UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON D.C. 20460
OFFICE OF THE ADMINISTRATOR
SCIENCE ADVISORY BOARD
October 12, 2007
EPA-SAB-08-001
Honorable Stephen L. Johnson
Administrator
U.S. Environmental Protection Agency
1200 Pennsylvania Avenue, N.W.
Washington, D.C. 20460
Subject: SAB Advisory on EPA's Issues in Valuing Mortality Risk Reduction
Dear Administrator Johnson,
The EPA National Center for Environmental Economics (NCEE) requested the Science
Advisory Board's advice on how the Agency should use meta-analysis to combine estimates of
the value of reducing mortality risks (i.e., estimates of the Value of a Statistical Life (VSL). The
NCEE also asked the SAB for advice on how the Agency should incorporate information on
remaining life expectancy when valuing reductions in risk of death. To respond to this advisory
request, the SAB's Environmental Economics Advisory Committee (EEAC) was augmented
with SAB chartered members as well as members of the Advisory Council on Clean Air
Compliance Analysis. The SAB Panel reviewed two NCEE papers on these subjects: Report of
the EPA Workgroup on VSL Meta Analysis, and Willingness to Pay for Environmental Health
Risk Reductions When There are Varying Degrees of Life Expectancy: A White Paper.
In answer to the meta-analysis charge questions, the SAB does not believe that meta-
regression—a particular form of meta-analysis—is an appropriate way to combine VSL
estimates for use in policy analyses. The SAB does, however, agree that meta-regression is a
useful statistical technique for identifying various aspects of study design or population
characteristics that are associated with differences in VSL estimates. Once important sample
characteristics, model and estimation factors affecting the VSL have been identified, the Agency
must determine a set of criteria for what constitutes a set of acceptable empirical studies of the
VSL. The SAB urges the Agency to establish such criteria. The Agency must also determine
which studies are appropriate for estimating the VSL in a specific policy context, depending on
the nature of the risk addressed by a policy and the population affected. Once these criteria have
been determined, and an acceptable sample of VSL estimates from the literature has been
formed, appropriate statistical techniques can be used to combine these estimates. Two that have
been used to weight individual study estimates include the random effects and the empirical
Bayes estimator.
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In addition, the SAB believes that both stated preference and revealed preference studies
should be considered in valuing mortality risks and that weight should be given to each of them
in proportion to how well they each address the policy question at hand. Both approaches have
strengths and weaknesses in a particular context, and, as a result, we do not believe that the
Agency should rely exclusively on one or the other in all contexts. Furthermore, the SAB
believes that the Agency should make needed adjustments when using VSL estimates from the
literature and consider reasonable priors regarding the magnitude of the VSL when including or
excluding the results from previous studies.
Regarding the role of life expectancy in valuing mortality risks, the Committee notes that
economic theory, in general, places no restrictions on the relationship between the VSL and
remaining life expectancy: the VSL may increase, decrease or remain constant as life
expectancy decreases. The relationship between the VSL and life expectancy is therefore an
empirical matter. In practice, because life expectancy is difficult to observe, the Agency will
have to relate the VSL to factors related to life expectancy—namely age and health status.
Although the literature on the relationship between age and the VSL is growing, the Committee
does not believe that it is sufficiently robust to allow the Agency to use a VSL that varies with
age. The Committee also believes that the use of a constant Value of a Statistical Life Year
(VSLY), which assumes that the VSL is strictly proportional to remaining life expectancy, is
unwarranted. If there is insufficient information to indicate that the VSL declines with age, there
is not sufficient information to indicate that the VSL is strictly proportional to remaining life
expectancy. Thus, the SAB recommends that at present the Agency use an age-independent VSL
to value mortality risk reductions. However, we also urge the Agency to report the age
distribution of statistical lives saved and the average remaining life expectancies of persons in
each age group.
The SAB urges the Agency to fund more research on empirical estimates of the VSL.
Reductions in risk of death constitute the majority of benefits from air pollution and drinking
water regulations. Accurately estimating the value of these benefits is crucial to promoting
efficient environmental policy, both now and in the future.
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Finally, we remind the Agency, that there is a much larger normative element in the
selection of VSL for regulatory evaluation and analysis than arises for many of the other issues
with which the Science Advisory Board deals. For example, while there is no denying the reality
of income effects, it is a policy judgment, not a scientific question, whether the same VSL should
be employed in all regulatory decisions across a society or different values should be chosen
depending upon the preferences and income of the population affected by a specific regulation.
Thank you for the opportunity to provide advice on this important and timely topic. The
SAB looks forward to receiving your response to this advisory.
Sincerely,
/signed/ /signed/
Dr. M. Granger Morgan, Chair, Dr. Maureen Cropper, Chair
EPA Science Advisory Board Environmental Economics Advisory
Committee
in
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NOTICE
This report has been written as part of the activities of the EPA Science Advisory
Board, a public advisory committee providing extramural scientific information and
advice to the Administrator and other officials of the Environmental Protection Agency.
The SAB is structured to provide balanced, expert assessment of scientific matters related
to problems facing the Agency. This report has not been reviewed for approval by the
Agency and, hence, the contents of this report do not necessarily represent the views and
policies of the Environmental Protection Agency, nor of other agencies in the Executive
Branch of the federal government. Mention of trade names or commercial products does
not constitute a recommendation for use. Reports of the EPA SAB are posted at:
http://www.epa.gov/sab.
IV
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Roster
U.S. Environmental Protection Agency
Science Advisory Board
Advisory on
EPA's Issues in Valuing Mortality Risk Reduction
CHAIR
Dr. Maureen Cropper, Professor of Economics, University of Maryland, College Park, MD and
Consultant, World Bank, Washington, DC
MEMBERS of EEAC1
Dr. Anna Alberini, Associate Professor, Agricultural and Resource Economics, University of
Maryland, College Park, MD
Dr. Michael Greenstone, Associate Professor, Economics Department, Massachusetts Institute
of Technology, Cambridge, MA
Dr. W. Michael Hanemann, Chancellor Professor, Department of Agricultural and Resource
Economics, University of California, Berkeley, CA
Dr. Gloria Helfand, Associate Professor, School of Natural Resources and Environment,
University of Michigan, Ann Arbor, MI
Dr. Billy Pizer, Fellow, Quality of Environment Division, Resources for the Future,
Washington, DC
OTHER MEMBERS
Ms. Laurie Chestnut, Managing Economist, Stratus Consulting, Boulder, CO
Dr. James K. Hammitt, Director, Harvard Center for Risk Analysis and Professor, Economics
and Decision Sciences, Harvard University, Cambridge, MA
Dr. F. Reed Johnson, Senior Fellow, Research Triangle Institute, Research Triangle Park, NC
Dr. Kathy Segerson, Professor, Department of Economics, University of CT, Storrs, CT
Dr. V. Kerry Smith, Professor, Economics, Arizona State University, Tempe, AZ
DESIGNATED FEDERAL OFFICER
Dr. Holly Stallworth, Science Advisory Board Staff Office, Washington, DC
1 / Members during Fiscal Year 2006.
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Table of Contents
Introduction 1
Meta-analysis of Mortality Risk Valuation Estimates: Charge Questions and Responses 2
Life Expectancy and Mortality Risk Valuation: Charge Questions and Responses 10
Appendix to Life Expectancy Charge Questions 14
Survival Curves and Life Expectancy 14
Implications of the Life-Cycle Model for Age and the VSL 14
References 17
VI
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Introduction
Reductions in mortality risk constitute the largest quantifiable category of benefits for
many EPA rules and regulations. As such, mortality risk valuation estimates are an important
input to the Agency's benefit cost analysis. The EPA uses a value of statistical life (VSL) to
express the benefits of mortality risk reductions in monetary terms for use in cost-benefit
analyses of its rules and regulations. EPA has used the same central default value (adjusted for
inflation) in its primary analyses since 1999 when the Agency updated its Guidelines for
Preparing Economic Analyses (2000). Prior to the release of the Guidelines, EPA sought advice
from the Science Advisory Board on the appropriateness of this estimate and its derivation. In
2000, EPA also consulted with the SAB on the appropriateness of making adjustments to VSL
estimates to capture risk and population characteristics associated with fatal cancer risks (An SAB
Report on EPA 's White Paper Valuing the Benefits of Fatal Cancer Risk Reductions, (EP A-
SAB-EEAC-00-013, July 27, 2000.). Again in 2004, the SAB's Environmental Economics
Advisory Committee (EEAC) held a consultation to respond to the National Center for
Environmental Economies' (NCEE) charge questions on meta-analysis and valuing mortality
risk reductions. In 2006, the EEAC, augmented with economists from the chartered SAB and the
Advisory Council on Clean Air Compliance Analysis, met to discuss specific charge questions
related to two NCEE papers: Report of the EPA Workgroup on VSL Meta Analysis, and
Willingness to Pay for Environmental Health Risk Reductions When There are Varying Degrees
of Life Expectancy: A White Paper. Both of these papers may be found at
http://yosemite.epa. gov/EE/epa/eerm.nsf/vwRepNumLookup/.
NCEE's charge questions and the SAB Panel's responses are provided below.
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Meta-analysis of Mortality Risk Valuation Estimates: Charge Questions and Responses
1. In light of the workgroup's findings, what approach or approaches are the most
scientifically appropriate to derive summary estimates of mortality risk valuation for use
in environmental policy analysis? Should meta-regression techniques be applied to
selected estimates or are other methods (e.g., fitting distributions) more appropriate?
Please specify which methods, aside from or in addition to meta-regression techniques
the Agency should explore.
We believe that, once EPA has assembled a set of studies that are applicable to the
population affected by a regulation and that meet appropriate criteria for a well-executed study, it
is appropriate to combine these using meta-analysis. For example, the VSL estimates could be
combined using a random effects estimator, in which individual VSL estimates are weighted in
inverse proportion to their variance. We do not, however, believe that meta-regression—a
particular form of meta-analysis—is an appropriate way to combine VSL estimates for use in
policy analysis, or to perform benefits transfer, for reasons described below. Meta-regression is,
however, a useful technique for understanding what factors may explain variation in VSL
estimates across studies.
A meta-regression, in which the characteristics of study participants (e.g., percent female,
percent over 65) and study design (e.g., does an hedonic wage study control for a worker's
industry) are used as covariates is useful in understanding what factors affect empirical estimates
of the VSL. It can be thought of as an empirical literature review which may highlight factors
affecting the VSL that would not otherwise be detected. By highlighting correlates of the VSL,
meta-regression may suggest features of study design for which criteria should be established.
For example, it might be determined that an acceptable hedonic wage study must control for the
worker's industry at the 2-digit level because this has a significant effect on the VSL estimate
obtained in an hedonic wage study.
It is, however, another matter to treat a meta-regression as a reduced-form model that can
be used for obtaining the VSL for a given sub-population or the VSL conditional on an
appropriate study design. To illustrate, a meta-regression may control for the functional form of
the dependent variable in an hedonic wage regression by setting a dummy variable equal to 1 if
the dependent variable is the log of wage rather than the wage. If researchers believe that the
appropriate form of the equation is to use the log of the wage, this should be one criterion for an
acceptable study and only studies satisfying the criterion should be combined in the meta-
analysis. Setting the dummy equal to 1 in the meta-regression is not equivalent to altering the
functional form of the underlying studies.
Similar problems exist when population characteristics in the meta-regression are used
for benefits transfer. Suppose that one of the covariates on the right-hand side (RHS) of a meta-
regression is the proportion of the study sample over 65. It is one thing for estimates of the VSL
across studies to show that this coefficient is negative and statistically significant, suggesting that
the VSL is lower for persons over 65, and another to set this variable equal to 1 to compute the
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VSL for persons over the age of 65. The latter treats the meta-regression as a reduced-form
model that can be used for benefits transfer. If the meta-regression suggests that age is
important, EPA should use the results of studies that control for age, and other factors that are
correlated with age, using individual data. These factors (e.g., wealth and income) are controlled
for imperfectly in a meta-regression in which the population characteristics are summarized by
an aggregate number for each study. The results of various studies may be combined in a
structural model, but this is not what is happening in a meta-regression.
How should studies be combined in lieu of using meta-regression? A weighting scheme
needs to be selected for calculating a central estimate from the selected study results. One
possibility is to combine the estimates in inverse proportion to their variance, i.e., to use a
random effects estimator. Another approach would be to use an empirical Bayes estimator
(Kochi, Hubbell and Kramer 2006) which weights individual study estimates using measures of
between as well as within study variability. Other approaches may also be appropriate
depending on the nature of the data and the policy application context. The analyst should
explain the rationale for the selected approach.
When studies are combined to inform a particular regulation, it is imperative that (a) the
studies pertain to the population affected by the regulation; and (b) that the studies satisfy
appropriate criteria regarding their design. We urge EPA to establish such criteria. For example,
EPA may wish to specify criteria to minimize the possibility that fatal job risk in an hedonic
wage study is correlated with the error term (i.e., that fatal risk is endogenous), which would
cause estimates of the VSL to be biased.2 In combining studies we do not recommend the use of
quality weights, other than the 0-1 weights that are implicit in deciding which studies are of
sufficiently high quality to be included in the meta-analysis. Although, in principle, there is no
reason why weights should not vary between 0 and 1, in practice determining these weights is
likely to be difficult. In the interests of transparency, we urge that a set of criteria for acceptable
studies be established and then applied to the literature.
Formulating a list of criteria for an acceptable study and applying them to the literature
will necessarily involve expert judgment. Expert elicitation is also useful in determining whether
it is appropriate to transfer a VSL estimate in the literature to a specific policy context. The SAB
Panel does not, however, recommend expert elicitation for combining estimates from the
literature that are amenable to quantitative assessment with meta-analysis techniques. EPA
should not directly elicit appropriate VSL values from experts, asking them, for example, to
specify a range of acceptable VSL values and/or a mean value based on their knowledge of the
literature, if there are published estimates of sufficient number and quality to support a meta-
analysis. When adequate empirical estimates are available, expert elicitation would require that
the expert mentally combine the results of dozens of studies, thus losing transparency in the
process.
2/ Fatal risk may be correlated with the error term in an hedonic wage study for several reasons:
unobserved worker characteristics may be correlated with fatal job risk if more able workers choose safer
jobs; or objective risk may be mismeasured (Black et al. 2003).
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2. Using the approach identified above, what measures/estimates should be combined? VSL
estimates? The coefficient on fatal risk? Other? How should the Agency select the
measures to be combined? Should a single, preferred estimate be selected from each
study or should all estimates be included?
We believe that a meta-analysis (e.g., a random effects estimator) should be used to pool
VSL estimates from acceptable studies that pertain to the population affected by a regulation.
The SAB Panel recommends that normally only one estimate should be selected from a study
that reports several models all estimated from the same dataset. Which estimate should be
selected when a study reports several estimates of the VSL depends on the set of criteria that the
Agency establishes to determine what is an acceptable study. For example, if different models
use different sets of covariates, the Agency should select the model with the preferred set of
covariates.
3. Should original studies be required to use a common empirical specification (functional
form and choice of covariates) in order to be included in a meta-analysis? What data are
required of the original studies to be included?
For compensating wage studies, the SAB Panel recommends that original studies report
the results of a common specification of the compensating wage regression, in addition to the
author(s)' own specifications. The compensating wage study report or article should also report
the estimate of the VSL calculated by the authors and its standard error—the latter being
essential for creating the weights to be deployed in the meta-analysis—and ample details on how
exactly both were calculated. Listed below is additional information that should be provided
about compensating wage and stated preference studies that are included in a meta-analysis. We
emphasize that all studies included in a meta-analysis should satisfy criteria specified by the
Agency as to what constitutes an acceptable study. These criteria are not limited to the
information listed below.
We recommend that the compensating wage studies ultimately to be included in a meta-
analysis:
• provide information on the source of data on risk to include both information on the death
statistics as well as how that data is converted to a risk rate, worker pay (including
whether the workers are paid an hourly rate) and worker characteristics;
• include codes for creating the sample used for the compensating wage regressions and for
transforming variables;
• report detailed statistics on risk, such as mean, mode, minimum/maximum rates and
standard deviation and average pay for the sample;
• explain whether the author(s) did or did not include non-fatal risks in the compensating
wage regression, in addition to the fatal risks variable;
• explain whether the sample contains only union workers, or if union membership was
controlled for in the regression;
• explain whether high-risk workers (e.g., police officers, firefighters, etc.) are included or
excluded from the sample;
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• explain clearly whether the researcher(s) included a quadratic term in risk, and
interactions between risk and other variables, in the regression; and
• explain clearly all covariates included in the regressions. For example, if a set of dummy
variables are included for the industry and occupation of the worker, details should be
provided on each category included in the model.
For stated preference studies, we recommend that the answers to the following questions be
included:
• Was the study a (i) contingent valuation survey, (ii) conjoint choice experiments, or (iii)
another type of hypothetical valuation exercise?
• What was the mode of administration of the survey?
• What was the sampling frame? Was a specific population targeted, or was the sample
supposed to mirror the general population?
• What was the age of the respondents, split by gender, income, education, health status (if
available)?
• What was the type of risk reduction respondents were to value in the SP study? (Was it a
reduction in the risk of dying for all causes? Cardiovascular/respiratory causes? Road-
traffic accidents?)
• Was the risk reduction immediate and incurred over the next year, or was it delayed into
the future?
• Were respondents asked to consider a private risk reduction or one delivered by a public
program? What was the payment vehicle (e.g., out-of-pocket costs of medical treatment,
taxes, increases in the prices of products or the cost of living)?
• Was the payment one-time or an annual payment to be repeated each year for a number
of years? How many years?
• Did each respondent have to value more than one risk reduction in the survey?
• Was the size of the (annual) risk reduction varied across respondents in the study? If so,
(i) report the min, max and average risk reductions used in the study, and (ii) did WTP
pass the scope test?
4. Given the various approaches used in the literature, ~what is the most scientifically
appropriate measure to derive when combining estimates from multiple studies? A single
central point estimate, a single distribution, or a range of estimates in economic
analyses? How can such a measure best reflect the uncertainty and variability in
mortality risk valuation estimates?
Meta-analysis should be used to provide a description of the probability distribution of
the estimates. The resulting probability distribution can be used for uncertainty analysis, and the
expected value and other relevant point estimates (e.g., median, 5th and 95th percentiles) can be
drawn from it.
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5. How should stated preference studies and revealed preference studies be considered
together in a scientifically appropriate method to derive summary estimates of mortality
risk valuation?
The SAB Panel believes that both stated preference (SP) and revealed preference (RP)
studies should be considered in valuing mortality risks and that weight should be given to each of
them in proportion to how well they each address the policy question at hand. For example, the
analyst may have greater confidence in the mean estimates from the wage-risk studies, but they
are limited to a working age population and an on-the-job risk context. For some EPA policy
questions, SP studies may be a better match to the policy question, such as for an elderly
population and an illness-related risk context, although the analyst may have less confidence in
the specific mean results from the SP studies. This implies some weighting based on analyst
judgment is necessary. We elaborate below on the fact that the two types of studies may, in
practice, measure different concepts. We also discuss the strengths and weaknesses of each
approach.
Revealed preference (RP) studies, such as compensating wage studies, measure the rate
of substitution between risk and wealth. Stated preference (SP) studies measure ex ante
willingness to pay for a discrete risk change and can involve changes in other aspects of a
respondent's health conditions, such as a period of morbidity or a latency period for a fatal
disease. This additional information presented as part of the stated preference questions may
influence the measures of ex ante willingness to pay. The mechanism offered for reducing the
risk may be a plan or a policy that may also influences the responses and thus the estimated
willingness to pay. All of these factors affect comparability among VSL estimates from SP and
wage hedonic studies.
Both RP and SP studies rely on several important maintained assumptions. Some
economists prefer the SP framework because it is possible to describe the circumstances giving
rise to the risk and the health outcomes involved that more closely correspond to the actual
expected benefits of environmental regulations. However, other economists are skeptical of
whether respondents treat the choice situations presented as "real" in the sense that the choices
made correspond to what actually would happen if the same individual confronted an actual
choice. In addition, some SP studies have demonstrated respondents' difficulty in providing
consistent answers to valuation questions, especially those involving small probabilities of
serious outcomes. RP studies on the other hand rest on the maintained hypothesis that
individuals correctly perceive risks as the researcher measures them—for example, that parents
correctly perceive the reduction in risk of death from a child wearing a helmet when riding a
bicycle. The assumption that people have good quantitative estimates of small risks has little
empirical support. It is also the case that compensating wage studies must infer the VSL by
controlling for many other factors that affect wages, such as worker ability and risk of nonfatal
injury, which may be measured inaccurately but also may be correlated with risk of fatal injury
on the job. Because different economists weight SP and RP advantages and disadvantages
differently, there is no professional consensus about these methodological alternatives. Thus we
do not recommend that the Agency rely exclusively on either SP or RP studies, but rather give
some consideration to results from both types of studies.
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6. How should the Agency use studies based on specific sub-samples (e.g., elderly) in
developing summary estimates of mortality valuation estimates for environmental policy
analysis?
As the SAB Panel noted in answering Life Expectancy Charge Questions 1 and 2, EPA
should aim to distinguish the VSL according to age and, possibly, health status, the empirical
correlates of life expectancy. This implies that separate meta-analyses would be performed for
studies of different populations, for example, persons 30-65 and persons 65 and over if sufficient
numbers of such studies are available. However, it is an empirical question as to what
population subgroups may have significantly different valuations for mortality risk reductions.
Identifying such subgroups should be based on empirical evidence, not assumption. Meta-
analyses may be helpful in identifying population characteristics that are important when
determining whether a study's results are applicable for a particular policy analysis.
7. Most studies that combine estimates adjust the data from the original studies to some
extent. For example, some studies adjust for after-tax wages, whereas others do not. Is
there a set of such modifications that the SAB-EEAC believes to be critical when deriving
summary estimates from the literature? Are there some data modifications that are
generally incompatible with a sound approach to synthesizing existing estimates? What
are the implications for interpreting results?
In synthesizing estimates from multiple studies, it is important to adjust as well as
possible for differences among the studies, especially for differences in the monetary units used
in the studies. Such adjustments can be made to studies before including their estimates in a
meta-analysis.
One adjustment that can and should be made is to adjust for monetary inflation between
studies by converting all nominal monetary values into real values. Because there is uncertainty
about the best estimate of inflation over a period (reflected, for example, in different measures
such as the various consumer price indices and the GDP deflator), the best adjustment is not
clear. However, if one relies only on relatively recent studies (that are likely to be most relevant
to the evaluation of current policy), differences between the alternative indices are likely to be
modest and contribute little to uncertainty about the appropriate valuation compared with other
factors. Similarly, if valuation estimates using other currencies are included, it is necessary to
adjust for the purchasing power of the currencies (again, uncertainty about the best conversion
rate is not likely to be a major concern). In the case of wages, differences in fringe benefit
provisions across countries may be pronounced and must also be considered.
Other adjustments that are in principle desirable are more difficult to make, and so the
SAB Panel recognizes our current empirical abilities may not permit these adjustments. One is
to adjust for differences in real income and wealth between study populations. Since the value of
reducing mortality risk increases with income and wealth, differences in these factors are
expected to yield differences in estimated valuation. However, the appropriate magnitude of
adjustment is not clear, because of uncertainty about the value(s) of the income elasticity and
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very little empirical evidence concerning the relationship between wealth and mortality
valuation.
A second potential adjustment is to convert all estimates into marginal changes in
consumer income (net of taxes and benefits). In hedonic-wage studies, workers' choices are in
principle driven by comparing the total incremental compensation with the total incremental risk
between jobs, where total compensation includes wages, health insurance, retirement income,
compensation conditional on injury, and other benefits, all evaluated post tax. In stated-
preference studies, respondents are likely to view payments as coming from post-tax income (in
principle, respondents may be asked about payments that would be made using either pre- or
post-tax income; this detail is usually not specified but may be inferred from question wording).
Adjustment for these factors is difficult because of variation in marginal tax rates and benefit
schedules across populations, and so the SAB Panel does not view it as critical, but suggests that
research attention be directed toward determining whether such adjustments can be made.
8. What reporting and other protocols should the researchers conducting the combination
study follow? How should the analysis handle zero or negative mortality risk valuation
estimates from studies that otherwise meet its selection criteria for inclusion?
The purpose of the combination study should be clearly defined. For what population is
the study attempting to combine estimates? There should also be an explicit description of the
rules for the inclusion and exclusion of items in the combination study, and of the search rule by
which the candidate studies were identified in the first place.
There should be systematic coding of important features of the items included in the
combination study, for example the metric in which wages are expressed, the metric for risk
itself, the other variables included in models involving VSL, and the populations for which VSL
was evaluated.
In general, the preferred approach for selecting studies is based on study design criteria,
not study results, but there may be limited circumstances when it is appropriate to exclude
studies based on results. One of these is a finding of statistically significant negative values for
mortality risk reduction (implying the population would prefer a shorter lifespan to a longer
one—an implausible result for anything but extreme circumstances). Obtaining statistically
insignificant results, implying zero value for an incremental risk reduction, is on the other hand,
a theoretically plausible result and is not sufficient reason for exclusion of a study. Implausibly
high valuations may raise concerns about study design problems that may not have been
identified, but it is very difficult to determine a criterion for exclusion based on "high" results. A
preferable approach would be to include an analysis of the effects of outliers on the estimates of
mean values and some eventual judgment about how much weight may be appropriate to give
the outliers.
9. What future research or additional data would offer the most improvement in the
Agency's ability to derive summary estimates of mortality risk valuation for
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environmental policy analyses over the short run? What longer-term research is most
needed for improved summary mortality risk valuation estimates?
• Fund more studies that will examine how the VSL varies with age and health status,
the empirical correlates of life expectancy.
• Fund more studies that will shed light on the relationship between wealth and
mortality valuation (income elasticity of VSL).
• Reanalyze the Pope et al. data to determine whether the impact of air pollution on
mortality varies with age, rather than using a constant proportional hazard model).
• Attempt to improve hedonic wage estimates of the value of mortality risk reductions.
Existing estimates, as pointed out by Dan Black and co-authors, suffer from omitted
variable bias problems and problems of measurement error (in measuring risk of
death), which cause estimates of the VSL to be biased.
• Fund studies to assess the advantages and disadvantages of combining RP and SP
estimates of the VSL, for example, using structural approach.
• Fund studies to clarify the relationship between: (a) private willingness to pay to
reduce own mortality risk (e.g., a private good), (b) private willingness to pay for
programs that reduce mortality risk in the community (e.g., a public good) that may
incorporate altruistic preferences, and (c) social preferences over programs that
reduce mortality risk to people with different characteristics or risks from different
sources. Some studies of each of these concepts have been published, but the
literature is insufficient to identify possible systematic differences among results and
to judge their relevance for EPA decisions.
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Life Expectancy and Mortality Risk Valuation: Charge Questions3 and Responses
1. What is the most appropriate methodology to use when valuing changes in mortality risk
for persons with different remaining life expectancies? Is it appropriate to use a
standard VSL to value reductions in mortality risk when information on remaining life
expectancy is not available?
2. It is anticipated that EPA will need to issue rules affecting persons who differ in their
remaining life expectancies in a relatively short time-frame. What does existing research
imply about approaches to valuing mortality risk when people have life expectancies of
varying lengths? How applicable and relevant is the existing literature and how does the
existing theoretical and empirical literature inform these issues?
According to standard welfare economics the value of a reduction in mortality risk (e.g.,
in the probability of dying over a stated period) is what a person is willing to pay for it. This
amount may be affected by a person's remaining life expectancy, but theory (e.g., the lifecycle
consumption model with uncertain lifetime) has little to say about the relationship between
willingness to pay (WTP) and remaining life expectancy. Under specific assumptions, the
lifecycle model predicts WTP for mortality risk reduction to be first increasing with age and then
decreasing with age (an inverted U shape over the adult lifespan). Only in very special cases can
it be said that WTP should be an increasing function of remaining life expectancy.4 However,
there are offsetting influences and it is not possible to predict based on theoretical analysis alone
whether WTP is increasing, decreasing, or unchanged over a person's lifetime.
The relationship between WTP for mortality risk changes and remaining life expectancy
is, therefore, an empirical matter. Unfortunately, this relationship is difficult to measure since
remaining life expectancy is not observable while an individual is still alive. Individuals could
be asked in a stated preference study what they would pay to reduce their probability of dying,
assuming different life expectancies. However, this is a difficult question. In revealed and stated
preference studies all that can be observed ex ante are correlates of life expectancy: viz., age and
health status. So, one could try to measure how WTP varies with age and health status.
This suggests that EPA may, in principle, want to allow WTP to vary with age and health
status. It is, however, the SAB Panel's judgment that the empirical literature is not advanced
enough at present to provide clear guidance as to how age and health status affect WTP for
changes in mortality risk.
Krupnick (2007) and Aldy and Viscusi (2007) provide recent summaries of the empirical
literature on age and the VSL. Aldy and Viscusi (2007) focus on revealed preference studies
while Krupnick (2007) summarizes the stated preference literature. Aldy and Viscusi (2007)
3/ In some cases, the charge questions were slightly revised to better reflect the Agency's intent, as
discussed with the National Center for Environmental Economics.
/ The Appendix to this report discusses the implications of the life-cycle model with uncertain lifetime for the
value of mortality risk reductions, explaining that, in general, theory places no restriction on the relationship
between WTP and age or remaining life expectancy.
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review compensating wage studies by Smith et al. (2004), Kniesner et al. (2006) and Aldy and
Viscusi (2006).5 Smith et al. (2004) find that the VSL is higher for workers aged 61-65 than for
younger workers. Kniesner et al. find a VSL declines slightly after age 50 and then reaches a
plateau, whereas Aldy and Viscusi (2006) find a significantly lower VSL for workers 55-62 than
for younger workers. Krupnick (2007) reviews 35 studies, 20 of which find some evidence of
the VSL declining with age and 15 of which do not. He concludes that, "Thus, considering the
weight of the evidence, the implication is that for countries that apply a single VSL to adults of
all ages, there is insufficient information and consensus to make a reasoned decision to switch to
using either different VSLs for different ages (in a private good context) or a VSLY, which
imposes a linear (discounted) relationship between life-years remaining and the VSL." The SAB
Panel agrees with this statement.
We suggest that EPA should, at present, use an age-independent VSL to value mortality
risk reductions according to the conventional paradigm. However, we also urge the Agency to
report the age distribution of statistical lives saved and the average remaining life expectancies of
persons in each age group.
3. Are there other areas of the literature that should be examined and how would they
inform this issue in the short tern (i.e., less than 6 months)?
The SAB Panel agrees that the White Paper by Dockins, Maguire, and Simon covered the
appropriate literature.
4. What type of long-term research can inform these issues?
The SAB Panel agrees that willingness to pay for risk reduction is likely to be affected by
remaining life expectancy, which is related to both age and baseline health status. The existing
evidence on these relationships is weak and occasionally contradictory. The SAB Panel
recommends that additional research be funded to improve these estimates.
5. What paradigms should be considered in valuing changes in mortality risk for person with
different life expectancies? How will these paradigms inform us in the short term?
One paradigm that is commonly used to allow remaining life expectancy to affect the
value of a reduction in mortality risk is the Value of a Statistical Life Year (VSLY). As applied in
practice, the VSLY assumes that the value of mortality risk reductions is proportional to
remaining life expectancy (or discounted remaining life expectancy) and uses this assumption to
calculate a value per life year saved. More specifically, the VSLY is derived by dividing the
VSL by the discounted expected number of life years remaining for the average individual
studied. This approach assumes that the VSL is the sum of the present value of each life year
(the VSLY) weighted by the probability that an individual survives to that year, which is
5 Although many compensating wage studies interact worker age with fatality risk, they do not measure
risk of death by age. Aldy and Viscusi (2007) note that these early studies may therefore yield biased
estimates of how the VSL changes with age.
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equivalent to assuming that the value of each remaining life year is constant.6 The resulting
VSLY is then applied to the expected number of discounted life years saved by the regulation
(i.e., to the predicted increase in discounted life expectancy).
This procedure is difficult to justify on either theoretical or empirical grounds, if the
appropriate valuation concept is what a person would pay to reduce his own risk of dying. There
is no empirical evidence to suggest that the VSLY is constant, or that the VSL declines in
proportion to remaining life expectancy, which the constant VSLY implies. (See answer to
charge question 1.) To apply the VSLY correctly would require first estimating how the VSLY
varies with age. If this can be done, it would be simpler to use an age-adjusted VSL than using
an age-adjusted VSL to calculate and age-adjusted VSLY.
6. More generally, based on the economics literature, under what conditions is it most
important to provide information on life expectancy and baseline risks as part of an
economic analysis of environmental policy? If the information cannot be incorporated
directly into monetized benefits estimates, how might it best be provided as a
supplemental analysis?
In general, the measure of benefits based on WTP should reflect the WTP of the
population that is affected by the change. The central VSL EPA has used in their most recent
RIAs (PM and ozone NAAQS) is a midpoint between $1 million and $10 million. The former is
the lower interquartile estimate from Mrozek and Taylor (2002)'s meta-analysis and the latter is
the upper interquartile estimate from Viscusi and Aldy (2003)'s meta-analysis. The Agency
notes that the midpoint ($5.5 million in 1999 dollars and 1990 income levels) is very similar to
the mean estimate from the Kochi et al. (2006) meta-analysis, which also included stated
preference studies. The wage studies obviously reflect a population of working individuals,
which implies at least some minimal health status (i.e., healthy enough to work) and a specific
age distribution (i.e., working age adults) with an associated average life expectancy (estimated
to be 35 years). If the population most affected by an EPA regulation or policy change differs
from the population represented in these studies, then the WTP estimates generated by these
studies may be a biased estimated of the true WTP of the affected population. Whenever this is
the case, it will be important to provide information on the life expectancy and baseline risk7 of
the affected population as part of an economic analysis of the policy.
Unfortunately, the current economics literature does not provide convincing evidence
regarding the direction of the bias that would exist if the baseline risk and life expectancy of the
affected population differ from those of the population included in the WTP studies, i.e., there is
mixed evidence on whether increases in baseline risk or reductions in life expectancy increase or
6
Formally, the approach assumes that the VSL at age j is, VSLj = ^qjt(l + <5y 'VSLY, where qjt is
t=j
the probability that an individual at age j survives to age t and 8 is the discount rate. VSLY can be
T
factored out of this expression, and ^<77 • t(l + 5) '~' is discounted remaining life expectancy.
1
Strictly speaking, the term baseline risk refers to the survival curves of the members of the population
affected by the regulation.
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decrease WTP estimates (see discussion of other charge questions). Nonetheless, it is important
to include these characteristics of the affected population for two reasons: (1) to highlight the
potential for bias, even if it is not possible to predict its direction, and (2) to highlight the fact
that the policy is likely to affect certain sub-populations disproportionately. While this latter
information may not be formally incorporated into the benefit-cost analysis (e.g., by providing
WTP estimates that are specific to affected sub-populations), it would provide the basis for an
equity assessment, which in many cases is required by statute, executive order, or agency policy.
Information about disproportionate impacts can be important input into policy decisions.
The information about baseline risk and life expectancy is most useful if provided in the
form of a distribution (rather than simply an average) across the affected population. This is
particularly true when the distribution is bi-modal. A bi-modal distribution would exist, for
example, in cases where the very young and the very old are susceptible to pollution effects.
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Appendix to Life Expectancy Charge Questions
This Appendix consists of two parts. The first describes the concept of a survival curve
and its relationship to life expectancy. The second presents the life-cycle consumption saving
model with uncertain lifetime, which forms the theoretical basis for examining the relationship
between the Value of a Statistical Life, age and remaining life expectancy.
Survival Curves and Life Expectancy
The effects of an environmental intervention on mortality risk can be summarized using
survival curves. Survival curves can be constructed for an individual or a population. An
individual survival curve plots the probability that an individual is still alive as a function of her
age (or calendar date). A population survival curve plots the fraction of people who are still
alive as a function of date. A survival curve can be constructed beginning at any age or date and
slopes downward (or is constant) everywhere. A steeper downward slope corresponds to greater
mortality risk. The area under an individual's survival curve equals his remaining life
expectancy.
Any pattern of change in mortality risk over time can be characterized as a shift in the
survival curve. For example, a one year reduction in mortality risk (e.g., from reducing exposure
to an acutely lethal pollutant such as carbon monoxide) flattens the survival curve for that year
and hence increases its height for later time periods. A risk reduction having only delayed effects
(e.g., reducing exposure to a pollutant that causes cancer to develop after a latency period) has no
effect on the curve for the time between the change in exposure and the end of the latency period
but flattens the curve and increases its height for subsequent periods. Any change in the survival
curve produces a unique expected number of life years saved or lost (the change in the area
under the curve).
What is typically valued in empirical studies is a change in the probability of dying over
the coming year. As explained above, a reduction in the probability of dying over the coming
year raises the individual's survival curve for all future years and thereby increases his life
expectancy. The next section discusses how a rational, expected-utility maximizing individual
would value this change in the context of the life-cycle consumption saving model.
Implications of the Life-Cycle Model for Age and the VSL
This section uses the life-cycle model with uncertain lifetime to derive WTP for a change
in the conditional probability of dying at any age (Cropper and Sussman, 1990; Cropper and
Freeman, 1991) and to examine how this might vary with age and remaining life expectancy.
The model assumes that at agey the individual chooses his future consumption stream to
maximize expected lifetime utility,
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where Vj is the present value of expected utility of lifetime consumption, Ut(Ct} is utility of
consumption at age t, q} t is the probability that the individual survives to age ^, given that he is
alive at agey, and 5 is the subjective rate of time preference. We assume that (1) is maximized
subject to a budget constraint that allows the individual to invest in annuities and to borrow via
life-insured loans (Yaari, 1965). This is equivalent to assuming that the present value of
expected consumption equals the present value of expected earnings plus initial wealth,
y]<7 .t (\ + r)J^Ct =^]q tQ + t")^'yt +W., (2)
t=i t=j
where r is the riskless rate of interest, yt is income at time t and W'j is initial wealth.
Now consider a program that alters Dk, the conditional probability of dying at age k,
given that the individual survives to that age. Since qiit = (l-Dj)(l-Dj+i). . . (l-Dt-i), any
program that alters Dk will necessarily alter the probability of surviving to all future ages. For
small changes in Dk, willingness to pay may be written as the product of the rate at which the
individual is willing to trade wealth Wj for a change in Dk, which we term VSLj^, times the size
of the change in Dk,
dV /dD,
WTP , = i -dD, = VSL ,dD, . (3)
/ K TT 7- I TTT7" K 1 K K \ s
dV]ldW]
Applying the Envelope Theorem to the Lagrangian function formed by (1) and (2), the
rate at which the individual substitutes current wealth for Dk may be written (Cropper and
Sussman, 1990) as:
VSLj,k= -L- ix,[c + *)'-'tf,(W +V + ry-'(yt -C,)]. (4)
Equation (4) says that the value of a change in the probability of dying at age k equals the loss in
expected utility from age k+1 onward, converted to dollars by dividing by the marginal utility of
income (/I/). Added to this is the effect of a change in Dk on the budget constraint. Cropper and
Sussman (1990) show that, by substituting first-order conditions for utility maximization into (4)
and rearranging terms, the VSL at agey for a risk reduction at agey equals
Ct]. (5)
If the individual does not have access to fair annuities, but can save at the riskless rate r (i.e., he
can never be a net borrower), then the expression in (5) holds without the last two terms inside
the brackets.
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It is VSLjj that is estimated in compensating wage studies. Most stated preference studies
measure (3) (withy=&). The question is how (5) changes withy. If Ut(C) = U(C) for all t, and r
= d, then Ct is constant for all t. In the case in which the individual can save at rate r (but never
be a net borrower), the term in brackets is constant and VSLjj
becomes
VSLjj = -±- 2X( 0 + 0' " \U(C) I V" (C)] . (6)
1 U] t=i+\
In this special case, if (1-Dj)'1 is close to 1, VSLjj is likely to decline with age, 7. Since
represents discounted remaining life expectancy, VSLjj is approximately proportional to
discounted remaining life expectancy, which would justify the use of a constant VSLY.
Equation (6) is, however, a very special case.
In general, as equation (5) demonstrates, one cannot make any statement regarding how
VSLjj varies with age/ This depends entirely on the pattern of consumption and utility of
consumption over the lifecycle.
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References
Aldy, Joseph E. and W. Kip Viscusi (2007a). "Age Differences in the Value of a Statistical Life:
Revealed Preference Estimates," Review of Environmental Economics and Policy 1(2):
forthcoming.
Aldy, Joseph E. and W. Kip Viscusi (2006). "Adjusting the Value of a Statistical Life for Age
and Cohort Effects," Resources for the Future Discussion Paper 06-19. [Review of Economics
and Statistics, forthcoming.]
Black, Dan et al. (2003). How Robust are Hedonic Wage Estimates of the Price of Risk? Final
Report to the USEPA, June 2003.
Cropper, Maureen L. and A. Myrick Freeman (1991). "Valuing Environmental Health Effects,"
in John Braden and Charles Kolstad (eds.) Measuring the Demand for Environmental
Commodities. Amsterdam: North-Holland.
Cropper, Maureen L. and Frances G. Sussman (1990). "Valuing Future Risks to Life," Journal
of Environmental Economics and Management 19:160-174.
Kniesner, Thomas J., W. Kip Viscusi and James P. Ziliak (2006). "Life-cycle Consumption and
the Age-Adjusted Value of a Statistical Life," Contributions to Economic Analysis and Policy
5(1). B.E. Press.
Kochi Ikuho, Bryan Hubbell and Randall Kramer (2006). "An Empirical Bayes Approach to
Combining and Comparing Estimates of the Value of a Statistical Life for Environmental Policy
Analysis," Environmental & Resource Economics 34:385-406.
Krupnick, Alan (2007). "Mortality Risk Valuation and Age: Stated Preference Evidence,"
Review of Environmental Economics and Policy 1(2): forthcoming.
Mrozek, J.R. and L.O. Taylor (2002). "What Determines the Value of Life? A Meta-Analysis,"
Journal of Policy Analysis and Management 21(2):253-270.
Smith, V. Kerry, Mary F. Evans, Hyun Kim and Donald H. Taylor (2004). "Do the 'Near
Elderly' Value Mortality Risks Differently?" Review of Economics and Statistics 86(1): 423-429.
U.S. EPA (2006). Regulatory Impact Analysis: 2006 National Ambient Air Quality Standards for
Particle Pollution. U.S. Environmental Protection Agency, Office of Air Quality Planning and
Standards, October 6. Available: http://www.epa.gov/ttn/ecas/ria.html.
Viscusi, W.K. and J.E. Aldy (2003). "The Value of Statistical Life: A Critical Review of Market
Estimates Throughout the World," Journal of Risk and Uncertainty 27(l):5-76.
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