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# Valuing Mortality Risk Reductions for Environmental Policy: A White Paper

U.S. Environmental Protection Agency, National Center for Environmental Economics

DRAFT D ecember 10, 2010

For consultation with the Science Advisory Board

– Environmental Economics Advisory CommitteeSAB Review Draft

2 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 Re commendations 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 Parametr ic 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

1SAB Review Draft

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## 1 Introduction 2

The valuation of human health benefits is often a crucial, but sometimes controversial, aspect of 3
the application of benefit

- cost analysis to environmental policies. Valuing the reduced risks of mortality, 4
in particular, poses a special set of conceptual, analytical, ethical and empi rical challenges for economists 5
and policy analysts. This white paper addresses current and recent U.S. Environmental Protection 6
Agency (EPA) practices regarding the valuation of mortality risk reductions, focusing especially on 7
empirical estimates of the ‚value of a statistical life‛ (VSL) from stated preference and hedonic wage 8
studies and how they might be summarized and applied to new policy cases using some form of benefit 9
transfer. Benefit transfer concepts will be highlighted throughout the paper, since any application of 10
existing empirical estimates of values for health risk reductions to new policy cases is inherently a benefit 11
transfer problem. 12
The main intended audience for this paper is EPA’s Science Advisory Board

- Environmental 13

Economics Advis ory Committee (EEAC). The main objectives of the paper are to highlight some key 14
topics related to the valuation of mortality risks, and to describe several possible approaches for 15
synthesizing the empirical estimates of values for mortality risk reductio ns from existing hedonic wage 16
and stated preference studies for the purpose of valuing mortality risk reductions associated with future 17
EPA policies. Some of these approaches could be implemented in the short term, but others will likely 18
require longer te rm research. We are soliciting general feedback and specific recommendations from the 19

SAB

- EEAC on each of these key topics and approaches. 20



### 1.1 Key topics 21

We highlight several issues in this paper, offering preliminary recommendations where we feel 22

conclusions can be supported by existing data and methods. In other cases we describe alternative 23
methods, data and data gaps, and possible future directions, with the intention of soliciting meaningful 24SAB Review Draft

4 feedback from the EEAC. The key topics addressed in this paper

— loosely ordered from short

- to longer

25

term tasks

— include: 26
Improving communication by reporting value estimates in terms of risk changes rather than “statistical lives.” 27
We fear, as do others, that the prevalence of such terms of art as ‚the value of a st atistical life‛ has 28
contributed to unnecessary confusion and consternation among decision

- makers and members of the 29
general public. We aim to ease these communication difficulties by replacing the VSL terminology 30
with the straightforward term ‚value of mo rtality risk‛ (VMR). The ‚units‛ associated with the 31
mortality risk change must be clearly delineated and in this paper we report the units in terms of 32
willingness to pay for a reduced risk of 1/1,000,000 or a ‚micro

- risk,‛ following Cameron (2008) and 33

Ho ward (1989). We believe that this term provides a more accurate description of the fundamental 34
valuation concept that underlies the marginal willingness to pay for risk reduction, and that this 35
choice of measurement unit is a more natural one considering the typically small (relative to the full 36
suite of risks from all hazards) changes in individual

- level risks resulting from most environmental 37
policies. 38
Alternative approaches for updating EPA’s best central estimate, or range of estimates, of the willingn ess

- to

39
pay for mortality risk reductions for use in regulatory impact analyses. EPA is interested in updating its 40
guidance to better reflect the existing estimates of mortality risk reduction values in the revealed and 41
stated preference literatures. Spec ifically, how can the empirical results (described below in Section 42
4) be used to revise EPA’s mortality risk valuation guidance in the form of a revised point estimate or 43
range or benefit transfer function? 44
Incorporating a cancer differential into morta lity risk valuation guidance. We discuss the possibility of 45
adding a ‚cancer differential‛ (often called a ‚cancer premium‛ in the literature) to the standard 46
(non

- cancer) estimates of mortality risk reduction values, specifically for use in analyzing pol icies 47
expected to reduce carcinogenic pollutants. EPA first raised the issue of a cancer premium with the 48SAB Review Draft

5 EEAC in 2000 (USEPA 2000b), but the literature has developed considerably since that time. Given 49
its importance for the valuation of environmental h ealth risks in particular, we review the current 50
literature and recommend including a cancer differential in future guidance. 51
The role of altruism in valuing risk reductions. The role of altruistic motives for improved health and 52
safety is typically igno red in most benefit

- cost analyses but may have important implications for 53
estimating individuals’ willingness to pay for environmental improvements. We review several 54

recent studies that examine the role of altruism in benefit

- cost analysis and highlight the potential 55
relevance of these findings for the valuation of mortality risk reductions, in particular their 56
implications for interpreting and transferring stated preference estimates of ‚public‛ versus ‚private‛ 57

risk reductions. 58
Toward functional benefit transfer. We discuss specific issues that we expect to arise in applying both 59
classical and Bayesian meta

- regression techniques to new datasets of stated preference and hedonic 60
wage value estimates described in this paper, as possible approaches for devel oping a benefit transfer 61
function. We also discuss the structural benefit transfer approach, which involves specifying a direct 62
or indirect utility function, including parameters that can describe the relevant attributes of the risk to 63

be evaluated, and t hen deriving analytical expressions for observable economic variables that can be 64
used to calibrate the parameters of the preference function. Developing a valid benefit transfer 65
function, using either meta

- regression or a structural approach or some comb ination of these, is a 66
longer

- term task than the others mentioned above, but EEAC feedback on these issues would be very 67
helpful in shaping EPA’s research agendas in these areas. 68



### 1.2 Roadmap 69

The remainder of this white paper is organized as follows. Before we address our key topics in 70
more detail, Section 2 provides background discussion that (1) describes the valuation challenge facing 71
the Agency and the differences in the contexts underlying existing mortality risk reduction value 72SAB Review Draft

6 estimates and the policy sc enarios we seek to analyze; (2) briefly summarizes EPA’s most recent 73
guidelines for valuing mortality risk reductions (USEPA 2008); 1 and (3) recaps the main 74
recommendations from several recent expert advisory committees to EPA on the valuation of human 75

hea lth risk reductions and the use of meta

- analyses for combining estimates from different studies. 76
With this context in mind, in Section 3 we describe and discuss three of the key topics of this 77
whitepaper: terminology and metrics, cancer risk valuation, a nd altruism. In Section 4, we review the 78
empirical mortality risk value estimates from the stated preference and hedonic wage literatures, 79
including recent meta

- analyses of these literatures. The discussion of the stated preference literature 80

includes a newly assembled database of stated preference estimates of mortality risk reduction values in 81
anticipation of an updated meta

- analysis. We also review and extract value estimates and other 82
attributes from hedonic wage studies that have provided estimates of the VSL, with selected studies 83
spanning 1974 to the present. We discuss strengths and weaknesses of these studies for application to 84
environmental policies. 85
In Section 5 we discuss alternative approaches for synthesizing the estimates from these 86

lite ratures as a necessary step for updating EPA guidance. A longer term goal is to develop a benefit 87
transfer function for valuing mortality risk reductions, rather than relying on the current practice of 88
transferring a single central point estimate. We dis cuss two basic approaches for developing such a 89

benefit transfer function: meta

- analysis and structural benefit transfer. Meta

- analysis uses statistical 90
regression techniques to quantify the influence of study, policy, demographic, and possibly other 91

vari ables on the willingness to pay for health risk reductions. The structural benefit transfer approach 92
involves specifying a direct or indirect utility function and then deriving analytical expressions for 93

observable economic variables that can be used to c alibrate the parameters of the preference function. 94

1 These are reflected in EPA’s revised Guidelines for Preparing Economic Analyses (2008)

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7 Section 6 concludes with summaries of the key topics and needs for both short

- term guidance and longer

95

term research. 96



## 2 Background 97



### 2.1 The valuation challenge 98

Benefit cost analysis is a useful tool that provi des detailed information on a wide variety of 99
consequences associated with environmental policies. Benefits are based on what individuals would be 100
willing to pay for risk reductions or for other improvements from pollution reduction. Costs are 101

determined using the value of the resources directed to pollution reduction. As safeguar ding human 102
health is among the EPA’s primary goals, to develop more complete and more accurate benefit

- cost 103
analyses of its policies, EPA must estimate individuals’ willingness t o pay for reductions in health risks 104
from environmental harms. Ideally, benefit

- cost analysis of policies that reduce health risks would 105
account for all of the factors that may cause willingness to pay to vary across different types of policies 106

and indivi dual characteristics and circumstances. The literature has indicated that these factors may 107
include the sources of risk affected by the policy (e.g., hazardous air pollutants, water contamination, 108
etc.), the resulting health conditions (e.g., cancer, card io

- respiratory diseases, gastro

- intestinal diseases, 109
etc.), how the policy affects the timing of morbidity and mortality risks across each individuals’ life span 110
(i.e., how it shifts the ‚survival curve‛), the income and other personal characteristics of t he affected 111
individuals, and how the changes in risks are perceived by those individuals. While addressing all of 112
these factors simultaneously is currently empirically infeasible, there are three challenges that we 113
highlight for their direct relevance to EPA. 114
First, fundamental to this valuation challenge is that the risk reductions provided by EPA policies 115
are inherently public in nature, unlike, for example, private purchase decisions. The distinction is 116
important because individuals may reasonably valu e risk reductions from public policies differently than 117SAB Review Draft

8 those from private actions even if their own mortality risks are affected in a quantitatively identical 118
manner. Such differences could be due to differences in ‚controllability,‛ ‚dread,‛ or other ta ngible or 119
intangible factors (e.g., Slovic 1987 , Savage 1993 , Chilton et al. 2006 ). Furthermore, public policies raise 120

issues about altruistic values for risk reductions to others, something that may be of particular relevance 121
for environmental risks. EPA would like to use the existing literature to evaluate the extent and nature of 122
altruistic values and consider how to formulate mortality risk valuation guidance accordingly. We 123
address altruism in greater detail in Section 6.3

. 124
A second major challenge for the valuation of mortality risk reductions for environmental 125
policies is the intertwined nature of morbidity and mortality risks. Environmental policies generally do 126
not reduce the risks of fatal workplace or automobile accidents, for example, which provide the context 127
for many of the mortality valuation estimates in the literature and generally have little or no 128
accompanying morbidity or period of illness. Ideally, we would use an integrated model that could 129
estimate willingness to pay for mortality and associated morbidity risk reductions simultaneously. 130
Developing such a model is beyond the scope of this white paper and c urrent guidance development 131
effort, and is near the frontier of the empirical valuation literature. Nevertheless, to the extent possible 132
with currently available data and models, we would like to account for how individuals consider 133
morbidity in existing estimates of mortality risk reduction values when they always occur together. It 134
also is important to capture some related losses that may not be reflected in willingness to pay estimates, 135
depending on context in which they were estimated. For example, r educed health from illness preceding 136
death is certainly a loss to an individual and his or her quality of life, but may not be reflected in VSL 137
estimates from the hedonic wage literature, which are based on the risks of workplace injuries that lead to 138

deat h. Society also is worse off because of the illness due to the individual’s lost productivity, something 139
that may not be reflected in revealed or stated willingness to pay estimates, depending upon the type of 140
insurance held by the individual and possibly the scenario description. 141SAB Review Draft

9 This issue is of particular relevance to EPA when addressing reductions in cancer risks since 142
many EPA policies focus on reducing exposure to carcinogens. Ten years ago EPA reviewed the 143
economic literature on valuing fatal cancer risk reductions and discussed a number of risk characteristics 144
that may influence people’s values, including but not limited to the timing of the risks ( USEPA 2000b ,c). 145
The committee recognized many of the issues reviewe d by EPA as theoretically valid but empirically 146
ambiguous, and therefore recommended that ‚the only risk characteristic for which adjustments to the 147
VSL can be made is the timing of the risk‛ ( USEPA 2000c p 1). In particular, t his recommendation 148
advised against the application of any differential to reflect preferences for reducing cancer risks relative 149
to other types of risk because of dread or other factors. With an additional decade of valuation literature 150
to draw upon, EPA is seeking to re

- examine this question using data from the stated and revealed 151
preference studies described below, as well as other relevant empirical results. We will discuss cancer 152

valuation in more detail in Section 6.4

. 153
Finally, the empirical literature may allow us to account for the extent to which individuals value 154
different categories of risks differ ently in a systematic transfer of benefits. For example, if environmental 155
risk reductions are valued differently from workplace or auto accidents, regardless of whether the 156
mitigation is from private or public actions, our guidance should reflect this dif ference. 157
It is important to keep the overarching valuation challenge in mind as we begin discussing recent 158
studies and value estimates. Each study reflects an attempt to measure the value of a reduction in 159
mortality risk from a specific cause (or small se t of causes), in a specific context, among a specific 160
population. By now there is ample theoretical and empirical evidence to indicate that values for health 161

risk reductions are not ‚one

- size

- fits

- all‛

— that is, they are ‚individuated‛ (e.g., Sunstein 2004 , Evans and 162

Smith 2008 , Scotton and Taylor 2009 ). For this reason, we believe that there is great scope for improving 163
upon the point value benefit t ransfer approach that has traditionally been applied to mortality risk 164
reductions based on a central estimate of the VSL. Therefore, we ultimately are seeking both short

- term 165SAB Review Draft

10 recommendations as well as advice on a longer

- term research agenda on how these heterogeneous 166
studies can best be synthesized for systematic benefit transfers to improve the application of benefit

- cost 167
analysis to future environmental policies. 168



### 2.2 Existing EPA Guidance 169

EPA’s draft Guidelines for Preparing Econo mic Analyses (2008) (hereafter, the draft Guidelines ) 170

retains the recommendation from the 2000 version, a default central VSL value $4.8 million in 1990 real 171
dollars. This estimate, after adjusting for inflation and real income growth, is to be applied to mortality 172
risk reductions for all types of policies, no matter the source of the risk. 2 The estimate is based on the 173
mean of a probability distribution fit to twenty

- six published VSL estimates. The draft Guidelines also 174

indicates that the distribution itself can be used for formal uncertainty analysis. The underlying studies, 175
the probability distribution parameters, and other useful information are available in Appendix B of the 176

draft Guidelines ( USEPA 2008 ). 177

The draft Guidelines also retains the 2000 version recommendation that the VSL for mortality risk 178
reductions should not be adjusted for differences in sources of risk or population characteristics

— rather, 179
these factors should be examined qualitatively. In some case s, the analysis may include a quantitative 180
sensitivity analysis. Analysts should account for timing when valuing mortality risk reductions, and 181

should discount the benefits of future risk reductions at the same rate used to discount other costs and 182

benefi ts. Because the VSL represents the marginal willingness to pay for contemporaneous risk 183
reductions, this is typically done by estimating the lag between reduced exposure and reduced mortality 184
risks, calculating willingness to pay in all future periods wh en mortality risks are reduced, and 185
discounting back to the present. 186
Finally, EPA’s draft Guidelines also recommends accounting for increases over time in average 187
income. This is done by using projections of real GDP per capita and applying an income elas ticity 188

2 We report all estimates in 2009 US dollars unless otherwise noted.SAB Review Draft

11 estimate. The resulting future (real) VSL will therefore reflect the idea that health risk reductions are 189
normal goods and so willingness to pay will increase with income. 190



### 2.3 Recommendations from prior expert committees 191

This white paper is one stage i n a detailed process that EPA has undertaken with the SAB

- EEAC 192
to improve the Agency’s ability to value health risk reductions. Since its review of EPA’s Guidelines for 193
Preparing Economic Analyses ( USEPA 2000a ) the SAB has offer ed several specific sets of recommendations 194
on valuing risk reductions, particularly for mortality risks. 195
In July 2000 the SAB

- EEAC released an advisory report in response to EPA’s white paper, Valuing 196
the Benefits of Fatal Cancer Risk Reduction , which foc used on benefit transfer issues associated with using 197
existing mortality risk values to estimate the benefits of EPA actions on carcinogens, including potential 198
adjustments that could be made to existing risk values to account for this category of benefits ( USEPA 199

2000b ). As noted earlier, after reviewing the white paper and current economics literature, the SAB 200
concluded that, while many of the issues raised in the white paper were theoretically valid and 201
potentially important, the empirical literature supported only accounting for latency and for income 202
growth over time. The SAB

- EEAC did not consider other adjustments to EPA’s default mortality risk 203
value to be appropriate for the Agency’s primary analyses, but could be address ed separately using 204
sensitivity analysis. 205
An August 2001 SAB report, Arsenic Rule Benefits Analysis: An SAB Review ( USEPA 2001 ) , 206
generally supported EPA’s estimate of the marginal willingness to pay for mortality risk reduction s. The 207

SAB also offered additional recommendations to account for the time between reduced exposure and 208
reduced mortality risks. This report coined the term ‚cessation lag‛ for this concept and offered specific 209
recommendations for estimating cessation la gs based on the types of risk data available. The SAB review 210
also clarified that reductions in exposure to carcinogens

— that is, exposure per se , aside from the increased 211
cancer risks that the exposure causes

— are not a separate benefit category under a dam age function 212SAB Review Draft

12 approach to valuing reduced risks. The board noted that it is possible that there is an existence value for 213
protected drinking water; however, without sufficient empirical evidence to estimate the magnitude of 214

this value, it cannot be include d in the quantitative benefits analysis. Finally, the report indicated that it 215
is appropriate to add the costs of illness to t he willingness to pay for mortality risk reductions when 216
estimating the benefits of reduced cancer mortality. 217

EPA further consult ed with the SAB

- EEAC on additional mortality risk valuation issues in 2004, 218
developing a strategy to gather additional information on meta

- analysis to inform both the SAB

- EEAC 219
and EPA ( USEPA 2004b ). In 2006, EPA returned to the SAB

- EEAC with two documents for formal 220
review: a white paper addressing how remaining life expectancy affects willingness to pay for mortality 221
risk reductions, and an expert report on the use of meta

- analysis for combining existing mortality risk 222

value es timates. A 2007 report, SAB Advisory on EPA's Issues in Valuing Mortality Risk Reduction , 223
responded to both topics ( USEPA 2007). 224
On the subject of life expectancy, the SAB

- EEAC noted that there was theoretical ambiguity on 225

how w illingness to pay might change with age (and, hence, remaining life expectancy). The committee 226
concluded that the existing economics literature does not provide clear theoretical or empirical support 227
for using different values for mortality risk reduction s for differently

- aged adults or a constant ‚value of 228
statistical life year‛ (VSLY). Thus, the SAB

- EEAC recommended that EPA continue using its traditional 229
assumption of an age

- independent willingness to pay for mortality risk reductions. 230

To address meta

- analysis, EPA assembled a work group of expert statisticians in December 2005 231

to discuss the meta

- analysis of VSL estimates and to examine three existing meta

- analyses: Mrozek and 232
Taylor (2002) , Viscusi and Aldy (2003) , and Kochi et al. (2006) . While the expert workgroup did not 233
endorse any one of these studies, the panel did encourage the use of meta

- analytic techniques for the 234
analysis of the existing literature on VSL. The workgroup recommended analyzing stated preference and 235SAB Review Draft

13 hedonic wage data separately, and offered a set of principles that should be followed in conducting such 236
an analysis ( USEPA 2007 ). 237

The SAB

- EEAC review of the Meta

- analysis workgroup’s report stated that meta

- regression is ‚a 238

useful statist ical technique for identifying various aspects of study design or population characteristics 239

that are associated with differences in VSL,‛ but concluded that meta

- regression is ‚not appropriate *for+ 240
combin*ing+ VSL estimates‛ into a summary measure ( USEPA 2007 p i). Rather, the SAB

- EEAC 241
suggested using meta

- regression to examine how study design characteristics influence the VSL estimates 242
and relying on other statistical techniques to determine a central estimate or range of est imates for use in 243
benefit transfer to new policy cases. 244
Based on these expert recommendations and other considerations, we believe that updated 245

reviews and meta

- analyses of the stated preference and hedonic wage literatures could help refine the 246
Agency’s c entral estimate(s) or range of estimates of the marginal willingness to pay for mortality risk 247
reductions. Studies have shown that values for health risk reductions may depend on differences among 248
policies and the affected individuals. These factors incl ude the sources of risk affected by the policy (e.g., 249
hazardous air pollutants, water contamination, etc.), the resulting health conditions (e.g., cancer, cardio

250
respiratory diseases, gastro

- intestinal diseases, etc.), as well as how the policy affects the timing of 251
morbidity and mortality risks across each individuals’ life span (i.e., how it shifts the ‚survival curve‛). 252
Therefore, as is widely recognized in most other contexts where some form of benefit transfer is used for 253
policy analysis, we believe a functional benefit transfer approach should be more accurate than a single 254
point estimate applied in all circumstances. Consequently, we are interested in exploring approaches for 255
developing benefit transfer functions that can account for some or all of t hese factors. 256SAB Review Draft

14 

## 3 Key Issues for EPA 257



### 3.1 Fundamental Concepts and Recommended Terminology Changes 258

3.1.1 Fundamental Valuation Concept 259
We begin by identifying the fundamental valuation concept that economists aim to estimate 260
using non

- market valuation methods and apply i n benefit

- cost analyses of policies that reduce human 261
health risks. Consider a general utility function for an individual i with income and some health risk 262

among the arguments:

. The vector is included to emphasize that, in addition 263

to income and risk, the individual’s utility (and therefore the willingness to pay for health risk 264
reductions) also may be influenced by many other factors specific to t he case at hand. We will highlight 265
several of these factors throughout this white paper. The individual’s marginal rate of substitution between 266

income and risk is: 267

. 268

This marginal rate of substitution, , also can be interpreted as the individual’s marginal 269

willingness to pay ( wtp ) for a change in risk

— that is, the amount of money the individual would be willing 270
to swap for a small change in risk on the margin. 3 This is the fundamental value concept that must be 271

estimated for use in benefit

- cost analyses of policies that may improve human health. With estimates of 272
these quantities, conditioned as necessary on possibly many observable characteristics of the policy and 273

the affected individuals, it is strai ghtforward to calculate the total willingness to pay for the risk 274
reductions that are expected to be produced by the policy: , where i indexes all individuals 275

affected by the policy, and and are the estimated marginal willingness to pay and risk 276

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 willin gness to pay amounts, which will have units of $.SAB Review Draft

15 reduction for individual i , both of which may depend on individual

- level characteristics and 277

circumstances. 4 278
It is important to emphasize that this is a marginal value concept

— a dollar v alue per unit change in 279

risk . These values should be thought of as the slope of a curve at a point, rather than the height of the 280

curve. 5 For practical purposes, the units used to report estimates of these slope values are of no 281
consequence. They could be reported as dollars per nano

- risk ( ), or micro

- risk ( ), or mili

- risk ( 282
), etc. As long as the measurement units are known, then the risk changes to be valued can be 283
expressed in the same units and the correct total value can be calculated. The conventional measurement 284
units used for reporting these slope estimates are (effe ctively) ‚dollars per mortality‛ risk changes, 285
usually simply written as ‚$,‛ where ‚per mortality‛ is understood (or misunderstood, depending on the 286
audience). This quantity was often referred to as the ‚value of life‛ in the early literature on the subj ect 287
(e.g., Rice and Cooper 1967 ). While the terminology varies, the quantity is now typically called the ‚value 288
of a statistical life,‛ or VSL, where ‚statistical‛ has been added to emphasize that valuation is based on 289
changes in risk rather than the loss of life with certainty. 6 290

3.1.2 Change in metric and terminology 291
Despite its widespread usage, this particular selection of measurement units for the denominator 292
of the marginal rate of substitution between income and risk, and the VSL label that has been attached to 293

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. Then 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.SAB Review Draft

16 it, have caused or contributed to needless confusion and controversy, especially among non

- economists 294
(Cameron 2009 ). Most economists recognize that the ‚units‛ associated with the VSL reflect the 295
aggregation of the small risk reductions across many individuals until that aggreg ate reflects a total of 296

1.0, or one statistical life. However, for non

- specialists this potentially subtle point is often lost; the 297
addition of the word ‚statistical‛ to the terminology does not seem sufficient to clarify the concept. 7 298
To help reduce t he misconceptions that seem to be inspired or aggravated by the VSL 299
terminology, we propose a change in EPA standard practice such that estimates of health values will be 300
referred to as the ‚value of mortality risk‛ (VMR), and report the associated units u sing standard metric 301
prefixes to indicate the size of the risk change and the associated time scale, e.g., $/μr/person/yr (dollars 302
per micro[10

- 6 ]

- risk per person per year) ( Howard 1989 , Cameron 200 9 ). 8 303
As noted earlier the choice of risk increment for aggregating and reporting risk changes is mainly 304
one of convenience. However, we believe that explicitly labeling the units of the VMR in this way more 305
clearly emphasizes that these values refer to s mall changes in individual

- level risks over a definite time 306
span rather than how much money any single individual or group would be willing to pay to prevent the 307
certain death of any particular person. It also should be emphasized that the use of a standa rdized 308

7 A recent e xample of the confusion surrounding this concept in the popular press can be found in an A P 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. T his story quickly spread throughout the media even app earing 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 ( μ r). 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 valuatio n of marginal changes in fatality risks specific to the type of the risk affected by the policy‛ (p 23).SAB Review Draft

17 measurement unit for reporting values for health risk reductions should neither be taken to imply that 309
the values themselves are invariant across individuals or contexts, nor that these marginal values will be 310
constant across the full range of relev ant risk changes. 311
For the remainder of this paper we will use the general term ‚value of mortality risk‛ whenever 312
possible. We will report estimates as VMRs, as defined above, to the extent possible, using the VSL 313
terminology only as necessary in disc ussing the previous literature. 314



### 3.2 Altruism and willingness to pay for mortality risk reductions 315

We now turn to an overarching conceptual issue that may affect the conduct of benefit

- cost 316
analysis more generally: altruism. The default assumption for most a pplications of revealed and stated 317
preference methods for non

- market valuation is that individuals’ (or households’) well

- being depends on 318
their own consumption (interpreted broadly to include market and non

- market goods and services) and 319
is not directly i nfluenced by the consumption or well

- being of others. If this assumption is invalid, we 320
may be concerned that our standard methods of estimating willingness to pay assuming ‚atomistic‛ 321
individuals or households may give misleading results in benefit

- cost analysis. 322
There are at least two ways that altruism may be relevant for the valuation of mortality risk 323
reductions. First, some stated preference studies are based on surveys that make a distinction between 324
‚public‛ and ‚private‛ risk reductions. 9 The di fference, if any, between WTP for public versus private 325
risk reductions may be partly due to altruism, but other factors could be at work as well. For example, a 326
distrust of government may lead some respondents to express a lower WTP for public risk reduc tions 327
provided through government programs compared to those provided through private initiatives. While 328
stated preference studies may in principle be able to distinguish altruistic preferences from other 329

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 ca tegory: 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 reduc tions in highway safety

- related deaths, are ‚public.‛ See section 6.1 for more details on the stated preference studies.SAB Review Draft

18 confounding factors, it is difficult to draw clear conclusions from the existing literature because most 330
studies that have been conducted to date were not designed to examine altruism per se. 10 Therefore, the 331
proper application of the results of these stated preference studies may depend in part on how al truism 332

should be treated in benefit

- cost analyses. Second, since hedonic wage studies are focused on 333
compensation received by individual workers for taking on private, job

- related risk, the mortality risk 334
values from hedonic wage studies do not incorporat e altruism. Therefore, if (some forms of) altruistic 335
preferences should be included in benefit

- cost analysis, then hedonic wage

- based estimates of mortality 336
risk values may need to be supplemented with separate value estimates that capture altruistic pref erences 337
alone. On the other hand, if (some forms of) altruistic preferences should be excluded from benefit

- cost 338
analyses, then this may influence whether (or how) some stated preference studies should be used for 339

benefit transfers. 340

EPA’s Guidelines for Preparing Economic Analyses (USEPA 2000a) discussed the role of altruism in 341
estimating the total benefits of public actions, and noted the key distinctions between paternalistic (or 342
‚safety focused‛) and non

- paternalistic (or ‚pr eference respecting‛) forms of altruism. 11 If altruistic 343

motives are non

- paternalistic, then individuals care not only about the benefits others receive, but also 344
the costs they bear, and most economists who have studied this issue have concluded that it i s generally 345
inappropriate to add these altruistic values for benefits others receive to total willingness to pay. Doing 346

so could lead to ‚double

- counting‛ some of the benefits and/or costs. Paternalistic altruism, on the other 347

hand, should be included in the calculation of total benefits. EPA’s Guidelines ( USEPA 2000 a p 61) 348

describes the issue as follows: 349

10 Stated preference studies and the treatment of altruism also may hold promise for identifying preferences related to equity or env ironmental 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 id entified 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.SAB Review Draft

19 While benefits are generally calculated by summing each individual's WTP for his or her own 350 welfare, there are conditions under which it is appropriate to include altruistic values, or individuals' 351 WTP for the welfare of others. Economic theory concludes that if one cares about a neighbor but 352 respects the neighbor's preferences, and if the neighbor would have to pay for the policy action being 353 analyzed, then altruistic benefits should not be counted in a benefit

- cost analysis. The intuition 354 behind this result is that, if one respects the neighbor's preferences, one cares about both the benefits 355 and the costs the neighbor fac es. It is therefore inappropriate to add the value one attaches to the 356 neighbor's benefits without considering the cost implications of doing so. Comparing individual 357 benefits and costs in this case is the appropriate decision rule. 358 359 Altruistic benefits m ay be counted either when altruism toward one's neighbor is paternalistic or 360 when one will in fact bear the costs of the project but the neighbor will not. In the first case 361 (paternalistic altruism), one cares about the benefits the neighbor will enjoy, e .g., from a health or 362 safety project, but not about the costs the project will impose on him. An example of the second case 363 would be a project whose costs are borne entirely by the current generation; i.e., the project imposes 364 no costs on future generation s. In this case, altruism toward future generations by the current 365 generation could legitimately be counted as a benefit. 366 367 The conclusions in the Guidelines were based largely on Bergstrom (1982) and McConnell (1997) 368
who demonstrated that the optimal provision of public goods based upon selfish preferences is a 369
necessary and sufficient condition for the optimal provision based on social preferences (including 370
altruistic preferences). However, since the publication of the Guidelines , Flores (2002) has challenged the 371
conventional wisdom that (non

- paternalistic) altruism should be excluded from benefit

- cost analysis. 372
Flores showed that passing a private values benefit

- cost test is a sufficient but not a necessary condition 373

for non

- marginal policies to be potentially Pareto improving, except under special circumstances. That is, 374

even if all altruism is non

- paternalistic, failure to include altruistic values may lead to the rejection of 375
policies that are potentially Pareto improving. Flores concluded that ‚benefit

- cost analysis with altruism 376
cannot simply be conducted independent of who pays.‛ In a more recent study, Bergstrom (2006) 377

concl uded that ‚The assumptions under which the private values benefit

- cost test is necessary for 378
potential Pareto improvements need not always be satisfied;‛ nevertheless, ‚Despite these 379
qualifications< for a broad class of economies, a comparison of the sum o f private values to the cost of a 380
project is the appropriate test for determining whether it can lead to a Pareto improvement‛ (p 348

- 349). 381SAB Review Draft

20 Bergstrom’s conclusion seems to summarize the prevailing view regarding non

- paternalistic 382

altruism in benefit

- cost analysis, especially for policies that would cause marginal changes in 383
environmental quality (since Flores’ counter

- examples involved non

- marginal changes). Therefore, the 384
main relevance of altruism for mortality risk valuation lies in the distinction bet ween the paternalistic and 385

non

- paternalistic forms. Including the former but excluding the latter may require supplementing 386
revealed preference estimates of health risk valuations with a careful selection of results from previous 387
stated preference studies . Stated preference surveys that elicit only private willingness to pay would 388
exclude both forms of altruism. One way to include paternalistic but exclude non

- paternalistic altruism 389
would be to design a survey that would inform respondents about health i mprovements that others 390
would experience from the policy, but also ask each respondent to assume that all others would be taxed 391
an amount equal to their private willingness to pay for the policy, so that their utility remains unchanged 392
(Johansson 1994). I t is not clear which if any of existing stated preference studies (many of which are 393
reviewed below in Section 6.1) were designed this way, so the current body of empirical results cannot 394
support the separation of paternalistic from non

- paternalistic altru ism. We recommend additional 395
research in this area to help estimate paternalistic willingness to pay for environmental policies that 396
reduce health risks. Additional examination of existing studies may shed light on this issue in the 397

relative short

- term, and we are interested in feedback on this issue. 398



### 3.3 Valuing cancer risks 399
As noted in our description of EPA’s valuation challenge, willingness to pay for cancer risk 400
reductions may be systematically different than that for workplace or auto accidents or oth er risks not 401
associated with a lengthy and painful illness. This difference is sometimes referred to as a a ‚cancer 402
premium,‛ but we will use the more general term ‚cancer differential.‛ While not often defined 403
precisely, the differential is posited as c apturing elements of dread and fear of cancer, as well as the pain 404SAB Review Draft

21 and suffering from the period of illness preceding death. It might also include income and household 405
productivity losses over this period of morbidity. 406

Several authors have recommended a ccounting for this differential in benefit

- cost analysis of 407
policies that reduce exposure to carcinogens (e.g., Revesz 1999 , Sunstein 2004 ). To the extent that existing 408
policy guidance on valuing m ortality risk reductions is based on non

- cancer risk

- wealth tradeoffs, this 409
would involve an ‚adjustment‛ to the default (generic, non

- cancer) mortality risk reduction value. 410
Governmental analyses in the UK have adopted this approach, applying a 100% diff erential for cancer 411
risks ( HM Treasury 2003 ). 12 In addition, the European Commission has recommended a 50% differential 412
for carcinogenic pollutants over its default value of preventing a fatality ( European Commission 2000 ). 413
For the purpose of developing guidance, we are interested in assessing the valuation literature on 414
cancer risks and any cancer risk differential, both in the short

- term and the longer term. Ultimately, this 415

literat ure could inform the development of a benefit transfer function, in combination with the stated 416
preference and hedonic wage estimates described in greater detail below. While such longer

- term 417
research is being conducted, we believe it is reasonable that e vidence of systematically different 418
preferences for cancer risk reductions be part of any recommended short

- term guidance. 419

To inform this discussion, this section contains a somewhat more detailed assessment of the 420
empirical literature on cancer risk valu ation, with a particular emphasis on studies that examine risks in 421

both cancer and non

- cancer contexts. These studies are described in Table 1 in the following categories: 422
studies comparing values for cancer and non

- cancer fatal risk reductions 423

- stated pre ference studies that estimate willingness to pay 424

- risk

- risk studies 425
stated preference studies of cancer risks without internal comparisons, and 426
related hedonic property and hedonic wage studies. 427

12 Specifically, this adjustment is applied for the benefits from asbestos proposals by the UK Health and Safety Executive (HSE).SAB Review Draft

22 The first of these categories contains the most direct evidence on any cancer differentials. 428
Note on Cessation Lag and Latency 429
Reduced exposure to carcinogens results in reduced cancer incidence after a period of time that 430
EPA has referred to as ‚cessation lag,‛ a term originally coined by the SAB in its revi ew of the Agency’s 431
arsenic in drinking water benefits analysis. Cessation lag addresses only reduced risks from reduced 432
exposure and thus applies best to populations currently at risk. The time between initial exposure and 433

increased cancer incidence is r eferred to as ‚latency‛ in recent EPA analyses, but it is often used in the 434
literature in a broader sense to refer to the time difference between a change in exposure and a change in 435

risk. 436

Prior SAB

- EEAC advice and agency practice has been to estimate c essation lag and latency from 437
available epidemiologic data, apply a value of statistical life estimate at the time at which cancer mortality 438
reductions occur, and discount this value back to the present at the rates prescribed in Agency guidance. 439
The prac tice has generally been supported by research findings suggesting that individuals discount over 440
these lag times at rates generally consistent with market rates, although some recent stated preference 441

studies find near

- zero discount rates over latency peri ods (Hammitt and Haninger, 2010; Alberini and 442
Scasny, 2010a). 443
An important issue in estimating a cancer differential is the potential need to consider 444
differences in the time profile of mortality risks between cancer and non

- cancer cases. Earlier studie s 445
were often silent on the issue, but more recent ones have attempted to address it explicitly. Our focus in 446

this section is on a potential cancer differential that captures the difference in marginal willingness to pay 447
for reduction of cancer mortality r isks relative to that of a non

- specific mortality risk holding timing 448
equal. That is, the differential, in principle, compares a contemporaneous non

- cancer risk reduction with 449
a contemporaneous cancer risk reduction. We recognize that timing may be inter twined with how people 450SAB Review Draft

23 perceive and value risk reductions, something that should be considered more fully in any rigorous, 451
systematic benefit

- transfer exercise as we develop guidance. 452
Stated Preference studies including cancer and non

- cancer risks 453

Several stated preference studies have estimated willingness to pay for both cancer and non

454
cancer risks, in large part to examine a possible cancer differential. A few studies have focused only on 455
cancer risk reductions without an internal comparison to other t ypes of risk. The results of these studies 456

are somewhat mixed

— some have found evidence of a cancer differential ( Hammitt and Liu 2004 , Tsuge 457

et al. 2005 , Alberini and Scasny 2010a, an d Alberini and Scasny 2010b), while a few others found no such 458
evidence ( Hammitt and Haninger 2010 , Adamowicz et al. 200 8) when looking at whole

- household or 459
public risks. Cameron and DeShazo (2008) found evidence of a differential for some cancers (breast and 460
prostate) over other cancers (colon, lung, and skin), but not over other health endpoints (heart attacks and 461
disease). 462

There ha ve been two risk

- risk tradeoff studies specifically examining how preferences for cancer 463
risk reduction compare to those for automobile accident risk reductions. By asking respondents to choose 464
among different bundles of risks, these simplified choice exp eriments aim to estimate the relative values 465
of various types of risk reductions. They do not, however, provide a willingness to pay for either risk 466
type and therefore are not included in our reviews of the willingness to pay literature above. Van 467

Houtve n et al. (2008) found a strong preference for avoiding cancer risks relative to automobile accidents 468
even after controlling for latency and morbidity periods. With a 5

- year latency, values for reductions in 469
fatal cancer risk were approximately three times larger than those for immediate accident risks, declining 470
to fifty percent larger for a 25

- year latency. By contrast, in a study by Magat et al. (1996), the median 471
respondent was indifferent between fatality risk from auto accidents and lymphoma, suggest ing that 472
cancer mortality is no more ‘dreaded’ than accidental mortality. It is difficult to draw firm conclusions, 473
however, because the study did not specify the timing of the risks, and, in particular, any latency 474SAB Review Draft

24 associated with cancer. Therefore, if respondents assumed that cancer risks would be realized after a 475
latency period then the results suggest that any preference for cancer reductions was approximately 476
offset by discounting future risks. 477
Three additional stated preference studies focus on WTP for cancer risks without direct 478
comparisons to other risks. These do not internally address the question of how cancer risks are valued 479
differently from non

- cancer risks, but may be combined with the results from other studies to address 480
this question. Focusing on cancer risks from hazardous waste sites Alberini, et al. (2010) estimated a 481
cancer VSL of approximately $5.6 million (2009 dollars) using the results of choice experiments in Italy. 482

Carson and Mitchell (2006) examined willingness to pay for installing a water filtration system to remove 483
trihalomethanes (THM) in public drinking water. Estimated values depend upon an assumed latency 484
and discount rate, as well as the specific risk reduction, but generally range from $3.4 to $8.0 at the 485
smallest risk changes for a 25

- year latency. Buzby et al. (1995) used a telephone

- mail survey to examine 486
the value of reduced fatal cancer risk from exposure to pesticides in grapefruit, and estimated a value of 487

statistical cancer fatality at $6.99 million based on exposure assumptions. 488
Related Hedonic Property and Wage Studies 489
There are a small number of studies that have estimated WTP for reduced cancer risks using 490
revealed preference approaches. The results have generally shown that the value of a statistical cancer 491
case is similar to prevailing VSL estimates from hedonic wage studies. Direct comparison, however, is 492
difficult without additional assumptions about latency or cessation lag and cancer fatality rates, as noted 493
for each study. 494

In the context of hazardous waste, Gayer et al. (2000) and Gayer et al. (2002) employed a hedonic 495
property framework to estimate the implicit value of a statistical cancer case from surrounding 496
Superfund sites. In the first study, the value of a statistical cancer case was approximately $5.5 million, 497
but did not include any assumptions or information on latency or fatality. The 2002 study calculated 498SAB Review Draft

25 estimates under a variety of latency and discounting as sumptions with results ranging from $5.2 million 499
to $10.0 with no latency, and from $6.2 to $11.8 million using a 3% discount rate and 10

- year latency 500
period. 501
Davis (2004) used housing price responses to an observed cancer clus ter in Nevada to estimate 502
marginal willingness to pay for a change in lifetime pediatric leukemia risk ranging from $3.7 million to 503
$11.1 million, which is generally consistent with the Gayer et al. studies, although the leukemia values are 504
specific to chi ldren. Ho and Hite (2008) included risks from air toxics and hazardous waste sites in a 505
hedonic property model and estimated the implicit value of cancer mortality to be $6.0 million. Finally, 506
Lott and Manning (2000) exp lored the presence of compensating wage differentials for carcinogenic 507
exposures in the workplace using the hedonic wage framework, finding that workers were being 508
compensated for carcinogenic exposures. By making assumptions about the proportion of cance r deaths 509
that arise from occupational exposures they calculated a cancer

- specific VSL of $12.4 million. 13 510
Because reducing environmental cancer risk is an important part of EPA’s mission to protect 511
human health, a key question is how the results from the e mpirical literature summarized here, along 512
with other literature described in this report, can be systematically synthesized to account for individuals’ 513
preferences for reducing cancer risks relative to other types of health risks. As a first

- cut, the sim ple 514
average of the central estimates of the cancer differential from the subset of studies in Table 1 that 515
reported values for both cancer and non

- cancer risks is 52%. 14 This is a preliminary estimate and should 516
be refined or replaced with a more systemati c synthesis of the literature, possibly incorporating results 517

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 0.5 2

.SAB Review Draft

26 from other relevant studies. In the meantime, a cancer differential of 50% might be a reasonable 518
placeholder value for use in upcoming RIAs. 15 519



## 4 Review of stated preference and hedonic wage st udies 520
Our reviews of the literature in the sections that follow focus on results from stated preference 521
and hedonic wage and studies. This reflects where the majority of potentially relevant empirical 522
estimates are found and is consistent with prior consu ltations and advisory reports. The hedonic wage 523
approach is well

- established and vetted and remains influential in informing guidance across the federal 524
government. However, the approach is limited to work

- related risks and the associated risk 525

characteri stics, many of which differ from EPA policy scenarios, as has been detailed many times in the 526

economics literature. 527
There has been a tremendous growth in the number of stated preference studies to estimate 528
values for mortality risk reductions in recent years; certainly there is now a far larger and more 529
sophisticated body of literature to draw upon than was available at the time of EPA’s last revision of its 530
guidance. These developments potentially allow for an examination of important valuation dimensi ons 531
including risk source (e.g., environmental, traffic

- related); type of illness (e.g., any cancer differential or 532
associated morbidity); and altruism. Our review of the empirical literature and how it can be synthesized 533
attempts to address these issues. 534
However, additional studies exist that may supplement the reviews of the stated preference and 535
hedonic wage literatures below. First, some stated preference studies do not seek to estimate willingness 536
to pay or accept, but rather relative preferences for different types of mortality risk reduction. Two 537
examples addressing cancer risks are described more completely above ( Magat et al. 1996 and Van 538

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 differen tial implicitly assumes that the income elasticity of the absolute cancer differential equals that for the non

- cancer VSL.SAB Review Draft

27 Houtven et al. 2008). The study results do not estimate willingness to pay, but it may be possible to 539
combine the estimates from the studies on relative tradeoffs with the willingness to pay literature to 540

refine our benefit transfers. 541
Another segment of the literature that we do not examine in detail here includes studies that 542

ev aluate only public preferences for risk reducing policies. Examples from this literature include 543
Cropper et al. (1994) and Subramanian and Cropper (2000) , who used survey meth ods to examine how 544
respondents would allocate a given public budget to public programs for lifesaving and risk reduction; 545

and Bosworth et al. (2009) who assessed community

- level preferences for public programs to improve 546
health and safety. The SAB previously concluded that these studies can be informative in their own right, 547
but cannot be directly related to individual willingness to pay and used directly for benefit

- cost analysis 548
( USEPA 2001 ). EPA is open to suggestions on whether and how this literature may be effectively and 549
appropriately synthesized with the results of other studies for the development of guidance on mortality 550

risk valuation. 551
The hedonic property method has been used to es timate the value of environmental amenities 552
and disamenities including mortality risks. A major challenge has been to limit the analysis to risk 553
reduction rather than more comprehensive measures or indicators of environmental quality, such as air 554
quality (e.g., Chay and Greenstone 2005 ) or the presence of or distance to hazardous waste sites (e.g., 555
Greenstone and Gallagher 2008 ). These studies can be useful for evaluati ng some policies directly, such 556
as the remediation of hazardous sites, but cannot be directly informative for mortality risk valuation. 557
Willingness to pay for reduced mortality risks have been estimated in hedonic property studies, as first 558

described and demonstrated in Portney (1981) , who examined the relationship between housing prices 559
and mortality risks from air quality. Four other studies, described more completely above in this paper, 560
estimate marginal willingness to pay for cancer risk (Gayer et al. 2000 , 2002 ; Davis 2004; and Ho and Hite 561
2008). 562SAB Review Draft

28 Finally, implicit values for risk reductions can be estimated in ‚averting behavior‛ studies, 563
wherein an individual or household uses the good as an input into the production of health or safety. 564
Blomquist (2004) conducted a n extensive review of this literature and concluded, with some caveats, that 565
the findings are broadly similar to hedonic wage estimates. Recent additions to the literature are 566
generally consistent with this conclusion (e.g., Andersson 2005 , 2008 (automobile risks); Hakes and 567

Viscusi 2007 (seatbelt use)). Key concerns about averting behavior studies include issues of risk 568
perception and the separability of joint benefits and costs ( USEPA 2000 b). Viscusi (1992) explicitly 569

excluded these studies from consideration in his meta

- analysis of VSL estimates. Further, the lack of 570

available studies on environm entally

- related risks limits the usefulness of this class of studies for the 571
present purpose of developing guidance for mortality risk valuation. 16 572



### 4.1 Stated preference studies 573

Stated preference (SP) is a survey

- based method for estimating willingness to pay o r accept for 574

non

- market goods or services. SP methods are widely used to value environmental amenities or 575
improvements in human health endpoints that may be difficult or impossible to estimate using revealed 576
preference methods because of long lag times, u nclear causality, or other factors. For example, SP studies 577
have been used to elicit willingness to pay for reductions in the risks of dying from cancer and cardio

578
vascular disease. SP studies vary widely in terms of the types of risk considered, payment vehicles, 579
latency periods, mode of survey administration, etc. The number of and variation among existing SP 580
studies is now large enough that the variation in their results can be analyzed statistically, although this 581

involves a number of data collection and model estimation challenges. 582

16 Note that there are some studies that relate averting behaviors to environmental quality or even related risks (e.g., Dickie and G erking, 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.SAB Review Draft

29 4.1.1 Recent meta

- analyses of SP studies 583

Three recent meta

- analyses examined the stated preference literature using statistical methods. 584
Kochi et al. (2006) used both stated and revealed preference studies in an empirical Bayes framework. 585
Dekker et al. (2008) focused exclusively on stated preference studies, also with Bayesian methods. 586

Br aathen et al. (2009) conducted a meta

- regression analysis of a wide variety of stated preference studies 587
using classical econometric tools. Each of these studies is discussed in more detail below. 588
Kochi et al. (2006) use d an empirical Bayes estimation method to generate predicted VSL 589
estimates using multiple estimates from both stated preference and hedonic wage studies. Here we focus 590
on the analysis and results for the stated preference data in their study. Study selec tion criteria were 591
similar to those used by Viscusi (1992) , including the use of studies for the general population and those 592
conducted in high income countries only, and a minimum sample size. 17 Another important criterion was 593
the use of estimates for immediate risk reductions; specifically, estimates for risks involving a latency 594
period were excluded. 595
Kochi et al. analyzed 45 VSL estimates drawn from 14 stated preference studies. The authors 596

recorded all estimates from each study and then separated them into ‚homogeneous subsets.‛ 597
Specifically, they grouped estimates by lead study author and used a Q

- test for homogeneity to 598
determine whether the estimates within a group are homogenoeous. After completing the separation of 599
the estimates into homogenous subsets, they recalculated the VSL for the subset to create a unique VSL 600
for that author. The recalculated mean reflects a weighted VSL of the estimates in the homogeneous 601
subset, where the weights are based on the standard e rrors for the estimates. 18 This technique is intended 602
to address the troubling issue of choosing among multiple estimates from each study when those 603

17 Viscusi (1992) excluded two studies with sample size s 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.SAB Review Draft

30 estimates may be based on overlapping samples. The process of creating homogeneous subsets resulted 604

in 18 stated preference VSL estimates with a mean of $3.5 million and a standard error of $0.67 million (in 605
2009 dollars). 606
Dekker et al. (2008) examined the influence of risk context (i.e., deaths from automobile

- related 607

acciden ts, air pollution, and all causes) on willingness to pay estimates from SP studies. The authors 608
discussed the benefits transfer challenge associated with applying estimates from one context (e.g., auto 609
risks) to another (e.g., air pollution), particularly when there is limited empirical evidence on the size and 610
direction of the effects. Employing Bayesian techniques in a meta

- regression, they compared willingness 611
to pay or accept estimates in three different risk contexts

— air pollution, traffic safety, an d 612
environment/general

— while attempting to control for the size of the risk change and other respondent 613
and study characteristics. Several study design decisions by Dekker et al. were based on 614

recommendations from the EPA meta

- analysis work group ( USEPA 2006 ). 615
The authors used existing meta

- analyses and additional literature searches to identify stated 616
preference studies for auto, air pollution, or context

- free (unspecified) mortality risk reductions. After 617
searching the liter ature and applying screening criteria, a final database was assembled containing 98 618
VSL estimates from 27 studies, including three studies from the U.S. Seventy

- one of the estimates were 619
based on studies of road safety, seven on studies of air pollution, and twenty on studies of ‚general 620
mortality‛ (presumably deaths from all, or unspecified, causes). The authors drew multiple estimates 621
from each study, although it appears that they attempted to ensure that those estimates were from non

622
overlapping subsam ples. Because of the small sample size that results from this approach they use 623
Bayesian techniques suitable for these situations. 624
The analysis by Dekker et al. focused on explaining variation in willingness to pay for discrete 625
changes in mortality risk reductions rather than the VSL and therefore includes as an independent 626
variable the magnitude of the risk change associated with each estimate. They found that willingness to 627SAB Review Draft

31 pay estimates are lower when the commodity is described as a public good and that there is a premium 628
for risk reductions from air/general context over automobile risks. 629
Braathen et al. (2009) reviewed an d conducted a meta

- analysis of 75 studies with 900 estimates 630
from developed and developing countries. The authors recorded a variety of attributes for each estimate: 631
type of risk, country, survey mode, type of study, etc. The purpose of the study was to examine how 632
these attributes influence the resulting VSL estimates. Using classical econometric techniques, their 633
results show that methodological variables (i.e., type of payment questions, survey mode) explain 70 634
percent of the variation in the estimate s. Of particular relevance to EPA, the authors found that health 635

risks are valued lower than traffic and environmental risks, in contrast to the results of Dekker et al. 636
However, risks to individuals are valued higher than risks to the public, similar to the results of Dekker et 637
al. (2008) . The work of Braathen et al. still is preliminary and, like the Dekker et al. meta

- analysis, it 638

includes studies f rom both developed and developing countries. 639

4.1.2 A new meta

- analysis dataset 640
In an effort to both update the estimate or range of estimates used by EPA, we have constructed a 641
new dataset containing information from a set of studies reflecting the current lit erature appropriate for 642
application to U.S. environmental policy. 19 We used EconLit, conference proceedings, published and 643
unpublished meta

- analyses, working paper series, and personal contacts to identify and generate a 644
comprehensive list of stated prefer ence mortality risk valuation studies from 1974 and later. 20 645
Each study was screened to ensure that it provided empirical estimates of the value of mortality 646
risk reductions (i.e., purely theoretical studies and those that only examined morbidity were not 647
included). Following the advice from the SAB

- EEAC ( USEPA 2007 ), we established a set of selection 648

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

.SAB Review Draft

32 criteria that determined which studies to include in our final data set. These criteria are based on 649

information from other meta

- analyses, as well as our own best judgment regarding study features 650
necessary for application to valuing mortality risk reductions when analyzing U.S. environmental 651
policies. The criteria we applied are as follows: 652
minimum sample size of 100, 653
sample fram e based on general population, 654
conducted in a high

- income country, 21 655

results based on exclusive dataset, 656
written in English, 657
provides enough information to calculate a WTP estimate if one is not reported in the paper, 658
provides estimates for willingness to pay (willingness to accept estimates were not included), 22 659

and 660
provides estimates for willingness to pay for risk reductions to adults (estimates for risk 661
reductions to children are not included). 662
We focus on studies with a sample size of at least 100 bec ause smaller samples tend to suffer from 663
small sample size problems (e.g., less precision) and are less likely to be representative of the general 664
population. Because the purpose of this exercise is to determine an estimate or range of estimates for use 665

i n environmental policy, we limit our studies to those of the general population as opposed to specialized 666
subgroups, like students or business owners. In addition, because our focus is on U.S. environmental 667
policy we choose to limit our studies to those c onducted in high

- income countries. Socio

- economic and 668
cultural differences between the U.S. and most developing countries may be too large for reliable 669

21 High

- income count ries 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. T hese studies also report WTP estimates so we do not reject any study based solely on this criterion.SAB Review Draft

33 transfers of value estimates. Our own language limitations required that we restrict ourselves to stud ies 670
written in English. Finally, we limit our investigation to willingness to pay estimates for adults only. 671
Thirty

- three studies published between 1988 and 2009 23 meet the selection criteria described 672
above, yielding nearly 450 willingness to pay estima tes. For each of the studies we recorded all 673
willingness to pay and value of statistical life estimates that were reported in the study, as well as those 674
we could calculate based on information available in the study. 24 The meta

- analyses using stated 675
pref erence studies we described earlier draw multiple estimates from each study, and each has a different 676
way to address the fact that these estimates are almost always drawn from overlapping samples (e.g., 677
authors report multiple results from different estima tion exercises or sub

- samples within their data). 678
However, we believe that the issues associated with using multiple estimates from each study are 679
sufficiently problematic to warrant selection of independent estimates from each study. 25 Table 3 reports 680

se lected data for each study with detailed footnotes to describe the decisions to support the selected 681

estimates. 26 This exercise results in 40 independent estimates. We report select characteristics for each 682
estimates along with the willingness to pay and standard errors (reported in $/μr). The willingness to 683
pay for micro

- risks are either directly extracted from the underlying studies (when the information was 684
reported in the papers) or calculated by dividing the VSL estimates by 10

- 6 when the WTP estima tes are 685
not reported. 686
All estimates were recorded in the currency and dollar year presented in the study. If the dollar 687
year was not noted or could not be gleaned from other information in the study then we assumed that it 688

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 r ejection. 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 mul tiple 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 includi ng estimates by age group

– if this was determined to be an important dimension to the analysis.SAB Review Draft

34 was the year prior to the releas e or publication of the paper. All estimates are for individuals; when it 689
was clear that an estimate reflected a household willingness to pay, we divided those estimates by the 690
average household size for the country and year when the study was conducted. We then converted all 691
estimates to U.S. dollars using the Purchasing Power Parity Index for the dollar year of the estimates. 692
Next, all estimates were converted to 2009 dollars using the Consumer Price Index (CPI) and adjusted for 693
income growth over time assuming an income elasticity of 0.5. 694
In addition to the willingness to pay estimates and standard errors (when available), we 695
quantified and recorded as much information as we could for each study. Our data set includes whether 696
or not the study was pu blished in a peer

- reviewed journal, the year it was conducted and published or 697
released, the country where the study was conducted, sample characteristics, risk reduction information 698
(e.g., magnitude, type of risk), scope tests, public versus private risk reductions, etc. See Table 2 for a 699
description of many of the variables in our data set. Much of this information is only available for a 700
subset of studies, particularly information on the demographic characteristics of the sample

. 701
Twenty

- two studies were published in journals, with 13 published in the Journal of Risk and 702
Uncertainty. Six of the remaining studies are unpublished reports or working papers and five are book 703
chapters. We identified nine different sources of mortality risk represented in the studies, including 704
automobile accidents, air pollution, drinking water, hazardo us waste sites, and food. The studies were 705
predominantly conducted in the U.S. and Europe. Other countries represented in the data include 706
Canada, Japan, Taiwan, and New Zealand. 707
Most of the studies are contingent valuation studies where the choice q uestion involves stating a 708
response (e.g., yes/no to a dichotomous choice question, open

- ended response) to a scenario with a fixed 709
set of attributes. Several studies are choice experiments in which respondents choose one option from 710

several in which the attributes, including the magnitude of the risk reductions and the cost, vary across 711
the options. 712SAB Review Draft

35 The average sample size for the estimates is 814 observations with a range of 13 to over 2,000. 27 713

Most studies were conducted with a self

- administered mode via web

- TV or a centralized computer 714
facility. The second most common mode is an in

- person survey. Other modes represented in the data 715
include mail, telephone, and a combination of the two. A scope test was performed or calculated for 716

about half of the estimates, and of those about 90 percent passed a weak form of the test (i.e., willingness 717
to pay estimates exhibited a statistically significant increase with the size of the risk reduction, but was 718
not necessarily proportional). Fifteen percent passed a strong form of the scope test (i.e., willingness to 719
pay was proportional or nearly proportional to the size of the risk reduction). 720



### 4.2 Hedonic wage studies 721

In their recommendations to EPA, the SAB

- EEAC and the Meta

- Analysis workgroup clearly 722

stated that bo th revealed hedonic wage and stated preference studies should be considered when 723
deriving estimates of mortality risk values (USEPA 2006 , 2007 ). Both groups also recommended that the 724
two segments of th e literature be analyzed separately. In this section we focus on the hedonic wage 725

literature. 726
Hedonic pricing models use statistical methods to measure the contribution of a good’s 727
characteristics to its price. As applied to the labor market, hedonic wag e studies (also known as 728
compensating wage studies) are based on the premise that heterogeneous goods and services can be 729
viewed as ‚bundles‛ of attributes and are differentiated from each other by the quantity and quality of 730

these attributes. Fatal and n onfatal risks are among the many attributes that differ across jobs. All else 731
equal, we would expect riskier jobs to pay higher wages. Therefore, it should be possible to estimate the 732
value associated with reduced occupational fatality risk using data on wage and risk differentials among 733

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.SAB Review Draft

36 jobs, controlling for other factors that might influence the wage. A standard regression equation in the 734
hedonic wage literature is 735

, 736

where is the wage for individual i , is a vector of explanatory variables including various 737

characteristics for the individual and her job, is the probability of dying on the job, and and are 738
parameters to be estimated. If the prevailing wages are the result of a market equilibrium in which 739
individuals have sorted themselves among jobs to optimize their individual

- level trade offs be tween 740
wages and risks, then the slope of the hedonic wage function with respect to the risk variable, , 741
will equal the individuals’ marginal willingness to swap wages for risks. 742

4.2.1 Data sources 743
Some of the principal differences betwe en hedonic wage studies arise from the data sources used 744
to characterize workers and the job risks they face ( Bellavance et al. 2009 ). Since no large data sets exist 745

that contain both worker and risk information, rese archers must match observations from various 746
sources, which requires judgments on how best to combine data that are often reported at different levels 747
of aggregation. Most hedonic wage studies conducted in the U.S. rely on one of two datasets for 748

informat ion on wages, other job characteristics, and worker characteristics: the Panel Study of Income 749
Dynamics (PSID) and the Current Population Survey (CPS). Until recently, most studies had relied on 750
two primary sources of risk characteristics: the Bureau of L abor Statistics (BLS) Survey of Working 751
Conditions and the National Institute of Occupational Safety and Health (NIOSH) National Traumatic 752
Occupational Fatality Survey. The BLS data are reported as annual counts of deaths by three

- digit 753
occupation or indu stry while the NIOSH data provide rates of death, averaged over five years, by one

754
digit occupation or industry by state. Users of these data necessarily consider risks by broad industry 755SAB Review Draft

37 classifications (assigning all occupations within an industry the sa me risk) or by broad occupational 756
classification (ignoring potential differences within an occupation across industries). 757

A number of recent studies, however, have turned to the Bureau of Labor Statistics’ Census of 758
Fatal Occupational Injuries (CFOI) as t he source for workplace risk characteristics. The CFOI data are 759
considered the most comprehensive data on workplace fatalities available (Viscusi 2004), compiling 760
detailed information since 1992 from all states and the District of Columbia. Not only are the counts of 761
these fatal events reported by 3

- digit occupation and 4

- digit industry classifications, but the 762
circumstances of the fatal events as well as other characteristics of the workers involved (e.g., age, gender, 763
race) also are recorded. 28 To ensur e the veracity and completeness of the reported data, multiple sources 764

are consulted and cross

- referenced, including death certificates, workers’ compensation reports and 765
Federal and State administration reports. To form a complete dataset for estimation, these data still must 766
be paired with worker samples drawn from another source (often the Current Population Survey) and 767
fatality rates still must be constructed by the researcher using estimates of the number of workers, as with 768

the other BLS data. 769

4.2.2 Esti mation issues 770
Recently, EPA funded a study to examine the hedonic wage methodology and to provide a 771
quantitative assessment of the robustness of the resulting value estimates for mortality risk reductions. 772

The results of this research are summarized in Black et al. (2003) and were subsequently published in 773

Black and Kniesner (2003). These studies examined the roles of the functional form of the estimating 774
equation, measurement error, and unobservable characteristics using various commonly used data sets. 775
Their findings highlighted a number of potential problems with previou s hedonic wage studies. First, 776
they found that estimates of the value of risk reductions can be very sensitive to seemingly minor changes 777
in the specification of the regression equation. In fact, many specifications lead to negative estimates, 778

28 More information on the CFOI data is available at: http://www.bls.gov/iif/oshfat1.htm.SAB Review Draft

38 which woul d suggest that people would be willing to accept lower wages for jobs with higher risks. They 779
were unable to alleviate this problem using more flexible functional forms, so they concluded that this 780
instability is not due to equation mis

- specification. In stead, they found strong evidence that the job risk 781

estimates contain considerable measurement error. 782
Black and Kniesner (2003) examined both the BLS SWC and NIOSH data sets (the CFOI dataset 783
had not been widely use d by that time). Their res ults indicate that, while both datasets have advantages 784
and disadvantages, they both also are subject to considerable measurement error. They identified three 785

sources of measurement error in the two data sets: 786
sampling variation within industry and occupation cells given the small size of some of the cells 787
(in recognition of this problem, BLS and NIOSH suppress data when the number of fatalities is 788
low), 789
heterogeneity in job risks and non

- random assignment of those risks within o ccupations (e.g., late 790
night convenience store clerks tend to be male and older), and 791
industry and occupation are not measure d accurately, especially at the three

- digit level. 792
Moreover, they found that the measurement error is correlated with covariates co mmonly used in the 793
wage equations and is likely correlated with the regression error as well. They concluded that studies 794
that do not control for measurement error suffer from attenuation bias, resulting in under

- estimates of 795
mortality risk values. They also concluded that the NIOSH data produce results most consistent with 796
economic theory. 797

4.2.3 Recent meta

- analyses of hedonic wage studies 798
In addition to the methodological assessment conducted by Black and others, several meta

799
analyses of the hedonic wage lite rature have been conducted in recent years. We focus here on four 800
recent studies, three of which were reviewed by the Meta

- analysis workgroup convened by EPA. The 801
fourth was published after their deliberations. 802SAB Review Draft

39 Mrozek and Taylor (2002) used multiple observations from 47 hedonic wage studies. Variables 803

included in their meta

- regressions were of three types: (1) those which may influence wage/risk tradeoffs 804
(e.g., mean hourly earnings), (2) those describing the sa mple, and (3) methodological choices of the 805
original researchers (e.g., if a risk

- squared term was included in the estimating equation). 806
The authors used weighted least squares where the weights were the number of estimates 807
provided by the study. This en sured that each study was weighted equally, regardless of the number of 808

observations drawn from it. Four meta

- regression models were estimated, each using log(VSL) as the 809
dependent variable. All four models indicated a positive and significant relationsh ip between the mean 810

risk and VSL. The authors used the meta

- analysis results to ‚predict‛ the VSL as if the original studies 811
had all followed a set of ‚best practice‛ assumptions. The predicted values range from $1.78 million to 812
$15.4 million (2009 dolla rs). Those assuming the use of National Institute for Occupational Safety and 813
Health (NIOSH) data are higher than those assuming use of Bureau of Labor Statistics (BLS) data. The 814
authors concluded that the evidence best supports an estimate of $2.69 mill ion at the average 815
occupational risk level of 0.5 per 10,000 (2009 dollars). 816
While this study provides a comprehensive overview of the hedonic wage literature, it includes 817
studies using older (and possibly unreliable) occupational risk data. In addition, the authors excluded 818
estimates in original studies that were statistically insignificant or negative. 819
Viscusi and Aldy (2003) conducted a review of more than 60 hedonic wage studies of values for 820
mortality risk reduc tions across 10 countries (including 52 from the U.S.), examining a number of 821
econometric issues, the effects of unionization on risk premiums, and the effects of age and income on 822
VSL estimates. No studies were eliminated from the sample, and no attempt was made to modify the 823
original VSL estimates. Point estimates extracted from each study were those based on the ‚whole 824
sample‛ and the original authors’ preferred model specification. Viscusi and Aldy generated summ ary 825
VSL estimates by using the estimated coefficients from the meta

- analysis to predict the natural logarithm 826SAB Review Draft

40 of VSL for each original study, then study

- specific predicted

- VSLs were averaged to produce an overall 827

mean estimate. Predicted U.S. mean values were constructed based on regression samples using all 828
countries, but with averaging across U.S. studies only. The predicted values in the study for the U.S. 829
range from $6.85 million to $9.47 million (2009 dollars), and the median predicted values were ge nerally 830
very close to the means. 831
Kochi et al. (2006) used an empirical Bayes estimation method to generate predicted VSL 832
estimates based on previous hedonic and stated preference studies. Here we focus on the analysis an d 833
results for the hedonic wage data. Using selection criteria similar to those from Viscusi (1992) , the 834
analysis included 162 VSL estimates from 31 hedonic wage studies. All possible VSL estimates and 835

associated standard erro rs for each included study were re

- estimated based on information provided in 836
each original study. Estimates without standard errors were not included. The homogeneous subsetting 837
method described earlier also was applied to the hedonic wage estimates (th e hedonic and stated 838
preference data were analyzed together), resulting in 42 VSL estimates from hedonic wage studies with a 839
mean of $11.96 million and a standard error of $0.62 million (2009 dollars). Because of the subsetting 840
technique employed to pool the estimates, Kochi et al . could not explicitly account for study design and 841
population characteristics in their analysis. 842
Bellavance et al. (2009) is the most recent meta

- analysis o f the hedonic wage literature. The 843
authors’ principle objective was to better understand the variability in VSL estimates from hedonic wage 844
studies, which is described as ranging from $0.5 to $50 million. Thirty

- nine VSL estimates from 37 845

studies were as sembled based on those used in prior meta

- analyses and further searches of several 846
economics databases. The resulting dataset contains sixteen studies from the U.S., seven from Canada, 847

and three or fewer from each of several other countries. The earliest study is from 1974 and the most 848
recent is Viscusi (2004). 849SAB Review Draft

41 The authors draw only one VSL estimate from each study. Standard errors were recorded or 850
computed for 32 of the 39 estimates. Criteria were established to chose the specification within each 851

stud y, including: (1) no interaction terms between the probability of death and other explanatory 852
variables (in order to more easily compute the standard error), (2) similarity of specification to other 853
included studies, (3) larger samples with characteristics most similar to other studies, and (4) the 854
recommendations of authors of prior meta

- analyses. Bellavance et al. acknowledged that the source for 855
U.S. risk data varies and has evolved over time from early BLS surveys to NIOSH to BLS’ Census of Fatal 856
Occupational Injuries (CFOI). However, their analysis did not control for the data source other than for 857
the use of Society of Actuaries (SOA) data, which was found to have a significant impact on the estimated 858

VSL. Sensi tivity analyses were conducted with and without studies using SOA risk data. 859
Using a mixed effects model (random intercept with fixed effects for study characteristics), the 860
authors regressed the VSL estimates on average income, probability of death, and several study design 861
variables. The mean weighted average VSL is approximately $7.23 million (2009 dollars). Other key 862
findings include that the VSL is significantly higher for studies that treat risk as endogenous, and there is 863

some evidence that the VS L declines with the baseline risk. 864

4.2.4 A new meta

- analysis of hedonic wage studies 865
Using Appendix 1 from Bellevance et al. as a starting point, we constructed a new data set of 866
hedonic wage studies, augmenting the informa tion contained therein with data from Kochi et al. (2006) 867

and Viscusi and Aldy (2003) . We also conducted a full text search in JSTOR for ‚Census of Fatal 868
Occupational Injuries‛ and ‚CF OI‛ in order to develop a comprehensive list of studies using these data. 869
A total of 14 CFOI studies were reviewed, with those actually using the CFOI data in an original, hedonic 870
wage analysis retained for further assessment. These seven studies were fu rther augmented with an 871
unpublished manuscript using the CFOI data, for a total of eight additional studies. 872SAB Review Draft

42 Additional searches were conducted in JSTOR for studies published in 2000 or later using the key 873
words ‚hedonic wage‛ and ‚compensating wage.‛ We also conducted a search in the Social Science 874
Citations Index for studies citing Viscusi (2004), a paper that derives mortality risk valuation estimates 875
controlling for occupation and industry using the CFOI data. 876
In constructing our data set, we general ly employed the same selection criteria used in Bellavance 877
et al. (2009) , with some exceptions based on our own judgment and to ensure consistency with the criteria 878
used for the stated preference data set. First, we limited our data to those studies with a sample size of 879
100 or more. We also retained only those studies conducted in a high

- income country as defined by the 880
World Bank. Third, we omitted studies that rely on Society of Actuaries data as the source of ri sk 881
information as these data are thought to reflect broader risks than those experienced on the job ( Viscusi 882

1992 , Kochi et al. 2006 ). We further limited our data by excluding those studies tha t focus on extremely 883
dangerous jobs (e.g., police officers), since the risk preferences of individuals who take these jobs may 884
differ substantially from those of the general public. We do, however, apply the other selection criteria 885
employed by Bellavance et al. , including retaining only those studies using a model specification similar 886
to that given near the beginning of this section, excluding studies based on specific causes of death, 887
excluding studies using the sam e samples as other studies, and excluding studies failing to report enough 888
information to calculate the value of mortality risk reductions and/or the average probability of death. 889
Applying all of these criteria resulted in the selection of 37 studies. 890

For each of our selected studies we recorded the following key variables: year of publication, the 891
country in which the sample was drawn, sample size, average income, average annual probability of 892

death, source of risk information, the estimated coefficient o n the risk variable, whether the sample was 893
exclusively male, manufacturing, blue collar and white, as well as whether the regression controlled for 894
nonfatal risks, union status, and worker compensation. We calculated VMRs for each study by deriving 895

the V SL and dividing these estimates by 10 6 . As with our stated preference data, all estimates are 896SAB Review Draft

43 reported in 2009 dollars after adjusting for inflation using CPI and accounting for income growth over 897
time assuming an income elasticity of 0.5. 898

Similar to the stated preference data, we capture only one specification per study in our database, 899
following the criteria established by Bellavance et al. 29 Because the hedonic studies are more 900
homogeneous in their design than the stated preference studies, we are able to be more selective in which 901
specifications to include. Although one motivation here is to minimize the influence of each individual 902
study, it does not necessarily rid us entirely of the problem of overlapping subs amples as many of the 903
studies draw their samples from the same source. 904
Table 4 lists key characteristics for our selected studies. 30 A total of 24 studies out of 37 were 905
conducted in the U.S. with 3 using NIOSH data, 13 using BLS data and 8 using CFOI dat a as the source of 906
occupational risk. Seven of these twenty

- four studies rely on the Panel Study of Income Dynamics (PSID) 907
as a source for worker characteristics with another 11 using CPS data. Twenty

- six studies included 908
women in their samples and 7 focu sed on blue collar workers only. Three studies restricted their samples 909
to union members only. Average sample size across studies was 17,741, and the average income was 910
$40,508 per year (2009 dollars). The mean probability of occupational death across st udies was 0.00014. 911



## 5 Income Elasticity Considerations 912
EPA first attempted to address the income elasticity of VSL issue in its analysis of The Benefits and 913
Costs of the Clean Air Act, 1990 to 2010 (US EPA, 1999), which made a distinction between application of 914
income adjustments for longitudinal changes in income over time and cross

- sectional income differences 915
for benefit transfer. The report applied a range of VSL income elasticities in a sensitivity analysis to 916
project the value of reduced mortality risks in the year 2010. 917

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).SAB Review Draft

44 The issue was further developed in EPA’s White Paper Valuing the Benefits of Fatal Cancer Risk 918

Reductions , where income was one of the many benefit transfer issues to be addressed. The SAB

- EEAC 919
review of the White Paper concluded: ‚Wi th regard to population characteristics, the Committee believes 920
that it is appropriate to adjust the value of the projected statistical lives saved in future years to reflect 921
higher incomes in those years, but not for cross

- sectional differences in income, because of the sensitivity 922
of making such distinctions.‛ 31 The SAB

- EEAC recommended that any appropriate adjustments for 923
income growth should be part of the Agency’s main analysis. 924
Based on a review of the empirical literature on the cross

- sectional i ncome elasticity of VSL 925
literature originally developed for use in The Benefits and Costs of the Clean Air Act, 1990 to 2010 report, 926
EPA analyses have typically applied a range of estimates with a low end of 0.08, a central value of 0.4, 927
and a high end of 1.0. Many analyses characterize this range with a triangular distribution with a 928
resulting mean estimate of approximately 0.48. Income elasticity is then typically paired with projections 929
of growth in real US GDP per capita. 930

More recent information on the income elasticity of VSL has come primarily from meta

- analyses 931
of hedonic wage studies. The results in Mrozek and Taylor (2002) suggest income elasticities ranging 932
from 0.37 to 0.49, although the authors note that these results should be interpreted w ith caution because 933
of measurement error in the income variable and the functional form used by many hedonic wage studies 934

included in their meta

- analysis . As described earlier in this paper, more recent work from Viscusi and 935
Aldy (2003) estimates the inco me elasticity of the VSL in the range of 0.5 to 0.6, slightly higher than the 936
mean value used in many EPA analyses. None of the 95 percent confidence bounds on the Viscusi and 937
Aldy estimates include a VSL income elasticity as high as 1.0. The Bellevance et al . (2009) meta

- analysis, 938

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 relati onship between wealth and mortality valuation.‛ US EPA 2007, page D

- 7.SAB Review Draft

45 also described earlier, predicts somewhat higher elasticity estimates ranging from 0.84 to 1.08 depending 939
upon the model. 940
Some recent theoretical research has examined the relationship between the income elasticity of 941

the VSL a nd the coefficient of relative risk aversion and noted that these two quantities should be very 942
close in magnitude. This can be seen most easily in a simple two

- period model. Let ‚lifetime‛ utility be 943

the expected discounted sum of utility in both periods: , where is utility in period , 944

is the probability of survival between periods 1 and 2, and is the utility discount factor . Also assume 945

that depends on income in period and takes the standard ‚constant relative risk aversion‛ (CRRA) 946

form: , where is the coefficient of relative risk aversion

. The VSL is the marginal rate 947
of substitution between the individual’s first period income and her probability of survival to the second 948
period, i.e., , and so the income elasticity of the VSL is 949

. Kaplow (2005) examined a more realistic version of this model by allowing 950

for self

- defensive expenditures that could increase the individual’s survival probability. Using th at 951

elaborated model, Kaplow showed that the income elasticity of the VSL should be at le ast as large as 1 952

when , and at least as large as when

. 953
Empirical estimates of the coefficient of relative risk aversion span a wide range

— from around 954
0.5 to 1 at the lower end (e.g., She pard and Zeckhauser 1984, Eeckhoudt and Hammit 2001, Chetty 2006) 955
to 10 or more at the high end (e.g., Kocherlakota 1990)

— but most estimated or assumed values for 956
seem to fall in the range of 1 to 3. For example, Hall and Jones (200 8) and Hall (2010) estimated to be 957
around 2, based on the recent trend of income growth and the more rapid growth in hea lth care 958
expenditures in the United States

. Szpiro (1986), Feldstein and Ranguelova (2001), Barro (2006), and 959
Layard et al . (2008), among others, also estimate or use values of in this range. And in the 960SAB Review Draft

46 contemporary climate change economics literature, t he most commonly used values of are 2 to 3 (e.g., 961

Ar row 2007 ; Nordhaus 2008 ; Dasgupta 2008 ; Weitzman 2009, 2010 a,b ). 962
The theoretical considerations combined with (most of) the empirical estimates of relative risk 963
aversion cited above are at odds with the early estimates of the income elasticity of the VSL in the 964
neighborhood of 0.5 cited above. In a more recent study, Kneisner et al . (2009) applied a quantile 965
regression approach to a dataset assembled from the Panel Study of Income Dynamics (PSID) and the 966
Census of Fatal Occupational Injuries (CFOI). The ir preferred regression model produced estimates of 967
the income elasticity of the VSL between 1.23, for the lowest quantile, to 2.24, for the highest quantile. 968

Kneisner et al . note that ‚Our estimates of a large income elasticity of VSL are consistent with the simple 969
theoretical models that have been developed *by Kaplow (2005)+,‛ and ‚With recent estimates of the 970
coefficient of relative risk aversion being around 2 based on the labor supply analysis of Chetty (2006) 971
and the consumption analysis of Kneisner and Ziliak (2002), one would expect the VSL to be income 972

elastic, which is what the results above indicate.‛ 973
Based on theoretical considerations such as those examined by Kaplow (2005) and the new 974
empirical results of Kneisner et al . (2009), EPA believes that its recommended estimate of the income 975
elasticity of the VSL appears to be on the low end of the range of estimates and may need to be updated 976
to a higher value or range of values. 977

978 

## 6 Methods for Combining Data 979
The values for mortality risk reductions estimated in the stated preference and hedonic wage 980
studies described above constitute a current empirical summary of the literature, which can be used to 981
inform the revision of EPA’s mortality risk valuation guidan ce. These studies could be combined or 982
synthesized in a number of ways, from a simple point estimate to range, distribution, or systematically 983
combined in a more rigorous meta

- analysis. Our objective in this section is to outline analytical options 984SAB Review Draft

47 that can be implemented in the longer term for updating the estimate or range of estimates used by EPA 985
in our guidance on valuing morality risk reductions. We begin with meta

- analysis methods, including 986
methods similar to those used in our current guidance and extending to more rigorous application of 987

meta

- regression techniques. This is followed by the structural benefit transfer approach, which involves 988
calibrating a direct or indirect utility function so that it is consistent with summary estimates of values for 989
health risk. Our goal is to provide enough information on the analytical options and key issues to receive 990

clear recommendations from the SAB

- EEAC on an approach to implement for updating our guidance and 991

on future research directions. 992



### 6.1 Meta

- analysi s 993

There are several options for obtaining simple summary statistics or ranges from the existing 994
data. We outline these options and key issues in order of increasing complexity. 995

6.1.1 Parametric distribution 996
EPA’s current guidance took one best estimate from each of five stated preference and twenty

997
one hedonic wage studies and then fit a parametric distribution to the values. The resulting mean and 998
distribution has become EPA’s default estimate for valuing mortality risk reductions. To replicate this 999

approa ch we could use the databases of SP and HW studies discussed above and then separately 1000
characterize the resulting distributions in a curve

- fitting exercise. Based on these distributions we could 1001
define a range of default values for the value of mortality risk for EPA policies. Key choices and 1002
principles are: 1003
Use all “independent estimates” from the studies rather than one estimate per study

. Because many studies 1004
provide estimates for different subpopulations or other treatments, we can often include mult iple 1005
study estimates without gross violations of independence. An alternative is to rely upon a single 1006
estimate per study, which has been done for several meta

- analysis. 1007SAB Review Draft

48 Update all study estimates to a common year, including the effect of real income (GD P per capita) growth over 1008
time and the estimates income elasticity of the VSL. The review of the literature in the prior section 1009
already includes this update. 1010
Limit SP study estimates to those that are non

- cancer and non

- latent. In so doing, we will prod uce a ‚base 1011
value‛ that should be more consistent with estimates stemming from the hedonic wage literature. 1012
We will attempt to address any systematic difference in value between reduced cancer risks and 1013
other types of risk separately. In part, this is si mply recognizing that EPA policies affect both cancer 1014

and non

- cancer mortality risks and different values for each may be appropriate. Similarly, EPA 1015
policies address risk reductions varying from the near

- immediate to those delayed over many years, 1016

a bene fit

- transfer aspect that we address by discounting over estimated latency periods. Including 1017
latent risks in this simple aggregation would double

- count the effects of timing on value. 1018
Include public

- risk studies or rely only on private

- risk SP studies

. Most EPA regulations result in public 1019

risk reductions. To avoid under

- counting benefits, we would want to err toward inclusion, basing 1020
guidance on the full set of relevant studies including those that incorporate altruism even if we 1021
cannot distinguish whe ther it is paternalistic or non

- paternalistic. On the other hand, to avoid 1022

double

- counting of benefits we would want to use only those studies that capture private willingness 1023
to pay for mortality risk reduction. Clear recommendations from the EEAC on th is issue in particular 1024
would be very helpful. 1025

6.1.2 Classical econometrics 1026
A second approach to combining the information from multiple studies

— to determine the 1027
characteristics of the studies that influence the value estimates or to generate a benefit transfer f unction

— 1028
is to perform a meta

- regression using classical econometrics. Two issues arise when considering this 1029
approach. First, the analyst must decide which observations to include in the analysis. Some previous 1030

meta

- regression studies have used all rele vant observations in the analysis (e.g., Nelson and Kennedy 1031SAB Review Draft

49 2008 , Braathen et al. 2009 , Mrozek and Taylor 2002 ). This approach incorporates all available 1032
information, but runs the risk of including estimates from overlapping samples (and therefore non

1033
independent observations). For example, the same individual(s) may be represented multiple times in 1034
the data when a paper reports multiple esti mates using different modeling assumptions. Restricting the 1035

data to non

- overlapping samples is a non

- trivial exercise because choosing the most appropriate 1036
estimate(s) from each study involves subjective judgment. In addition, small sample size problems

— 1037
already a hurdle in meta

- analysis

— are exacerbated when the sample is limited in this way. The stated 1038
preference and hedonic wage meta

- analysis datasets described in Section 4 draw independent samples 1039
based on procedures outlined above. However, a very st rict interpretation of the requirement for non

1040
overlapping subsamples for the hedonic wage studies could result in just a handful of estimates for use in 1041

a meta

- analysis given the reliance by authors on the same sources of data. 1042

Second, there are econome tric issues to consider when analyzing these data. Nelson and 1043
Kennedy (2008) discuss ‚factual‛ versus ‚methodological heterogeneity.‛ Factual heterogeneity arises 1044
because of real differences in what the primary stu dies are measuring. For example, the wtp for auto risks 1045
may factually differ from that for cancer risks. Similarly, the wtp for occupational risks for male blue

1046
collar workers may factually differ from that estimated for a more inclusive sample. Methodo logical 1047
heterogeneity arises because of different study design choices, such as the use of different models to 1048
estimate willingness to pay. When these sources of heterogeneity are unobserved, errors may be 1049
correlated. It also is likely that estimates pro duced by different surveys and designed by different 1050
authors have different variances, making heteroskedasticity a concern. Classical econometrics provides 1051
several approaches for dealing with correlated errors and heteroskedasticity. A fixed effects mode l 1052
assumes that the unobserved heterogeneity among studies can be captured with an intercept shift. By 1053
including a dummy variable for all but one of the studies, the intercept shift is estimated directly. This 1054
approach can result in low degrees of freedom if each study contributes a small number of estimates. An 1055SAB Review Draft

50 alternative approach that does not require a new independent variable for each study is the random 1056
effects model. Using the ‚composite error‛ exposition of the random effects model, the estimatin g 1057
equation is 1058

1059

where is WTP estimate j from study i, is the row of data for that estimate, and is a vector of 1060

coefficients. The error term has the following structure 1061

, where and

. 1062

is a composite error term with components u, which can vary between studies but has the sa me value 1063

within studies, and , which can vary within and across studies. 1064
If heteroskedasticity also is a concern, there will be two potential violations of the classical 1065
assumption of spherical errors. In this setting, coeffic ient estimates will be consistent but inefficient and 1066
standard error estimates may be inconsistent. One solution to this problem is to estimate the model in the 1067
traditional way but calculate standard errors that are robust to heteroskedasticity. White st andard errors 1068
are robust to heteroskedasticity ( Greene 1997 p 503

- 505), and there is a class of robust standard errors that 1069
imposes the panel structure on the calculation and is thus robust to correlation within clusters as well. 1070
Statistical packages such as Stata and SAS are able to produce ‚cluster

- robust‛ stan dard errors. 1071
A second way to address heteroskedasticity is via weighted least squares, where the weights are 1072
inversely proportional to the variance of the willingness to pay estimate. However, since a number of the 1073

studies in our meta

- analysis datasets d o not provide standard errors of the estimates, we can use the 1074
number of estimates drawn from a single study (assuming we draw multiple estimates per study) as a 1075
proxy for variance. The rationale for this proxy is that studies reporting a large number of estimates are 1076
more likely to report all possible willingness to pay estimates based on different characteristics of the 1077
sample, versions of the survey, etc., and these estimates may be less precise than those from a study that 1078SAB Review Draft

51 presents a few, select estima tes. Mrozek and Taylor (2002) used this approach, as discussed above. This 1079
insures that each study is given equal weight, as opposed to each estimate. The sample size for each 1080
estimate also could be used to generat e weights. Observations that arise from larger samples should be 1081
more precise, all else equal. However, sample sizes are not available for all observations in our meta

1082
analysis datasets. Mrozek and Taylor (2002) us ed the level of significance of the VSL estimate to create a 1083

t

- statistic weight in an appendix to their paper. The estimating equation for this approach is: 1084

1085

where is the number of estimates or sample size f rom the i th study. This technique provides more 1086

efficient estimates than unweighted estimation of the analogous model. 1087
Considering the data issues common to meta

- analyses of willingness to pay estimates for 1088
mortality risk reductions, we propose two classi cal approaches meant to address both heteroskedasticity 1089
and correlated errors arising from unobserved study heterogeneity when multiple estimates are drawn 1090
from each study. Weighted least squares estimation, as discussed above, can correct for 1091

heteroskeda sticity. However, relevant statistics may not be reported to construct the ideal weights. If 1092
weighted least squares is used, we suggest testing for heteroskedasticity and using standard errors that 1093
are robust to clustering. Alternatively, one could esti mate a study

- level panel model to account for 1094
unobserved heterogeneity and calculate standard errors that are robust to heteroskedasticity. Since many 1095
studies provide just a few estimates, a fixed effects model may not be feasible while a random effects 1096

m odel would preserve degrees of freedom. We are particularly interested in EEAC comments on these 1097

alternatives. 1098

6.1.3 Bayesian estimation 1099
In the previous section we discussed how classical estimation techniques could be used to 1100

estimate a meta

- regression of valu es for reductions in mortality risks while addressing heteroskedasticity 1101SAB Review Draft

52 and correlated errors. However, if we use data sets with non

- overlapping estimates

— as has been 1102
recommended by the Meta

- analysis workgroup, and as is reflected in the summary of state d preference 1103
and hedonic wage estimates in Tables 3 and 4

— our data selection criteria leave us with relatively small 1104
samples for meta

- regression. The combination of small sample size and non

- spherical errors presents a 1105
particular problem for classical app roaches to estimation. Specification tests, including those for 1106
heteroskedasticity, and calculations of robust standard errors rely on asymptotic relationships and 1107
therefore may not be reliable when the sample size is small ( Moeltner and Woodward 2009 ). Bayesian 1108
estimation has desirable small sample properties and can more easily accommodate general error 1109

structures. 1110
Bayesian analogs to the classical approaches discussed above have been developed and can be 1111

used to estimate a meta

- regression model to improve value estimates and provide richer inference into 1112

the results. Koop (2003 p 124

- 129) presented a Bayesian pooled regression model with an error structure 1113
general enough to be robust to correlated errors and heteroskedasticity even when the form of 1114
heteroskedasticity is unknown. Moeltner and Woodward (2009) use this model to estimate a meta

1115
regression of wetland valuation estimates from a sample of just 12 values from 9 studies. They use Gibbs 1116
sampling to estimate the model 1117

, 1118

where is WTP reported in study j , is a row vector of population and other characteristics 1119

associated with study j , is a vector of regression coefficients, is a zero mean regression error with 1120

variance , and IG denotes the inverse

- gamma distribution. This approach allows the authors to 1121

estimate study

- specific variances by estimating a single parameter ν and drawing in a data 1122

augmentation step. Moeltner and Woodward (2009) showed that Bayesian estimation can be used to 1123SAB Review Draft

53 conduct meta

- regression on small heteroskedastic samples and produce consistent and efficient 1124
parameter estimates. 1125
A Bayesian analogue to the study

- level panel model is also de veloped by Koop (2003 p 149

- 157). 1126
Bayesian estimation of a study

- level panel model with a non

- hierarchical prior is analogous to the fixed 1127
effects model in classical econometrics because the unobserved heterogeneity between studies is 1128

attributed to a cons tant (intercept shift) for each study. If the number of studies is large relative to the 1129
number of estimates from each study then, just as would be the case under classical assumptions, the 1130
high

- dimensional parameter space can be problematic. In these ca ses it may be beneficial to use a 1131

hierarchical prior which places more structure on the unobserved heterogeneity by assuming the study

1132
level effects can be drawn from a distribution, thus only the parameters of that distribution, and not the 1133

individual eff ects themselves, need to be estimated. Bayesian estimation of a panel model with a 1134
hierarchical prior is analogous to the classical random effects panel model. In both cases the error 1135
structure imposed on the model is general enough to be robust to non

- s pherical errors due to correlation 1136
within studies and heteroskedasticity. 1137



### 6.2 Structural benefit transfer 1138

Thus far we have discussed meta

- analysis, including classical and Bayesian approaches to 1139
estimating a meta

- regression model, which then could be used for functional benefit transfers. Using 1140

meta

- regression, the form of the estimating equation, and therefore the transfer function, typically would 1141
be based on a combination of statistical tests and qualitative theorizing about the important variables to 1142

i nclude in the model. The resulting function can be viewed as a low

- order Taylor series approximation to 1143
the ‚true‛ preference function within the range of the data used to estimate it. 1144

In contrast to the meta

- regression approach, structural benefit

- tran sfer (also known as preference 1145

calibration ) involves first specifying a direct or indirect utility function for a representative individual, 1146
then deriving analytical expressions for observable economic outcomes from the utility function (Smith et 1147SAB Review Draft

54 al. 2002 , 2006 ). Such observable outcomes could include labor

- leisure tradeoffs, demand for related 1148
market commodities, equilibrium wage schedules for jobs with differing risk or other characteristi cs, 1149
responses to stated preference survey questions, etc. The parameters of the utility function are calibrated 1150
using data on such outcomes, and the calibrated model then can be used to predict willingness to pay or 1151
accept for any policy changes that can be described by variations in one or more of the parameters that 1152
appear in the calibrated preference function. 1153
The key advantages of the structural benefit transfer approach are that it provides a means of 1154
combining estimates from separate studies that u se different benefit concepts (e.g., marginal or non

1155
marginal willingness to pay or accept, consumer surplus, compensating or equivalent variation, etc.), and 1156
it assures the economic consistency of transfers (Smith et al. 2 002 , 2006 ). In this context ‚economic 1157
consistency‛ means, for example, that estimated willingness to pay will never exceed income, that value 1158
estimates will always be responsive to scope (the size of the postulated change in quantity or quality), 1159

that WTP and WTA will always stand in the proper relationship to each other, and so forth. The way that 1160
such consistency is achieved is through the ex ante imposition of a specific form for the utility function, 1161
from which all subsequent value estimates and behavioral res ponses are then derived. One way to think 1162

about the contrast between meta

- regression and structural benefit transfer is that the former uses 1163
relatively more data and fewer theoretical assumptions, while the latter uses relatively fewer data (or 1164
more highl y aggregated data) and stronger theoretical assumptions. Therefore, the meta

- regression 1165
approach may give more accurate value estimates within the range of the data used to estimate the 1166
function, while the structural benefit transfer approach may be more accurate in out

- of

- sample transfers. 1167
Thus, the choice of one approach over the other may depend in part on whether the policy case(s) to be 1168
examined fall largely within or largely outside of the range of data available for a meta

- regression 1169

transfer funct ion. 1170SAB Review Draft

55 6.2.1 Static preference functions 1171
A simplistic example may help clarify the structural benefit transfer approach. Here we follow 1172
Smith et al. ( 2003 , 2006 ) and use a static model of the tradeoff be tween income and survival. (In the next 1173

sub

- section we will consider a more general dynamic life

- cycle model.) Assume that utility conditional 1174
on survival is proportional to the log of scaled income, so expected utility is , whe re p is the 1175

individual’s survival probability. Using this functional form, the marginal willingness to pay for an 1176
increase in the probability of survival is . Next suppose that, 1177

based on a comprehensive review of the hedonic wag e literature, wtp is estimated to be $8/μr (i.e., the 1178
VSL is $8,000,000) for individuals with average annual income 35,000 $/yr and average annual survival 1179
probability p = 0.984. This allows calibration of the single unknown parameter of the utility funct ion: 1180
= 214.5, which gives a function that can be transferred to individuals with different 1181

background mortality risk levels. This function could vary by age and other personal and environmental 1182

characteristics, and/or different i ncome levels by adjusting p and/or Y , respectively. Using this functional 1183

form, wtp is inversely proportional to the baseline survival probability (and therefore increases with the 1184
background mortality risk) and is (nearly) proportional to income. 1185

We also can use the calibrated utility function to calculate willingness to pay for changes in 1186
mortality risks of any magnitude, rather than relying on the first

- order approximation represented by the 1187

wtp . In this case the willingness to pay function is . Note that 1188

for large enough ’s the marginal approximation may exceed total income while the actual WTP 1189

cannot. 32 As noted by Smith et al. (2006) , this is one of the key advantages of a structural benefit transfer 1190

32 Letting go to its maximum value gives , which is necessarily less than Y. Also

note that, in this mode l, the smaller is p the larger is WTP , approaching Y as p goes to zero

. This gives a simple illustration of the ‚dead

- anyway effect‛ ( Pratt and Zeckhauser 1996 ).SAB Review Draft

56 approach: it can produce more realistic predictions of WTP well outside of the range of data used to 1191
estimate marginal willingness to pay. (Additional numerical examples are provided in Appendix A .) 1192
Another advantage of the structural approach is that it can help to account for potential 1193
behavioral responses. We can illustrate this by extending the simple model given above. Again 1194
following the hedonic wage l iterature, suppose that wages, W , are an increasing function of job

- related 1195
mortality risk, m . Specifically, suppose that . Total income is comprised of wages plus 1196

non

- wage income, y . With this extension, expected utility is , where 1197

is the background (non

- job related) survival probability. Now suppose that after careful examination 1198

of the hedonic wage literature we estimate that, for a sample of individuals of prime working a ge (say, 1199
around 40 years old), y = 5,000 $/yr, W = 30,000 $/yr, = 0.99, m = 0.006, and = $8/μr. So, 1200

for example, if = 0.5, then and 1201

= . (Note that with two estimates of wtp at two levels of job risk, we could 1202

calibrate and simultaneously.) Now recall the standard assumption underlying the hedonic wage 1203
literature that the individual has chosen her job

- risk level optimally, and assume she is able to adjust that 1204

level to re

- optimize her expected utility after a policy intervention changes by some amount . To 1205

determine the maximum willingness to pay for an exogenous change in mortality risk, we must solve the 1206

two

- equation system comprised of (1) the equality between expected utility with and without the policy, 1207
and (2) the first

- order condition for maximi zed expected utility with respect to job

- risk with the policy 1208
and a reduction in income equal to WTP

. 1209
Results from some simple numerical experiments with this model are given in Appendix A . The 1210
main lesson from these example s is that if individuals are able to adjust their job risk level, then WTP 1211
generally will be higher and the total number of ‚statistical lives saved‛ will be lower than otherwise 1212SAB Review Draft

57 predicted under the assumption of no behavioral response. The numerical exam ples in Appendix A are 1213
not intended to represent any specific real

- world case; nevertheless, they clearly illustrate that the 1214
structural benefit transfer approach is able to capture these effects. 1215

6.2.2 Life

- cycle preference function s 1216
The structural benefit transfer function illustrated above was based on the simplifying 1217
assumption that the representative individual looks ahead only one period at a time

— that is, utility 1218
depends only on the probability of survival to the next period and expected consumption in the next 1219
period. A more realistic framework would account for expectations of survival and consumption in all 1220
future periods. This brings us to the life

- cycle consumption modeling approach. A life

- cycle 1221
consumption model represen ts consumption

- versus

- saving (and possibly other) choices by an individual 1222

over the course of her lifetime. Life

- cycle models are inherently dynamic, with age

- specific mortality 1223
probabilities included as key parameters. Individuals are assumed to maximiz e the expected present 1224
value of discounted utility, where the expectation is conditional on the probabilities of living to all 1225
possible future ages (e.g., Yaari 1964 , Shepard and Zeckha user 1984 , Rosen 1988 , Cropper and Sussman 1226

1990 , Ehrlich 2000 , Johansson 2002 , Aldy and Smyt h 2006 , Murphy and Topel 2006 , Hall and Jones 2007 , 1227

USEPA 2007 p. 14

- 16). 1228

A life

- cycle consumption modeling framework could be used as the basis for a generalized 1229
structural benefit transfer function. Such a transfer function would allow calculation of willingness to 1230
pay for any marginal or non

- marginal changes in the individual’s mortality profile (i.e., ‚survival curve‛) 1231
at any point in the life cycle . As emphasized by Hammit (2007 p. 232) , ‚the survival curve and how it 1232
shifts are the fundamental concepts; the number of life

- years saved and lives saved in a specified time 1233
period are the alternative and partial summary mea sures of the shift.‛ The life

- cycle consumption 1234

framework is tailor

- made to account for shifts in the survival curve, and it can easily account for the age 1235SAB Review Draft

58 and lifetime income profile of the individual and the latency and cessation lag characteristics of the 1236
policy. 1237
As in any structural benefit transfer application, it may be necessary to calibrate the parameters 1238

of a life

- cycle consumption model using only a few aggregate data

— for example, summary statistics on 1239

labor

- leisure tradeoffs, average rates of saving over a representative individual’s life span, average 1240
market wage differentials for more versus less risky jobs, summary results from stated preference surveys 1241

on risk tradeoffs, etc. Thus, like other structural

- benefit transfer functions, one base d on the life

- cycle 1242
consumption framework would necessarily sacrifice statistical sophistication for theoretical consistency, 1243
so many of the advantages and disadvantages of structural benefit

- transfer functions discussed by Smith 1244
et al. ( 2002 , 2006 ) will apply to life

- cycle models as well. 1245
An important potential advantage of using a life

- cycle consumption framework for structural 1246
benefit transfers is that it could help to avoid the transfer errors that may arise from using a single VSL 1247
point estimate for all varieties of mortality risk reduc tions. As shown in Appendix A , the life

- cycle 1248
framework allows calculation of the marginal willingness to pay at any age a for risk reductions at any 1249
later age b , . VSL estimates from hedonic wage st udies may be most plausibly interpreted as the 1250

marginal willingness to pay for contemporaneous mortality risk reductions for adults of prime working 1251

age, e.g., . It may be inaccurate to use such estimates to calculate the willing ness to pay for, say, a 1252

20 year

- old who will experience mortality risk reductions at ages 55 through the end of life. In contrast, a 1253

schedule of estimates based on a calibrated life

- cycle consumption model would give a ready 1254

mea ns of calculating total willingness to pay for any exogenous shift in the survival curve for individuals 1255
of any age. Furthermore, this approach can properly account for all latency and cessation lag effects 1256
associated with the specific pattern of mortalit y risk changes caused by the policy, without the need for 1257
possibly inaccurate transfers of a VSL point estimate to earlier and later ages and across individuals with 1258

different levels of wealth and income. 1259SAB Review Draft

59 Implementing such a structural life

- cycle benefit transfer function would be challenging. 1260
Estimating or calibrating such a model would require specifying or solving for the life

- cycle pattern of 1261
consumption, and specifying a functional form for the utility function as well as calibrating or estimating 1262

it s parameters. Any structural benefit transfer approach

— whether based on a life

- cycle consumption 1263
framework or something else

— would represent a significant departure from the traditional point 1264
estimate transfer approach typically used for mortality risk va luations, mainly based on the VSL. To 1265
accelerate the development of such an approach, we recommend conducting additional case studies 1266
applying existing structural benefit transfer functions (e.g., Smith et al. 2002, 2003, 2006) to a wider range 1267

of illustr ative policy scenarios, and additional research aimed at expanding and refining the calibration of 1268
existing benefit transfer functions or developing new ones for potential use in future policy analyses. The 1269
scholarly research on structural benefit transfe r methods is still in an early stage, so we are especially 1270

interested in EEAC recommendations in this area. 1271



## 7 Conclusions 1272
EPA continually strives to improve the quality of its economic analyses of proposed 1273
environmental policies. This is especially import ant in the area of human health valuation, in particular 1274
the value of mortality risk reductions, since such a large fraction of the (monetized) benefits of EPA rules 1275
are based on this category of impacts. This white paper represents the latest round of li terature review 1276
and study by EPA’s National Center for Environmental Economics on this topic, submitted to the SAB

1277
EEAC for feedback. Advice from the committee will be carefully considered as EPA updates its 1278
Guidelines for Preparing Economic Analyses

. 1279



### 7.1 Add ressing key issues: terminology, altruism, cancer valuation 1280

EPA plans to change its metric and terminology for mortality risk valuation in benefit

- cost 1281
analysis to better reflect the risk

- dollar tradeoffs faced by individuals as evaluated in the economics 1282SAB Review Draft

60 literature, and risk reductions provided by environmental policies. As detailed in section 3.1.2 of this 1283
white paper, for valuation purposes we will report changes in risk reductions valued in terms of the 1284
value of mortality risk (VMR), scaled to micro

- ri sk reductions. This is consistent with recent suggestions 1285
in the economics literature and is aimed at reducing confusion about how mortality risks are evaluated in 1286

benefit

- cost analysis. 1287
A second key issue for EPA is the valuation of cancer risk reductio ns and how these risks are 1288
valued systematically differently from the more immediate risks typically considered in WTP studies. 1289
Our review of the cancer literature, while not conclusive, suggests a ‚cancer differential‛ of roughly 50% 1290

over immediate accid ental or ‚generic‛ risk valuation estimates. We recommend including a differential 1291
of this general magnitude as part of Agency benefits analyses for reduced cancer risks. Specific guidance 1292
on the application of this differential will be developed by the Agency at a later date. 1293



### 7.2 Longer term analytical directions 1294

In the longer term, EPA plans to perform analysis to better and more rigorously synthesize the 1295
existing mortality risk valuation literature. Two key directions include meta

- analysis and structural 1296

benefit

- transfer. 1297

7.2.1 Meta

- analysis 1298
Section 5.1 described simplified approaches to aggregating the existing empirical valuation data, 1299
along with some key issues to consider in this process. These include whether to (i) use multiple 1300
estimates from studies, (ii ) update all studies to a common year accounting for real income growth, and 1301
(iii) limit SP studies to avoid double

- counting the effects of cancer risks and latency or cessation lag. The 1302
suggested approach evaluates the RP and SP studies separately, from which EPA would develop a range 1303
of default values for the value of mortality risk (VMR). 1304SAB Review Draft

61 Alternatively, a new addition to the discussion of mortality risk meta

- analysis with the SAB

1305
EEAC is the potential for Bayesian meta

- regression, and we are particula rly interested in the SAB

- EEAC 1306
comments on the potential advantages and disadvantages of this approach. Another key question to 1307
consider is how the results of any meta

- regression would be used to inform guidance, and the merits of 1308
developing a statistical benefit

- transfer function from these results. 1309

7.2.2 Structural Benefit Transfer 1310

An alternative to meta

- regression and other largely statistical approaches to synthesizing 1311
literature results for policy, is to impose more structure on the benefit

- transfer problem and then calibrate 1312
a preference function based on a specified utility function and data on observable outcomes. This is a 1313
relatively new approach that has been developed and demonstrated in only a few previous studies. We 1314
recommended conducting addition al scoping studies and further research to develop structural benefit 1315
transfer functions, possibly based on a life

- cycle consumption framework, suitable for application in 1316

benefit

- cost analyses of future EPA policies. 1317



### 7.3 Other research directions 1318

We see thre e other areas where more research would be valuable in developing guidance for 1319
mortality risk valuation, and we welcome SAB

- EEAC comment on these (as requested in the 1320
accompanying charge questions). 1321
First, additional applied research on the altruistic comp onents of WTP for public risk reductions 1322
would be a valuable contribution, potentially allowing EPA to rigorously include theoretically

1323
appropriate altruistic values and better reflect the public value of environmental policies. We 1324
acknowledge that this i s a difficult task. The economics literature on the proper treatment of altruism in 1325

benefit

- cost analysis is well

- developed, enumerating the conditions under which it is appropriate to 1326
include altruistic values in evaluating the benefits of public program s. EPA programs are inherently 1327SAB Review Draft

62 public and ideally should include paternalistic altruism. However, while the empirical literature has 1328
been able to capture some altruistic values for public risk reductions, it has not generally been able to 1329
distinguish amo ng types of altruism sufficiently well for the values to be included neatly in applied 1330
analysis. 1331
Second, more and more research reflects the general understanding that value of reducing 1332
mortality risks is not ‚one

- size

- fits

- all.‛ Rather, these values ar e heterogeneous, or ‚individuated,‛ and 1333
depend upon a wide array of individual and risk characteristics. More detailed research in this area also 1334
will provide data needed for developing more general and more accurate benefit

- transfer functions. 1335

Third and finally, most of the valuation literature, and many theoretical frameworks, have 1336
treated mortality and morbidity risks separately, focusing on just one of these endpoints at a time. 1337
However, some recent work also suggests that changes in health risks may be best framed as changes in 1338
health risk profiles that include both mortality and morbidity. Individuals may value different 1339
combinations of changes in risk or illness and risk of death in complex ways. Systematic empirical work 1340

to evaluate these relatio nships could lead to much more robust and complete benefits analysis. 1341SAB Review Draft

63 

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74 

## 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 & Haninger (2010) Choice experiment Latency periods of 1, 10, 20 years
Implied discount rates not stat diff from zero (

- 1.2 to 3.9) 1⁄2 sample: no

symptom descriptions;
1⁄2 sample: 150

- 200 word descriptions

Self

- assessed severity based on EQ

- 5D and visual analog scales Not separately treated Pesticide risks from

food. Safer food from Pesticide Safety System (not organic)

Auto accident for whole family simultaneously from ‚product‛ on next car purchase. Adult selves

Adult others

Children Organ: brain,

liver, bladder, lymphocytes
Mortality only (no

non

- fatal outcomes) No statistical difference

by cancer/non

- cancer; target organ; auto/other risks (for protecting whole family simultaneously).

Child VSL=1.8 Adult Other VSL=1.15 Self
Insensitivity to number of people for the ‚whole household‛ question. Alberini & Scasny (2010a) ‚Labels & Perceptions . . .‛

Choice experiment Latency periods of 0, 2, 5, 10 years

Discount rate = zero (may reflect changes in future baseline risk) Description of

morbidity or illness
Focus of study is mortality risk Rated subjectively by respondents for each type of risk ‚cancer‛ designation

varied independently from dread
Private good v. nationwide public program Other independent variables: salience(‚familiarity‛) exposure, sensitivity to illness, beliefs in prevalence Adults

Children (Italy) Respiratory

fatality

Cancer fa tality
Auto fatality EC Cancer differential of

50% relative to ‚general‛ VSL is consistent with findings.

Auto accident risks valued less than respiratory or cancer
VSL higher for public v. private (if public programs are effective)
‚cancer‛ designatio n effect persists after controlling for other risk characteristics.SAB Review Draft

75 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)

Premiu m 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).SAB Review Draft

76 discount rate estimated. by length and

severity (pain, disability) Can cer (5 types)

Auto accidents
Tsuge et al. (2005) Choice experiment Latency periods of 0, 5, 10 years
Implied d iscount 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 hear t 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 ‚ac cident‛ 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 ca ncer

risks vs. auto

- accident risks. Adults Fatal cancer (stomach, liver, brain); Significant cancer

differential (3x over auto accidents at 5

- yearSAB Review Draft

77 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 f rom 2008 survey in Milan

Cancer VSL of ~$5.6mSAB Review Draft

78 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 statisticalSAB Review Draft

79 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 millionSAB Review Draft

80 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; 1=published in a peer

- review outlet (includes book chapters) JRU 0=does not appear in Journal of Risk and Uncertainty (JRU); 1=published in JRU ALBSERIES 0=not part of the Alberini, Krupnick, Cropper and Simon series of studies; 1=part of this series AUTO 0=non

- auto/traffic risk; 1=auto/traffic risk ENVIRONMENTAL 0=non

- environmental risk source; 1=environmental

- related risk (i.e., air pollution, drinking water, hazardous waste site, or unspecified general death risk) P UBLIC 0=risk affects individual only; 1=risk affects public CANCER 0=non

- cancer death; 1=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 conducte d US 0=non

- US study; 1=US study CV 0=choice experiment; 1=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, 1=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, 1=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, 1=survey administered with an interviewer (e.g., in

- person, telephone DOTS 0=ladder, bar chart used for visual aid; 1=grid used for visual aid SCOPE 0=no scope test performed or calculated, 1=scope test performed or calculated WEAK 0=does not pass a weak scope test, 1=passes a weak test, but WTP is less than proportional to the size of the risk reductionSAB Review Draft

81 Variable Name Description STRONG 0=does not pass a strong scope test, 1=passes a strong test; WTP is proportional to the size of the risk reductionSAB Review Draft

82 Table 3. Stated preference dataset

Study

Country Sample Size Risk Characteristics

Risk reduction WTP

(2009$)* SE Cancer Public Latency (yrs) Auto risk Env. risk Unspec. Source Other risk type

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) 0.48SAB Review Draft

83 Study

Country Sample Size Risk Characteristics

Risk reduction WTP

(2009$)* SE Cancer Public Latency (yrs) Auto risk Env. risk Unspec. Source Other risk type

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 f or 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 independe nt estima tes 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) b ased 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)SAB Review Draft

84 (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)SAB Review Draft

85 Table 4: Hedonic Wage dataset

Study Country Sample Sample Size Sample

Characteristics

Risk Variable Mean Risk Nonfatal

Risk Included (1=Yes) Workers'

Comp Included? (1=Yes) WTP

(2009$) SE Union White Male Manual/Mfg Blue Collar

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 3.47SAB Review Draft

86 Study Country Sample Sample Size Sample

Characteristics

Risk Variable Mean Risk Nonfatal

Risk Included (1=Yes) Workers'

Comp Included? (1=Yes) WTP

(2009$) SE Union White Male Manual/Mfg Blue Collar

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 BLS 1972

- 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 1.34SAB Review Draft

87 Study Country Sample Sample Size Sample

Characteristics

Risk Variable Mean Risk Nonfatal

Risk Included (1=Yes) Workers'

Comp Included? (1=Yes) WTP

(2009$) SE Union White Male Manual/Mfg Blue Collar

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 8.82SAB Review Draft

88 Study Country Sample Sample Size Sample

Characteristics

Risk Variable Mean Risk Nonfatal

Risk Included (1=Yes) Workers'

Comp Included? (1=Yes) WTP

(2009$) SE Union White Male Manual/Mfg Blue Collar

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 CFOI 1992

- 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 CFOI 1996

- 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 BLS 1993 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

. 895 E

- 05 1 0 6.16 1.89SAB Review Draft

89 

## 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 reductio ns 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 [ ]. The final six columns in the table show WTP [$] and [yr

- 1 ] (explained

below) for a range of ’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 utilit y with and without the policy,

,

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.,

,

where is the job

- risk level that the individual would choose if her baseline survival probability were
increased by and if she were charged the amount WTP for this change. The level of m that she would

actual ly 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 = 1 and if each i ndividual wereSAB Review Draft

90 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

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 live s saved would be positive, though the latter still would be

less than . 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 h igher 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 fr om 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 (mul ti

- 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

, where is utility in period t (assumed here to depend on

consumption , health status , and possibly age t ), is the probability of surviving to the beginning

of age given that the individual is alive at the beginning of age , , 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

.SAB Review Draft

91 To help interpret this willingness to pay measure, we can break the value function into two parts

a t some future age t = b , , then re

- write second term

on the right hand side of this equation in terms of the value function at age b ,

, which means

. 33 Thus, the marginal

willingness to pay at age a for a reduction in mortality risk at some future age b is

. 34 This is the expected remaining lifetime utility at the beginning of age b ,

discounted by the survival probability and t he 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 calibra ting 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 cons umption 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 condition s

— 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 Dire ct inspection of this equation suggests some simple comparative static results: (1) decreases with the latency period because all elements of the numerator

— , , and

— decrease and the denominator does not change. (2) could increase or decrease with a because, while and 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 would unambiguously decrease with age. However, observed consumption patterns generally are not flat; consumption typically is low in the early (adu lt) years, high in middle age, and lower again in later years, which, all else equal, would tend to increase then decrease

.SAB Review Draft

92 functional form for the period utility function and cal ibrating 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 ra ndom 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, r ace,
geographic region, etc., as appropriate for the exposed sub

- population relevant for the policy to be

examined.
2.) Set 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:

. Then either

a. set 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 pa y 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 and d simu ltaneously.

Such a calibrated life

- cycle model then could be used to calculate for all combinations of a and b

for each representative individual identified in step 1. These estimates then could be transferred to any

pattern o f mortality risk changes that are projected for one or more policies under consideration. More
sophisticated versions of this approach could specify as a function of age and/or health status, which

might facilitate a link to the QALY literature.SAB Review Draft

93SAB Review Draft

94 Table A1 . Maximum willingness to pay for a range of changes in survival probabilities, , based on a marginal approximation ( ) and direct calculation ( ), with and without a behavioral response. Baseline job risk is m = 0.006. Estimates of the adjusted job risk with a behavioral response ( ) 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

[yr

1 ] [$] [$] [$] [yr

1 ] [$] [yr

1 ] [$] [yr

1 ]
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 0.0110000SAB Review Draft

95