish between one-
and two-day occurrences of symptoms, but approximately one-half of the
occurrences were reported as two day occurrences. As a consequence, the
value estimates obtained were divided by 1.5 to convert to daily values.
Two tests were performed prior to estimating values of symptom and air
pollution reduction. First, calculations were made for both normal and
impaired subsamples to ensure that relevant ratios of incremental products
of private goods in reducing symptoms bracketed the corresponding price
ratio. Recall from the discussion in Section II that this condition
guarantees that value estimates for reducing both types of symptoms are
positive. A problem in making this calculation is that estimates of
incremental rates of technical substitution vary across individuals
(incremental products are functions of individual characteristics), but no

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21
respondent specific price information is available. As just indicated,
dealers in Glendora provided the basis for a plausible range of prices to
be constructed for each good. If midpoints of relevant price ranges are
used together with incremental rates of technical substitution taken from
Tables 2 and 3, the bracketing condition is met for all 100 respondents in
the normal subsample and 117 of 126 respondents in the impaired subsample.
Of course, alternative price ratios selected from this range meet the
bracketing condition for different numbers of respondents.
Second, possible singularity of the symptom technology matrix was
18
analyzed using a Wald test (see Judge et al. 1985, p. 215 for details).
In the context of estimates in Tables 2 and 3, the distribution of the test
statistic (X) is difficult to evaluate because relevant derivatives are
functions of covariate values and specific to individual respondents.
However, if derivatives are evaluated in terms of the underlying latent
variable model, they can be expressed in terms of parameters only and A is
2
distributed as x with 1 degree of freedom. Adopting this simpler
approach, p-values for the Wald test statistic are large: p = .742 for the
impaired subsample equations and p = .610 for the normal subsample
19
equations. As a consequence, the null hypothesis of singularity of the
symptom technology matrix is not rejected at conventional levels. This
result suggests that in both subsamples, there does not appear to be an
independent technology for reducing the two types of symptoms, budget
constraints are nondifferentiable, and separate value estimates for
chest and throat and other symptoms should not be calculated.
A common value for reducing chest and throat and other symptoms still
can be obtained by aggregating the two categories and re-estimating
production functions in a univariate tobit framework. Table 4 shows

-------
results based on using the same covariates as those reported in Tables 2
and 3 and retaining the variance components error structure. The Table 4
equations also make use of a constraint requiring that if m > n = 1, the
marginal rate of technical substitution must equal the input price ratio to
insure that values of marginal willingness to pay to avoid a symptom must
be identical no matter which private good is used as the basis for the
calculation. In the case where m = 2 and n = 1, as discussed in Section
II this single value is -Uj/X = -(P^sj) = -(P^/S*). In the impaired
subsample, the restriction can be tested under the null hypothesis,
H0 : SACCAR = ^PACCAR/PACHOME^ BACHOME' where the are coefficients of
ACCAR and ACHOME in the latent model and the P^ are midpoints from the
estimated range of two day prices for the private goods. In corresponding
notation, the null hypothesis to test in the normal subsample is,
H0 : 6ACCAR = ^ACCAR^NOTGASCK^NOTGASCK' Both hyPotheses are tested
against the alternative that coefficients of private qoods are
unconstrained parameters, using a likelihood ratio test.
P-values for the parameter restrictions are comparatively large;
P = .623 in the impaired subsample and P = .562 in the normal subsample.
Thus , the above null hypotheses are not rejected at conventional
significance levels. This result supports a critical implication of the
previously presented household production model, namely that individuals
equate marginal rates of technical substitution in production with relevant
price ratios. Moreover, coefficients of private good variables defined
under the null hypotheses for the two subsamples have t-statistics
exceeding two in absolute value. Performance of remaining variables is
roughly comparable to the bivariate tobit estimates. A notable exception,
however, is that in the normal subsample univariate tobit estimates,

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23
coefficients of 03 and N02 are positive with t-statistics exceeding 1.6.
This outcome suggests that persons with normal respiratory function tend to
experience more symptoms when air pollution levels are high, whereas those
with impaired respiratory function experience symptoms with such regularity
that there is no clear relationship to fluctuations in air quality.
Intensity of particular symptoms may be greater in both subsamples when
pollution levels are high, but this aspect is not directly measured.
Table 5 presents estimates of marginal willingness to pay to avoid
symptoms and to reduce two air pollutants. Unconditional values of
relieving symptoms and reducing air pollution are calculated for each
respondent from observed univariate tobit models. Table 5 reports the
mean, median, and range of respondents' marginal willingness to pay to
eliminate one health symptom for one day as well as mean marginal
willingness to pay to reduce air pollutants by one unit for one day for the
normal subsample. Symptom reduction values range from $0.81 to $1.90 in
the impaired subsample and from $0.49 to $1.22 in the normal subsample with
means of $1.12 and $0.73 in the two subsamples, respectively. ^ Also ,
values of willingness to pay to reduce one hour daily maximum levels of 03
and N02 by one part per ten million are $0.31 and $0.91 in the normal
subsample. Corresponding calculations are not reported for the impaired
subsample because, as shown in Table 4, coefficients of air pollution
variables are not significant at conventional levels.
V. Conclusion
Willingness to pay values of symptom reduction and air quality
improvement just presented should be viewed as illustrative approximations
for two reasons. First, private goods used in computing the estimates are

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24
likely to be direct sources of utility. Second, symptom experience and
private good purchase decisions are likely to be jointly determined.
Nevertheless, these estimates still are of interest because aspects of
joint production are taken into account. A key finding is that independent
technologies for home producing symptoms are difficult to identify, thus
greatly limiting the number of individual symptoms for which values can be
computed. In fact, the 26 symptoms analyzed here had to be aggregated into
a single group before willingness to pay values could be computed.
This outcome appears to have implications for estimating willingness
to pay for nonmarket commodities in other contexts. An obvious example
concerns previous estimates of willingness to pay to avoid health symptoms.
Berger et al. (1987) report one day willingness to pay values for
eliminating each of seven minor health symptoms, such as stuffed up
sinuses, cough, headache and heavy drowsiness that range from $27 per day
to $142 per day. Green et al. (1978) present estimates of willingness to
pay to avoid similarly defined symptoms ranging from $26 per day to $79 per
day. In both studies, however, willingness to pay estimates were obtained
symptom by symptom in a contingent valuation framework that ignores whether
independent technologies are available to produce each. Thus, respondents
simply may have lumped total willingness to pay for broader health concerns
onto particular symptoms. Some respondents may also have inadvertently
stated their willingness to pay to avoid symptoms for periods longer than
one day.
Another example relates to emerging research aimed at splitting
willingness to pay to reduce air pollution into health, visibility, and
possibly other components. From a policy standpoint, this line of inquiry
is important because the Clean Air Act and its subsequent amendments focus

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25
primarily on health and give less weight to other reasons why people may
want lower air pollution levels. Analyzing location choice within
metropolitan areas, for example, may not provide enough information to
decompose total willingness to pay into desired components. Instead,
survey procedures must be designed in which respondents are either reminded
of independent technologies that can be used to home produce air pollution
related goods or else confronted with believable hypothetical situations
that allow one good to vary while others are held constant.

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26
REFERENCES
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Pollution Using Information on Defensive Expenditures," Journal of
Environmental Economics and Management (March 1988), 111-127.
Berger, M. C., G. C. Blomquist, D. Kenkel, and G. S. Tolley, "Valuing
Changes in Health Risks: A Comparison of Alternative Measures,"
Southern Economic Journal 53 (April 1987), 967-984.
Berndt, E. R., B. H. Hall, R. E. Hall, and J. A. Hausman, "Estimation
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Bockstael, N., and R. McConnell, "Welfare Measurement in the Household
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806-814.
Chamberlain, G., "Analysis of Covariance with Qualitative Data," Review of
Economic Studies 47 (1980), 225-238.
Chestnut, L., and D. Violette, Estimates of Willingness to Pay for
Pollution-Induced Changes in Morbidity: A Critique for Benefit Cost
Analysis of Pollution Regulation, EPA-68-01-6543 (1984).
Courant, P. N., and R. C. Porter, "Averting Expenditure and the Cost of
Pollution," Journal of Environmental Economics and Management 8
(December 1981), 321-329.

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Detels, R., S. Rokaw, A. Coulson, D. Tashkin, J. Sayre, and F. Massey, Jr.,
"The UCLA Population Studies of Chronic Obstructive Respiratory
Disease I. Methodology," American Journal of Epidemiology 109 (1979),
33-58.
Detels, R., J. Sayre, A. Coulson, et al., "The UCLA Population Studies of
Chronic Obstructive Respiratory Disease IV. Respiratory Effects of
Long Term Exposure to Photochemical Oxidants," American Review of
Respiratory Disease 124 (1981), 673-68(30
Dickie, M., S. Gerking, G. McClelland, and W. Schulze, "Valuing
Morbidity: An Overview and State of the Art Assessment," Volume I of
Improving Accuracy and Reducing Costs of Environmental Benefit
Assessments, U.S. Environmental Protection Agency, Cooperative
Agreement #CR812054-01-2, December 1987(a).
Dickie, M., S. Gerking, W. Schulze, A. Coulson, and D. Tashkin, "Value
of Symptoms of Ozone Exposure: An Application of the Averting
Behavior Method," Volume II of Improving Accuracy and Reducing Costs
of Environmental Benefit Assessments, U.S. Environmental Protection
Agency, Cooperative Agreement #CR812054-01-2, December 1987(b).
Frisch, R., Theory of Production (Chicago: Rand McNally & Company, 1965).
Gerking, S., A. Coulson, W. Schulze, D. Tashkin, D. Anderson, M. Dickie,
and D. Brookshire, "Estimating Benefits of Reducing Community
Low-Level Ozone Exposure: A Feasibility Study," Volume III of
Experimental Methods for Assessing Environmental Benefits, U.S.
Environmental Protection Agency, Cooperative Agreement
#CR-811077-01-0, September 1984.

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28
Graham, J. W., and C. A. Green, "Estimating the Parameters of a Household
Production Function With Joint Products," Review of Economics and
Statistics 66 (May 1984), 277-282.
Green, A. E. S., S. V. Berg, E. T. Loehman, M. E. Shaw, R. W. Fahien,
R. H. Hedinger, A. A. Arroyo, and V. H. De, An Interdisciplinary
Study of the Health, Social and Environmental Economics of Sulfur
Oxide Pollution in Florida, Interdisciplinary Center for Aeronomy and
(other) Atmospheric Sciences, University of Florida, Gainesville,
Florida, 1978.
Gregory, A. W., and M. R. Veall, "Formulating Wald Tests of Nonlinear
Restrictions," Econometrica 53 (November 1985), 1465-1468.
Grossman, M., "On the Concept of Health Capital and the Demand for Health,"
Journal of Political Economy 80 (March 1972), 223-255.
Harford, J. D., "Averting Behavior and the Benefits of Reduced Soiling,"
Journal of Environmental Economics and Management 11 (September 1984),
296-302.
Harrington, W., and P. R. Portney, "Valuing the Benefits of Health and
Safety Regulation," Journal of Urban Economics 22 (July 1987),
101-112.
Hori, H., "Revealed Preference for Public Goods," American Economic Review
65 (December 1975), 947-954.
Hsiao, C., Analysis of Panel Data (Cambridge: Cambridge University Press,
1986).
Judge, G. G., W. E. Griffiths, R. C. Hill, H. Lutkepohl, and T. C. Lee,
The Theory and Practice of Econometrics, 2nd Edition (New York: John
Wiley and Sons, 1985).

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Maddala, G. S., "Limited Dependent Variable Models Using Panel Data,"
Journal of Human Resources 22 (Summer 1987), 307-338.
McDonald, J. F., and R. A. Moffit, "The Uses of Tobit Analysis," Review of
Economics and Statistics 62 (May 1980), 318-321.
Mundlak, Y., "On the Pooling of Time Series and Cross-Section Data,"
Econometrica 46 (January 1978), 69-85.
Pollak, R. A., and M. L. Wachter, "The Relevance of the Household
Production Function Approach and Its Implications for the Allocation
of Time," Journal of Political Economy 83 (April 1975), 255-277.
Rosenzweig, Y. R., and T. P. Schultz, "The Behavior of ^Mothers as Inputs
to Child Health: The Determinants of Birth Weight, Gestation, and
Race of Fetal Growth," in Victor R. Fuchs (ed.), Economic Aspects of
Health (Chicago: The University of Chicago Press, 1982).
Rosenzweig, M. R., and T. P. Schultz, "Estimating a Household Production
Function: Heterogeneity, the Demand for Health Inputs, and Their
Effects on Birth Weight," Journal of Political Economy 91 (October
1983), 723-746.
Samuelson, P. A., "The Pure Theory of Public Expenditures," Review of
Economics and Statistics 36 (November 1954), 387-389.
Wilcox-Gok, V. L., "The Determination of Child Health: An Application of
Sibling and Adoption Data," Review of Economics and Statistics 65 (May
1983), 266-273.
Wilcox-Gok, V. L., "Mother's Education, Health Practices and Children's
Health Needs: A Variance Components Model," Review of Economics and
Statistics 67 (November 1985), 706-710.

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30
FOOTNOTES
1
Another, possibly troublesome, aspect of joint production occurs if
some or all elements of V are arguments in the utility function. This
complication is discussed momentarily.
2
Hori identifies three sources of nondifferentiability of the budget
surface under joint production. The first occurs if the number of private
goods is less than the number of commodities. The second arises because of
nonnegativity restrictions on the private goods. This is not treated
directly in the present paper, but if each private good is purchased in
positive quantities, the chosen commodity bundle will not lie at the second
type of kink. Hori's third cause of nondifferentiability implies linear
dependence among the rows of the technology matrix, a possibility
considered below.
3
Notice that this point on aggregation may apply to other valuation
methods as well. Using contingent valuation surveys, for example, Green et
al. (1978) and Berger et al. (1987) obtained value estimates of several
specific symptoms; however, issues relating to existence of independent
symptom technologies never was faced. Future contingent valuation surveys
may do well to consider this point prior to eliciting estimates of
willingness to pay.
4
For example, suppose m = n = 2 and both private goods are direct
sources of utililty. If equation (6) is used to solve for the U./A, then:
(1) if the two marginal rates of technical substitution (MRTS) do not
bracket the price ratio, then the value of the commodity whose

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31
MRTS is closer in magnitude to the price ratio will be overestimated,
while the value of the other commodity will be underestimated; (2) if
the two MRTS values do bracket the price ratio, then the value of
either one or both of the commodities will be overestimated; and (3)
in no case will the value of both commodities be underestimated.
s
Both questionnaires are presented and extensively discussed m Volume
II of Dickie et al. (1987(b)).
6
Chest and throat symptoms include (1) cough, (2) throat irritation,
(3) husky voice, (4) phlegm, sputum or mucous, (5) chest tightness, (6)
could not take a deep breath, (7) pain on deep respiration, (8) out of
breath easily, (9) breathing sounds wheezing or whistling. Other symptoms
are (1) eye irritation, (2) could not see as weH as usual, (3) eyes
sensitive to bright light, (4) ringing in ears (5) pain in ears, (6) sinus
pain, (7) nosebleed, (8) dry and painful nose, (9) runny nose, (10) fast
heartbeat at rest, (11) tired easily, (12) faintness or dizziness, (13)
felt spaced out or disoriented, (14) headache, (15) chills or fever, (16)
nausea, and (17) swollen glands.
An alternative to counting the number of different symptoms
experienced in the two days prior to the interview would be to consider the
number of symptom/days experienced. Both approaches were used to construct
empirical estimates; however, to save space, only those based on counts of
different symptoms are reported. Both approaches yield virtually identical
value estimates for symptom and air pollution reduction.
8
Cooking with a fuel other than natural gas reduces exposure because
gas stoves emit nitrogen dioxide.

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32
9
The equations also were estimated after defining the pollution
variables as the largest of the one hour maxima on the two days; similar
results were obtained.
10
Although there is a linear relationship between the latent dependent
variables and the private goods in the tobit model, the relationship
between the observed dependent variables and the private goods has the
usual properties of a production function. The expected number of
symptoms is decreasing and convex (nonstrictly) in the private goods.
11
Rosenzweig and Schultz also initially specify their production
functions in translog form and then test whether restrictions to CES and
Cobb-Douglas forms are justified. This type of analysis is not pursued
here as most of the covariates used are 0-1 dummy variables. Squaring
these variables does not alter their values. Interaction variables of
course, still could be computed.
12
Wilcox-Gok used variance components to control for family-specific
effects in pooled sibling data rather than for individual-specific effects
in pooled cross section-time series data.
13
The tobit coefficients and variances of the model are estimated by
maximizing the likelihood function using the method of Berndt, Hall, Hall,
and Hausman (1974). The score vectors are specified analytically and the
information matrix is approximated numerically using the summed outer
products of the score vectors. Starting values for the coefficients and
the standard deviations of the transitory error components were obtained
from two independent tobit regressions with no permanent error component.
In preliminary runs a starting value of unity was used for the standard
deviation of the permanent error component, but the starting value was

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33
adjusted to 1.5 after the initial estimate was consistently greater than
one.
14
The following discussion draws heavily on Hsiao (1986) and Maddala
(1987) .
15
Covariates in the reduced form regressions are: ASTHMA, BRONCH,
FLEMCO, SHRTWZ, HAYFEV, BURB, AGE, EXPWORK, years of education, number of
dependents, household income, and an occupation dummy variable measuring
whether respondent is a blue collar worker.
16
In the impaired subsample, inclusion of EXPWORK frequently caused
the bivariate tobit algorithm to fail to converge. This problem arose in
the specification presented in Table 2; consequently the EXPWORK variable
was excluded.
^The estimated two-day prices are: $2.34 for ACCEN, $1.00 for ACCAR,
$0.80 for NOTGASCK. The discount rate was assumed to be 5 percent. For
further details of the procedure used to estimate prices, see Dickie et al.
(1987(a)).
1 8
The Wald test was chosen because its test statistic can be computed
using only the unconstrained estimates. Since the likelihood and
constraint functions both are nonlinear, re-estimating the model with
the constraint imposed would be considerably more difficult than computing
the Wald test statistic. Gregory and Veall (1985) identified a problem
with Wald tests of nonlinear restrictions: changing the restriction into a
form that is algebraically equivalent under the null hypothesis will change
the p-value of the test. To check for this problem, the constraint was
tested in two forms. The first, reported in the text, is
^0 : ^1^2 ~ ^2^1 =	seconc* -'-s	~ S^/S? = 0. In all cases both
tests yielded nearly identical p-values.

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34
19
In other estimates of symptom production functions not reported
here, corresponding p-values also are large, almost always exceeding .25
and sometimes the .80-.90 range.
20
For comparison purposes, mean values also were estimated at
subsample means of all explanatory variables. Results differ little with
means computed over respondents. Evaluated at subsample means, willingness
to pay to eliminate one symptom for one day is $1.05 in the impaired
subsample and $0.70 in the normal subsample.

-------
0
1
2
3
4
5
6
8
9
10
11
12
13
14
15
16
17
e :
1 .--FREQUENCY DISTRIBUTIONS OF SYMPTOMS BY SUBSAMPLE
Number of Chest and
Throat Symptoms
Experienced in Past
	Two Days	
Impaired	Normal
351
408
CO
0^
41
64
18
48
15
37
9
26
4
16
6
8
2
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.348	0.453
Number of Other
Symptoms Experienced
In Past Two Days
Impaired	Normal
257
338
123
79
85
42
73
18
45
12
28
5
14
6
9
2
4
1
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1.668	0.692

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TABLE 2. --BIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES:
IMPAIRED SUBSAMPLE2

Chest and Throat
Symptoms
Other
Symptoms
CONSTANT
-3.085
-2.043

(-3.035)
(-2.125)
ASTHMA
0.8425
0.6724

(2.328)
(1.851)
BRONCH
3.774
2.936

(7.663)
(6.668)
SHRTWHZ
1.494
1.235

(3.683)
(3.428)
FLEMCO
1.458
0.2526

(4:038)
(0.8558)
HAYFEV
1.110
0.6613

(3.509)
(2.365)
BURB
-1.431
-0.7330

(-2.728)
(-1.539)
ACE
0.2986
2.042

(0.1596)
(1.177)
EXPWORK
— b
— b
ACCAR
-0.3485
-0.4395

(-0.8885)
(-1.364)
ACCEN
-1,9961
-0.6291

(-2.834)
(-1,829)
03
-0.1672
0.1252

(-0.5638)
(-.4475)
CO
1.279
-0.06285

(1.259)
(-0.06356)
N02
0.5475
0.6384

(0.7744)
(0.9282)

2.617
2.454
V
(HJO)
(20.81)
a,,
1.827

u
(21.17)

Chi-Square0
148.7

P-Value for


Wald Test
0.742

Number of


1 terati ons
21

aThe dependent variables are the numbers of symptoms reported m the "chest and throat"
category and in the "other" category. Asymptotic t-ratios are in parentheses. AGE is
measured in centuries, CO in parts per hundred thousand , and 03 and N02 in parts per ten
million. All remaining explanatory variables are dummies. Note the long term health
status dummies do not represent mutually exclusive categories.
^Omitted due to convergence problems.
°The chi-square test statistic is -21 nA, where \ is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
^The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.

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TABLE 3. --BIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES:
NORMAL SUBSAMPLEa
Chest and Throat	Other
Symptoms	Symptoms
CONSTANT
-5,
.789
-5.479

(-2.
.157)
(-2.790)
HAYFEV
0
L .
.316
1.461

(1:
614)
(1.871)
BURB
-1.
,388
-0.6248

-1.
,180)
(-0.8470
ACE
4.
143
7.075

(0,
.7873)
(2.091)
EXPWORK
0.
,8707
1.329

(1
.157)
(2.297)
ACCAR
-1.
,949
-0.6705

(-2.
,905)
-1.057)
NOTGASCK
-0.
,4613
-0.8565

(-0.
,6312)
(-1.594)
03
0,
.2757
0.3592

(0
.5867)
(0.9674)
CO
0,
.1788
-0.07200

(0,
.07729)
(-0.05241)
N02
1.
841
1.069

(1
.162)
(1.127)
0v
3.
,204
2.435
(10.
15)
(11.31)
G„
1
.828


(10.
,44)

Chi -Square'3
69.
81

P-Value for



Wald Test
0,
.610

Number of



1terati onsc
20


aThe dependent variables are the numbers of symptoms reported in the "chest and throat"
category and in the "other" category. Asymptotic t-ratios are in parentheses. AGE is
measured in centuries, CO in parts per hundred thousand , and 03 and N02 in parts per ten
million. All remaining explanatory variables are dummies.
^The chi-sguare test statistic is -21nX, where A is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
°The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.

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TABLE 4. --UNIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES3

Impaired
Normal

Subsample
Subsample
CONSTANT
-2.253
-6.085

(-1.263)
(-2.329)
ASTHMA
1.0333
(1.953)

BRONCH
4.649
(7.708)

SHRTWHZ
1.909
(3.242)

FLEMCO
1.769
(3.607)

HAYFEV
1.574
2.216

(3.137)
(2.378)
BURB
-1.830
-13623

(-2.927)
(-1.126)
ACE
1.200
6.351

(0.40jS4)
(1.165)
EXPWORK

1.725
(2.039)
ACCAR
-0.5900
-1.260

(-2.585)
(-2.425)
03
0.1629
0.5941

(0.4846)
(1.616)
CO
1.013
0.3722

(0.8041)
(0.2163)
U02
0.8930
1.726

(1.130)
(1.784)

3.684
3.790
(37.29)
(22.47)
CTli
2.582
2.516
(15.84)
(8.822)
Chi-Squarec
77.88
36.45
P-Value for


Parameter Restrictions
0.623
0.562
Number of


1 terati oris
8
5
aThe dependent variable is the total number of symptoms reported. Asymptotic t-ratios are in
parentheses. ACE is measured in centuries, CO in parts per hundred thousand, and 03 and N02
in parts per ten million. All remaining explanatory variables are dummies. Note the long
term health status dummies do not represent mutually exclusive categories.
^Omitted due to convergence problems.
°The chi-square test statistic is -21 nA, where X is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
^The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.

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TABLE 5. --MARGINAL WILLINGNESS TO PAY TO RELIEVE SYMPTOMS AND
AVOID AIR POLLUTION
Impaired Subsample
Symptoms	03	N02	CO
Mean
Median
Maximum
Minimum
Normal Subsample
Symptoms	03	N02	CO
Mean	$0.73	$0.31b	$0.91b
Median	$0.70
Maximum	$1.22
Minimum	$0.49
a_	...
Denotes coefficient not significantly different from zero at 10 percent
level using one tail test in estimated equations presented in Table 4.
b
Estimates of willingness to pay for reduced air pollution do not vary
across sample members. In the computational ratio, respondent specific
information appears both in the numerator and denominator and therefore
cancels out.
$1.12
$1.09
$1.90
$0.81

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