SAB Review Draft
Valuing Mortality Risk Reductions
for Environmental Policy:
A White Paper
U.S. Environmental Protection Agency,
National Center for Environmental Economics
DRAFT
December 10, 2010
For consultation with the Science Advisory Board-Environmental Economics Advisory Committee
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1 Introduction 3
1.1 Key topics 3
1.2 Roadmap 5
2 Background 7
2.1 The valuation challenge 7
2.2 Existing EPA Guidance 10
2.3 Recommendations from prior expert committees 11
3 Key Issues for EPA 14
3.1 Fundamental Concepts and Recommended Terminology Changes 14
3.1.1 Fundamental Valuation Concept 14
3.1.2 Change in metric and terminology 15
3.2 Altruism and willingness to pay for mortality risk reductions 17
3.3 Valuing cancer risks 20
4 Review of stated preference and hedonic wage studies 26
4.1 Stated preference studies 28
4.1.1 Recent meta-analyses of SP studies 29
4.1.2 A new meta-analysis dataset 31
4.2 Hedonic wage studies 35
4.2.1 Data sources 36
4.2.2 Estimation issues 37
4.2.3 Recent meta-analyses of hedonic wage studies 38
4.2.4 A new meta-analysis of hedonic wage studies 41
5 Methods for Combining Data 46
5.1 Meta-analysis 47
5.1.1 Parametric distribution 47
5.1.2 Classical econometrics 48
5.1.3 Bayesian estimation 51
5.2 Structural benefit transfer 53
5.2.1 Static preference functions 55
5.2.2 Life-cycle preference functions 57
6 Conclusions 59
6.1 Addressing key issues: terminology, altruism, cancer valuation 59
6.2 Longer term analytical directions 60
6.2.1 Meta-analysis 60
6.2.2 Structural Benefit Transfer 61
6.3 Other research directions 61
References 63
Tables and figures 74
Appendix A 89
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1 Introduction
The valuation of human health benefits is often a crucial, but sometimes controversial, aspect of
the application of benefit-cost analysis to environmental policies. Valuing the reduced risks of mortality,
in particular, poses a special set of conceptual, analytical, ethical and empirical challenges for economists
and policy analysts. This white paper addresses current and recent U.S. Environmental Protection
Agency (EPA) practices regarding the valuation of mortality risk reductions, focusing especially on
empirical estimates of the "value of a statistical life" (VSL) from stated preference and hedonic wage
studies and how they might be summarized and applied to new policy cases using some form of benefit
transfer. Benefit transfer concepts will be highlighted throughout the paper, since any application of
existing empirical estimates of values for health risk reductions to new policy cases is inherently a benefit
transfer problem.
The main intended audience for this paper is EPA's Science Advisory Board-Environmental
Economics Advisory Committee (EEAC). The main objectives of the paper are to highlight some key
topics related to the valuation of mortality risks, and to describe several possible approaches for
synthesizing the empirical estimates of values for mortality risk reductions from existing hedonic wage
and stated preference studies for the purpose of valuing mortality risk reductions associated with future
EPA policies. Some of these approaches could be implemented in the short term, but others will likely
require longer term research. We are soliciting general feedback and specific recommendations from the
SAB-EE AC on each of these key topics and approaches.
1.1 Key topics
We highlight several issues in this paper, offering preliminary recommendations where we feel
conclusions can be supported by existing data and methods. In other cases we describe alternative
methods, data and data gaps, and possible future directions, with the intention of soliciting meaningful
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feedback from the EEAC. The key topics addressed in this paper—loosely ordered from short- to longer-
term tasks—include:
• Improving communication by reporting value estimates in terms of risk changes rather than "statistical lives."
We fear, as do others, that the prevalence of such terms of art as "the value of a statistical life" has
contributed to unnecessary confusion and consternation among decision-makers and members of the
general public. We aim to ease these communication difficulties by replacing the VSL terminology
with the straightforward term "value of mortality risk" (VMR). The "units" associated with the
mortality risk change must be clearly delineated and in this paper we report the units in terms of
willingness to pay for a reduced risk of 1/1,000,000 or a "micro-risk," following Cameron (2008) and
Howard (1989). We believe that this term provides a more accurate description of the fundamental
valuation concept that underlies the marginal willingness to pay for risk reduction, and that this
choice of measurement unit is a more natural one considering the typically small (relative to the full
suite of risks from all hazards) changes in individual-level risks resulting from most environmental
policies.
• Alternative approaches for updating EPA's best central estimate, or range of estimates, of the willingness-to-
pay for mortality risk reductions for use in regulatory impact analyses. EPA is interested in updating its
guidance to better reflect the existing estimates of mortality risk reduction values in the revealed and
stated preference literatures. Specifically, how can the empirical results (described below in Section
4) be used to revise EPA's mortality risk valuation guidance in the form of a revised point estimate or
range or benefit transfer function?
• Incorporating a cancer differential into mortality risk valuation guidance. We discuss the possibility of
adding a "cancer differential" (often called a "cancer premium" in the literature) to the standard
(non-cancer) estimates of mortality risk reduction values, specifically for use in analyzing policies
expected to reduce carcinogenic pollutants. EPA first raised the issue of a cancer premium with the
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EEAC in 2000 (USEPA 2000b), but the literature has developed considerably since that time. Given
its importance for the valuation of environmental health risks in particular, we review the current
literature and recommend including a cancer differential in future guidance.
• The role of altruism in valuing risk reductions. The role of altruistic motives for improved health and
safety is typically ignored in most benefit-cost analyses but may have important implications for
estimating individuals' willingness to pay for environmental improvements. We review several
recent studies that examine the role of altruism in benefit-cost analysis and highlight the potential
relevance of these findings for the valuation of mortality risk reductions, in particular their
implications for interpreting and transferring stated preference estimates of "public" versus "private"
risk reductions.
• Toward functional benefit transfer. We discuss specific issues that we expect to arise in applying both
classical and Bayesian meta-regression techniques to new datasets of stated preference and hedonic
wage value estimates described in this paper, as possible approaches for developing a benefit transfer
function. We also discuss the structural benefit transfer approach, which involves specifying a direct
or indirect utility function, including parameters that can describe the relevant attributes of the risk to
be evaluated, and then deriving analytical expressions for observable economic variables that can be
used to calibrate the parameters of the preference function. Developing a valid benefit transfer
function, using either meta-regression or a structural approach or some combination of these, is a
longer-term task than the others mentioned above, but EEAC feedback on these issues would be very
helpful in shaping EPA's research agendas in these areas.
1.2 Roadmap
The remainder of this white paper is organized as follows. Before we address our key topics in
more detail, Section 2 provides background discussion that (1) describes the valuation challenge facing
the Agency and the differences in the contexts underlying existing mortality risk reduction value
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estimates and the policy scenarios we seek to analyze; (2) briefly summarizes EPA's most recent
guidelines for valuing mortality risk reductions (USEPA 2008);1 and (3) recaps the main
recommendations from several recent expert advisory committees to EPA on the valuation of human
health risk reductions and the use of meta-analyses for combining estimates from different studies.
With this context in mind, in Section 3 we describe and discuss three of the key topics of this
whitepaper: terminology and metrics, cancer risk valuation, and altruism. In Section 4, we review the
empirical mortality risk value estimates from the stated preference and hedonic wage literatures,
including recent meta-analyses of these literatures. The discussion of the stated preference literature
includes a newly assembled database of stated preference estimates of mortality risk reduction values in
anticipation of an updated meta-analysis. We also review and extract value estimates and other
attributes from hedonic wage studies that have provided estimates of the VSL, with selected studies
spanning 1974 to the present. We discuss strengths and weaknesses of these studies for application to
environmental policies.
In Section 5 we discuss alternative approaches for synthesizing the estimates from these
literatures as a necessary step for updating EPA guidance. A longer term goal is to develop a benefit
transfer function for valuing mortality risk reductions, rather than relying on the current practice of
transferring a single central point estimate. We discuss two basic approaches for developing such a
benefit transfer function: meta-analysis and structural benefit transfer. Meta-analysis uses statistical
regression techniques to quantify the influence of study, policy, demographic, and possibly other
variables on the willingness to pay for health risk reductions. The structural benefit transfer approach
involves specifying a direct or indirect utility function and then deriving analytical expressions for
observable economic variables that can be used to calibrate the parameters of the preference function.
1 These are reflected in EPA's revised Guidelines for Preparing Economic Analyses (2008).
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Section 6 concludes with summaries of the key topics and needs for both short-term guidance and longer-
term research.
2 Background
2.1 The valuation challenge
Benefit cost analysis is a useful tool that provides detailed information on a wide variety of
consequences associated with environmental policies. Benefits are based on what individuals would be
willing to pay for risk reductions or for other improvements from pollution reduction. Costs are
determined using the value of the resources directed to pollution reduction. As safeguarding human
health is among the EPA's primary goals, to develop more complete and more accurate benefit-cost
analyses of its policies, EPA must estimate individuals' willingness to pay for reductions in health risks
from environmental harms. Ideally, benefit-cost analysis of policies that reduce health risks would
account for all of the factors that may cause willingness to pay to vary across different types of policies
and individual characteristics and circumstances. The literature has indicated that these factors may
include the sources of risk affected by the policy (e.g., hazardous air pollutants, water contamination,
etc.), the resulting health conditions (e.g., cancer, cardio-respiratory diseases, gastro-intestinal diseases,
etc.), how the policy affects the timing of morbidity and mortality risks across each individuals' life span
(i.e., how it shifts the "survival curve"), the income and other personal characteristics of the affected
individuals, and how the changes in risks are perceived by those individuals. While addressing all of
these factors simultaneously is currently empirically infeasible, there are three challenges that we
highlight for their direct relevance to EPA.
First, fundamental to this valuation challenge is that the risk reductions provided by EPA policies
are inherently public in nature, unlike, for example, private purchase decisions. The distinction is
important because individuals may reasonably value risk reductions from public policies differently than
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those from private actions even if their own mortality risks are affected in a quantitatively identical
manner. Such differences could be due to differences in "controllability," "dread," or other tangible or
intangible factors (e.g., Slovic 1987, Savage 1993, Chilton et al. 2006). Furthermore, public policies raise
issues about altruistic values for risk reductions to others, something that may be of particular relevance
for environmental risks. EPA would like to use the existing literature to evaluate the extent and nature of
altruistic values and consider how to formulate mortality risk valuation guidance accordingly. We
address altruism in greater detail in Section 6.3.
A second major challenge for the valuation of mortality risk reductions for environmental
policies is the intertwined nature of morbidity and mortality risks. Environmental policies generally do
not reduce the risks of fatal workplace or automobile accidents, for example, which provide the context
for many of the mortality valuation estimates in the literature and generally have little or no
accompanying morbidity or period of illness. Ideally, we would use an integrated model that could
estimate willingness to pay for mortality and associated morbidity risk reductions simultaneously.
Developing such a model is beyond the scope of this white paper and current guidance development
effort, and is near the frontier of the empirical valuation literature. Nevertheless, to the extent possible
with currently available data and models, we would like to account for how individuals consider
morbidity in existing estimates of mortality risk reduction values when they always occur together. It
also is important to capture some related losses that may not be reflected in willingness to pay estimates,
depending on context in which they were estimated. For example, reduced health from illness preceding
death is certainly a loss to an individual and his or her quality of life, but may not be reflected in VSL
estimates from the hedonic wage literature, which are based on the risks of workplace injuries that lead to
death. Society also is worse off because of the illness due to the individual's lost productivity, something
that may not be reflected in revealed or stated willingness to pay estimates, depending upon the type of
insurance held by the individual and possibly the scenario description.
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This issue is of particular relevance to EPA when addressing reductions in cancer risks since
many EPA policies focus on reducing exposure to carcinogens. Ten years ago EPA reviewed the
economic literature on valuing fatal cancer risk reductions and discussed a number of risk characteristics
that may influence people's values, including but not limited to the timing of the risks (USEPA 2000b,c).
The committee recognized many of the issues reviewed by EPA as theoretically valid but empirically
ambiguous, and therefore recommended that "the only risk characteristic for which adjustments to the
VSL can be made is the timing of the risk" (USEPA 2000c p 1). In particular, this recommendation
advised against the application of any differential to reflect preferences for reducing cancer risks relative
to other types of risk because of dread or other factors. With an additional decade of valuation literature
to draw upon, EPA is seeking to re-examine this question using data from the stated and revealed
preference studies described below, as well as other relevant empirical results. We will discuss cancer
valuation in more detail in Section 6.4.
Finally, the empirical literature may allow us to account for the extent to which individuals value
different categories of risks differently in a systematic transfer of benefits. For example, if environmental
risk reductions are valued differently from workplace or auto accidents, regardless of whether the
mitigation is from private or public actions, our guidance should reflect this difference.
It is important to keep the overarching valuation challenge in mind as we begin discussing recent
studies and value estimates. Each study reflects an attempt to measure the value of a reduction in
mortality risk from a specific cause (or small set of causes), in a specific context, among a specific
population. By now there is ample theoretical and empirical evidence to indicate that values for health
risk reductions are not "one-size-fits-all"—that is, they are "individuated" (e.g., Sunstein 2004, Evans and
Smith 2008, Scotton and Taylor 2009). For this reason, we believe that there is great scope for improving
upon the point value benefit transfer approach that has traditionally been applied to mortality risk
reductions based on a central estimate of the VSL. Therefore, we ultimately are seeking both short-term
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recommendations as well as advice on a longer-term research agenda on how these heterogeneous
studies can best be synthesized for systematic benefit transfers to improve the application of benefit-cost
analysis to future environmental policies.
2.2 Existing EPA Guidance
EPA's draft Guidelines for Preparing Economic Analyses (2008) (hereafter, the draft Guidelines)
retains the recommendation from the 2000 version, a default central VSL value $4.8 million in 1990 real
dollars. This estimate, after adjusting for inflation and real income growth, is to be applied to mortality
risk reductions for all types of policies, no matter the source of the risk.2 The estimate is based on the
mean of a probability distribution fit to twenty-six published VSL estimates. The draft Guidelines also
indicates that the distribution itself can be used for formal uncertainty analysis. The underlying studies,
the probability distribution parameters, and other useful information are available in Appendix B of the
draft Guidelines (USEPA 2008).
The draft Guidelines also retains the 2000 version recommendation that the VSL for mortality risk
reductions should not be adjusted for differences in sources of risk or population characteristics—rather,
these factors should be examined qualitatively. In some cases, the analysis may include a quantitative
sensitivity analysis. Analysts should account for timing when valuing mortality risk reductions, and
should discount the benefits of future risk reductions at the same rate used to discount other costs and
benefits. Because the VSL represents the marginal willingness to pay for contemporaneous risk
reductions, this is typically done by estimating the lag between reduced exposure and reduced mortality
risks, calculating willingness to pay in all future periods when mortality risks are reduced, and
discounting back to the present.
Finally, EPA's draft Guidelines also recommends accounting for increases over time in average
income. This is done by using projections of real GDP per capita and applying an income elasticity
2 We report all estimates in 2009 US dollars unless otherwise noted.
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estimate. The resulting future (real) VSL will therefore reflect the idea that health risk reductions are
normal goods and so willingness to pay will increase with income.
2.3 Recommendations from prior expert committees
This white paper is one stage in a detailed process that EPA has undertaken with the SAB-EEAC
to improve the Agency's ability to value health risk reductions. Since its review of EPA's Guidelines for
Preparing Economic Analyses (USEPA 2000a) the SAB has offered several specific sets of recommendations
on valuing risk reductions, particularly for mortality risks.
In July 2000 the SAB-EEAC released an advisory report in response to EPA's white paper, Valuing
the Benefits of Fatal Cancer Risk Reduction, which focused on benefit transfer issues associated with using
existing mortality risk values to estimate the benefits of EPA actions on carcinogens, including potential
adjustments that could be made to existing risk values to account for this category of benefits (USEPA
2000b). As noted earlier, after reviewing the white paper and current economics literature, the SAB
concluded that, while many of the issues raised in the white paper were theoretically valid and
potentially important, the empirical literature supported only accounting for latency and for income
growth over time. The SAB-EEAC did not consider other adjustments to EPA's default mortality risk
value to be appropriate for the Agency's primary analyses, but could be addressed separately using
sensitivity analysis.
An August 2001 SAB report, Arsenic Rule Benefits Analysis: An SAB Review (USEPA 2001),
generally supported EPA's estimate of the marginal willingness to pay for mortality risk reductions. The
SAB also offered additional recommendations to account for the time between reduced exposure and
reduced mortality risks. This report coined the term "cessation lag" for this concept and offered specific
recommendations for estimating cessation lags based on the types of risk data available. The SAB review
also clarified that reductions in exposure to carcinogens—that is, exposure per se, aside from the increased
cancer risks that the exposure causes—are not a separate benefit category under a damage function
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approach to valuing reduced risks. The board noted that it is possible that there is an existence value for
protected drinking water; however, without sufficient empirical evidence to estimate the magnitude of
this value, it cannot be included in the quantitative benefits analysis. Finally, the report indicated that it
is appropriate to add the costs of illness to the willingness to pay for mortality risk reductions when
estimating the benefits of reduced cancer mortality.
EPA further consulted with the SAB-EEAC on additional mortality risk valuation issues in 2004,
developing a strategy to gather additional information on meta-analysis to inform both the SAB-EEAC
and EPA (USEPA 2004b). In 2006, EPA returned to the SAB-EEAC with two documents for formal
review: a white paper addressing how remaining life expectancy affects willingness to pay for mortality
risk reductions, and an expert report on the use of meta-analysis for combining existing mortality risk
value estimates. A 2007 report, SAB Advisory on EPA's Issues in Valuing Mortality Risk Reduction,
responded to both topics (USEPA 2007).
On the subject of life expectancy, the SAB-EEAC noted that there was theoretical ambiguity on
how willingness to pay might change with age (and, hence, remaining life expectancy). The committee
concluded that the existing economics literature does not provide clear theoretical or empirical support
for using different values for mortality risk reductions for differently-aged adults or a constant "value of
statistical life year" (VSLY). Thus, the SAB-EEAC recommended that EPA continue using its traditional
assumption of an age-independent willingness to pay for mortality risk reductions.
To address meta-analysis, EPA assembled a work group of expert statisticians in December 2005
to discuss the meta-analysis of VSL estimates and to examine three existing meta-analyses: Mrozek and
Taylor (2002), Viscusi and Aldy (2003), and Kochi et al. (2006). While the expert workgroup did not
endorse any one of these studies, the panel did encourage the use of meta-analytic techniques for the
analysis of the existing literature on VSL. The workgroup recommended analyzing stated preference and
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hedonic wage data separately, and offered a set of principles that should be followed in conducting such
an analysis (USEPA 2007).
The SAB-EEAC review of the Meta-analysis workgroup's report stated 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," but concluded that meta-regression is "not appropriate [for]
combin[ing] VSL estimates" into a summary measure (USEPA 2007 p i). Rather, the SAB-EEAC
suggested using meta-regression to examine how study design characteristics influence the VSL estimates
and relying on other statistical techniques to determine a central estimate or range of estimates for use in
benefit transfer to new policy cases.
Based on these expert recommendations and other considerations, we believe that updated
reviews and meta-analyses of the stated preference and hedonic wage literatures could help refine the
Agency's central estimate(s) or range of estimates of the marginal willingness to pay for mortality risk
reductions. Studies have shown that values for health risk reductions may depend on differences among
policies and the affected individuals. These factors include the sources of risk affected by the policy (e.g.,
hazardous air pollutants, water contamination, etc.), the resulting health conditions (e.g., cancer, cardio-
respiratory diseases, gastro-intestinal diseases, etc.), as well as how the policy affects the timing of
morbidity and mortality risks across each individuals' life span (i.e., how it shifts the "survival curve").
Therefore, as is widely recognized in most other contexts where some form of benefit transfer is used for
policy analysis, we believe a functional benefit transfer approach should be more accurate than a single
point estimate applied in all circumstances. Consequently, we are interested in exploring approaches for
developing benefit transfer functions that can account for some or all of these factors.
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3 Key Issues for EPA
3.1 Fundamental Concepts and Recommended Terminology Changes
3.1.1 Fundamental Valuation Concept
We begin by identifying the fundamental valuation concept that economists aim to estimate
using non-market valuation methods and apply in benefit-cost analyses of policies that reduce human
health risks. Consider a general utility function for an individual i with income X and some health risk
R, among the arguments: L/ = U Y, R. , Z . The vector Z; is included to emphasize that, in addition
to income and risk, the individual's utility (and therefore the willingness to pay for health risk
reductions) also may be influenced by many other factors specific to the case at hand. We will highlight
several of these factors throughout this white paper. The individual's marginal rate of substitution between
income and risk is:
eu ,v dUn dX dU/dR,
dU:=—dY- +—dR = 0 => —L = L.
8Yi dRi dRi dU/dY,
This marginal rate of substitution, dYJdR., also can be interpreted as the individual's marginal
willingness to pay (wtp) for a change in risk—that is, the amount of money the individual would be willing
to swap for a small change in risk on the margin.3 This is the fundamental value concept that must be
estimated for use in benefit-cost analyses of policies that may improve human health. With estimates of
these quantities, conditioned as necessary on possibly many observable characteristics of the policy and
the affected individuals, it is straightforward to calculate the total willingness to pay for the risk
reductions that are expected to be produced by the policy: ^. wtp{ x AR;, where i indexes all individuals
affected by the policy, and wtp{ and AR, are the estimated marginal willingness to pay and risk
3 Throughout this white paper, we will use "wtp" to refer to marginal willingness to pay, which will have units of
$/change in risk, and we will use "WTP" to refer to discrete willingness to pay amounts, which will have units of $.
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reduction for individual i, both of which may depend on individual-level characteristics and
circumstances.4
It is important to emphasize that this is a marginal value concept—a dollar value per unit change in
risk. These values should be thought of as the slope of a curve at a point, rather than the height of the
curve.5 For practical purposes, the units used to report estimates of these slope values are of no
consequence. They could be reported as dollars per nano-risk (10 9), or micro-risk (10 ' ), or mili-risk (
10 ), etc. As long as the measurement units are known, then the risk changes to be valued can be
expressed in the same units and the correct total value can be calculated. The conventional measurement
units used for reporting these slope estimates are (effectively) "dollars per mortality" risk changes,
usually simply written as "$," where "per mortality" is understood (or misunderstood, depending on the
audience). This quantity was often referred to as the "value of life" in the early literature on the subject
(e.g., Rice and Cooper 1967). While the terminology varies, the quantity is now typically called the "value
of a statistical life," or VSL, where "statistical" has been added to emphasize that valuation is based on
changes in risk rather than the loss of life with certainty.6
3.1.2 Change in metric and terminology
Despite its widespread usage, this particular selection of measurement units for the denominator
of the marginal rate of substitution between income and risk, and the VSL label that has been attached to
4 For ease of exposition we ignore the time dimension here. We will allude to some of the complications that arise in
the more realistic dynamic case, using a life-cycle model, in Section 6.2.2 and Appendix A.
5 Also note that if the risk changes to be valued are large, then the slope of the willingness to pay function may
change over the relevant range and so the marginal willingness to pay ' the change in risk may not give an accurate
estimate of total willingness to pay. For the most part in this white paper we will ignore this complication, though
we do come back to it in an illustrative example in Section 5.2.1.
6 A common way of explaining the meaning of the VSL is based on a population's aggregate willingness to pay for an
aggregate risk reduction. For example, suppose in a town of 1,000 people a policy is enacted that reduces each
person's risk of dying by 1 in 1,000 in a year. Lhen the expected number of avoided deaths (lives saved) by the policy
for the year would be equal to one—a so-called "statistical life." Suppose further that we know (from a survey or
other study) that the average amount that people in the town would be willing to pay for the risk reduction of 1 in
1,000 was $8,000. We then know that the aggregate willingness to pay is $8,000,000 for saving the one statistical life,
so the "value of a statistical life" would be $8,000,000.
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it, have caused or contributed to needless confusion and controversy, especially among non-economists
(Cameron 2009). Most economists recognize that the "units" associated with the VSL reflect the
aggregation of the small risk reductions across many individuals until that aggregate reflects a total of
1.0, or one statistical life. However, for non-specialists this potentially subtle point is often lost; the
addition of the word "statistical" to the terminology does not seem sufficient to clarify the concept.7
To help reduce the misconceptions that seem to be inspired or aggravated by the VSL
terminology, we propose a change in EPA standard practice such that estimates of health values will be
referred to as the "value of mortality risk" (VMR), and report the associated units using standard metric
prefixes to indicate the size of the risk change and the associated time scale, e.g., $/|jr/person/yr (dollars
per micro[10'6]-risk per person per year) (Howard 1989, Cameron 2009).8
As noted earlier the choice of risk increment for aggregating and reporting risk changes is mainly
one of convenience. However, we believe that explicitly labeling the units of the VMR in this way more
clearly emphasizes that these values refer to small changes in individual-level risks over a definite time
span rather than how much money any single individual or group would be willing to pay to prevent the
certain death of any particular person. It also should be emphasized that the use of a standardized
7 A recent example of the confusion surrounding this concept in the popular press can be found in an AP story titled,
"American Life Worth Less Today" (Bornstein 2008) that opened by saying "[EPA] has decided that an American life
isn't worth what it used to be." The story was referring to an alternate analysis in some air regulatory impact
analyses that used a more recent review of the literature to report a lower VSL than is reflected in EPA's 2000
Guidelines. This story quickly spread throughout the media even appearing on the Colbert Report as EPA's efforts
to "devalue life." Video clip at http://www.colbertnation.com/the-colbert-report-videos/176175/july-14-2008/the-
word—priceless (04:06) Posted on 7/14/2008.
8 Other alternatives to the VSL to better describe marginal wealth-risk tradeoffs have been used or proposed as well.
For example, the UK government uses the term "value of prevented fatality (VPF)," but as described by Wolfe (2007)
this designation confronts the same misinterpretations as VSL. Cameron (2009) suggests a greater departure from
standard terminology not only to communicate that "lives" are not being valued, but also to clarify that "value" itself
should be understood in terms of opportunity costs. After considering several alternatives, the term suggested is
"willingness to swap (WTS) other goods and services for a micro-risk reduction," abbreviated WTS (|-ir). In recent
empirical work, Cameron and DeShazo (2008) report results in terms of micro-risk reductions. Scotton and Taylor
(2009) use the term "value of a risk reduction" (VRR), noting that "explicit consideration of the heterogeneous values
for heterogeneous risks underscores the importance of moving the policy discussion from 'a VSL' to valuation of
marginal changes in fatality risks specific to the type of the risk affected by the policy" (p 23).
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measurement unit for reporting values for health risk reductions should neither be taken to imply that
the values themselves are invariant across individuals or contexts, nor that these marginal values will be
constant across the full range of relevant risk changes.
For the remainder of this paper we will use the general term "value of mortality risk" whenever
possible. We will report estimates as VMRs, as defined above, to the extent possible, using the VSL
terminology only as necessary in discussing the previous literature.
3.2 Altruism and willingness to pay for mortality risk reductions
We now turn to an overarching conceptual issue that may affect the conduct of benefit-cost
analysis more generally: altruism. The default assumption for most applications of revealed and stated
preference methods for non-market valuation is that individuals' (or households') well-being depends on
their own consumption (interpreted broadly to include market and non-market goods and services) and
is not directly influenced by the consumption or well-being of others. If this assumption is invalid, we
may be concerned that our standard methods of estimating willingness to pay assuming "atomistic"
individuals or households may give misleading results in benefit-cost analysis.
There are at least two ways that altruism may be relevant for the valuation of mortality risk
reductions. First, some stated preference studies are based on surveys that make a distinction between
"public" and "private" risk reductions.9 The difference, if any, between WTP for public versus private
risk reductions may be partly due to altruism, but other factors could be at work as well. For example, a
distrust of government may lead some respondents to express a lower WTP for public risk reductions
provided through government programs compared to those provided through private initiatives. While
stated preference studies may in principle be able to distinguish altruistic preferences from other
9 Few studies explicitly address the public versus private issue. However, for most of the studies it is possible to
assign the estimates to one category: estimates that accrue to an individual only, such as an individual health risk
reduction or the decision to wear a seatbelt or purchase a health care treatment, are "private" and estimates that can
accrue to the individual and others, such as reductions in highway safety-related deaths, are "public." See section 6.1
for more details on the stated preference studies.
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confounding factors, it is difficult to draw clear conclusions from the existing literature because most
studies that have been conducted to date were not designed to examine altruism per se.10 Therefore, the
proper application of the results of these stated preference studies may depend in part on how altruism
should be treated in benefit-cost analyses. Second, since hedonic wage studies are focused on
compensation received by individual workers for taking on private, job-related risk, the mortality risk
values from hedonic wage studies do not incorporate altruism. Therefore, if (some forms of) altruistic
preferences should be included in benefit-cost analysis, then hedonic wage-based estimates of mortality
risk values may need to be supplemented with separate value estimates that capture altruistic preferences
alone. On the other hand, if (some forms of) altruistic preferences should be excluded from benefit-cost
analyses, then this may influence whether (or how) some stated preference studies should be used for
benefit transfers.
EPA's Guidelines for Preparing Economic Analyses (USEPA 2000a) discussed the role of altruism in
estimating the total benefits of public actions, and noted the key distinctions between paternalistic (or
"safety focused") and non-paternalistic (or "preference respecting") forms of altruism.11 If altruistic
motives are non-paternalistic, then individuals care not only about the benefits others receive, but also
the costs they bear, and most economists who have studied this issue have concluded that it is generally
inappropriate to add these altruistic values for benefits others receive to total willingness to pay. Doing
so could lead to "double-counting" some of the benefits and/or costs. Paternalistic altruism, on the other
hand, should be included in the calculation of total benefits. EPA's Guidelines (USEPA 2000a p 61)
describes the issue as follows:
10 Stated preference studies and the treatment of altruism also may hold promise for identifying preferences related
to equity or environmental justice (EJ) concerns. For example, preferences for reductions in risks for others,
particularly those who may be disproportionately exposed to pollutants (which are often low income and minority
groups typically associated with EJ) could be identified through a well designed stated preference study.
11 Formally, the utility function of non-paternalistic altruists includes others' utility, while the utility function of
paternalistic altruists includes others' consumption of one or more types of private or public goods or services.
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While benefits are generally calculated by summing each individual's WTP for his or her own
welfare, there are conditions under which it is appropriate to include altruistic values, or individuals'
WTP for the welfare of others. Economic theory concludes that if one cares about a neighbor but
respects the neighbor's preferences, and if the neighbor would have to pay for the policy action being
analyzed, then altruistic benefits should not be counted in a benefit-cost analysis. The intuition
behind this result is that, if one respects the neighbor's preferences, one cares about both the benefits
and the costs the neighbor faces. It is therefore inappropriate to add the value one attaches to the
neighbor's benefits without considering the cost implications of doing so. Comparing individual
benefits and costs in this case is the appropriate decision rule.
Altruistic benefits may be counted either when altruism toward one's neighbor is paternalistic or
when one will in fact bear the costs of the project but the neighbor will not. In the first case
(paternalistic altruism), one cares about the benefits the neighbor will enjoy, e.g., from a health or
safety project, but not about the costs the project will impose on him. An example of the second case
would be a project whose costs are borne entirely by the current generation; i.e., the project imposes
no costs on future generations. In this case, altruism toward future generations by the current
generation could legitimately be counted as a benefit.
The conclusions in the Guidelines were based largely on Bergstrom (1982) and McConnell (1997)
369 who demonstrated that the optimal provision of public goods based upon selfish preferences is a
370 necessary and sufficient condition for the optimal provision based on social preferences (including
371 altruistic preferences). However, since the publication of the Guidelines, Flores (2002) has challenged the
372 conventional wisdom that (non-paternalistic) altruism should be excluded from benefit-cost analysis.
373 Flores showed that passing a private values benefit-cost test is a sufficient but not a necessary condition
374 for non-marginal policies to be potentially Pareto improving, except under special circumstances. That is,
375 even if all altruism is non-paternalistic, failure to include altruistic values may lead to the rejection of
376 policies that are potentially Pareto improving. Flores concluded that "benefit-cost analysis with altruism
377 cannot simply be conducted independent of who pays." In a more recent study, Bergstrom (2006)
378 concluded that "The assumptions under which the private values benefit-cost test is necessary for
379 potential Pareto improvements need not always be satisfied;" nevertheless, "Despite these
380 qualifications... for a broad class of economies, a comparison of the sum of private values to the cost of a
381 project is the appropriate test for determining whether it can lead to a Pareto improvement" (p 348-349).
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Bergstrom's conclusion seems to summarize the prevailing view regarding non-paternalistic
altruism in benefit-cost analysis, especially for policies that would cause marginal changes in
environmental quality (since Flores' counter-examples involved non-marginal changes). Therefore, the
main relevance of altruism for mortality risk valuation lies in the distinction between the paternalistic and
non-paternalistic forms. Including the former but excluding the latter may require supplementing
revealed preference estimates of health risk valuations with a careful selection of results from previous
stated preference studies. Stated preference surveys that elicit only private willingness to pay would
exclude both forms of altruism. One way to include paternalistic but exclude non-paternalistic altruism
would be to design a survey that would inform respondents about health improvements that others
would experience from the policy, but also ask each respondent to assume that all others would be taxed
an amount equal to their private willingness to pay for the policy, so that their utility remains unchanged
(Johansson 1994). It is not clear which if any of existing stated preference studies (many of which are
reviewed below in Section 6.1) were designed this way, so the current body of empirical results cannot
support the separation of paternalistic from non-paternalistic altruism. We recommend additional
research in this area to help estimate paternalistic willingness to pay for environmental policies that
reduce health risks. Additional examination of existing studies may shed light on this issue in the
relative short-term, and we are interested in feedback on this issue.
3.3 Valuing cancer risks
As noted in our description of EPA's valuation challenge, willingness to pay for cancer risk
reductions may be systematically different than that for workplace or auto accidents or other risks not
associated with a lengthy and painful illness. This difference is sometimes referred to as a a "cancer
premium," but we will use the more general term "cancer differential." While not often defined
precisely, the differential is posited as capturing elements of dread and fear of cancer, as well as the pain
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and suffering from the period of illness preceding death. It might also include income and household
productivity losses over this period of morbidity.
Several authors have recommended accounting for this differential in benefit-cost analysis of
policies that reduce exposure to carcinogens (e.g., Revesz 1999, Sunstein 2004). To the extent that existing
policy guidance on valuing mortality risk reductions is based on non-cancer risk-wealth tradeoffs, this
would involve an "adjustment" to the default (generic, non-cancer) mortality risk reduction value.
Governmental analyses in the UK have adopted this approach, applying a 100% differential for cancer
risks (HM Treasury 2003).12 In addition, the European Commission has recommended a 50% differential
for carcinogenic pollutants over its default value of preventing a fatality (European Commission 2000).
For the purpose of developing guidance, we are interested in assessing the valuation literature on
cancer risks and any cancer risk differential, both in the short-term and the longer term. Ultimately, this
literature could inform the development of a benefit transfer function, in combination with the stated
preference and hedonic wage estimates described in greater detail below. While such longer-term
research is being conducted, we believe it is reasonable that evidence of systematically different
preferences for cancer risk reductions be part of any recommended short-term guidance.
To inform this discussion, this section contains a somewhat more detailed assessment of the
empirical literature on cancer risk valuation, with a particular emphasis on studies that examine risks in
both cancer and non-cancer contexts. These studies are described in Table 1 in the following categories:
• studies comparing values for cancer and non-cancer fatal risk reductions
stated preference studies that estimate willingness to pay
risk-risk studies
• stated preference studies of cancer risks without internal comparisons, and
• related hedonic property and hedonic wage studies.
12 Specifically, this adjustment is applied for the benefits from asbestos proposals by the UK Health and Safety
Executive (HSE).
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The first of these categories contains the most direct evidence on any cancer differentials.
Note on Cessation Lag and Latency
Reduced exposure to carcinogens results in reduced cancer incidence after a period of time that
EPA has referred to as "cessation lag," a term originally coined by the SAB in its review of the Agency's
arsenic in drinking water benefits analysis. Cessation lag addresses only reduced risks from reduced
exposure and thus applies best to populations currently at risk. The time between initial exposure and
increased cancer incidence is referred to as "latency" in recent EPA analyses, but it is often used in the
literature in a broader sense to refer to the time difference between a change in exposure and a change in
risk.
Prior SAB-EEAC advice and agency practice has been to estimate cessation lag and latency from
available epidemiologic data, apply a value of statistical life estimate at the time at which cancer mortality
reductions occur, and discount this value back to the present at the rates prescribed in Agency guidance.
The practice has generally been supported by research findings suggesting that individuals discount over
these lag times at rates generally consistent with market rates, although some recent stated preference
studies find near-zero discount rates over latency periods (Hammitt and Haninger, 2010; Alberini and
Scasny, 2010a).
An important issue in estimating a cancer differential is the potential need to consider
differences in the time profile of mortality risks between cancer and non-cancer cases. Earlier studies
were often silent on the issue, but more recent ones have attempted to address it explicitly. Our focus in
this section is on a potential cancer differential that captures the difference in marginal willingness to pay
for reduction of cancer mortality risks relative to that of a non-specific mortality risk holding timing
equal. That is, the differential, in principle, compares a contemporaneous non-cancer risk reduction with
a contemporaneous cancer risk reduction. We recognize that timing may be intertwined with how people
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perceive and value risk reductions, something that should be considered more fully in any rigorous,
systematic benefit-transfer exercise as we develop guidance.
Stated Preference studies including cancer and non-cancer risks
Several stated preference studies have estimated willingness to pay for both cancer and non-
cancer risks, in large part to examine a possible cancer differential. A few studies have focused only on
cancer risk reductions without an internal comparison to other types of risk. The results of these studies
are somewhat mixed—some have found evidence of a cancer differential (Hammitt and Liu 2004, Tsuge
et al. 2005, Alberini and Scasny 2010a, and Alberini and Scasny 2010b), while a few others found no such
evidence (Hammitt and Haninger 2010, Adamowicz et al. 2008) when looking at whole-household or
public risks. Cameron and DeShazo (2008) found evidence of a differential for some cancers (breast and
prostate) over other cancers (colon, lung, and skin), but not over other health endpoints (heart attacks and
disease).
There have been two risk-risk tradeoff studies specifically examining how preferences for cancer
risk reduction compare to those for automobile accident risk reductions. By asking respondents to choose
among different bundles of risks, these simplified choice experiments aim to estimate the relative values
of various types of risk reductions. They do not, however, provide a willingness to pay for either risk
type and therefore are not included in our reviews of the willingness to pay literature above. Van
Houtven et al. (2008) found a strong preference for avoiding cancer risks relative to automobile accidents
even after controlling for latency and morbidity periods. With a 5-year latency, values for reductions in
fatal cancer risk were approximately three times larger than those for immediate accident risks, declining
to fifty percent larger for a 25-year latency. By contrast, in a study by Magat et al. (1996), the median
respondent was indifferent between fatality risk from auto accidents and lymphoma, suggesting that
cancer mortality is no more 'dreaded' than accidental mortality. It is difficult to draw firm conclusions,
however, because the study did not specify the timing of the risks, and, in particular, any latency
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associated with cancer. Therefore, if respondents assumed that cancer risks would be realized after a
latency period then the results suggest that any preference for cancer reductions was approximately
offset by discounting future risks.
Three additional stated preference studies focus on WTP for cancer risks without direct
comparisons to other risks. These do not internally address the question of how cancer risks are valued
differently from non-cancer risks, but may be combined with the results from other studies to address
this question. Focusing on cancer risks from hazardous waste sites Alberini, et al. (2010) estimated a
cancer VSL of approximately $5.6 million (2009 dollars) using the results of choice experiments in Italy.
Carson and Mitchell (2006) examined willingness to pay for installing a water filtration system to remove
trihalomethanes (THM) in public drinking water. Estimated values depend upon an assumed latency
and discount rate, as well as the specific risk reduction, but generally range from $3.4 to $8.0 at the
smallest risk changes for a 25-year latency. Buzby et al. (1995) used a telephone-mail survey to examine
the value of reduced fatal cancer risk from exposure to pesticides in grapefruit, and estimated a value of
statistical cancer fatality at $6.99 million based on exposure assumptions.
Related Hedonic Property and Wage Studies
There are a small number of studies that have estimated WTP for reduced cancer risks using
revealed preference approaches. The results have generally shown that the value of a statistical cancer
case is similar to prevailing VSL estimates from hedonic wage studies. Direct comparison, however, is
difficult without additional assumptions about latency or cessation lag and cancer fatality rates, as noted
for each study.
In the context of hazardous waste, Gayer et al. (2000) and Gayer et al. (2002) employed a hedonic
property framework to estimate the implicit value of a statistical cancer case from surrounding
Superfund sites. In the first study, the value of a statistical cancer case was approximately $5.5 million,
but did not include any assumptions or information on latency or fatality. The 2002 study calculated
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estimates under a variety of latency and discounting assumptions with results ranging from $5.2 million
to $10.0 with no latency, and from $6.2 to $11.8 million using a 3% discount rate and 10-year latency
period.
Davis (2004) used housing price responses to an observed cancer cluster in Nevada to estimate
marginal willingness to pay for a change in lifetime pediatric leukemia risk ranging from $3.7 million to
$11.1 million, which is generally consistent with the Gayer et al. studies, although the leukemia values are
specific to children. Ho and Hite (2008) included risks from air toxics and hazardous waste sites in a
hedonic property model and estimated the implicit value of cancer mortality to be $6.0 million. Finally,
Lott and Manning (2000) explored the presence of compensating wage differentials for carcinogenic
exposures in the workplace using the hedonic wage framework, finding that workers were being
compensated for carcinogenic exposures. By making assumptions about the proportion of cancer deaths
that arise from occupational exposures they calculated a cancer-specific VSL of $12.4 million.13
Because reducing environmental cancer risk is an important part of EPA's mission to protect
human health, a key question is how the results from the empirical literature summarized here, along
with other literature described in this report, can be systematically synthesized to account for individuals'
preferences for reducing cancer risks relative to other types of health risks. As a first-cut, the simple
average of the central estimates of the cancer differential from the subset of studies in Table 1 that
reported values for both cancer and non-cancer risks is 52%.14 This is a preliminary estimate and should
be refined or replaced with a more systematic synthesis of the literature, possibly incorporating results
13 As stated earlier, all figures have been updated to 2009 dollars using the Consumer Price Index, unless otherwise
noted.
14 Specifically, the summary point estimates that we drew from each of the nine studies in Table 1 that
reported results pertaining directly to the cancer differential (i.e., VSLcancer / VSLnon-cancer -1) are: 0
(Hammit & Hanninger 2010), 0.5 (Alberini & Scansy 2010a), 0.85 (Alberini & Scansy 2010b), -0.15
(Adamowiz et al. 2008), 0 (Cameron & Deshazo 2008), 0.2 (Tsuge et al. 2005), 0.3 (Hammitt & Liu 2004), 3
(Van Houtven et al. 2008), and 0 (Magat et al. 1996). The average of these figures is 0.52.
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from other relevant studies. In the meantime, a cancer differential of 50% might be a reasonable
placeholder value for use in upcoming RIAs.15
4 Review of stated preference and hedonic wage studies
Our reviews of the literature in the sections that follow focus on results from stated preference
and hedonic wage and studies. This reflects where the majority of potentially relevant empirical
estimates are found and is consistent with prior consultations and advisory reports. The hedonic wage
approach is well-established and vetted and remains influential in informing guidance across the federal
government. However, the approach is limited to work-related risks and the associated risk
characteristics, many of which differ from EPA policy scenarios, as has been detailed many times in the
economics literature.
There has been a tremendous growth in the number of stated preference studies to estimate
values for mortality risk reductions in recent years; certainly there is now a far larger and more
sophisticated body of literature to draw upon than was available at the time of EPA's last revision of its
guidance. These developments potentially allow for an examination of important valuation dimensions
including risk source (e.g., environmental, traffic-related); type of illness (e.g., any cancer differential or
associated morbidity); and altruism. Our review of the empirical literature and how it can be synthesized
attempts to address these issues.
However, additional studies exist that may supplement the reviews of the stated preference and
hedonic wage literatures below. First, some stated preference studies do not seek to estimate willingness
to pay or accept, but rather relative preferences for different types of mortality risk reduction. Two
examples addressing cancer risks are described more completely above (Magat et al. 1996 and Van
15 Another possible way to represent the cancer differential would be to estimate the absolute (rather than fractional)
increment of the cancer mortality risk values over the values for non-cancer risks (i.e., VSLcancer - VSLnon-cancer).
This would require an additional step of estimating the income elasticity of this absolute cancer differential.
Estimating the fractional cancer differential implicitly assumes that the income elasticity of the absolute cancer
differential equals that for the non-cancer VSL.
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Houtven et al. 2008). The study results do not estimate willingness to pay, but it may be possible to
combine the estimates from the studies on relative tradeoffs with the willingness to pay literature to
refine our benefit transfers.
Another segment of the literature that we do not examine in detail here includes studies that
evaluate only public preferences for risk reducing policies. Examples from this literature include
Cropper et al. (1994) and Subramanian and Cropper (2000), who used survey methods to examine how
respondents would allocate a given public budget to public programs for lifesaving and risk reduction;
and Bosworth et al. (2009) who assessed community-level preferences for public programs to improve
health and safety. The SAB previously concluded that these studies can be informative in their own right,
but cannot be directly related to individual willingness to pay and used directly for benefit-cost analysis
(USEPA 2001). EPA is open to suggestions on whether and how this literature may be effectively and
appropriately synthesized with the results of other studies for the development of guidance on mortality
risk valuation.
The hedonic property method has been used to estimate the value of environmental amenities
and disamenities including mortality risks. A major challenge has been to limit the analysis to risk
reduction rather than more comprehensive measures or indicators of environmental quality, such as air
quality (e.g., Chay and Greenstone 2005) or the presence of or distance to hazardous waste sites (e.g.,
Greenstone and Gallagher 2008). These studies can be useful for evaluating some policies directly, such
as the remediation of hazardous sites, but cannot be directly informative for mortality risk valuation.
Willingness to pay for reduced mortality risks have been estimated in hedonic property studies, as first
described and demonstrated in Portney (1981), who examined the relationship between housing prices
and mortality risks from air quality. Four other studies, described more completely above in this paper,
estimate marginal willingness to pay for cancer risk (Gayer et al. 2000, 2002; Davis 2004; and Ho and Hite
2008).
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Finally, implicit values for risk reductions can be estimated in "averting behavior" studies,
wherein an individual or household uses the good as an input into the production of health or safety.
Blomquist (2004) conducted an extensive review of this literature and concluded, with some caveats, that
the findings are broadly similar to hedonic wage estimates. Recent additions to the literature are
generally consistent with this conclusion (e.g., Andersson 2005, 2008 (automobile risks); Hakes and
Viscusi 2007 (seatbelt use)). Key concerns about averting behavior studies include issues of risk
perception and the separability of joint benefits and costs (USEPA 2000b). Viscusi (1992) explicitly
excluded these studies from consideration in his meta-analysis of VSL estimates. Further, the lack of
available studies on environmentally-related risks limits the usefulness of this class of studies for the
present purpose of developing guidance for mortality risk valuation.16
4.1 Stated preference studies
Stated preference (SP) is a survey-based method for estimating willingness to pay or accept for
non-market goods or services. SP methods are widely used to value environmental amenities or
improvements in human health endpoints that may be difficult or impossible to estimate using revealed
preference methods because of long lag times, unclear causality, or other factors. For example, SP studies
have been used to elicit willingness to pay for reductions in the risks of dying from cancer and cardio-
vascular disease. SP studies vary widely in terms of the types of risk considered, payment vehicles,
latency periods, mode of survey administration, etc. The number of and variation among existing SP
studies is now large enough that the variation in their results can be analyzed statistically, although this
involves a number of data collection and model estimation challenges.
16 Note that there are some studies that relate averting behaviors to environmental quality or even related risks (e.g.,
Dickie and Gerking, 2009; Um, Kwak, and Kim, 2002), but, as documented in Blomquist, 2006, relatively few studies
estimate WTP for reduced mortality risks in an environmental context.
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4.1.1 Recent meta-analyses of SP studies
Three recent meta-analyses examined the stated preference literature using statistical methods.
Kochi et al. (2006) used both stated and revealed preference studies in an empirical Bayes framework.
Dekker et al. (2008) focused exclusively on stated preference studies, also with Bayesian methods.
Braathen et al. (2009) conducted a meta-regression analysis of a wide variety of stated preference studies
using classical econometric tools. Each of these studies is discussed in more detail below.
Kochi et al. (20061 used an empirical Bayes estimation method to generate predicted VSL
estimates using multiple estimates from both stated preference and hedonic wage studies. Here we focus
on the analysis and results for the stated preference data in their study. Study selection criteria were
similar to those used by Viscusi (1992), including the use of studies for the general population and those
conducted in high income countries only, and a minimum sample size.17 Another important criterion was
the use of estimates for immediate risk reductions; specifically, estimates for risks involving a latency
period were excluded.
Kochi et al. analyzed 45 VSL estimates drawn from 14 stated preference studies. The authors
recorded all estimates from each study and then separated them into "homogeneous subsets."
Specifically, they grouped estimates by lead study author and used a Q-test for homogeneity to
determine whether the estimates within a group are homogenoeous. After completing the separation of
the estimates into homogenous subsets, they recalculated the VSL for the subset to create a unique VSL
for that author. The recalculated mean reflects a weighted VSL of the estimates in the homogeneous
subset, where the weights are based on the standard errors for the estimates.18 This technique is intended
to address the troubling issue of choosing among multiple estimates from each study when those
17 Viscusi (1992) excluded two studies with sample sizes of around 30. Kochi et al. (2006) chose a minimum sample
size of 100 for their analysis.
18 Another implicit selection criterion in this study was the use of estimates with reported standard errors. In the
assembly of our new meta-analysis dataset, described in Section 4.1.2 below, we find that this may be a highly
constraining selection criterion.
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estimates may be based on overlapping samples. The process of creating homogeneous subsets resulted
in 18 stated preference VSL estimates with a mean of $3.5 million and a standard error of $0.67 million (in
2009 dollars).
Dekker et al. (20081 examined the influence of risk context (i.e., deaths from automobile-related
accidents, air pollution, and all causes) on willingness to pay estimates from SP studies. The authors
discussed the benefits transfer challenge associated with applying estimates from one context (e.g., auto
risks) to another (e.g., air pollution), particularly when there is limited empirical evidence on the size and
direction of the effects. Employing Bayesian techniques in a meta-regression, they compared willingness
to pay or accept estimates in three different risk contexts—air pollution, traffic safety, and
environment/general—while attempting to control for the size of the risk change and other respondent
and study characteristics. Several study design decisions by Dekker et al. were based on
recommendations from the EPA meta-analysis work group (USEPA 2006).
The authors used existing meta-analyses and additional literature searches to identify stated
preference studies for auto, air pollution, or context-free (unspecified) mortality risk reductions. After
searching the literature and applying screening criteria, a final database was assembled containing 98
VSL estimates from 27 studies, including three studies from the U.S. Seventy-one of the estimates were
based on studies of road safety, seven on studies of air pollution, and twenty on studies of "general
mortality" (presumably deaths from all, or unspecified, causes). The authors drew multiple estimates
from each study, although it appears that they attempted to ensure that those estimates were from non-
overlapping subsamples. Because of the small sample size that results from this approach they use
Bayesian techniques suitable for these situations.
The analysis by Dekker et al. focused on explaining variation in willingness to pay for discrete
changes in mortality risk reductions rather than the VSL and therefore includes as an independent
variable the magnitude of the risk change associated with each estimate. They found that willingness to
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pay estimates are lower when the commodity is described as a public good and that there is a premium
for risk reductions from air/general context over automobile risks.
Braathen et al. (2009) reviewed and conducted a meta-analysis of 75 studies with 900 estimates
from developed and developing countries. The authors recorded a variety of attributes for each estimate:
type of risk, country, survey mode, type of study, etc. The purpose of the study was to examine how
these attributes influence the resulting VSL estimates. Using classical econometric techniques, their
results show that methodological variables (i.e., type of payment questions, survey mode) explain 70
percent of the variation in the estimates. Of particular relevance to EPA, the authors found that health
risks are valued lower than traffic and environmental risks, in contrast to the results of Dekker et al.
However, risks to individuals are valued higher than risks to the public, similar to the results of Dekker et
al. (2008). The work of Braathen et al. still is preliminary and, like the Dekker et al. meta-analysis, it
includes studies from both developed and developing countries.
4.2.2 A new meta-analysis dataset
In an effort to both update the estimate or range of estimates used by EPA, we have constructed a
new dataset containing information from a set of studies reflecting the current literature appropriate for
application to U.S. environmental policy.19 We used EconLit, conference proceedings, published and
unpublished meta-analyses, working paper series, and personal contacts to identify and generate a
comprehensive list of stated preference mortality risk valuation studies from 1974 and later.20
Each study was screened to ensure that it provided empirical estimates of the value of mortality
risk reductions (i.e., purely theoretical studies and those that only examined morbidity were not
included). Following the advice from the SAB-EEAC (USEPA 2007), we established a set of selection
19 There is substantial overlap between our data set and those reflected in the meta-analyses reviewed in this section.
Differences are due to different selection criteria and new studies that have appeared since the other meta-analysis
studies were conducted.
20 The earliest study that forms the basis of the recommendations of the existing EPA Guidelines (2000a) was
conducted in 1974. Therefore, we limited our search for relevant literature to this starting date, assuming that the
earlier literature had been vetted and judged to be obsolete prior to the release of the 2000 Guidelines.
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criteria that determined which studies to include in our final data set. These criteria are based on
information from other meta-analyses, as well as our own best judgment regarding study features
necessary for application to valuing mortality risk reductions when analyzing U.S. environmental
policies. The criteria we applied are as follows:
• minimum sample size of 100,
• sample frame based on general population,
• conducted in a high-income country,21
• results based on exclusive dataset,
• written in English,
• provides enough information to calculate a WTP estimate if one is not reported in the paper,
• provides estimates for willingness to pay (willingness to accept estimates were not included),22
and
• provides estimates for willingness to pay for risk reductions to adults (estimates for risk
reductions to children are not included).
We focus on studies with a sample size of at least 100 because smaller samples tend to suffer from
small sample size problems (e.g., less precision) and are less likely to be representative of the general
population. Because the purpose of this exercise is to determine an estimate or range of estimates for use
in environmental policy, we limit our studies to those of the general population as opposed to specialized
subgroups, like students or business owners. In addition, because our focus is on U.S. environmental
policy we choose to limit our studies to those conducted in high-income countries. Socio-economic and
cultural differences between the U.S. and most developing countries may be too large for reliable
21 High-income countries are defined as having a gross national income per-capita of $11,906 (2008 US dollars)
according to the World Bank reports (www.worldbank.org). The most recent World Bank data is for 2008.
22 Three studies report willingness to accept estimates. These studies also report WTP estimates so we do not reject
any study based solely on this criterion.
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transfers of value estimates. Our own language limitations required that we restrict ourselves to studies
written in English. Finally, we limit our investigation to willingness to pay estimates for adults only.
Thirty-three studies published between 1988 and 200923 meet the selection criteria described
above, yielding nearly 450 willingness to pay estimates. For each of the studies we recorded all
willingness to pay and value of statistical life estimates that were reported in the study, as well as those
we could calculate based on information available in the study.24 The meta-analyses using stated
preference studies we described earlier draw multiple estimates from each study, and each has a different
way to address the fact that these estimates are almost always drawn from overlapping samples (e.g.,
authors report multiple results from different estimation exercises or sub-samples within their data).
However, we believe that the issues associated with using multiple estimates from each study are
sufficiently problematic to warrant selection of independent estimates from each study.25 Table 3 reports
selected data for each study with detailed footnotes to describe the decisions to support the selected
estimates.26 This exercise results in 40 independent estimates. We report select characteristics for each
estimates along with the willingness to pay and standard errors (reported in $/|jr). The willingness to
pay for micro-risks are either directly extracted from the underlying studies (when the information was
reported in the papers) or calculated by dividing the VSL estimates by 10 6 when the WTP estimates are
not reported.
All estimates were recorded in the currency and dollar year presented in the study. If the dollar
year was not noted or could not be gleaned from other information in the study then we assumed that it
23 While we set a start date of 1974 for inclusion in our data set, only studies published after 1988 met our selection
criteria.
24 For the most part, all possible estimates were calculated or recorded for each study. We did not, however, record
or calculate estimates for various levels of confidence respondents had in their responses, passing/failing quizzes
about risk, and various forms of scenario rejection. We felt that these estimates were designed mainly to test the
validity of the survey instrument and not to produce central estimates of mortality risk valuations per se.
25 Later we discuss in detail the various issues associated with using multiple estimates and how this can be
addressed econometrically.
26 In general we opted for the estimate(s) that were the most inclusive of all the data in the study. Alternatively, we
could select more estimates from each study - for example, by including estimates by age group - if this was
determined to be an important dimension to the analysis.
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was the year prior to the release or publication of the paper. All estimates are for individuals; when it
was clear that an estimate reflected a household willingness to pay, we divided those estimates by the
average household size for the country and year when the study was conducted. We then converted all
estimates to U.S. dollars using the Purchasing Power Parity Index for the dollar year of the estimates.
Next, all estimates were converted to 2009 dollars using the Consumer Price Index (CPI) and adjusted for
income growth over time assuming an income elasticity of 0.5.
In addition to the willingness to pay estimates and standard errors (when available), we
quantified and recorded as much information as we could for each study. Our data set includes whether
or not the study was published in a peer-reviewed journal, the year it was conducted and published or
released, the country where the study was conducted, sample characteristics, risk reduction information
(e.g., magnitude, type of risk), scope tests, public versus private risk reductions, etc. See Table 2 for a
description of many of the variables in our data set. Much of this information is only available for a
subset of studies, particularly information on the demographic characteristics of the sample.
Twenty-two studies were published in journals, with 13 published in the Journal of Risk and
Uncertainty. Six of the remaining studies are unpublished reports or working papers and five are book
chapters. We identified nine different sources of mortality risk represented in the studies, including
automobile accidents, air pollution, drinking water, hazardous waste sites, and food. The studies were
predominantly conducted in the U.S. and Europe. Other countries represented in the data include
Canada, Japan, Taiwan, and New Zealand.
Most of the studies are contingent valuation studies where the choice question involves stating a
response (e.g., yes/no to a dichotomous choice question, open-ended response) to a scenario with a fixed
set of attributes. Several studies are choice experiments in which respondents choose one option from
several in which the attributes, including the magnitude of the risk reductions and the cost, vary across
the options.
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The average sample size for the estimates is 814 observations with a range of 13 to over 2,000.27
Most studies were conducted with a self-administered mode via web-TV or a centralized computer
facility. The second most common mode is an in-person survey. Other modes represented in the data
include mail, telephone, and a combination of the two. A scope test was performed or calculated for
about half of the estimates, and of those about 90 percent passed a weak form of the test (i.e., willingness
to pay estimates exhibited a statistically significant increase with the size of the risk reduction, but was
not necessarily proportional). Fifteen percent passed a strong form of the scope test (i.e., willingness to
pay was proportional or nearly proportional to the size of the risk reduction).
4.2 Hedonic wage studies
In their recommendations to EPA, the SAB-EEAC and the Meta-Analysis workgroup clearly
stated that both revealed hedonic wage and stated preference studies should be considered when
deriving estimates of mortality risk values (USEPA 2006, 2007). Both groups also recommended that the
two segments of the literature be analyzed separately. In this section we focus on the hedonic wage
literature.
Hedonic pricing models use statistical methods to measure the contribution of a good's
characteristics to its price. As applied to the labor market, hedonic wage studies (also known as
compensating wage studies) are based on the premise that heterogeneous goods and services can be
viewed as "bundles" of attributes and are differentiated from each other by the quantity and quality of
these attributes. Fatal and nonfatal risks are among the many attributes that differ across jobs. All else
equal, we would expect riskier jobs to pay higher wages. Therefore, it should be possible to estimate the
value associated with reduced occupational fatality risk using data on wage and risk differentials among
27 This is the sample size for the recorded estimates. Most studies used a subset of the data when recording different
estimates (e.g., males only, younger respondents only). All studies meet the criteria of a minimum sample size of 100
respondents.
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jobs, controlling for other factors that might influence the wage. A standard regression equation in the
hedonic wage literature is
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classifications (assigning all occupations within an industry the same risk) or by broad occupational
classification (ignoring potential differences within an occupation across industries).
A number of recent studies, however, have turned to the Bureau of Labor Statistics' Census of
Fatal Occupational Injuries (CFOI) as the source for workplace risk characteristics. The CFOI data are
considered the most comprehensive data on workplace fatalities available (Viscusi 2004), compiling
detailed information since 1992 from all states and the District of Columbia. Not only are the counts of
these fatal events reported by 3-digit occupation and 4-digit industry classifications, but the
circumstances of the fatal events as well as other characteristics of the workers involved (e.g., age, gender,
race) also are recorded.28 To ensure the veracity and completeness of the reported data, multiple sources
are consulted and cross-referenced, including death certificates, workers' compensation reports and
Federal and State administration reports. To form a complete dataset for estimation, these data still must
be paired with worker samples drawn from another source (often the Current Population Survey) and
fatality rates still must be constructed by the researcher using estimates of the number of workers, as with
the other BLS data.
4.2.2 Estimation issues
Recently, EPA funded a study to examine the hedonic wage methodology and to provide a
quantitative assessment of the robustness of the resulting value estimates for mortality risk reductions.
The results of this research are summarized in Black et al. (2003) and were subsequently published in
Black and Kniesner (2003). These studies examined the roles of the functional form of the estimating
equation, measurement error, and unobservable characteristics using various commonly used data sets.
Their findings highlighted a number of potential problems with previous hedonic wage studies. First,
they found that estimates of the value of risk reductions can be very sensitive to seemingly minor changes
in the specification of the regression equation. In fact, many specifications lead to negative estimates,
28 More information on the CFOI data is available at: http://www.bls.gov/iif/oshfatl.htm.
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which would suggest that people would be willing to accept lower wages for jobs with higher risks. They
were unable to alleviate this problem using more flexible functional forms, so they concluded that this
instability is not due to equation mis-specification. Instead, they found strong evidence that the job risk
estimates contain considerable measurement error.
Black and Kniesner (2003) examined both the BLS SWC and NIOSH data sets (the CFOI dataset
had not been widely used by that time). Their results indicate that, while both datasets have advantages
and disadvantages, they both also are subject to considerable measurement error. They identified three
sources of measurement error in the two data sets:
• sampling variation within industry and occupation cells given the small size of some of the cells
(in recognition of this problem, BLS and NIOSH suppress data when the number of fatalities is
low),
• heterogeneity in job risks and non-random assignment of those risks within occupations (e.g., late
night convenience store clerks tend to be male and older), and
• industry and occupation are not measured accurately, especially at the three-digit level.
Moreover, they found that the measurement error is correlated with covariates commonly used in the
wage equations and is likely correlated with the regression error as well. They concluded that studies
that do not control for measurement error suffer from attenuation bias, resulting in under-estimates of
mortality risk values. They also concluded that the NIOSH data produce results most consistent with
economic theory.
4.2.3 Recent meta-analyses ofhedonic wage studies
In addition to the methodological assessment conducted by Black and others, several meta-
analyses of the hedonic wage literature have been conducted in recent years. We focus here on four
recent studies, three of which were reviewed by the Meta-analysis workgroup convened by EPA. The
fourth was published after their deliberations.
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Mrozek and Taylor (20021 used multiple observations from 47 hedonic wage studies. Variables
included in their meta-regressions were of three types: (1) those which may influence wage/risk tradeoffs
(e.g., mean hourly earnings), (2) those describing the sample, and (3) methodological choices of the
original researchers (e.g., if a risk-squared term was included in the estimating equation).
The authors used weighted least squares where the weights were the number of estimates
provided by the study. This ensured that each study was weighted equally, regardless of the number of
observations drawn from it. Four meta-regression models were estimated, each using log(VSL) as the
dependent variable. All four models indicated a positive and significant relationship between the mean
risk and VSL. The authors used the meta-analysis results to "predict" the VSL as if the original studies
had all followed a set of "best practice" assumptions. The predicted values range from $1.78 million to
$15.4 million (2009 dollars). Those assuming the use of National Institute for Occupational Safety and
Health (NIOSH) data are higher than those assuming use of Bureau of Labor Statistics (BLS) data. The
authors concluded that the evidence best supports an estimate of $2.69 million at the average
occupational risk level of 0.5 per 10,000 (2009 dollars).
While this study provides a comprehensive overview of the hedonic wage literature, it includes
studies using older (and possibly unreliable) occupational risk data. In addition, the authors excluded
estimates in original studies that were statistically insignificant or negative.
Viscusi and Aldv (20031 conducted a review of more than 60 hedonic wage studies of values for
mortality risk reductions across 10 countries (including 52 from the U.S.), examining a number of
econometric issues, the effects of unionization on risk premiums, and the effects of age and income on
VSL estimates. No studies were eliminated from the sample, and no attempt was made to modify the
original VSL estimates. Point estimates extracted from each study were those based on the "whole
sample" and the original authors' preferred model specification. Viscusi and Aldy generated summary
VSL estimates by using the estimated coefficients from the meta-analysis to predict the natural logarithm
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of VSL for each original study, then study-specific predicted-VSLs were averaged to produce an overall
mean estimate. Predicted U.S. mean values were constructed based on regression samples using all
countries, but with averaging across U.S. studies only. The predicted values in the study for the U.S.
range from $6.85 million to $9.47 million (2009 dollars), and the median predicted values were generally
very close to the means.
Kochi et al. (2006) used an empirical Bayes estimation method to generate predicted VSL
estimates based on previous hedonic and stated preference studies. Here we focus on the analysis and
results for the hedonic wage data. Using selection criteria similar to those from Viscusi (1992), the
analysis included 162 VSL estimates from 31 hedonic wage studies. All possible VSL estimates and
associated standard errors for each included study were re-estimated based on information provided in
each original study. Estimates without standard errors were not included. The homogeneous subsetting
method described earlier also was applied to the hedonic wage estimates (the hedonic and stated
preference data were analyzed together), resulting in 42 VSL estimates from hedonic wage studies with a
mean of $11.96 million and a standard error of $0.62 million (2009 dollars). Because of the subsetting
technique employed to pool the estimates, Kochi et al. could not explicitly account for study design and
population characteristics in their analysis.
Bellavance et al. (2009) is the most recent meta-analysis of the hedonic wage literature. The
authors' principle objective was to better understand the variability in VSL estimates from hedonic wage
studies, which is described as ranging from $0.5 to $50 million. Thirty-nine VSL estimates from 37
studies were assembled based on those used in prior meta-analyses and further searches of several
economics databases. The resulting dataset contains sixteen studies from the U.S., seven from Canada,
and three or fewer from each of several other countries. The earliest study is from 1974 and the most
recent is Viscusi (2004).
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The authors draw only one VSL estimate from each study. Standard errors were recorded or
computed for 32 of the 39 estimates. Criteria were established to chose the specification within each
study, including: (1) no interaction terms between the probability of death and other explanatory
variables (in order to more easily compute the standard error), (2) similarity of specification to other
included studies, (3) larger samples with characteristics most similar to other studies, and (4) the
recommendations of authors of prior meta-analyses. Bellavance et al. acknowledged that the source for
U.S. risk data varies and has evolved over time from early BLS surveys to NIOSH to BLS' Census of Fatal
Occupational Injuries (CFOI). However, their analysis did not control for the data source other than for
the use of Society of Actuaries (SOA) data, which was found to have a significant impact on the estimated
VSL. Sensitivity analyses were conducted with and without studies using SOA risk data.
Using a mixed effects model (random intercept with fixed effects for study characteristics), the
authors regressed the VSL estimates on average income, probability of death, and several study design
variables. The mean weighted average VSL is approximately $7.23 million (2009 dollars). Other key
findings include that the VSL is significantly higher for studies that treat risk as endogenous, and there is
some evidence that the VSL declines with the baseline risk.
4.2.4 A new meta-analysis ofhedonic wage studies
Using Appendix 1 from Bellevance et al. as a starting point, we constructed a new data set of
hedonic wage studies, augmenting the information contained therein with data from Kochi et al. (2006)
and Viscusi and Aldy (2003). We also conducted a full text search in JSTOR for "Census of Fatal
Occupational Injuries" and "CFOI" in order to develop a comprehensive list of studies using these data.
A total of 14 CFOI studies were reviewed, with those actually using the CFOI data in an original, hedonic
wage analysis retained for further assessment. These seven studies were further augmented with an
unpublished manuscript using the CFOI data, for a total of eight additional studies.
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Additional searches were conducted in JSTOR for studies published in 2000 or later using the key
words "hedonic wage" and "compensating wage." We also conducted a search in the Social Science
Citations Index for studies citing Viscusi (2004), a paper that derives mortality risk valuation estimates
controlling for occupation and industry using the CFOI data.
In constructing our data set, we generally employed the same selection criteria used in Bellavance
et al. (2009), with some exceptions based on our own judgment and to ensure consistency with the criteria
used for the stated preference data set. First, we limited our data to those studies with a sample size of
100 or more. We also retained only those studies conducted in a high-income country as defined by the
World Bank. Third, we omitted studies that rely on Society of Actuaries data as the source of risk
information as these data are thought to reflect broader risks than those experienced on the job (Viscusi
1992, Kochi et al. 2006). We further limited our data by excluding those studies that focus on extremely
dangerous jobs (e.g., police officers), since the risk preferences of individuals who take these jobs may
differ substantially from those of the general public. We do, however, apply the other selection criteria
employed by Bellavance et al., including retaining only those studies using a model specification similar
to that given near the beginning of this section, excluding studies based on specific causes of death,
excluding studies using the same samples as other studies, and excluding studies failing to report enough
information to calculate the value of mortality risk reductions and/or the average probability of death.
Applying all of these criteria resulted in the selection of 37 studies.
For each of our selected studies we recorded the following key variables: year of publication, the
country in which the sample was drawn, sample size, average income, average annual probability of
death, source of risk information, the estimated coefficient on the risk variable, whether the sample was
exclusively male, manufacturing, blue collar and white, as well as whether the regression controlled for
nonfatal risks, union status, and worker compensation. We calculated VMRs for each study by deriving
the VSL and dividing these estimates by 106. As with our stated preference data, all estimates are
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reported in 2009 dollars after adjusting for inflation using CPI and accounting for income growth over
time assuming an income elasticity of 0.5.
Similar to the stated preference data, we capture only one specification per study in our database,
following the criteria established by Bellavance et al.29 Because the hedonic studies are more
homogeneous in their design than the stated preference studies, we are able to be more selective in which
specifications to include. Although one motivation here is to minimize the influence of each individual
study, it does not necessarily rid us entirely of the problem of overlapping subsamples as many of the
studies draw their samples from the same source.
Table 4 lists key characteristics for our selected studies.30 A total of 24 studies out of 37 were
conducted in the U.S. with 3 using NIOSH data, 13 using BLS data and 8 using CFOI data as the source of
occupational risk. Seven of these twenty-four studies rely on the Panel Study of Income Dynamics (PSID)
as a source for worker characteristics with another 11 using CPS data. Twenty-six studies included
women in their samples and 7 focused on blue collar workers only. Three studies restricted their samples
to union members only. Average sample size across studies was 17,741, and the average income was
$40,508 per year (2009 dollars). The mean probability of occupational death across studies was 0.00014.
5 Income Elasticity Considerations
EPA first attempted to address the income elasticity of VSL issue in its analysis of The Benefits and
Costs of the Clean Air Act, 1990 to 2010 (US EPA, 1999), which made a distinction between application of
income adjustments for longitudinal changes in income over time and cross-sectional income differences
for benefit transfer. The report applied a range of VSL income elasticities in a sensitivity analysis to
project the value of reduced mortality risks in the year 2010.
29 Note that some hedonic studies report results for multiple non-overlapping subsamples (e.g., male vs. female,
union vs. non-union) within the study. Rather than capture these multiple observations, we have elected to
implement the selection criteria used by Bellavance et al.
30 Information reported in the table was adapted from Bellavance et al. (2009).
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The issue was further developed in EPA's White Paper Valuing the Benefits of Fatal Cancer Risk
Reductions, where income was one of the many benefit transfer issues to be addressed. The SAB-EEAC
review of the White Paper concluded: "With regard to population characteristics, the Committee believes
that it is appropriate to adjust the value of the projected statistical lives saved in future years to reflect
higher incomes in those years, but not for cross-sectional differences in income, because of the sensitivity
of making such distinctions."31 The SAB-EEAC recommended that any appropriate adjustments for
income growth should be part of the Agency's main analysis.
Based on a review of the empirical literature on the cross-sectional income elasticity of VSL
literature originally developed for use in The Benefits and Costs of the Clean Air Act, 1990 to 2010 report,
EPA analyses have typically applied a range of estimates with a low end of 0.08, a central value of 0.4,
and a high end of 1.0. Many analyses characterize this range with a triangular distribution with a
resulting mean estimate of approximately 0.48. Income elasticity is then typically paired with projections
of growth in real US GDP per capita.
More recent information on the income elasticity of VSL has come primarily from meta-analyses
of hedonic wage studies. The results in Mrozek and Taylor (2002) suggest income elasticities ranging
from 0.37 to 0.49, although the authors note that these results should be interpreted with caution because
of measurement error in the income variable and the functional form used by many hedonic wage studies
included in their meta-analysis. As described earlier in this paper, more recent work from Viscusi and
Aldy (2003) estimates the income elasticity of the VSL in the range of 0.5 to 0.6, slightly higher than the
mean value used in many EPA analyses. None of the 95 percent confidence bounds on the Viscusi and
Aldy estimates include a VSL income elasticity as high as 1.0. The Bellevance et al. (2009) meta-analysis,
31 "An SAB Report on EPA's White Paper Valuing the Benefits of Fatal Cancer Risk Reduction," US EPA, 2000, page 7. A
2007 SAB review also noted the empirical difficulties of accounting for differences in real income and wealth across
populations due, in part, to "uncertainty about the value(s) of income elasticity and very little empirical evidence
concerning the relationship between wealth and mortality valuation." US EPA 2007, page D-7.
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also described earlier, predicts somewhat higher elasticity estimates ranging from 0.84 to 1.08 depending
upon the model.
Some recent theoretical research has examined the relationship between the income elasticity of
the VSL and the coefficient of relative risk aversion and noted that these two quantities should be very
close in magnitude. This can be seen most easily in a simple two-period model. Let "lifetime" utility be
the expected discounted sum of utility in both periods: U = Ux 4- p/3u2, where ut is utility in period t,
p is the probability of survival between periods 1 and 2, and is the utility discount factor. Also assume
that ut depends on income in period t and takes the standard "constant relative risk aversion" (CRRA)
form: ut = C',' " J — 77, where t) is the coefficient of relative risk aversion. The VSL is the marginal rate
of substitution between the individual's first period income and her probability of survival to the second
period, i.e., VSL = / dP~2^U/ dyl j= yl (3 Q2'1 2 C —y and so the income elasticity of the VSL is
CVSL/dyl ~jf. ^'|/VSL j= 77 . Kaplow (2005) examined a more realistic version of this model by allowing
for self-defensive expenditures that could increase the individual's survival probability. Using that
elaborated model, Kaplow showed that the income elasticity of the VSL should be at least as large as 1
when 0 < rj < 1, and at least as large as rj when 77 > 1.
Empirical estimates of the coefficient of relative risk aversion span a wide range—from around
0.5 to 1 at the lower end (e.g., Shepard and Zeckhauser 1984, Eeckhoudt and Hammit 2001, Chetty 2006)
to 10 or more at the high end (e.g., Kocherlakota 1990)—but most estimated or assumed values for rj
seem to fall in the range of 1 to 3. For example, Hall and Jones (2008) and Hall (2010) estimated rj to be
around 2, based on the recent trend of income growth and the more rapid growth in health care
expenditures in the United States. Szpiro (1986), Feldstein and Ranguelova (2001), Barro (2006), and
Layard et al. (2008), among others, also estimate or use values of T] in this range. And in the
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contemporary climate change economics literature, the most commonly used values of // are 2 to 3 (e.g.,
Arrow 2007; Nordhaus 2008; Dasgupta 2008; Weitzman 2009, 2010a,b).
The theoretical considerations combined with (most of) the empirical estimates of relative risk
aversion cited above are at odds with the early estimates of the income elasticity of the VSL in the
neighborhood of 0.5 cited above. In a more recent study, Kneisner et al. (2009) applied a quantile
regression approach to a dataset assembled from the Panel Study of Income Dynamics (PSID) and the
Census of Fatal Occupational Injuries (CFOI). Their preferred regression model produced estimates of
the income elasticity of the VSL between 1.23, for the lowest quantile, to 2.24, for the highest quantile.
Kneisner et al. note that "Our estimates of a large income elasticity of VSL are consistent with the simple
theoretical models that have been developed [by Kaplow (2005)]," and "With recent estimates of the
coefficient of relative risk aversion being around 2 based on the labor supply analysis of Chetty (2006)
and the consumption analysis of Kneisner and Ziliak (2002), one would expect the VSL to be income
elastic, which is what the results above indicate."
Based on theoretical considerations such as those examined by Kaplow (2005) and the new
empirical results of Kneisner et al. (2009), EPA believes that its recommended estimate of the income
elasticity of the VSL appears to be on the low end of the range of estimates and may need to be updated
to a higher value or range of values.
6 Methods for Combining Data
The values for mortality risk reductions estimated in the stated preference and hedonic wage
studies described above constitute a current empirical summary of the literature, which can be used to
inform the revision of EPA's mortality risk valuation guidance. These studies could be combined or
synthesized in a number of ways, from a simple point estimate to range, distribution, or systematically
combined in a more rigorous meta-analysis. Our objective in this section is to outline analytical options
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that can be implemented in the longer term for updating the estimate or range of estimates used by EPA
in our guidance on valuing morality risk reductions. We begin with meta-analysis methods, including
methods similar to those used in our current guidance and extending to more rigorous application of
meta-regression techniques. This is followed by the structural benefit transfer approach, which involves
calibrating a direct or indirect utility function so that it is consistent with summary estimates of values for
health risk. Our goal is to provide enough information on the analytical options and key issues to receive
clear recommendations from the SAB-EEAC on an approach to implement for updating our guidance and
on future research directions.
6.1 Meta-analysis
There are several options for obtaining simple summary statistics or ranges from the existing
data. We outline these options and key issues in order of increasing complexity.
6.1.1 Parametric distribution
EPA's current guidance took one best estimate from each of five stated preference and twenty-
one hedonic wage studies and then fit a parametric distribution to the values. The resulting mean and
distribution has become EPA's default estimate for valuing mortality risk reductions. To replicate this
approach we could use the databases of SP and HW studies discussed above and then separately
characterize the resulting distributions in a curve-fitting exercise. Based on these distributions we could
define a range of default values for the value of mortality risk for EPA policies. Key choices and
principles are:
• Use all "independent estimates" from the studies rather than one estimate per study. Because many studies
provide estimates for different subpopulations or other treatments, we can often include multiple
study estimates without gross violations of independence. An alternative is to rely upon a single
estimate per study, which has been done for several meta-analysis.
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• Update all study estimates to a common year, including the effect of real income (GDP per capita) growth over
time and the estimates income elasticity of the VSL. The review of the literature in the prior section
already includes this update.
• Limit SP study estimates to those that are non-cancer and non-latent. In so doing, we will produce a "base
value" that should be more consistent with estimates stemming from the hedonic wage literature.
We will attempt to address any systematic difference in value between reduced cancer risks and
other types of risk separately. In part, this is simply recognizing that EPA policies affect both cancer
and non-cancer mortality risks and different values for each may be appropriate. Similarly, EPA
policies address risk reductions varying from the near-immediate to those delayed over many years,
a benefit-transfer aspect that we address by discounting over estimated latency periods. Including
latent risks in this simple aggregation would double-count the effects of timing on value.
• Include public-risk studies or rely only on private-risk SP studies. Most EPA regulations result in public
risk reductions. To avoid under-counting benefits, we would want to err toward inclusion, basing
guidance on the full set of relevant studies including those that incorporate altruism even if we
cannot distinguish whether it is paternalistic or non-paternalistic. On the other hand, to avoid
double-counting of benefits we would want to use only those studies that capture private willingness
to pay for mortality risk reduction. Clear recommendations from the EEAC on this issue in particular
would be very helpful.
6.1.2 Classical econometrics
A second approach to combining the information from multiple studies—to determine the
characteristics of the studies that influence the value estimates or to generate a benefit transfer function-
is to perform a meta-regression using classical econometrics. Two issues arise when considering this
approach. First, the analyst must decide which observations to include in the analysis. Some previous
meta-regression studies have used all relevant observations in the analysis (e.g., Nelson and Kennedy
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2008, Braathen et al. 2009, Mrozek and Taylor 2002). This approach incorporates all available
information, but runs the risk of including estimates from overlapping samples (and therefore non-
independent observations). For example, the same individual(s) may be represented multiple times in
the data when a paper reports multiple estimates using different modeling assumptions. Restricting the
data to non-overlapping samples is a non-trivial exercise because choosing the most appropriate
estimate(s) from each study involves subjective judgment. In addition, small sample size problems —
already a hurdle in meta-analysis—are exacerbated when the sample is limited in this way. The stated
preference and hedonic wage meta-analysis datasets described in Section 4 draw independent samples
based on procedures outlined above. However, a very strict interpretation of the requirement for non-
overlapping subsamples for the hedonic wage studies could result in just a handful of estimates for use in
a meta-analysis given the reliance by authors on the same sources of data.
Second, there are econometric issues to consider when analyzing these data. Nelson and
Kennedy (2008) discuss "factual" versus "methodological heterogeneity." Factual heterogeneity arises
because of real differences in what the primary studies are measuring. For example, the wtp for auto risks
may factually differ from that for cancer risks. Similarly, the wtp for occupational risks for male blue-
collar workers may factually differ from that estimated for a more inclusive sample. Methodological
heterogeneity arises because of different study design choices, such as the use of different models to
estimate willingness to pay. When these sources of heterogeneity are unobserved, errors may be
correlated. It also is likely that estimates produced by different surveys and designed by different
authors have different variances, making heteroskedasticity a concern. Classical econometrics provides
several approaches for dealing with correlated errors and heteroskedasticity. A fixed effects model
assumes that the unobserved heterogeneity among studies can be captured with an intercept shift. By
including a dummy variable for all but one of the studies, the intercept shift is estimated directly. This
approach can result in low degrees of freedom if each study contributes a small number of estimates. An
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alternative approach that does not require a new independent variable for each study is the random
effects model. Using the "composite error" exposition of the random effects model, the estimating
equation is
ytj
where yi}- is WTP estimate j from study i, x;/ is the row of data for that estimate, and P is a vector of
coefficients. The error term sj}- has the following structure
Etj =ui + Vy, where u ~ N 0,
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presents a few, select estimates. Mrozek and Taylor (2002) used this approach, as discussed above. This
insures that each study is given equal weight, as opposed to each estimate. The sample size for each
estimate also could be used to generate weights. Observations that arise from larger samples should be
more precise, all else equal. However, sample sizes are not available for all observations in our meta-
analysis datasets. Mrozek and Taylor (2002) used the level of significance of the VSL estimate to create a
f-statistic weight in an appendix to their paper. The estimating equation for this approach is:
1 1
— yV =— XyP
//; nt
where nt is the number of estimates or sample size from the /"' study. This technique provides more
efficient estimates than unweighted estimation of the analogous model.
Considering the data issues common to meta-analyses of willingness to pay estimates for
mortality risk reductions, we propose two classical approaches meant to address both heteroskedasticity
and correlated errors arising from unobserved study heterogeneity when multiple estimates are drawn
from each study. Weighted least squares estimation, as discussed above, can correct for
heteroskedasticity. However, relevant statistics may not be reported to construct the ideal weights. If
weighted least squares is used, we suggest testing for heteroskedasticity and using standard errors that
are robust to clustering. Alternatively, one could estimate a study-level panel model to account for
unobserved heterogeneity and calculate standard errors that are robust to heteroskedasticity. Since many
studies provide just a few estimates, a fixed effects model may not be feasible while a random effects
model would preserve degrees of freedom. We are particularly interested in EEAC comments on these
alternatives.
6.1.3 Bayesian estimation
In the previous section we discussed how classical estimation techniques could be used to
estimate a meta-regression of values for reductions in mortality risks while addressing heteroskedasticity
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and correlated errors. However, if we use data sets with non-overlapping estimates—as has been
recommended by the Meta-analysis workgroup, and as is reflected in the summary of stated preference
and hedonic wage estimates in Tables 3 and 4—our data selection criteria leave us with relatively small
samples for meta-regression. The combination of small sample size and non-spherical errors presents a
particular problem for classical approaches to estimation. Specification tests, including those for
heteroskedasticity, and calculations of robust standard errors rely on asymptotic relationships and
therefore may not be reliable when the sample size is small (Moeltner and Woodward 2009). Bayesian
estimation has desirable small sample properties and can more easily accommodate general error
structures.
Bayesian analogs to the classical approaches discussed above have been developed and can be
used to estimate a meta-regression model to improve value estimates and provide richer inference into
the results. Koop (2003 p 124-129) presented a Bayesian pooled regression model with an error structure
general enough to be robust to correlated errors and heteroskedasticity even when the form of
heteroskedasticity is unknown. Moeltner and Woodward (2009) use this model to estimate a meta-
regression of wetland valuation estimates from a sample of just 12 values from 9 studies. They use Gibbs
sampling to estimate the model
yj=xB + sj with Cj N 0,cr2fc>; , and IG
fv v
.2 1,
where y^ is WTP reported in study j, X;- is a row vector of population and other characteristics
associated with study j, (3 is a vector of regression coefficients, Ł. is a zero mean regression error with
variance <7 COj, and IG denotes the inverse-gamma distribution. This approach allows the authors to
estimate study-specific variances by estimating a single parameter v and drawing ok in a data
augmentation step. Moeltner and Woodward (2009) showed that Bayesian estimation can be used to
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conduct meta-regression on small heteroskedastic samples and produce consistent and efficient
parameter estimates.
A Bayesian analogue to the study-level panel model is also developed by Koop (2003 p 149-157).
Bayesian estimation of a study-level panel model with a non-hierarchical prior is analogous to the fixed
effects model in classical econometrics because the unobserved heterogeneity between studies is
attributed to a constant (intercept shift) for each study. If the number of studies is large relative to the
number of estimates from each study then, just as would be the case under classical assumptions, the
high-dimensional parameter space can be problematic. In these cases it may be beneficial to use a
hierarchical prior which places more structure on the unobserved heterogeneity by assuming the study-
level effects can be drawn from a distribution, thus only the parameters of that distribution, and not the
individual effects themselves, need to be estimated. Bayesian estimation of a panel model with a
hierarchical prior is analogous to the classical random effects panel model. In both cases the error
structure imposed on the model is general enough to be robust to non-spherical errors due to correlation
within studies and heteroskedasticity.
6.2 Structural benefit transfer
Thus far we have discussed meta-analysis, including classical and Bayesian approaches to
estimating a meta-regression model, which then could be used for functional benefit transfers. Using
meta-regression, the form of the estimating equation, and therefore the transfer function, typically would
be based on a combination of statistical tests and qualitative theorizing about the important variables to
include in the model. The resulting function can be viewed as a low-order Taylor series approximation to
the "true" preference function within the range of the data used to estimate it.
In contrast to the meta-regression approach, structural benefit-transfer (also known as preference
calibration) involves first specifying a direct or indirect utility function for a representative individual,
then deriving analytical expressions for observable economic outcomes from the utility function (Smith et
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al. 2002, 2006). Such observable outcomes could include labor-leisure tradeoffs, demand for related
market commodities, equilibrium wage schedules for jobs with differing risk or other characteristics,
responses to stated preference survey questions, etc. The parameters of the utility function are calibrated
using data on such outcomes, and the calibrated model then can be used to predict willingness to pay or
accept for any policy changes that can be described by variations in one or more of the parameters that
appear in the calibrated preference function.
The key advantages of the structural benefit transfer approach are that it provides a means of
combining estimates from separate studies that use different benefit concepts (e.g., marginal or non-
marginal willingness to pay or accept, consumer surplus, compensating or equivalent variation, etc.), and
it assures the economic consistency of transfers (Smith et al. 2002, 2006). In this context "economic
consistency" means, for example, that estimated willingness to pay will never exceed income, that value
estimates will always be responsive to scope (the size of the postulated change in quantity or quality),
that WTP and WTA will always stand in the proper relationship to each other, and so forth. The way that
such consistency is achieved is through the ex ante imposition of a specific form for the utility function,
from which all subsequent value estimates and behavioral responses are then derived. One way to think
about the contrast between meta-regression and structural benefit transfer is that the former uses
relatively more data and fewer theoretical assumptions, while the latter uses relatively fewer data (or
more highly aggregated data) and stronger theoretical assumptions. Therefore, the meta-regression
approach may give more accurate value estimates within the range of the data used to estimate the
function, while the structural benefit transfer approach may be more accurate in out-of-sample transfers.
Thus, the choice of one approach over the other may depend in part on whether the policy case(s) to be
examined fall largely within or largely outside of the range of data available for a meta-regression
transfer function.
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6.2.1 Static preference functions
A simplistic example may help clarify the structural benefit transfer approach. Here we follow
Smith et al. (2003, 2006) and use a static model of the tradeoff between income and survival. (In the next
sub-section we will consider a more general dynamic life-cycle model.) Assume that utility conditional
on survival is proportional to the log of scaled income, so expected utility is U — pin aY , where p is the
individual's survival probability. Using this functional form, the marginal willingness to pay for an
increase in the probability of survival is wtp = dll/dp / dU/dY =Yln aY /p. Next suppose that,
based on a comprehensive review of the hedonic wage literature, wtp is estimated to be $8/|jr (i.e., the
VSL is $8,000,000) for individuals with average annual income 35,000 $/yr and average annual survival
probability p = 0.984. This allows calibration of the single unknown parameter of the utility function:
In a = pVSL / Y — In Y = 214.5, which gives a function that can be transferred to individuals with different
background mortality risk levels. This function could vary by age and other personal and environmental
characteristics, and/or different income levels by adjusting p and/or Y, respectively. Using this functional
form, wtp is inversely proportional to the baseline survival probability (and therefore increases with the
background mortality risk) and is (nearly) proportional to income.
We also can use the calibrated utility function to calculate willingness to pay for changes in
mortality risks of any magnitude, rather than relying on the first-order approximation represented by the
wtp. In this case the willingness to pay function is WTP — Y — ex p | pin aY / p + Ap / a. Note that
for large enough Ap's the marginal approximation may exceed total income while the actual WTP
cannot.32 As noted by Smith et al. (2006), this is one of the key advantages of a structural benefit transfer
32 Letting A p go to its maximum value 1 - p gives WTP = Y |jl -1 / a Y 1 p J, which is necessarily less than Y. Also
note that, in this model, the smaller is p the larger is WTP, approaching Y asp goes to zero. This gives a simple
illustration of the "dead-anyway effect" (Pratt and Zeckhauser 1996).
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approach: it can produce more realistic predictions of WTP well outside of the range of data used to
estimate marginal willingness to pay. (Additional numerical examples are provided in Appendix A.)
Another advantage of the structural approach is that it can help to account for potential
behavioral responses. We can illustrate this by extending the simple model given above. Again
following the hedonic wage literature, suppose that wages, W, are an increasing function of job-related
mortality risk, m. Specifically, suppose that W = W0 + amp . Total income is comprised of wages plus
non-wage income, y. With this extension, expected utility is U - p0 - m In a y + W0 + am" , where
p0 is the background (non-job related) survival probability. Now suppose that after careful examination
of the hedonic wage literature we estimate that, for a sample of individuals of prime working age (say,
around 40 years old), y = 5,000 $/yr, W = 30,000 $/yr, pQ = 0.99, m = 0.006, and wtp = dW / dm = $8/|jr. So,
for example, if (3 = 0.5, then 8W / dm — pam13'1 => a = 8 / 1CT6 / 2 / 0.006 = 6.67 x 108 and
W0 = W — am1' = -8.6 x 109. (Note that with two estimates of wtp at two levels of job risk, we could
calibrate a and (i simultaneously.) Now recall the standard assumption underlying the hedonic wage
literature that the individual has chosen her job-risk level optimally, and assume she is able to adjust that
level to re-optimize her expected utility after a policy intervention changes p0 by some amount Ap . To
determine the maximum willingness to pay for an exogenous change in mortality risk, we must solve the
two-equation system comprised of (1) the equality between expected utility with and without the policy,
and (2) the first-order condition for maximized expected utility with respect to job-risk with the policy
and a reduction in income equal to WTP.
Results from some simple numerical experiments with this model are given in Appendix A. The
main lesson from these examples is that if individuals are able to adjust their job risk level, then WTP
generally will be higher and the total number of "statistical lives saved" will be lower than otherwise
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predicted under the assumption of no behavioral response. The numerical examples in Appendix A are
not intended to represent any specific real-world case; nevertheless, they clearly illustrate that the
structural benefit transfer approach is able to capture these effects.
6.2.2 Life-cycle preference functions
The structural benefit transfer function illustrated above was based on the simplifying
assumption that the representative individual looks ahead only one period at a time—that is, utility
depends only on the probability of survival to the next period and expected consumption in the next
period. A more realistic framework would account for expectations of survival and consumption in all
future periods. This brings us to the life-cycle consumption modeling approach. A life-cycle
consumption model represents consumption-versus-saving (and possibly other) choices by an individual
over the course of her lifetime. Life-cycle models are inherently dynamic, with age-specific mortality
probabilities included as key parameters. Individuals are assumed to maximize the expected present
value of discounted utility, where the expectation is conditional on the probabilities of living to all
possible future ages (e.g., Yaari 1964, Shepard and Zeckhauser 1984, Rosen 1988, Cropper and Sussman
1990, Ehrlich 2000, Johansson 2002, Aldy and Smyth 2006, Murphy and Topel 2006, Hall and Jones 2007,
USEPA 2007 p. 14-16).
A life-cycle consumption modeling framework could be used as the basis for a generalized
structural benefit transfer function. Such a transfer function would allow calculation of willingness to
pay for any marginal or non-marginal changes in the individual's mortality profile (i.e., "survival curve")
at any point in the life cycle. As emphasized by Hammit (2007 p. 232), "the survival curve and how it
shifts are the fundamental concepts; the number of life-years saved and lives saved in a specified time
period are the alternative and partial summary measures of the shift." The life-cycle consumption
framework is tailor-made to account for shifts in the survival curve, and it can easily account for the age
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and lifetime income profile of the individual and the latency and cessation lag characteristics of the
policy.
As in any structural benefit transfer application, it may be necessary to calibrate the parameters
of a life-cycle consumption model using only a few aggregate data—for example, summary statistics on
labor-leisure tradeoffs, average rates of saving over a representative individual's life span, average
market wage differentials for more versus less risky jobs, summary results from stated preference surveys
on risk tradeoffs, etc. Thus, like other structural-benefit transfer functions, one based on the life-cycle
consumption framework would necessarily sacrifice statistical sophistication for theoretical consistency,
so many of the advantages and disadvantages of structural benefit-transfer functions discussed by Smith
et al. (2002, 2006) will apply to life-cycle models as well.
An important potential advantage of using a life-cycle consumption framework for structural
benefit transfers is that it could help to avoid the transfer errors that may arise from using a single VSL
point estimate for all varieties of mortality risk reductions. As shown in Appendix A, the life-cycle
framework allows calculation of the marginal willingness to pay at any age a for risk reductions at any
later age b, wtpa h. VSL estimates from hedonic wage studies may be most plausibly interpreted as the
marginal willingness to pay for contemporaneous mortality risk reductions for adults of prime working
age, e.g., wtp40 40. It may be inaccurate to use such estimates to calculate the willingness to pay for, say, a
20 year-old who will experience mortality risk reductions at ages 55 through the end of life. In contrast, a
schedule of wtya h estimates based on a calibrated life-cycle consumption model would give a ready
means of calculating total willingness to pay for any exogenous shift in the survival curve for individuals
of any age. Furthermore, this approach can properly account for all latency and cessation lag effects
associated with the specific pattern of mortality risk changes caused by the policy, without the need for
possibly inaccurate transfers of a VSL point estimate to earlier and later ages and across individuals with
different levels of wealth and income.
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Implementing such a structural life-cycle benefit transfer function would be challenging.
Estimating or calibrating such a model would require specifying or solving for the life-cycle pattern of
consumption, and specifying a functional form for the utility function as well as calibrating or estimating
its parameters. Any structural benefit transfer approach—whether based on a life-cycle consumption
framework or something else—would represent a significant departure from the traditional point
estimate transfer approach typically used for mortality risk valuations, mainly based on the VSL. To
accelerate the development of such an approach, we recommend conducting additional case studies
applying existing structural benefit transfer functions (e.g., Smith et al. 2002, 2003, 2006) to a wider range
of illustrative policy scenarios, and additional research aimed at expanding and refining the calibration of
existing benefit transfer functions or developing new ones for potential use in future policy analyses. The
scholarly research on structural benefit transfer methods is still in an early stage, so we are especially
interested in EEAC recommendations in this area.
7 Conclusions
EPA continually strives to improve the quality of its economic analyses of proposed
environmental policies. This is especially important in the area of human health valuation, in particular
the value of mortality risk reductions, since such a large fraction of the (monetized) benefits of EPA rules
are based on this category of impacts. This white paper represents the latest round of literature review
and study by EPA's National Center for Environmental Economics on this topic, submitted to the SAB-
EEAC for feedback. Advice from the committee will be carefully considered as EPA updates its
Guidelines for Preparing Economic Analyses.
7.1 Addressing key issues: terminology, altruism, cancer valuation
EPA plans to change its metric and terminology for mortality risk valuation in benefit-cost
analysis to better reflect the risk-dollar tradeoffs faced by individuals as evaluated in the economics
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literature, and risk reductions provided by environmental policies. As detailed in section 3.1.2 of this
white paper, for valuation purposes we will report changes in risk reductions valued in terms of the
value of mortality risk (VMR), scaled to micro-risk reductions. This is consistent with recent suggestions
in the economics literature and is aimed at reducing confusion about how mortality risks are evaluated in
benefit-cost analysis.
A second key issue for EPA is the valuation of cancer risk reductions and how these risks are
valued systematically differently from the more immediate risks typically considered in WTP studies.
Our review of the cancer literature, while not conclusive, suggests a "cancer differential" of roughly 50%
over immediate accidental or "generic" risk valuation estimates. We recommend including a differential
of this general magnitude as part of Agency benefits analyses for reduced cancer risks. Specific guidance
on the application of this differential will be developed by the Agency at a later date.
7.2 Longer term analytical directions
In the longer term, EPA plans to perform analysis to better and more rigorously synthesize the
existing mortality risk valuation literature. Two key directions include meta-analysis and structural
benefit-transfer.
7.2.2 Meta-analysis
Section 5.1 described simplified approaches to aggregating the existing empirical valuation data,
along with some key issues to consider in this process. These include whether to (i) use multiple
estimates from studies, (ii) update all studies to a common year accounting for real income growth, and
(iii) limit SP studies to avoid double-counting the effects of cancer risks and latency or cessation lag. The
suggested approach evaluates the RP and SP studies separately, from which EPA would develop a range
of default values for the value of mortality risk (VMR).
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Alternatively, a new addition to the discussion of mortality risk meta-analysis with the SAB-
EEAC is the potential for Bayesian meta-regression, and we are particularly interested in the SAB-EEAC
comments on the potential advantages and disadvantages of this approach. Another key question to
consider is how the results of any meta-regression would be used to inform guidance, and the merits of
developing a statistical benefit-transfer function from these results.
7.2.2 Structural Benefit Transfer
An alternative to meta-regression and other largely statistical approaches to synthesizing
literature results for policy, is to impose more structure on the benefit-transfer problem and then calibrate
a preference function based on a specified utility function and data on observable outcomes. This is a
relatively new approach that has been developed and demonstrated in only a few previous studies. We
recommended conducting additional scoping studies and further research to develop structural benefit
transfer functions, possibly based on a life-cycle consumption framework, suitable for application in
benefit-cost analyses of future EPA policies.
7.3 Other research directions
We see three other areas where more research would be valuable in developing guidance for
mortality risk valuation, and we welcome SAB-EEAC comment on these (as requested in the
accompanying charge questions).
First, additional applied research on the altruistic components of WTP for public risk reductions
would be a valuable contribution, potentially allowing EPA to rigorously include theoretically-
appropriate altruistic values and better reflect the public value of environmental policies. We
acknowledge that this is a difficult task. The economics literature on the proper treatment of altruism in
benefit-cost analysis is well-developed, enumerating the conditions under which it is appropriate to
include altruistic values in evaluating the benefits of public programs. EPA programs are inherently
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public and ideally should include paternalistic altruism. However, while the empirical literature has
been able to capture some altruistic values for public risk reductions, it has not generally been able to
distinguish among types of altruism sufficiently well for the values to be included neatly in applied
analysis.
Second, more and more research reflects the general understanding that value of reducing
mortality risks is not "one-size-fits-all." Rather, these values are heterogeneous, or "individuated," and
depend upon a wide array of individual and risk characteristics. More detailed research in this area also
will provide data needed for developing more general and more accurate benefit-transfer functions.
Third and finally, most of the valuation literature, and many theoretical frameworks, have
treated mortality and morbidity risks separately, focusing on just one of these endpoints at a time.
However, some recent work also suggests that changes in health risks may be best framed as changes in
health risk profiles that include both mortality and morbidity. Individuals may value different
combinations of changes in risk or illness and risk of death in complex ways. Systematic empirical work
to evaluate these relationships could lead to much more robust and complete benefits analysis.
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Tables and figures
Table 1: Cancer Valuation Literature Summary
Study
Timing
Treatment of
Morbidity
Dread
Risk context and
characteristics
Affected
Pop.
Other health
effects
Findings / Notes
Hammitt &
Latency periods
Yi sample: no
Not separately
Pesticide risks from
Adult selves
Organ: brain,
No statistical difference
Haninger (2010)
of 1,10, 20 years
symptom
treated
food. Safer food from
liver, bladder,
by cancer/non-cancer;
Choice experiment
descriptions;
Pesticide Safety
Adult others
lymphocytes
target organ; auto/other
Implied discount
System (not organic)
risks (for protecting
rates not stat diff
Vi sample: 150-200
Children
Mortality only (no
whole family
from zero ( -1.2
word descriptions
Auto accident for
non-fatal
simultaneously).
to 3.9)
Self-assessed
severity based on
EQ-5D and visual
analog scales
whole family
simultaneously from
"product" on next car
purchase.
outcomes)
Child VSL=1.8 Adult
Other VSL=1.15 Self
Insensitivity to number
of people for the "whole
household" question.
Alberini & Scasny
Latency periods
Description of
Rated
"cancer" designation
Adults
Respiratory
EC Cancer differential of
(2010a) "Labels &
of 0, 2, 5,10 years
morbidity or illness
subjectively
varied independently
fatality
50% relative to "general"
Perceptions . .
by
from dread
Children
VSL is consistent with
Discount rate =
Focus of study is
respondents
(Italy)
Cancer fatality
findings.
Choice experiment
zero (may reflect
mortality risk
for each type
Private good v.
changes in future
baseline risk)
of risk
nationwide public
program
Other independent
variables:
salience("familiarity")
exposure, sensitivity
to illness, beliefs in
prevalence
Auto fatality
Auto accident risks
valued less than
respiratory or cancer
VSL higher for public v.
private (if public
programs are effective)
"cancer" designation
effect persists after
controlling for other risk
characteristics.
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SAB Review Draft
VSL increases with
dread;
Alberini & Scasny
(2010b) "Context
and the VSL ..
Choice experiment
* The Italy sample
appears to overlap
with Alberini et al.
(2010a)
Yes (0, 2, 5,10
years)
Implicit discount
rates from 0.3 to
7.4%
Description of
morbidity or illness
Focus of study is
mortality risk
No
Public & Private
programs
Perceived
"effectiveness" of the
program
Finds that "risk
characteristics and
mode of delivery
primarily drive
heterogeneity in VSL"
Adults
Children
(CzechRep.
& Italy)
Respiratory illness
Cancer
Road-Traffic
accidents
"Evidence of cancer
premium":
~ 1.25x (Italy-children)
~ 1.90x (Italy-adults)
~ 1.75x (Czech-children)
~ 2.5 x (Czech-adults)
Premium for public
programs
Any premium for
reduced children's risk is
modest (small for cancer
risks, larger for other
causes).
Adamowicz et al.
(2008)
CVM and CE
Risks described
as community
deaths over a 35-
year time period
for microbials
and carcinogens
Symptoms
described for
microbial illness
and for bladder
cancer
Not addressed
Risk reductions are
strictly public
Describes tradeoffs
between reduced
microbials in DW and
reduced carcinogens
Households
(Canada)
Microbial illness
Microbial fatality
Bladder cancer
- fatal
- nonfatal
Modest cancer
"discount" (for
mortality)
Cancer VSL =
.85*Microbial VSL
Cancer illness = 20-50%
of cancer mortality
Cameron &
DeShazo (2008)
Choice experiment
Illness profile
over specific,
varying times
Results support
lower values for
longer latency.
No implicit
Health states
defined as:
- Current health
- Sickness
- Remission years
- Lost life-years
Illness characterized
Not addressed
Intervention is
generally a screening
and treatment
program to prevent
the given risk profile.
For auto accidents it is
a safety program.
Adults
12 major common
risks, including:
Heart disease,
heart attack,
stroke, respiratory
disease, diabetes,
Alzheimer's
Difficult to draw general
conclusions.
Heart attacks & heart
disease risks valued
similarly to some cancers
(and more than others).
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SAB Review Draft
discount rate
estimated.
by length and
severity (pain,
disability)
Cancer (5 types)
Auto accidents
Tsuge et al. (2005)
Choice experiment
Latency periods
of 0, 5,10 years
Implied discount
rate = 20%
Unclear, but does
not appear to be
detailed.
Focus is on
mortality.
Subjective
perceptions of
voluntariness,
controllability,
dread(pain),
dread(fear),
severity,
exposure
Adults
(Japan)
Accidents
Generalized
cancer
Heart disease
Non-specific
Unique formulation of
"quantity-based" VSL
distinguishing WTP for
opportunities for risk
reduction
Depends on model
specifications, but
perhaps 20% differential
over "general" risks;
reduced cancer risks
preferred to reduced
heart attack risk;
Hammitt & Liu
(2004)
CVM
Latent: 20 years
to onset of
symptoms
Acute: symptoms
"within a few
months"
Implied discount
rates of 1.5%
(with up to 3%
plausible)
brief description of
symptoms
progressive severity
over time from mild
to bedridden and
unable to care for
themselves
lasting 2-3 years
before mortality
Not addressed
directly
All symptoms held the
same except for
"cancer" designation:
Lung cancer v.
bronchitis (from
pollution from
factories)
Liver cancer v. liver
failure (from drinking
water contaminants)
Adults
(Taiwan)
Liver (failure v.
cancer)
Lung (bronchitis
v. cancer)
~30% differential for
cancer relative to
identical non-cancer
degenerative disease
(marginal significance)
Environmental context.
No "trauma" or
"accident" alternative for
comparison.
Philips et al. (1989)
No
No
No
No
Adults
(U.K.)
Motor vehicles
Heart disease
Fatal & Nonfatal
Mean estimates higher
for cancer; median
estimates are not
The following two studies are risk-risk studies
Van Houtven et al.
(2008)
Latency periods
of 5,15, 25-year
periods specified
Symptoms
described for three
types of cancer;
Not treated
separately
Organ-specific cancer
risks vs. auto-accident
risks.
Adults
Fatal cancer
(stomach, liver,
brain);
Significant cancer
differential (3x over auto
accidents at 5-year
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SAB Review Draft
Risk-Risk Survey
Morbidity varied
from 2 or 5 years
morbidity duration
varied separately
from latency
Fatal auto accident
latency; 1.5x at 25 years)
Differential declines with
length of latency;
Latency would need to
be 30+ years for
indifference
Magat et al. (1996)
risk-risk survey
Not addressed
explicitly
Symptoms
described for
lymphoma and
nerve disease
No
Included separate
treatments for non-
fatal lymphoma and
nerve disease
Respondents told not
to consider out of
pocket medical costs
Adults
Fatal lymphoma,
non-fatal
lymphoma;
fatal auto
accidents
nerve disease
No evidence of
differential for cancer
fatality (ratio of fatal
cancer: fatal auto is 1:1.)
Ratio of non-fatal cancer
to auto is ~.58.
The following studies examine cancer only (without comparison to other risks)
Carson & Mitchell
(2006)
Open-ended CVM
Not in survey;
VSL estimates
assume 25 years
No
No
Public/social decision
Cancer risks from
THM in drinking
water
Adults
(Household?
)
No
Cancer VSL depends
upon assumptions about
latency and discount
rate. Also sensitive to
risk reduction.
Assuming 0.4/100,000
reduction, 25-yr latency,
results range from
$3.4m at 3% to
$8.8m at 7%
Alberini et al.
(2010)
0, 2, 5,10 years
Employed a zero
discount rate for
estimation based
on prior work
Extent unclear
Unclear
Cancer risks from
hazardous waste in
Italy
Adults
Fatal Cancer (type
unspecified)
New estimates of the
cancer VSL using data
from 2008 survey in
Milan
Cancer VSL of ~$5.6m
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SAB Review Draft
About 20% higher if
delivered via public
program (if public
programs are considered
"effective").
Buzby et al. (1995)
No
No
No
Exposure to pesticides
in grapefruit
Grapefruit
customers
(Adults)
No
Makes assumptions
about lifetime exposure
to estimate VSL=$6.99m
Revealed Preference Cancer Valuation Studies
Study
Timing
Treatment of
Morbidity
Dread
Risk context and
characteristics
Affected
PoP-
Other health
effects
Findings / Notes
Gayer et al. (2000)
Hedonic Property
No
No
No
No; just "cancer" w/o
distinction between
fatal and non-fatal
cancers
Adults /
Household
near
Superfund
sites
No
cancer risk reductions
valued similarly to
workplace fatal risks
Gayer et al. (2002)
Hedonic Property
No
No
No
No; just "cancer" w/o
distinction between
fatal and non-fatal
cancers
Adults /
Household
near
Superfund
sites
No
$5.2m to $10.0m cancer
VSL with no latency (and
100% fatality.)
With 10-year latency:
-$6.2 to $11.7 at 3%
- $10.2 to $19.8 at 7%
Davis (2004)
Hedonic Property
Unclear
No
No
Pediatric leukemia
from cancer cluster; no
distinction between
fatal and non-fatal
Children
No
value of prevented
pediatric leukemia
ranges from $4.1m to
$11.5m depending on
model used
Ho and Hite (2008)
No
No
No
cancer mortality only
(didn't include non-
Adults
No
Hedonic property with
$6.0m Value of statistical
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SAB Review Draft
Hedonic Property
fatal)
cancer fatality (without
latency treatment or
assumptions).
Lott & Manning
(2000)
Hedonic wage
No
No
No
Cancer
Workers
No
Hedonic Wage
Cancer VSL = $12.4
million
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SAB Review Draft
Table 2. Select variables included in the stated preference meta-analysis dataset
Variable Name
Description
STUDY
Study identifier
PUBYEAR
Year study was published or released
PUBLISH
0=unpublished or working paper; l=published in a peer-review outlet
(includes book chapters)
JRU
0=does not appear in Journal of Risk and Uncertainty (JRU); l=published
in JRU
ALBSERIES
0=not part of the Alberini, Krupnick, Cropper and Simon series of
studies; l=part of this series
AUTO
O=non-auto/traffic risk; l=auto/traffic risk
ENVIRONMENTAL
O=non-environmental risk source; l=environmental-related risk (i.e., air
pollution, drinking water, hazardous waste site, or unspecified general
death risk)
PUBLIC
0=risk affects individual only; l=risk affects public
CANCER
0=non-cancer death; l=cancer death
ESTIMATES
Number of estimates reported or calculated from study
WTP
Willingness to pay for risk reduction (2009 US dollars)
WTP_SE
Standard error for WTP
VSL
VSL in millions, adjusted for inflation and income growth (2009 dollars)
SE
Standard error in millions of VSL estimate
MEAN
0=WTP/VSL is based on median WTP; 1=WTP/VSL is based on mean
WTP
YEARCONDUCT
Year study was conducted
US
0=non-US study; 1=US study
cv
0=choice experiment; l=contingent valuation
BASE
Baseline risk presented to survey respondents
REDUCE
Size of risk reduction presented to respondents
PCTREDUCE
Percent reduction in risk
TIMING
0=immediate risk reduction, l=latent risk reduction
LENGTH
Length of latency period in years (0=immediate risk reduction)
SIZE
Sample size used to calculate WTP/VS: estimate
MALE
0=female, l=male
AGE
Average age
RACE
Percent white
INCOME
Annual mean household income (thousands, 2007 US dollars)
HEALTH
Percent reporting exceptional or very good health, no reported disease
or illness, or non-smoker
NSCENARIO
Number of scenarios each respondent was asked to value
MODE
0= self administered survey mode, l=survey administered with an
interviewer (e.g., in-person, telephone
DOTS
0=ladder, bar chart used for visual aid; l=grid used for visual aid
SCOPE
0=no scope test performed or calculated, l=scope test performed or
calculated
WEAK
0=does not pass a weak scope test, l=passes a weak test, but WTP is less
than proportional to the size of the risk reduction
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SAB Review Draft
Variable Name
Description
STRONG
0=does not pass a strong scope test, l=passes a strong test; WTP is
proportional to the size of the risk reduction
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SAB Review Draft
Table 3. Stated preference dataset
Risk Characteristics
Study
Country
Sample Size
Cancer
Public
Latency (yrs)
Auto risk
Env. risk
Unspec. Source
Other risk type
Risk
reduction
WTP
(2009$)*
SE
Adamowicz et al. (2008)
USA
366
0
1
0
0
1
0
0
0.0000029
6.65 (1)
0.91
Adamowicz et al. (2008)
USA
366
1
1
10
0
1
0
0
0.0000029
6.03 (1)
0.75
Alberini and Chiabai (2007)
Italy
756
0
0
0
0
1
0
0
0.0001
6.03 (2)
Alberini et al. (2007)
Italy
782
0
1
0
0
1
0
0
0.000001
6.96 (1)
Alberini et al. (2004)
USA
548
0
0
0
0
0
1
0
0.0001
6.59 (3)
1.00
Alberini et al. (2004)
Canada
292
0
0
0
0
0
1
0
0.0001
5.05 (3)
0.66
Alberini et al. (2006a)
USA
403
0
0
10
0
0
1
0
0.0005
0.95 (4)
0.44
Alberini et al. (2006a)
Canada
589
0
0
10
0
0
1
0
0.0005
1.42 (4)
0.26
Alberini et al. (2006b)
France, Italy, UK
0
0
0
0
0
1
0
0.0005
3.22 (4)
0.57
Alberini and Scasny (2010)
Italy
1906
1
1
4.25
1
1
0
0
0.000425
4.68 (16)
0.30
Alberini and Scasny (2010)
Czech Republic
1506
1
1
4.25
1
1
0
0
0.000425
1.27 (16)
0.14
Alberini et al. (2006c)
Czech Republic
954
0
0
0
0
1
0
0
0.0003
3.11 (4)
0.21
Andersson and Lindberg (2009)
Sweden
216
0
0
0
1
0
0
0
0.0002
13.02 (5)
Andersson and Lindberg (2009)
Sweden
222
0
1
0
1
0
0
0
0.0002
7.45 (5)
Buzby et al. (1995)
USA
512
1
0
75
0
0
0
1
0.00000066
6.99 (6)
Cameron et al. (2008)
USA
1619
1
0
10
0
0
1
0
0.000001
0.86 (7)
Carson and Mitchell (2006)
USA
121
1
1
25
0
1
0
0
0.0000004
8.64 (8)
Corso et al. (2001)
USA
275
0
0
0
1
0
0
0
0.00005
4.29 (9)
Desaigues and Rabl (1995)
France
1000
0
1
0
1
0
0
0
0.000046
1.64 (1)
Gerking et al. (1988)
USA
861
0
0
0
0
0
0
1
0.00025
6.86 (6)
Gyrd-Hansen et al. (2007)
Norway
1168
0
0
0
0
0
0
1
0.0028
0.04 (1)
Hakes and Viscusi (2007)
USA
465
0
0
0
1
0
0
0
0.0001
7.22 (10)
Hammitt and Graham (1999)
USA
992
0
0
0
1
0
0
0
0.00005
2.96 (11)
0.32
Hammitt and Graham (1999)
USA
978
0
0
0
0
0
0
1
0.000073
2.72 (11)
0.56
Hammitt and Haninger (2010)
USA
1997
0.5
0
1
0
0
0
1
0.00015
6.77 (12)
1.24
Hammitt and Liu (2004)
Taiwan
1248
1
0
20
0
1
0
0
0.00005
1.94 (13)
Hultkrantz et al. (2006)
Sweden
225
0
0
0
1
0
0
0
0.000165
6.40 (14)
Itaoka et al. (2007)
Japan
248
0
0
0
0
0
1
0
0.001
2.92 (17)
0.76
Johannesson et al. (1997)
Sweden
2029
0
0
22.5
0
0
0.0002
5.13 (10)
Johannesson et al. (1996)
Sweden
389
0
0
0
1
0
0
0
0.000162
4.49 (18)
0.48
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SAB Review Draft
Risk Characteristics
Study
Country
Sample Size
Cancer
Public
Latency (yrs)
Auto risk
Env. risk
Unspec. Source
Other risk type
Risk
reduction
WTP
(2009$)*
SE
Johannesson et al. (1996)
Sweden
410
0
1
0
1
0
0
0
0.000162
3.73 (18)
0.48
Kidholm (1995)
Denmark
908
0
0
0
1
0
0
0
0.000022
2.38 (19)
Lanoie et al. (1995)
Canada
162
0
0
0
1
0
0
0
0.0002
2.92 (10)
Miller and Guria ((1991)
New Zealand
629
0
0
0
1
0
0
0
1.59 (21)
Morris and Hammitt (2001)
USA
167
0
0
20
0
0
0
1
0.046
0.19 (20)
Persson et al. (2001)
Sweden
675
0
0
0
1
0
0
0
0.00003
3.59 (1)
Philips et al. (1989)
U.K.
1563
1
0
0
1
1
0
0
6.90 (1)
Strand (2002)
Norway
0
0
1
0
1
0
0
0.57 (22)
Tsuge et al. (2005)
Japan
400
1
0
5
0
1
1
0.0001
3.62 (15)
Zhang, et al. (2009)
Canada
366
1
0
0
0
0
0
12.69 (23)
* The WTP and SE estimates reported in this table are adjusted for inflation (using the CPI) and income growth (using an elasticity of 0.5).
(1) author's preferred
(2) healthy 30-49 year old, based on mean and smaller risk reduction (from Table 7 in paper)
(3) based on mean and smaller risk reduction (Table 6 in paper)
(4) based on mean
(5) based on parametric estimation (Table 7 in paper)
(6) only estimate reported in paper
(7) 45 year old who is diagnosed with lung cancer 10 years after exposure, is sick for 5 years and then dies; estimate is chosen because it most
closely matches many EPA policy scenarios (Table 3 in paper)
(8) based on corrected mean for the smallest risk reduction (Table 19.2 in paper) (note: We could also obtain other independent estimates for
different risk reductions)
(9) from a model with co-variates for the smaller risk reduction using dots for a visual aid (Table 3 in paper)
(10) based on the full sample
(11) based on median (mean not reported) for the smallest risk reduction (Table 5 and 7 in paper)
(12) based on model of WTP for reductions in risk to self, which is based on median WTP, one year latency and cancer set to 0.5 and affected
organs set to 0.25 (options are brain, bladder, liver and lymphocytes) (Table 2 in paper)
(13) based on latent lung cancer from model with full set of co-variates (Table 3 in paper)
(14) based on private risk reduction (there is also an estimate for a public risk reduction, but they are not independent)
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(15) only estimate in paper; reflects the idea that wtp is independent of the source of risk; CE asks about cancer, accidents, heart disease, over
different latency periods
(16) based on pooled model (Table 5 in paper)
(17) based on smaller risk reduction with no latency from wave 2 (where smaller risk reduction was presented first (Table 7 in paper)
(18) based on standard estimates (Table 2 in paper)
(19) based on mean estimate for risk reduction provided through an air bag (assumed to be a private risk reduction) using the maximum WTP
results (Table 2 in paper)
(20) based on WTP for vaccine at age 60 (Table 3 in paper)
(21) based on WTP for a safer car (Table 3 in paper)
(22) based on WTP for private reductions in risk from environmental causes (Table 10 in paper)
(23) based on WTP for private cancer risk reductions assuming no treatment or purchase of bottled water (Table 9 in paper)
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Table 4: Hedonic Wage dataset
Sample
Characteristics
Study
Country
Sample
Sample
Size
Union
White
Male
Manual/Mfg
Blue Collar
Risk Variable
Mean
Risk
Nonfatal
Risk
Included
(l=Yes)
Workers'
Comp
Included?
(l=Yes)
WTP
(2009$)
SE
Smith (1974)
USA
CPS 1967; Census
of Manufactures
1960;
Employment and
Earnings 1963
3183
0
1
1
0
0
BLS 1966,1967
0.000125
1
0
14.06
5.87
Viscusi (1978)
USA
SWC 1969-1970
496
0
0
0
0
1
BLS, subjective
risk of job (SWC)
0.000118
1
0
3.72
2.15
Olson (1981)
USA
CPS 1978
5993
0
0
0
0
0
BLS 1973
0.0001
1
0
18.15
7.30
Viscusi (1981)
USA
PSID 1976
3977
0
0
0
0
0
BLS 1973-1976
0.000104
1
0
12.33
2.13
Marin and
Psacharopoulos
(1982)
UK
General
Household
Survey 1975
5509
0
0
0
0
0
OPCS
Occupational
Mortality
Decenniel Survey
1970-1972
0.00009
0
0
9.09
2.01
Dorsey and
Walzer (1983)
USA
CPS May 1978
1697
1
0
0
0
1
BLS 1976
0.000058
1
1
17.27
7.29
Dillingham and
Smith (1984)
USA
CPS May 1979
879
0
1
0
0
0
BLS industry data
1976,1979
0.00012
1
0
4.81
2.30
Leigh and Folsom
(1984)
USA
PSID 1974, QES
1977
1529
0
1
0
0
0
BLS
0.00014
1
0
15.12
6.40
Dillingham (1985)
USA
QES 1977
514
0
0
0
0
0
BLS 1976; NY
workers'
compensation
data 1970
0.00014
0
0
6.21
3.47
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Sample
Characteristics
Study
Country
Sample
Sample
Size
Union
White
Male
Manual/Mfg
Blue Collar
Risk Variable
Mean
Risk
Nonfatal
Risk
Included
(l=Yes)
Workers'
Comp
Included?
(l=Yes)
WTP
(2009$)
SE
Weiss et al. (1986)
Austria
Austrian
Microcensus File
of Central Bureau
of Statistics 1981
4225
0
0
0
0
0
Austrian Social
Insurance Data
on Job-related
Accidents 1977-
1984
0.00013
1
0
12.23
5.03
Moore and
Viscusi (1988)
USA
PSID 1982
1349
0
1
0
0
0
BLS1972-1982,
NIOSH National
NTOF Survey
1980-85
0.00008
0
1
13.15
5.21
Garen (1988)
USA
PSID 1981-1982
2863
0
0
0
0
1
BLS 1980,1981
0.000108
1
0
24.08
5.17
Meng (1989)
Canada
National Survey
of Class Structure
and Labour
Process 1981
718
0
0
0
0
0
Labour Canada
and Quebec
Occupational
Health and Safety
Board 1981
0.00019
0
0
6.85
3.99
Meng and Smith
(1990)
Canada
National Election
Survey
777
0
0
0
1
0
Labour Canada
and Quebec
Occupational
Health and Safety
Board 1981-83
0.00012
0
0
1.78
3.28
Berger and
Gabriel (1991)
USA
1980 Census
22837
0
0
1
0
0
BLS 1979
0.000097
0
0
11.17
1.95
Leigh (1991)
USA
PSID 1974,1981
1502
0
0
1
0
1
BLS 1979
0.000134
0
0
10.74
3.23
Kniesner and
Leeth (1991)
USA
CPS 1978
8868
0
0
0
1
0
NIOSH NTOF
Survey 1980-1985
0.000436
1
1
0.67
0.46
Gegax (1991)
USA
Authors' mail
survey 1984
228
1
0
0
0
0
Workers' assessed
fatality risk at
work 1984
0.00086
0
0
3.92
1.99
Martinello and
Meng (1992)
Canada
Labor Market
Activity Survey
1986
4352
0
0
0
1
0
Labor Canada
and Statistics
Canada 1986
0.00025
1
0
4.45
1.34
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Sample
Characteristics
Study
Country
Sample
Sample
Size
Union
White
Male
Manual/Mfg
Blue Collar
Risk Variable
Mean
Risk
Nonfatal
Risk
Included
(l=Yes)
Workers'
Comp
Included?
(l=Yes)
WTP
(2009$)
SE
Cousineau et al.
(1992)
Canada
Labor Canada
Survey 1979
32713
0
0
0
1
0
Quebec
Compensation
Board
7.64E-05
1
0
7.01
0.67
Siebert and Wei
(1994)
UK
General
Household
Survey 1983
1353
1
0
1
1
0
Health and Safety
Executive 1986-88
3.32E-05
1
0
20.70
9.85
Leigh (1995)
USA
PSID 1981
1528
0
0
1
0
1
NIOSH 1980-85
0.00011
0
0
16.23
3.04
Sandy and Elliot
(1996)
UK
Social Change
and Economic
Life Initiative
Survey 1986
440
0
0
1
1
0
OPCS
Occupational
Mortality
Decenniel Survey
1979/80-1982/83
4.52E-05
0
0
76.00
32.55
Milleret al. (1997)
Australia
Australian
Census of
Population and
Housing 1991
18,850
0
0
1
0
0
Worksafe
Australia,
National
Occupational
Health and Safety
Commission
1992-93
0.000068
0
0
23.86
1.82
Meng and Smith
(1999)
Canada
Labor Market
Activity Survey
1986
1503
0
0
0
0
0
Ontario Workers'
Compensation
Board
0.00018
1
1
3.33
0.86
Kim and Fishback
(1999)
South
Korea
Ministry of
Labor's Report on
Monthly Labor
Survey and
Survey on Basic
Statistics for the
Wage Structures
321
0
0
1
0
0
Ministry of
Labor's Analysis
for Industrial
Accidents
0.000485
1
1
2.20
0.45
Arabsheibani and
Marin (2000)
UK
General
Household
Survey (1980s)
3608
0
0
1
0
0
OPCS
Occupational
Mortality
Decennial Survey
1979-80
0.00005
1
0
43.88
8.82
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Sample
Characteristics
Study
Country
Sample
Sample
Size
Union
White
Male
Manual/Mfg
Blue Collar
Risk Variable
Mean
Risk
Nonfatal
Risk
Included
(l=Yes)
Workers'
Comp
Included?
(l=Yes)
WTP
(2009$)
SE
Gunderson and
Hyatt (2001)
Canada
Survey of Ontario
Workers with
Perma- nent
Impairment
2014
0
0
0
0
1
Ontario Workers'
Compensation
Board
0.000167
1
34.03
4.83
Viscusi (2003)
USA
CPS MORG 1997
83625
0
1
0
0
0
CFOI1992-1997
3.62E-05
1
1
21.45
2.01
Leeth and Ruser
(2003)
USA
CPS ORG 1996-98
45001
0
0
1
0
1
CFOI1996-1998
9.76E-05
1
1
3.61
0.80
Smith et al. (2004)
USA
Health &
Retirement
Survey (Wave 1)
3632
0
0
0
0
0
BLS1993
5.8E-05
0
0
7.97
Viscusi (2004)
USA
CPS MORG 1997
99033
0
0
0
0
0
CFOI 1992-1997
4.02E-05
1
1
6.79
0.80
Kniesner et al.
(2006)
USA
PSID 1997
1875
0
0
1
0
0
CFOI 1992-1997
0.00004
0
0
29.59
Viscusi and Aldy
(2007)
USA
CPS MORG 1992-
1997
120,008
0
0
0
0
0
CFOI 1992-1997
0.00004
1
1
12.23
Aldy and Viscusi
(2008)
USA
CPS MORG 1993-
1997
123,439
0
0
0
0
0
CFOI 1992-2000
1
1
13.09
Evans and Smith
(2008)
USA
Health &
Retirement
Survey
2,708
0
0
0
0
0
CFOI
0.000064
0
0
13.06
Scotton and
Taylor (2009)
USA
CPS MORG 1996-
1998
43,261
0
0
0
0
0
CFOI 1992-1997
4.895E-05
1
0
6.16
1.89
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Appendix A
This appendix gives some illustrative numerical examples using the simple static (single-period)
structural benefit transfer function from Section 5.2.1, and a more formal exposition of the life-cycle
modeling framework discussed in Section 5.2.2. Table B1 shows willingness to pay values for a range of
mortality risk reductions using the static model in Section 5.2.1. The first three columns in the table show
the difference between the marginal approximation and the exact WTP [$] for a range of changes in
baseline risks Ap [yr_1 ]. The final six columns in the table show WTP [$] and m" [yr-1] (explained
below) for a range of Ap's and three possible values of ('>, accounting for the behavioral response
described in Section 5.2.1. To determine the maximum willingness to pay for an exogenous change in
background mortality risks, we must solve the two-equation system comprised of the equality between
expected utility with and without the policy,
p0-m In a y + W0 + amp - p0+Ap- m* In a y + W0 + am- WTP ,
and the first-order condition for maximized expected utility with respect to job-risk with the policy and a
reduction in income equal to WTP, i.e.,
flam"13'1 p0+Ap- ra" / y + W0 + am- WTP - In a y + W0 + am"p - WTP = 0,
where m" is the job-risk level that the individual would choose if her baseline survival probability were
increased by Ap and if she were charged the amount WTP for this change. The level of m that she would
actually choose after the policy is implemented would depend on the actual cost of the policy to her.
The main lesson from these examples is that—when preferences for consumption and risk are not
separable, as in this example—if individuals are able to freely adjust their job risk level, then WTP
generally will be higher and the total number of "statistical lives saved" will be lower than otherwise
predicted under the assumption of no behavioral response. In fact, if (3 = 1 and if each individual were
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charged their maximum WTP for the change, then the individuals' behavioral responses would fully
offset the changes in their baseline mortality risk. In this extreme case, WTP would exactly equal
wtp ¦ Ap and, if each individual had to pay this full amount to fund the policy, then the number of "lives
saved" would be zero. If the full costs of the policy were less than the aggregate WTP, then both the net
social benefits and the number of statistical lives saved would be positive, though the latter still would be
less than ApxN . If the full costs of the policy were greater than the aggregate WTP, then of course the
net social benefits would be negative, but also note that the number of statistical lives "saved" would be
negative as well—that is, even though environmental risks were reduced, the policy would increase
overall mortality rates since people's behavioral responses to the increased costs would involve shifting
to jobs with higher mortality risks. The numerical results in Table B1 are not necessarily intended to be
realistic, especially considering that they involve mortality risk reductions that are much larger than
those we would typically expect from most environmental regulations, but they nevertheless highlight
the importance of calculating benefits and costs simultaneously for non-marginal policies when
behavioral adjustments are expected.
Next, a brief exposition of a generalized life-cycle (multi-period) model may help to describe the
potential usefulness of this framework as a basis for structural benefit transfers of mortality risk
reductions. Suppose that the value function for a representative individual is given by
T
Va = ct,ht,t sa te p ° , where u ct,ht,t is utility in period t (assumed here to depend on
t=a
consumption ct, health status ht, and possibly age t), sr is the probability of surviving to the beginning
of age t +1 given that the individual is alive at the beginning of age t , sat — ]~[^ Sr, and T is the
individual's maximum possible lifespan. Marginal willingness to pay at age a for mortality risk
reductions (or, equivalently, an increase in survival probability) at age b (> a) is wtp , h =
dca dVJ8sb
ds, dVJdc
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To help interpret this willingness to pay measure, we can break the value function into two parts
h-l T
at some future age t = b, Va = ZM ct,ht,t sate~pt~a + ct,ht,t sate pt " , then re-write second term
t=b
on the right hand side of this equation in terms of the value function at age b,
h-1 dV
Va = ^u ct,ht,t sate pt " +Vhsahe ph " , which means —- = Vbsa ble pb " -33 Thus, the marginal
t-a SS b
willingness to pay at age a for a reduction in mortality risk at some future age b is
V-p b-a
bSab-ie
uotp h = ,34 This is the expected remaining lifetime utility at the beginning of age b,
du c ,h ,a /dc
a' a' ' a
discounted by the survival probability and the pure rate of time preference between ages a and b, and
then monetized by the marginal utility of consumption at age a.
Developing a usable structural benefit-transfer function based on a lifecycle framework would be
challenging. Estimating or calibrating such a model would require specifying or solving for the life-cycle
pattern of consumption, calibrating or estimating the pure rate of time preference, and specifying a
33 Throughout this section we treat the path of consumption over the life cycle as exogenous; that is, we ignore any
behavioral responses to changes in mortality risks that would adjust the levels of consumption in future periods.
This simplification will be strictly valid only under some special conditions—namely, that that the individual can
never be a net borrower (Cropper and Sussman 1990, USEPA 2007 p D-15)— but it should provide a close
approximation for small changes in exogenous mortality risks. More specifically, we would expect it to provide a
close lower bound on willingness to pay in most cases of interest—a lower bound because it assumes that the
individual is constrained to maintain the same consumption path after the change, and a close approximation
because we would expected any adjustments in future consumption levels to be very small for reasonably small
changes in mortality risks.
34 Direct inspection of this equation suggests some simple comparative static results: (1) wtpa b decreases with the
latency period b-a because all elements of the numerator — Vb+1, sa hl, and e p h —decrease and the denominator
does not change. (2) wtpa a could increase or decrease with a because, while Va+1 and sa a l decrease with a, the
denominator could decrease or increase with a depending on the pattern of consumption and health status over the
life cycle (USEPA 2007 p D-16). If the pattern of consumption were perfectly flat over the life cycle, and if utility
depended only on consumption and not health status or age per se, then wtpa a would unambiguously decrease with
age. However, observed consumption patterns generally are not flat; consumption typically is low in the early
(adult) years, high in middle age, and lower again in later years, which, all else equal, would tend to increase then
decrease wtp .
r a,a
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functional form for the period utility function u c,, h,, t and calibrating or estimating its parameters.
The simplest reasonable implementation of such an approach might proceed as follows:
1.) Specify the lifetime pattern of consumption for a "representative" individual as the pattern of
average consumption levels for a random sample of individuals of various ages from the population
of interest. Alternatively, multiple representative life-cycle consumption patterns could be generated
based on average consumption levels for sub-samples of the population, e.g., by gender, race,
geographic region, etc., as appropriate for the exposed sub-population relevant for the policy to be
examined.
2.) Set p equal to a suitable central value from a relevant set of revealed or stated preference studies
(presumably somewhere between, say, 0% and 5% per year).
3.) Assume the utility function is of the standard CRRA form with a lower bound on utility:
ut = n - d1^ / 1 - Tj . Then either
a. set 71 equal to a suitable central value from a relevant set of revealed or stated preference studies
(presumably somewhere between, say, 0.5 and 3), and use at least one valid estimate of
willingness to pay for well-specified mortality risk changes from the revealed or stated
preference literature to calibrate d, or
b. use at least two valid estimates of marginal willingness to pay from the RP or SP literature to
calibrate i] and d simultaneously.
Such a calibrated life-cycle model then could be used to calculate wtpa b for all combinations of a and b
for each representative individual identified in step 1. These estimates then could be transferred to any
pattern of mortality risk changes that are projected for one or more policies under consideration. More
sophisticated versions of this approach could specify ut as a function of age and/or health status, which
might facilitate a link to the QALY literature.
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Table Al. Maximum willingness to pay for a range of changes in survival probabilities, Ap, based on a
marginal approximation (wtp ¦ Ap) and direct calculation (WTP ), with and without a behavioral
response. Baseline job risk is m = 0.006. Estimates of the adjusted job risk with a behavioral response (
m" ) assume that the individual's income is simultaneously reduced by WTP (that is, expected utility
without the policy is equal to that with the policy combined with the charge WTP).
No behavioral
response
With behavioral response
P =
0.33
P =
0.67
P
= 1
Ap [yr
wtp ¦ Ap
WTP
WTP
m" [yr
WTP
m" [yr
WTP
m" [yr
[$]
[$]
[$]
[$]
[$]
0.000005
40.0
25.0
40.0
0.0060034
400
0.0060040
40.0
0.0060050
0.00005
400.0
397.7
399.2
0.0060337
399.6
0.0060404
400.0
0.0060500
0.0005
4,000.0
3,778.1
3,926.6
0.0063399
3,956.7
0.0064062
4,000.0
0.0065000
0.005
40,000.0
23,773.6
33,977.6
0.0096250
36,431.3
0.0102351
40,000.0
0.0110000
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