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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

December 10, 2010

For consultation with the Science Advisory Board–Environmental Economics Advisory Committee
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1 Introduction........................................................................................................................................................3

1.1 Key topics .................................................................................................................................................3

1.2 Roadmap...................................................................................................................................................5

2 Background.........................................................................................................................................................7

2.1 The valuation challenge..........................................................................................................................7

2.2 Existing EPA Guidance.........................................................................................................................10

2.3 Recommendations from prior expert committees.............................................................................11

3 Key Issues for EPA...........................................................................................................................................14

3.1 Fundamental Concepts and Recommended Terminology Changes ..............................................14

3.1.1 Fundamental Valuation Concept....................................................................................................14

3.1.2 Change in metric and terminology.................................................................................................15

3.2 Altruism and willingness to pay for mortality risk reductions.......................................................17

3.3 Valuing cancer risks ..............................................................................................................................20

4 Review of stated preference and hedonic wage studies .............................................................................26

4.1 Stated preference studies ......................................................................................................................28

4.1.1 Recent meta-analyses of SP studies ................................................................................................29

4.1.2 A new meta-analysis dataset...........................................................................................................31

4.2 Hedonic wage studies ...........................................................................................................................35

4.2.1 Data sources.......................................................................................................................................36

4.2.2 Estimation issues...............................................................................................................................37

4.2.3 Recent meta-analyses of hedonic wage studies ............................................................................38

4.2.4 A new meta-analysis of hedonic wage studies .............................................................................41

5 Methods for Combining Data.........................................................................................................................46

5.1 Meta-analysis .........................................................................................................................................47

5.1.1 Parametric distribution ....................................................................................................................47

5.1.2 Classical econometrics......................................................................................................................48

5.1.3 Bayesian estimation..........................................................................................................................51

5.2 Structural benefit transfer.....................................................................................................................53

5.2.1 Static preference functions...............................................................................................................55

5.2.2 Life-cycle preference functions .......................................................................................................57

6 Conclusions.......................................................................................................................................................59

6.1 Addressing key issues: terminology, altruism, cancer valuation ...................................................59

6.2 Longer term analytical directions........................................................................................................60

6.2.1 Meta-analysis.....................................................................................................................................60

6.2.2 Structural Benefit Transfer...............................................................................................................61

6.3 Other research directions......................................................................................................................61

References ..................................................................................................................................................................63

Tables and figures.....................................................................................................................................................74

Appendix A ...............................................................................................................................................................89

1
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2 1 Introduction

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

4 the application of benefit-cost analysis to environmental policies. Valuing the reduced risks of mortality, 

5 in particular, poses a special set of conceptual, analytical, ethical and empirical challenges for economists 

6 and policy analysts. This white paper addresses current and recent U.S. Environmental Protection 

7 Agency (EPA) practices regarding the valuation of mortality risk reductions, focusing especially on 

8 empirical estimates of the ‚value of a statistical life‛ (VSL) from stated preference and hedonic wage 

9 studies and how they might be summarized and applied to new policy cases using some form of benefit 

10 transfer. Benefit transfer concepts will be highlighted throughout the paper, since any application of 

11 existing empirical estimates of values for health risk reductions to new policy cases is inherently a benefit 

12 transfer problem.

13 The main intended audience for this paper is EPA’s Science Advisory Board-Environmental 

14 Economics Advisory Committee (EEAC). The main objectives of the paper are to highlight some key 

15 topics related to the valuation of mortality risks, and to describe several possible approaches for 

16 synthesizing the empirical estimates of values for mortality risk reductions from existing hedonic wage 

17 and stated preference studies for the purpose of valuing mortality risk reductions associated with future 

18 EPA policies. Some of these approaches could be implemented in the short term, but others will likely 

19 require longer term research. We are soliciting general feedback and specific recommendations from the 

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

21 1.1 Key topics

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

23 conclusions can be supported by existing data and methods. In other cases we describe alternative 

24 methods, data and data gaps, and possible future directions, with the intention of soliciting meaningful 
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25 feedback from the EEAC. The key topics addressed in this paper—loosely ordered from short- to longer26 term tasks—include:

27 Improving communication by reporting value estimates in terms of risk changes rather than “statistical lives.” 

28 We fear, as do others, that the prevalence of such terms of art as ‚the value of a statistical life‛ has 

29 contributed to unnecessary confusion and consternation among decision-makers and members of the 

30 general public. We aim to ease these communication difficulties by replacing the VSL terminology 

31 with the straightforward term ‚value of mortality risk‛ (VMR). The ‚units‛ associated with the 

32 mortality risk change must be clearly delineated and in this paper we report the units in terms of 

33 willingness to pay for a reduced risk of 1/1,000,000 or a ‚micro-risk,‛ following Cameron (2008) and 

34 Howard (1989). We believe that this term provides a more accurate description of the fundamental 

35 valuation concept that underlies the marginal willingness to pay for risk reduction, and that this 

36 choice of measurement unit is a more natural one considering the typically small (relative to the full 

37 suite of risks from all hazards) changes in individual-level risks resulting from most environmental 

38 policies.

39 Alternative approaches for updating EPA’s best central estimate, or range of estimates, of the willingness-to40 pay for mortality risk reductions for use in regulatory impact analyses. EPA is interested in updating its 

41 guidance to better reflect the existing estimates of mortality risk reduction values in the revealed and 

42 stated preference literatures. Specifically, how can the empirical results (described below in Section 

43 4) be used to revise EPA’s mortality risk valuation guidance in the form of a revised point estimate or 

44 range or benefit transfer function? 

45 Incorporating a cancer differential into mortality risk valuation guidance. We discuss the possibility of 

46 adding a ‚cancer differential‛ (often called a ‚cancer premium‛ in the literature) to the standard 

47 (non-cancer) estimates of mortality risk reduction values, specifically for use in analyzing policies 

48 expected to reduce carcinogenic pollutants. EPA first raised the issue of a cancer premium with the 
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49 EEAC in 2000 (USEPA 2000b), but the literature has developed considerably since that time. Given 

50 its importance for the valuation of environmental health risks in particular, we review the current 

51 literature and recommend including a cancer differential in future guidance. 

52 The role of altruism in valuing risk reductions. The role of altruistic motives for improved health and 

53 safety is typically ignored in most benefit-cost analyses but may have important implications for 

54 estimating individuals’ willingness to pay for environmental improvements. We review several 

55 recent studies that examine the role of altruism in benefit-cost analysis and highlight the potential 

56 relevance of these findings for the valuation of mortality risk reductions, in particular their 

57 implications for interpreting and transferring stated preference estimates of ‚public‛ versus ‚private‛ 

58 risk reductions.

59 Toward functional benefit transfer. We discuss specific issues that we expect to arise in applying both 

60 classical and Bayesian meta-regression techniques to new datasets of stated preference and hedonic 

61 wage value estimates described in this paper, as possible approaches for developing a benefit transfer 

62 function. We also discuss the structural benefit transfer approach, which involves specifying a direct 

63 or indirect utility function, including parameters that can describe the relevant attributes of the risk to 

64 be evaluated, and then deriving analytical expressions for observable economic variables that can be 

65 used to calibrate the parameters of the preference function. Developing a valid benefit transfer 

66 function, using either meta-regression or a structural approach or some combination of these, is a 

67 longer-term task than the others mentioned above, but EEAC feedback on these issues would be very 

68 helpful in shaping EPA’s research agendas in these areas.

69 1.2 Roadmap

70 The remainder of this white paper is organized as follows. Before we address our key topics in 

71 more detail, Section 2 provides background discussion that (1) describes the valuation challenge facing 

72 the Agency and the differences in the contexts underlying existing mortality risk reduction value 
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73 estimates and the policy scenarios we seek to analyze; (2) briefly summarizes EPA’s most recent 

guidelines for valuing mortality risk reductions (USEPA 2008);1 74 and (3) recaps the main 

75 recommendations from several recent expert advisory committees to EPA on the valuation of human 

76 health risk reductions and the use of meta-analyses for combining estimates from different studies. 

77 With this context in mind, in Section 3 we describe and discuss three of the key topics of this 

78 whitepaper: terminology and metrics, cancer risk valuation, and altruism. In Section 4, we review the 

79 empirical mortality risk value estimates from the stated preference and hedonic wage literatures, 

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

81 includes a newly assembled database of stated preference estimates of mortality risk reduction values in 

82 anticipation of an updated meta-analysis. We also review and extract value estimates and other 

83 attributes from hedonic wage studies that have provided estimates of the VSL, with selected studies 

84 spanning 1974 to the present. We discuss strengths and weaknesses of these studies for application to 

85 environmental policies. 

86 In Section 5 we discuss alternative approaches for synthesizing the estimates from these 

87 literatures as a necessary step for updating EPA guidance. A longer term goal is to develop a benefit 

88 transfer function for valuing mortality risk reductions, rather than relying on the current practice of 

89 transferring a single central point estimate. We discuss two basic approaches for developing such a 

90 benefit transfer function: meta-analysis and structural benefit transfer. Meta-analysis uses statistical 

91 regression techniques to quantify the influence of study, policy, demographic, and possibly other 

92 variables on the willingness to pay for health risk reductions. The structural benefit transfer approach 

93 involves specifying a direct or indirect utility function and then deriving analytical expressions for 

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

 

1 These are reflected in EPA’s revised Guidelines for Preparing Economic Analyses (2008).
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95 Section 6 concludes with summaries of the key topics and needs for both short-term guidance and longer96 term research. 

97 2 Background

98 2.1 The valuation challenge

99 Benefit cost analysis is a useful tool that provides detailed information on a wide variety of 

100 consequences associated with environmental policies. Benefits are based on what individuals would be 

101 willing to pay for risk reductions or for other improvements from pollution reduction. Costs are 

102 determined using the value of the resources directed to pollution reduction. As safeguarding human 

103 health is among the EPA’s primary goals, to develop more complete and more accurate benefit-cost 

104 analyses of its policies, EPA must estimate individuals’ willingness to pay for reductions in health risks 

105 from environmental harms. Ideally, benefit-cost analysis of policies that reduce health risks would 

106 account for all of the factors that may cause willingness to pay to vary across different types of policies 

107 and individual characteristics and circumstances. The literature has indicated that these factors may 

108 include the sources of risk affected by the policy (e.g., hazardous air pollutants, water contamination, 

109 etc.), the resulting health conditions (e.g., cancer, cardio-respiratory diseases, gastro-intestinal diseases, 

110 etc.), how the policy affects the timing of morbidity and mortality risks across each individuals’ life span 

111 (i.e., how it shifts the ‚survival curve‛), the income and other personal characteristics of the affected 

112 individuals, and how the changes in risks are perceived by those individuals. While addressing all of 

113 these factors simultaneously is currently empirically infeasible, there are three challenges that we 

114 highlight for their direct relevance to EPA.

115 First, fundamental to this valuation challenge is that the risk reductions provided by EPA policies 

116 are inherently public in nature, unlike, for example, private purchase decisions. The distinction is 

117 important because individuals may reasonably value risk reductions from public policies differently than 
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118 those from private actions even if their own mortality risks are affected in a quantitatively identical 

119 manner. Such differences could be due to differences in ‚controllability,‛ ‚dread,‛ or other tangible or 

120 intangible factors (e.g., Slovic 1987, Savage 1993, Chilton et al. 2006). Furthermore, public policies raise 

121 issues about altruistic values for risk reductions to others, something that may be of particular relevance 

122 for environmental risks. EPA would like to use the existing literature to evaluate the extent and nature of 

123 altruistic values and consider how to formulate mortality risk valuation guidance accordingly. We 

124 address altruism in greater detail in Section 6.3.

125 A second major challenge for the valuation of mortality risk reductions for environmental 

126 policies is the intertwined nature of morbidity and mortality risks. Environmental policies generally do 

127 not reduce the risks of fatal workplace or automobile accidents, for example, which provide the context 

128 for many of the mortality valuation estimates in the literature and generally have little or no 

129 accompanying morbidity or period of illness. Ideally, we would use an integrated model that could 

130 estimate willingness to pay for mortality and associated morbidity risk reductions simultaneously. 

131 Developing such a model is beyond the scope of this white paper and current guidance development 

132 effort, and is near the frontier of the empirical valuation literature. Nevertheless, to the extent possible 

133 with currently available data and models, we would like to account for how individuals consider 

134 morbidity in existing estimates of mortality risk reduction values when they always occur together. It 

135 also is important to capture some related losses that may not be reflected in willingness to pay estimates, 

136 depending on context in which they were estimated. For example, reduced health from illness preceding 

137 death is certainly a loss to an individual and his or her quality of life, but may not be reflected in VSL 

138 estimates from the hedonic wage literature, which are based on the risks of workplace injuries that lead to 

139 death. Society also is worse off because of the illness due to the individual’s lost productivity, something 

140 that may not be reflected in revealed or stated willingness to pay estimates, depending upon the type of 

141 insurance held by the individual and possibly the scenario description. 
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142 This issue is of particular relevance to EPA when addressing reductions in cancer risks since 

143 many EPA policies focus on reducing exposure to carcinogens. Ten years ago EPA reviewed the 

144 economic literature on valuing fatal cancer risk reductions and discussed a number of risk characteristics 

145 that may influence people’s values, including but not limited to the timing of the risks (USEPA 2000b,c). 

146 The committee recognized many of the issues reviewed by EPA as theoretically valid but empirically 

147 ambiguous, and therefore recommended that ‚the only risk characteristic for which adjustments to the 

148 VSL can be made is the timing of the risk‛ (USEPA 2000c p 1). In particular, this recommendation 

149 advised against the application of any differential to reflect preferences for reducing cancer risks relative 

150 to other types of risk because of dread or other factors. With an additional decade of valuation literature 

151 to draw upon, EPA is seeking to re-examine this question using data from the stated and revealed 

152 preference studies described below, as well as other relevant empirical results. We will discuss cancer 

153 valuation in more detail in Section 6.4.

154 Finally, the empirical literature may allow us to account for the extent to which individuals value 

155 different categories of risks differently in a systematic transfer of benefits. For example, if environmental 

156 risk reductions are valued differently from workplace or auto accidents, regardless of whether the 

157 mitigation is from private or public actions, our guidance should reflect this difference.

158 It is important to keep the overarching valuation challenge in mind as we begin discussing recent 

159 studies and value estimates. Each study reflects an attempt to measure the value of a reduction in 

160 mortality risk from a specific cause (or small set of causes), in a specific context, among a specific 

161 population. By now there is ample theoretical and empirical evidence to indicate that values for health 

162 risk reductions are not ‚one-size-fits-all‛—that is, they are ‚individuated‛ (e.g., Sunstein 2004, Evans and 

163 Smith 2008, Scotton and Taylor 2009). For this reason, we believe that there is great scope for improving 

164 upon the point value benefit transfer approach that has traditionally been applied to mortality risk 

165 reductions based on a central estimate of the VSL. Therefore, we ultimately are seeking both short-term 
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166 recommendations as well as advice on a longer-term research agenda on how these heterogeneous 

167 studies can best be synthesized for systematic benefit transfers to improve the application of benefit-cost 

168 analysis to future environmental policies.

169 2.2 Existing EPA Guidance

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

171 retains the recommendation from the 2000 version, a default central VSL value $4.8 million in 1990 real 

172 dollars. This estimate, after adjusting for inflation and real income growth, is to be applied to mortality 

risk reductions for all types of policies, no matter the source of the risk.2 173 The estimate is based on the 

174 mean of a probability distribution fit to twenty-six published VSL estimates. The draft Guidelines also 

175 indicates that the distribution itself can be used for formal uncertainty analysis. The underlying studies, 

176 the probability distribution parameters, and other useful information are available in Appendix B of the 

177 draft Guidelines (USEPA 2008). 

178 The draft Guidelines also retains the 2000 version recommendation that the VSL for mortality risk 

179 reductions should not be adjusted for differences in sources of risk or population characteristics—rather, 

180 these factors should be examined qualitatively. In some cases, the analysis may include a quantitative 

181 sensitivity analysis. Analysts should account for timing when valuing mortality risk reductions, and 

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

183 benefits. Because the VSL represents the marginal willingness to pay for contemporaneous risk 

184 reductions, this is typically done by estimating the lag between reduced exposure and reduced mortality 

185 risks, calculating willingness to pay in all future periods when mortality risks are reduced, and 

186 discounting back to the present.

187 Finally, EPA’s draft Guidelines also recommends accounting for increases over time in average 

188 income. This is done by using projections of real GDP per capita and applying an income elasticity 

 

2

 We report all estimates in 2009 US dollars unless otherwise noted. 
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189 estimate. The resulting future (real) VSL will therefore reflect the idea that health risk reductions are 

190 normal goods and so willingness to pay will increase with income.

191 2.3 Recommendations from prior expert committees

192 This white paper is one stage in a detailed process that EPA has undertaken with the SAB-EEAC 

193 to improve the Agency’s ability to value health risk reductions. Since its review of EPA’s Guidelines for 

194 Preparing Economic Analyses (USEPA 2000a) the SAB has offered several specific sets of recommendations 

195 on valuing risk reductions, particularly for mortality risks.

196 In July 2000 the SAB-EEAC released an advisory report in response to EPA’s white paper, Valuing 

197 the Benefits of Fatal Cancer Risk Reduction, which focused on benefit transfer issues associated with using 

198 existing mortality risk values to estimate the benefits of EPA actions on carcinogens, including potential 

199 adjustments that could be made to existing risk values to account for this category of benefits (USEPA 

200 2000b). As noted earlier, after reviewing the white paper and current economics literature, the SAB 

201 concluded that, while many of the issues raised in the white paper were theoretically valid and 

202 potentially important, the empirical literature supported only accounting for latency and for income 

203 growth over time. The SAB-EEAC did not consider other adjustments to EPA’s default mortality risk 

204 value to be appropriate for the Agency’s primary analyses, but could be addressed separately using 

205 sensitivity analysis. 

206 An August 2001 SAB report, Arsenic Rule Benefits Analysis: An SAB Review (USEPA 2001), 

207 generally supported EPA’s estimate of the marginal willingness to pay for mortality risk reductions. The 

208 SAB also offered additional recommendations to account for the time between reduced exposure and 

209 reduced mortality risks. This report coined the term ‚cessation lag‛ for this concept and offered specific 

210 recommendations for estimating cessation lags based on the types of risk data available. The SAB review 

211 also clarified that reductions in exposure to carcinogens—that is, exposure per se, aside from the increased 

212 cancer risks that the exposure causes—are not a separate benefit category under a damage function 
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213 approach to valuing reduced risks. The board noted that it is possible that there is an existence value for 

214 protected drinking water; however, without sufficient empirical evidence to estimate the magnitude of 

215 this value, it cannot be included in the quantitative benefits analysis. Finally, the report indicated that it 

216 is appropriate to add the costs of illness to the willingness to pay for mortality risk reductions when 

217 estimating the benefits of reduced cancer mortality.

218 EPA further consulted with the SAB-EEAC on additional mortality risk valuation issues in 2004, 

219 developing a strategy to gather additional information on meta-analysis to inform both the SAB-EEAC 

220 and EPA (USEPA 2004b). In 2006, EPA returned to the SAB-EEAC with two documents for formal 

221 review: a white paper addressing how remaining life expectancy affects willingness to pay for mortality 

222 risk reductions, and an expert report on the use of meta-analysis for combining existing mortality risk 

223 value estimates. A 2007 report, SAB Advisory on EPA's Issues in Valuing Mortality Risk Reduction,

224 responded to both topics (USEPA 2007).

225 On the subject of life expectancy, the SAB-EEAC noted that there was theoretical ambiguity on 

226 how willingness to pay might change with age (and, hence, remaining life expectancy). The committee 

227 concluded that the existing economics literature does not provide clear theoretical or empirical support 

228 for using different values for mortality risk reductions for differently-aged adults or a constant ‚value of 

229 statistical life year‛ (VSLY). Thus, the SAB-EEAC recommended that EPA continue using its traditional 

230 assumption of an age-independent willingness to pay for mortality risk reductions. 

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

232 to discuss the meta-analysis of VSL estimates and to examine three existing meta-analyses: Mrozek and 

233 Taylor (2002), Viscusi and Aldy (2003), and Kochi et al. (2006). While the expert workgroup did not 

234 endorse any one of these studies, the panel did encourage the use of meta-analytic techniques for the 

235 analysis of the existing literature on VSL. The workgroup recommended analyzing stated preference and 
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236 hedonic wage data separately, and offered a set of principles that should be followed in conducting such 

237 an analysis (USEPA 2007). 

238 The SAB-EEAC review of the Meta-analysis workgroup’s report stated that meta-regression is ‚a 

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

240 that are associated with differences in VSL,‛ but concluded that meta-regression is ‚not appropriate *for+ 

241 combin*ing+ VSL estimates‛ into a summary measure (USEPA 2007 p i). Rather, the SAB-EEAC 

242 suggested using meta-regression to examine how study design characteristics influence the VSL estimates 

243 and relying on other statistical techniques to determine a central estimate or range of estimates for use in 

244 benefit transfer to new policy cases.

245 Based on these expert recommendations and other considerations, we believe that updated 

246 reviews and meta-analyses of the stated preference and hedonic wage literatures could help refine the 

247 Agency’s central estimate(s) or range of estimates of the marginal willingness to pay for mortality risk 

248 reductions. Studies have shown that values for health risk reductions may depend on differences among 

249 policies and the affected individuals. These factors include the sources of risk affected by the policy (e.g., 

250 hazardous air pollutants, water contamination, etc.), the resulting health conditions (e.g., cancer, cardio251 respiratory diseases, gastro-intestinal diseases, etc.), as well as how the policy affects the timing of 

252 morbidity and mortality risks across each individuals’ life span (i.e., how it shifts the ‚survival curve‛). 

253 Therefore, as is widely recognized in most other contexts where some form of benefit transfer is used for 

254 policy analysis, we believe a functional benefit transfer approach should be more accurate than a single 

255 point estimate applied in all circumstances. Consequently, we are interested in exploring approaches for 

256 developing benefit transfer functions that can account for some or all of these factors.
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257 3 Key Issues for EPA

258 3.1 Fundamental Concepts and Recommended Terminology Changes

259 3.1.1 Fundamental Valuation Concept

260 We begin by identifying the fundamental valuation concept that economists aim to estimate 

261 using non-market valuation methods and apply in benefit-cost analyses of policies that reduce human 

health risks. Consider a general utility function for an individual i with income 

Yi

262 and some health risk 

Ri

among the arguments: 

, , U U Y R i i i i Z . The vector 

Zi

263 is included to emphasize that, in addition 

264 to income and risk, the individual’s utility (and therefore the willingness to pay for health risk 

265 reductions) also may be influenced by many other factors specific to the case at hand. We will highlight 

266 several of these factors throughout this white paper. The individual’s marginal rate of substitution between 

267 income and risk is: 

/

0 

/

i i

i i i

i i i i

U U dY U R dU dY dR

Y R dR U Y

268 .

This marginal rate of substitution, 

i i

269

dY dR

, also can be interpreted as the individual’s marginal 

270 willingness to pay (wtp) for a change in risk—that is, the amount of money the individual would be willing 

to swap for a small change in risk on the margin.3 271 This is the fundamental value concept that must be 

272 estimated for use in benefit-cost analyses of policies that may improve human health. With estimates of 

273 these quantities, conditioned as necessary on possibly many observable characteristics of the policy and 

274 the affected individuals, it is straightforward to calculate the total willingness to pay for the risk 

reductions that are expected to be produced by the policy: 

i i i

275

wtp R

, where i indexes all individuals 

affected by the policy, and 

wtpi

and 

Ri

276 are the estimated marginal willingness to pay and risk 

 

3 Throughout this white paper, we will use ‚wtp‛ to refer to marginal willingness to pay, which will have units of 

$/change in risk, and we will use ‚WTP‛ to refer to discrete willingness to pay amounts, which will have units of $.
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277 reduction for individual i, both of which may depend on individual-level characteristics and 

circumstances.4 278

279 It is important to emphasize that this is a marginal value concept—a dollar value per unit change in 

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

curve.5 281 For practical purposes, the units used to report estimates of these slope values are of no 

consequence. They could be reported as dollars per nano-risk (

9

10

), or micro-risk (

6

282

10

), or mili-risk (

3

283

10

), etc. As long as the measurement units are known, then the risk changes to be valued can be 

284 expressed in the same units and the correct total value can be calculated. The conventional measurement 

285 units used for reporting these slope estimates are (effectively) ‚dollars per mortality‛ risk changes, 

286 usually simply written as ‚$,‛ where ‚per mortality‛ is understood (or misunderstood, depending on the 

287 audience). This quantity was often referred to as the ‚value of life‛ in the early literature on the subject 

288 (e.g., Rice and Cooper 1967). While the terminology varies, the quantity is now typically called the ‚value 

289 of a statistical life,‛ or VSL, where ‚statistical‛ has been added to emphasize that valuation is based on

changes in risk rather than the loss of life with certainty.6 290 

291 3.1.2 Change in metric and terminology

292 Despite its widespread usage, this particular selection of measurement units for the denominator 

293 of the marginal rate of substitution between income and risk, and the VSL label that has been attached to 

 

4 For ease of exposition we ignore the time dimension here. We will allude to some of the complications that arise in 

the more realistic dynamic case, using a life-cycle model, in Section 6.2.2 and Appendix A.

5 Also note that if the risk changes to be valued are large, then the slope of the willingness to pay function may 

change over the relevant range and so the marginal willingness to pay 

 ́

the change in risk may not give an accurate 

estimate of total willingness to pay. For the most part in this white paper we will ignore this complication, though 

we do come back to it in an illustrative example in Section 5.2.1.

6 A common way of explaining the meaning of the VSL is based on a population’s aggregate willingness to pay for an 

aggregate risk reduction. For example, suppose in a town of 1,000 people a policy is enacted that reduces each 

person’s risk of dying by 1 in 1,000 in a year. 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.
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294 it, have caused or contributed to needless confusion and controversy, especially among non-economists 

295 (Cameron 2009). Most economists recognize that the ‚units‛ associated with the VSL reflect the 

296 aggregation of the small risk reductions across many individuals until that aggregate reflects a total of 

297 1.0, or one statistical life. However, for non-specialists this potentially subtle point is often lost; the 

addition of the word ‚statistical‛ to the terminology does not seem sufficient to clarify the concept.7 298 

299 To help reduce the misconceptions that seem to be inspired or aggravated by the VSL 

300 terminology, we propose a change in EPA standard practice such that estimates of health values will be 

301 referred to as the ‚value of mortality risk‛ (VMR), and report the associated units using standard metric 

302 prefixes to indicate the size of the risk change and the associated time scale, e.g., $/μr/person/yr (dollars 

per micro[10-6]-risk per person per year) (Howard 1989, Cameron 2009).8 303 

304 As noted earlier the choice of risk increment for aggregating and reporting risk changes is mainly 

305 one of convenience. However, we believe that explicitly labeling the units of the VMR in this way more 

306 clearly emphasizes that these values refer to small changes in individual-level risks over a definite time 

307 span rather than how much money any single individual or group would be willing to pay to prevent the 

308 certain death of any particular person. It also should be emphasized that the use of a standardized 

 

7 A recent example of the confusion surrounding this concept in the popular press can be found in an AP story titled, 

‚American Life Worth Less Today‛ (Bornstein 2008) that opened by saying ‚*EPA+ has decided that an American life 

isn’t worth what it used to be.‛ The story was referring to an alternate analysis in some air regulatory impact 

analyses that used a more recent review of the literature to report a lower VSL than is reflected in EPA’s 2000 

Guidelines. This story quickly spread throughout the media even appearing on the Colbert Report as EPA’s efforts 

to ‚devalue life.‛ Video clip at http://www.colbertnation.com/the-colbert-report-videos/176175/july-14-2008/theword---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 (μr). In recent 

empirical work, Cameron and DeShazo (2008) report results in terms of micro-risk reductions. Scotton and Taylor 

(2009) use the term ‚value of a risk reduction‛ (VRR), noting that ‚explicit consideration of the heterogeneous values 

for heterogeneous risks underscores the importance of moving the policy discussion from ‘a VSL’ to valuation of 

marginal changes in fatality risks specific to the type of the risk affected by the policy‛ (p 23). 
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309 measurement unit for reporting values for health risk reductions should neither be taken to imply that 

310 the values themselves are invariant across individuals or contexts, nor that these marginal values will be 

311 constant across the full range of relevant risk changes. 

312 For the remainder of this paper we will use the general term ‚value of mortality risk‛ whenever 

313 possible. We will report estimates as VMRs, as defined above, to the extent possible, using the VSL 

314 terminology only as necessary in discussing the previous literature. 

315 3.2 Altruism and willingness to pay for mortality risk reductions

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

317 analysis more generally: altruism. The default assumption for most applications of revealed and stated 

318 preference methods for non-market valuation is that individuals’ (or households’) well-being depends on 

319 their own consumption (interpreted broadly to include market and non-market goods and services) and 

320 is not directly influenced by the consumption or well-being of others. If this assumption is invalid, we 

321 may be concerned that our standard methods of estimating willingness to pay assuming ‚atomistic‛ 

322 individuals or households may give misleading results in benefit-cost analysis.

323 There are at least two ways that altruism may be relevant for the valuation of mortality risk 

324 reductions. First, some stated preference studies are based on surveys that make a distinction between 

‚public‛ and ‚private‛ risk reductions.9 325 The difference, if any, between WTP for public versus private 

326 risk reductions may be partly due to altruism, but other factors could be at work as well. For example, a 

327 distrust of government may lead some respondents to express a lower WTP for public risk reductions 

328 provided through government programs compared to those provided through private initiatives. While 

329 stated preference studies may in principle be able to distinguish altruistic preferences from other 

 

9 Few studies explicitly address the public versus private issue. However, for most of the studies it is possible to 

assign the estimates to one category: estimates that accrue to an individual only, such as an individual health risk 

reduction or the decision to wear a seatbelt or purchase a health care treatment, are ‚private‛ and estimates that can 

accrue to the individual and others, such as reductions in highway safety-related deaths, are ‚public.‛ See section 6.1 

for more details on the stated preference studies.
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330 confounding factors, it is difficult to draw clear conclusions from the existing literature because most 

studies that have been conducted to date were not designed to examine altruism per se.10 331 Therefore, the 

332 proper application of the results of these stated preference studies may depend in part on how altruism 

333 should be treated in benefit-cost analyses. Second, since hedonic wage studies are focused on 

334 compensation received by individual workers for taking on private, job-related risk, the mortality risk 

335 values from hedonic wage studies do not incorporate altruism. Therefore, if (some forms of) altruistic 

336 preferences should be included in benefit-cost analysis, then hedonic wage-based estimates of mortality 

337 risk values may need to be supplemented with separate value estimates that capture altruistic preferences 

338 alone. On the other hand, if (some forms of) altruistic preferences should be excluded from benefit-cost 

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

340 benefit transfers. 

341 EPA’s Guidelines for Preparing Economic Analyses (USEPA 2000a) discussed the role of altruism in 

342 estimating the total benefits of public actions, and noted the key distinctions between paternalistic (or 

‚safety focused‛) and non-paternalistic (or ‚preference respecting‛) forms of altruism.11 343 If altruistic 

344 motives are non-paternalistic, then individuals care not only about the benefits others receive, but also 

345 the costs they bear, and most economists who have studied this issue have concluded that it is generally 

346 inappropriate to add these altruistic values for benefits others receive to total willingness to pay. Doing 

347 so could lead to ‚double-counting‛ some of the benefits and/or costs. Paternalistic altruism, on the other 

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

349 describes the issue as follows: 

 

10

 Stated preference studies and the treatment of altruism also may hold promise for identifying preferences related 

to equity or environmental justice (EJ) concerns. For example, preferences for reductions in risks for others, 

particularly those who may be disproportionately exposed to pollutants (which are often low income and minority 

groups typically associated with EJ) could be identified through a well designed stated preference study. 

11 Formally, the utility function of non-paternalistic altruists includes others’ utility, while the utility function of 

paternalistic altruists includes others’ consumption of one or more types of private or public goods or services.
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350 While benefits are generally calculated by summing each individual's WTP for his or her own 

351 welfare, there are conditions under which it is appropriate to include altruistic values, or individuals' 

352 WTP for the welfare of others. Economic theory concludes that if one cares about a neighbor but 

353 respects the neighbor's preferences, and if the neighbor would have to pay for the policy action being 

354 analyzed, then altruistic benefits should not be counted in a benefit-cost analysis. The intuition 

355 behind this result is that, if one respects the neighbor's preferences, one cares about both the benefits 

356 and the costs the neighbor faces. It is therefore inappropriate to add the value one attaches to the 

357 neighbor's benefits without considering the cost implications of doing so. Comparing individual 

358 benefits and costs in this case is the appropriate decision rule.

359

360 Altruistic benefits may be counted either when altruism toward one's neighbor is paternalistic or 

361 when one will in fact bear the costs of the project but the neighbor will not. In the first case 

362 (paternalistic altruism), one cares about the benefits the neighbor will enjoy, e.g., from a health or 

363 safety project, but not about the costs the project will impose on him. An example of the second case 

364 would be a project whose costs are borne entirely by the current generation; i.e., the project imposes 

365 no costs on future generations. In this case, altruism toward future generations by the current 

366 generation could legitimately be counted as a benefit.

367

368 The conclusions in the Guidelines were based largely on Bergstrom (1982) and McConnell (1997)

369 who demonstrated that the optimal provision of public goods based upon selfish preferences is a 

370 necessary and sufficient condition for the optimal provision based on social preferences (including 

371 altruistic preferences). However, since the publication of the Guidelines, Flores (2002) has challenged the 

372 conventional wisdom that (non-paternalistic) altruism should be excluded from benefit-cost analysis. 

373 Flores showed that passing a private values benefit-cost test is a sufficient but not a necessary condition 

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

375 even if all altruism is non-paternalistic, failure to include altruistic values may lead to the rejection of 

376 policies that are potentially Pareto improving. Flores concluded that ‚benefit-cost analysis with altruism 

377 cannot simply be conducted independent of who pays.‛ In a more recent study, Bergstrom (2006)

378 concluded that ‚The assumptions under which the private values benefit-cost test is necessary for 

379 potential Pareto improvements need not always be satisfied;‛ nevertheless, ‚Despite these 

380 qualifications< for a broad class of economies, a comparison of the sum of private values to the cost of a 

381 project is the appropriate test for determining whether it can lead to a Pareto improvement‛ (p 348-349). 
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382 Bergstrom’s conclusion seems to summarize the prevailing view regarding non-paternalistic 

383 altruism in benefit-cost analysis, especially for policies that would cause marginal changes in 

384 environmental quality (since Flores’ counter-examples involved non-marginal changes). Therefore, the 

385 main relevance of altruism for mortality risk valuation lies in the distinction between the paternalistic and 

386 non-paternalistic forms. Including the former but excluding the latter may require supplementing 

387 revealed preference estimates of health risk valuations with a careful selection of results from previous 

388 stated preference studies. Stated preference surveys that elicit only private willingness to pay would 

389 exclude both forms of altruism. One way to include paternalistic but exclude non-paternalistic altruism 

390 would be to design a survey that would inform respondents about health improvements that others 

391 would experience from the policy, but also ask each respondent to assume that all others would be taxed 

392 an amount equal to their private willingness to pay for the policy, so that their utility remains unchanged 

393 (Johansson 1994). It is not clear which if any of existing stated preference studies (many of which are 

394 reviewed below in Section 6.1) were designed this way, so the current body of empirical results cannot 

395 support the separation of paternalistic from non-paternalistic altruism. We recommend additional 

396 research in this area to help estimate paternalistic willingness to pay for environmental policies that 

397 reduce health risks. Additional examination of existing studies may shed light on this issue in the 

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

399 3.3 Valuing cancer risks

400 As noted in our description of EPA’s valuation challenge, willingness to pay for cancer risk 

401 reductions may be systematically different than that for workplace or auto accidents or other risks not 

402 associated with a lengthy and painful illness. This difference is sometimes referred to as a a ‚cancer 

403 premium,‛ but we will use the more general term ‚cancer differential.‛ While not often defined 

404 precisely, the differential is posited as capturing elements of dread and fear of cancer, as well as the pain 
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405 and suffering from the period of illness preceding death. It might also include income and household 

406 productivity losses over this period of morbidity. 

407 Several authors have recommended accounting for this differential in benefit-cost analysis of 

408 policies that reduce exposure to carcinogens (e.g., Revesz 1999, Sunstein 2004). To the extent that existing 

409 policy guidance on valuing mortality risk reductions is based on non-cancer risk-wealth tradeoffs, this 

410 would involve an ‚adjustment‛ to the default (generic, non-cancer) mortality risk reduction value. 

411 Governmental analyses in the UK have adopted this approach, applying a 100% differential for cancer 

risks (HM Treasury 2003).12 412 In addition, the European Commission has recommended a 50% differential 

413 for carcinogenic pollutants over its default value of preventing a fatality (European Commission 2000). 

414 For the purpose of developing guidance, we are interested in assessing the valuation literature on 

415 cancer risks and any cancer risk differential, both in the short-term and the longer term. Ultimately, this 

416 literature could inform the development of a benefit transfer function, in combination with the stated 

417 preference and hedonic wage estimates described in greater detail below. While such longer-term 

418 research is being conducted, we believe it is reasonable that evidence of systematically different 

419 preferences for cancer risk reductions be part of any recommended short-term guidance. 

420 To inform this discussion, this section contains a somewhat more detailed assessment of the 

421 empirical literature on cancer risk valuation, with a particular emphasis on studies that examine risks in 

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

423 studies comparing values for cancer and non-cancer fatal risk reductions

424 - stated preference studies that estimate willingness to pay

425 - risk-risk studies

426 stated preference studies of cancer risks without internal comparisons, and

427 related hedonic property and hedonic wage studies. 

 

12

 Specifically, this adjustment is applied for the benefits from asbestos proposals by the UK Health and Safety 

Executive (HSE). 
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428 The first of these categories contains the most direct evidence on any cancer differentials.

429 Note on Cessation Lag and Latency

430 Reduced exposure to carcinogens results in reduced cancer incidence after a period of time that 

431 EPA has referred to as ‚cessation lag,‛ a term originally coined by the SAB in its review of the Agency’s 

432 arsenic in drinking water benefits analysis. Cessation lag addresses only reduced risks from reduced 

433 exposure and thus applies best to populations currently at risk. The time between initial exposure and 

434 increased cancer incidence is referred to as ‚latency‛ in recent EPA analyses, but it is often used in the 

435 literature in a broader sense to refer to the time difference between a change in exposure and a change in 

436 risk. 

437 Prior SAB-EEAC advice and agency practice has been to estimate cessation lag and latency from 

438 available epidemiologic data, apply a value of statistical life estimate at the time at which cancer mortality 

439 reductions occur, and discount this value back to the present at the rates prescribed in Agency guidance. 

440 The practice has generally been supported by research findings suggesting that individuals discount over 

441 these lag times at rates generally consistent with market rates, although some recent stated preference 

442 studies find near-zero discount rates over latency periods (Hammitt and Haninger, 2010; Alberini and 

443 Scasny, 2010a).

444 An important issue in estimating a cancer differential is the potential need to consider 

445 differences in the time profile of mortality risks between cancer and non-cancer cases. Earlier studies 

446 were often silent on the issue, but more recent ones have attempted to address it explicitly. Our focus in 

447 this section is on a potential cancer differential that captures the difference in marginal willingness to pay 

448 for reduction of cancer mortality risks relative to that of a non-specific mortality risk holding timing 

449 equal. That is, the differential, in principle, compares a contemporaneous non-cancer risk reduction with 

450 a contemporaneous cancer risk reduction. We recognize that timing may be intertwined with how people 
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451 perceive and value risk reductions, something that should be considered more fully in any rigorous, 

452 systematic benefit-transfer exercise as we develop guidance.

453 Stated Preference studies including cancer and non-cancer risks

454 Several stated preference studies have estimated willingness to pay for both cancer and non455 cancer risks, in large part to examine a possible cancer differential. A few studies have focused only on 

456 cancer risk reductions without an internal comparison to other types of risk. The results of these studies 

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

458 et al. 2005, Alberini and Scasny 2010a, and Alberini and Scasny 2010b), while a few others found no such 

459 evidence (Hammitt and Haninger 2010, Adamowicz et al. 2008) when looking at whole-household or 

460 public risks. Cameron and DeShazo (2008) found evidence of a differential for some cancers (breast and 

461 prostate) over other cancers (colon, lung, and skin), but not over other health endpoints (heart attacks and 

462 disease).

463 There have been two risk-risk tradeoff studies specifically examining how preferences for cancer 

464 risk reduction compare to those for automobile accident risk reductions. By asking respondents to choose 

465 among different bundles of risks, these simplified choice experiments aim to estimate the relative values 

466 of various types of risk reductions. They do not, however, provide a willingness to pay for either risk 

467 type and therefore are not included in our reviews of the willingness to pay literature above. Van 

468 Houtven et al. (2008) found a strong preference for avoiding cancer risks relative to automobile accidents 

469 even after controlling for latency and morbidity periods. With a 5-year latency, values for reductions in 

470 fatal cancer risk were approximately three times larger than those for immediate accident risks, declining 

471 to fifty percent larger for a 25-year latency. By contrast, in a study by Magat et al. (1996), the median 

472 respondent was indifferent between fatality risk from auto accidents and lymphoma, suggesting that 

473 cancer mortality is no more ‘dreaded’ than accidental mortality. It is difficult to draw firm conclusions, 

474 however, because the study did not specify the timing of the risks, and, in particular, any latency 
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475 associated with cancer. Therefore, if respondents assumed that cancer risks would be realized after a 

476 latency period then the results suggest that any preference for cancer reductions was approximately 

477 offset by discounting future risks. 

478 Three additional stated preference studies focus on WTP for cancer risks without direct 

479 comparisons to other risks. These do not internally address the question of how cancer risks are valued 

480 differently from non-cancer risks, but may be combined with the results from other studies to address 

481 this question. Focusing on cancer risks from hazardous waste sites Alberini, et al. (2010) estimated a 

482 cancer VSL of approximately $5.6 million (2009 dollars) using the results of choice experiments in Italy. 

483 Carson and Mitchell (2006) examined willingness to pay for installing a water filtration system to remove 

484 trihalomethanes (THM) in public drinking water. Estimated values depend upon an assumed latency 

485 and discount rate, as well as the specific risk reduction, but generally range from $3.4 to $8.0 at the 

486 smallest risk changes for a 25-year latency. Buzby et al. (1995) used a telephone-mail survey to examine 

487 the value of reduced fatal cancer risk from exposure to pesticides in grapefruit, and estimated a value of 

488 statistical cancer fatality at $6.99 million based on exposure assumptions.

489 Related Hedonic Property and Wage Studies

490 There are a small number of studies that have estimated WTP for reduced cancer risks using 

491 revealed preference approaches. The results have generally shown that the value of a statistical cancer 

492 case is similar to prevailing VSL estimates from hedonic wage studies. Direct comparison, however, is 

493 difficult without additional assumptions about latency or cessation lag and cancer fatality rates, as noted

494 for each study. 

495 In the context of hazardous waste, Gayer et al. (2000) and Gayer et al. (2002) employed a hedonic 

496 property framework to estimate the implicit value of a statistical cancer case from surrounding 

497 Superfund sites. In the first study, the value of a statistical cancer case was approximately $5.5 million, 

498 but did not include any assumptions or information on latency or fatality. The 2002 study calculated 
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499 estimates under a variety of latency and discounting assumptions with results ranging from $5.2 million 

500 to $10.0 with no latency, and from $6.2 to $11.8 million using a 3% discount rate and 10-year latency 

501 period. 

502 Davis (2004) used housing price responses to an observed cancer cluster in Nevada to estimate 

503 marginal willingness to pay for a change in lifetime pediatric leukemia risk ranging from $3.7 million to 

504 $11.1 million, which is generally consistent with the Gayer et al. studies, although the leukemia values are 

505 specific to children. Ho and Hite (2008) included risks from air toxics and hazardous waste sites in a 

506 hedonic property model and estimated the implicit value of cancer mortality to be $6.0 million. Finally, 

507 Lott and Manning (2000) explored the presence of compensating wage differentials for carcinogenic 

508 exposures in the workplace using the hedonic wage framework, finding that workers were being 

509 compensated for carcinogenic exposures. By making assumptions about the proportion of cancer deaths 

that arise from occupational exposures they calculated a cancer-specific VSL of $12.4 million.13 510

511 Because reducing environmental cancer risk is an important part of EPA’s mission to protect 

512 human health, a key question is how the results from the empirical literature summarized here, along 

513 with other literature described in this report, can be systematically synthesized to account for individuals’ 

514 preferences for reducing cancer risks relative to other types of health risks. As a first-cut, the simple 

515 average of the central estimates of the cancer differential from the subset of studies in Table 1 that 

reported values for both cancer and non-cancer risks is 52%.14 516 This is a preliminary estimate and should 

517 be refined or replaced with a more systematic synthesis of the literature, possibly incorporating results 

 

13

 As stated earlier, all figures have been updated to 2009 dollars using the Consumer Price Index, unless otherwise 

noted. 

14 Specifically, the summary point estimates that we drew from each of the nine studies in Table 1 that 

reported results pertaining directly to the cancer differential (i.e., VSLcancer / VSLnon-cancer - 1) are: 0 

(Hammit & Hanninger 2010), 0.5 (Alberini & Scansy 2010a), 0.85 (Alberini & Scansy 2010b), -0.15 

(Adamowiz et al. 2008), 0 (Cameron & Deshazo 2008), 0.2 (Tsuge et al. 2005), 0.3 (Hammitt & Liu 2004), 3 

(Van Houtven et al. 2008), and 0 (Magat et al. 1996). The average of these figures is 0.52.
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518 from other relevant studies. In the meantime, a cancer differential of 50% might be a reasonable 

placeholder value for use in upcoming RIAs.15 519 

520 4 Review of stated preference and hedonic wage studies

521 Our reviews of the literature in the sections that follow focus on results from stated preference 

522 and hedonic wage and studies. This reflects where the majority of potentially relevant empirical 

523 estimates are found and is consistent with prior consultations and advisory reports. The hedonic wage 

524 approach is well-established and vetted and remains influential in informing guidance across the federal 

525 government. However, the approach is limited to work-related risks and the associated risk 

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

527 economics literature. 

528 There has been a tremendous growth in the number of stated preference studies to estimate 

529 values for mortality risk reductions in recent years; certainly there is now a far larger and more 

530 sophisticated body of literature to draw upon than was available at the time of EPA’s last revision of its 

531 guidance. These developments potentially allow for an examination of important valuation dimensions 

532 including risk source (e.g., environmental, traffic-related); type of illness (e.g., any cancer differential or 

533 associated morbidity); and altruism. Our review of the empirical literature and how it can be synthesized 

534 attempts to address these issues.

535 However, additional studies exist that may supplement the reviews of the stated preference and 

536 hedonic wage literatures below. First, some stated preference studies do not seek to estimate willingness 

537 to pay or accept, but rather relative preferences for different types of mortality risk reduction. Two 

538 examples addressing cancer risks are described more completely above (Magat et al. 1996 and Van 

 

15 Another possible way to represent the cancer differential would be to estimate the absolute (rather than fractional) 

increment of the cancer mortality risk values over the values for non-cancer risks (i.e., VSLcancer - VSLnon-cancer). 

This would require an additional step of estimating the income elasticity of this absolute cancer differential. 

Estimating the fractional cancer differential implicitly assumes that the income elasticity of the absolute cancer 

differential equals that for the non-cancer VSL.
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539 Houtven et al. 2008). The study results do not estimate willingness to pay, but it may be possible to 

540 combine the estimates from the studies on relative tradeoffs with the willingness to pay literature to 

541 refine our benefit transfers. 

542 Another segment of the literature that we do not examine in detail here includes studies that 

543 evaluate only public preferences for risk reducing policies. Examples from this literature include 

544 Cropper et al. (1994) and Subramanian and Cropper (2000), who used survey methods to examine how 

545 respondents would allocate a given public budget to public programs for lifesaving and risk reduction; 

546 and Bosworth et al. (2009) who assessed community-level preferences for public programs to improve

547 health and safety. The SAB previously concluded that these studies can be informative in their own right, 

548 but cannot be directly related to individual willingness to pay and used directly for benefit-cost analysis 

549 (USEPA 2001). EPA is open to suggestions on whether and how this literature may be effectively and 

550 appropriately synthesized with the results of other studies for the development of guidance on mortality 

551 risk valuation. 

552 The hedonic property method has been used to estimate the value of environmental amenities 

553 and disamenities including mortality risks. A major challenge has been to limit the analysis to risk 

554 reduction rather than more comprehensive measures or indicators of environmental quality, such as air 

555 quality (e.g., Chay and Greenstone 2005) or the presence of or distance to hazardous waste sites (e.g., 

556 Greenstone and Gallagher 2008). These studies can be useful for evaluating some policies directly, such 

557 as the remediation of hazardous sites, but cannot be directly informative for mortality risk valuation. 

558 Willingness to pay for reduced mortality risks have been estimated in hedonic property studies, as first 

559 described and demonstrated in Portney (1981), who examined the relationship between housing prices 

560 and mortality risks from air quality. Four other studies, described more completely above in this paper, 

561 estimate marginal willingness to pay for cancer risk (Gayer et al. 2000, 2002; Davis 2004; and Ho and Hite 

562 2008). 
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563 Finally, implicit values for risk reductions can be estimated in ‚averting behavior‛ studies, 

564 wherein an individual or household uses the good as an input into the production of health or safety. 

565 Blomquist (2004) conducted an extensive review of this literature and concluded, with some caveats, that 

566 the findings are broadly similar to hedonic wage estimates. Recent additions to the literature are 

567 generally consistent with this conclusion (e.g., Andersson 2005, 2008 (automobile risks); Hakes and 

568 Viscusi 2007 (seatbelt use)). Key concerns about averting behavior studies include issues of risk 

569 perception and the separability of joint benefits and costs (USEPA 2000b). Viscusi (1992) explicitly 

570 excluded these studies from consideration in his meta-analysis of VSL estimates. Further, the lack of 

571 available studies on environmentally-related risks limits the usefulness of this class of studies for the 

present purpose of developing guidance for mortality risk valuation.16 572

573 4.1 Stated preference studies

574 Stated preference (SP) is a survey-based method for estimating willingness to pay or accept for 

575 non-market goods or services. SP methods are widely used to value environmental amenities or 

576 improvements in human health endpoints that may be difficult or impossible to estimate using revealed 

577 preference methods because of long lag times, unclear causality, or other factors. For example, SP studies 

578 have been used to elicit willingness to pay for reductions in the risks of dying from cancer and cardio579 vascular disease. SP studies vary widely in terms of the types of risk considered, payment vehicles, 

580 latency periods, mode of survey administration, etc. The number of and variation among existing SP 

581 studies is now large enough that the variation in their results can be analyzed statistically, although this 

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

 

16

 Note that there are some studies that relate averting behaviors to environmental quality or even related risks (e.g., 

Dickie and Gerking, 2009; Um, Kwak, and Kim, 2002), but, as documented in Blomquist, 2006, relatively few studies 

estimate WTP for reduced mortality risks in an environmental context.
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583 4.1.1 Recent meta-analyses of SP studies

584 Three recent meta-analyses examined the stated preference literature using statistical methods. 

585 Kochi et al. (2006) used both stated and revealed preference studies in an empirical Bayes framework. 

586 Dekker et al. (2008) focused exclusively on stated preference studies, also with Bayesian methods. 

587 Braathen et al. (2009) conducted a meta-regression analysis of a wide variety of stated preference studies 

588 using classical econometric tools. Each of these studies is discussed in more detail below. 

589 Kochi et al. (2006) used an empirical Bayes estimation method to generate predicted VSL 

590 estimates using multiple estimates from both stated preference and hedonic wage studies. Here we focus 

591 on the analysis and results for the stated preference data in their study. Study selection criteria were 

592 similar to those used by Viscusi (1992), including the use of studies for the general population and those 

conducted in high income countries only, and a minimum sample size.17 593 Another important criterion was

594 the use of estimates for immediate risk reductions; specifically, estimates for risks involving a latency 

595 period were excluded. 

596 Kochi et al. analyzed 45 VSL estimates drawn from 14 stated preference studies. The authors 

597 recorded all estimates from each study and then separated them into ‚homogeneous subsets.‛ 

598 Specifically, they grouped estimates by lead study author and used a Q-test for homogeneity to 

599 determine whether the estimates within a group are homogenoeous. After completing the separation of 

600 the estimates into homogenous subsets, they recalculated the VSL for the subset to create a unique VSL 

601 for that author. The recalculated mean reflects a weighted VSL of the estimates in the homogeneous 

subset, where the weights are based on the standard errors for the estimates.18 602 This technique is intended 

603 to address the troubling issue of choosing among multiple estimates from each study when those 

 

17

 Viscusi (1992) excluded two studies with sample sizes of around 30. Kochi et al. (2006) chose a minimum sample 

size of 100 for their analysis. 

18

 Another implicit selection criterion in this study was the use of estimates with reported standard errors. In the 

assembly of our new meta-analysis dataset, described in Section 4.1.2 below, we find that this may be a highly 

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

605 in 18 stated preference VSL estimates with a mean of $3.5 million and a standard error of $0.67 million (in 

606 2009 dollars).

607 Dekker et al. (2008) examined the influence of risk context (i.e., deaths from automobile-related 

608 accidents, air pollution, and all causes) on willingness to pay estimates from SP studies. The authors 

609 discussed the benefits transfer challenge associated with applying estimates from one context (e.g., auto 

610 risks) to another (e.g., air pollution), particularly when there is limited empirical evidence on the size and 

611 direction of the effects. Employing Bayesian techniques in a meta-regression, they compared willingness 

612 to pay or accept estimates in three different risk contexts—air pollution, traffic safety, and 

613 environment/general—while attempting to control for the size of the risk change and other respondent 

614 and study characteristics. Several study design decisions by Dekker et al. were based on 

615 recommendations from the EPA meta-analysis work group (USEPA 2006). 

616 The authors used existing meta-analyses and additional literature searches to identify stated 

617 preference studies for auto, air pollution, or context-free (unspecified) mortality risk reductions. After 

618 searching the literature and applying screening criteria, a final database was assembled containing 98 

619 VSL estimates from 27 studies, including three studies from the U.S. Seventy-one of the estimates were 

620 based on studies of road safety, seven on studies of air pollution, and twenty on studies of ‚general 

621 mortality‛ (presumably deaths from all, or unspecified, causes). The authors drew multiple estimates 

622 from each study, although it appears that they attempted to ensure that those estimates were from non623 overlapping subsamples. Because of the small sample size that results from this approach they use 

624 Bayesian techniques suitable for these situations. 

625 The analysis by Dekker et al. focused on explaining variation in willingness to pay for discrete 

626 changes in mortality risk reductions rather than the VSL and therefore includes as an independent 

627 variable the magnitude of the risk change associated with each estimate. They found that willingness to 
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628 pay estimates are lower when the commodity is described as a public good and that there is a premium 

629 for risk reductions from air/general context over automobile risks. 

630 Braathen et al. (2009) reviewed and conducted a meta-analysis of 75 studies with 900 estimates 

631 from developed and developing countries. The authors recorded a variety of attributes for each estimate: 

632 type of risk, country, survey mode, type of study, etc. The purpose of the study was to examine how 

633 these attributes influence the resulting VSL estimates. Using classical econometric techniques, their 

634 results show that methodological variables (i.e., type of payment questions, survey mode) explain 70 

635 percent of the variation in the estimates. Of particular relevance to EPA, the authors found that health 

636 risks are valued lower than traffic and environmental risks, in contrast to the results of Dekker et al. 

637 However, risks to individuals are valued higher than risks to the public, similar to the results of Dekker et 

638 al. (2008). The work of Braathen et al. still is preliminary and, like the Dekker et al. meta-analysis, it 

639 includes studies from both developed and developing countries. 

640 4.1.2 A new meta-analysis dataset

641 In an effort to both update the estimate or range of estimates used by EPA, we have constructed a 

642 new dataset containing information from a set of studies reflecting the current literature appropriate for 

application to U.S. environmental policy.19 643 We used EconLit, conference proceedings, published and 

644 unpublished meta-analyses, working paper series, and personal contacts to identify and generate a 

comprehensive list of stated preference mortality risk valuation studies from 1974 and later.20 645 

646 Each study was screened to ensure that it provided empirical estimates of the value of mortality 

647 risk reductions (i.e., purely theoretical studies and those that only examined morbidity were not

648 included). Following the advice from the SAB-EEAC (USEPA 2007), we established a set of selection 

 

19 There is substantial overlap between our data set and those reflected in the meta-analyses reviewed in this section. 

Differences are due to different selection criteria and new studies that have appeared since the other meta-analysis 

studies were conducted. 

20 The earliest study that forms the basis of the recommendations of the existing EPA Guidelines (2000a) was 

conducted in 1974. Therefore, we limited our search for relevant literature to this starting date, assuming that the 

earlier literature had been vetted and judged to be obsolete prior to the release of the 2000 Guidelines.
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32

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

650 information from other meta-analyses, as well as our own best judgment regarding study features 

651 necessary for application to valuing mortality risk reductions when analyzing U.S. environmental 

652 policies. The criteria we applied are as follows:

653 minimum sample size of 100,

654 sample frame based on general population,

conducted in a high-income country,21 655

656 results based on exclusive dataset,

657 written in English,

658 provides enough information to calculate a WTP estimate if one is not reported in the paper, 

provides estimates for willingness to pay (willingness to accept estimates were not included),22 659

660 and

661 provides estimates for willingness to pay for risk reductions to adults (estimates for risk 

662 reductions to children are not included). 

663 We focus on studies with a sample size of at least 100 because smaller samples tend to suffer from 

664 small sample size problems (e.g., less precision) and are less likely to be representative of the general 

665 population. Because the purpose of this exercise is to determine an estimate or range of estimates for use 

666 in environmental policy, we limit our studies to those of the general population as opposed to specialized 

667 subgroups, like students or business owners. In addition, because our focus is on U.S. environmental 

668 policy we choose to limit our studies to those conducted in high-income countries. Socio-economic and 

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

 

21 High-income countries are defined as having a gross national income per-capita of $11,906 (2008 US dollars) 

according to the World Bank reports (www.worldbank.org). The most recent World Bank data is for 2008. 

22

 Three studies report willingness to accept estimates. These studies also report WTP estimates so we do not reject 

any study based solely on this criterion. 
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33

670 transfers of value estimates. Our own language limitations required that we restrict ourselves to studies 

671 written in English. Finally, we limit our investigation to willingness to pay estimates for adults only. 

Thirty-three studies published between 1988 and 2009 672 23 meet the selection criteria described 

673 above, yielding nearly 450 willingness to pay estimates. For each of the studies we recorded all 

674 willingness to pay and value of statistical life estimates that were reported in the study, as well as those 

we could calculate based on information available in the study.24 675 The meta-analyses using stated 

676 preference studies we described earlier draw multiple estimates from each study, and each has a different 

677 way to address the fact that these estimates are almost always drawn from overlapping samples (e.g., 

678 authors report multiple results from different estimation exercises or sub-samples within their data). 

679 However, we believe that the issues associated with using multiple estimates from each study are 

sufficiently problematic to warrant selection of independent estimates from each study.25 680 Table 3 reports 

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

estimates.26 682 This exercise results in 40 independent estimates. We report select characteristics for each 

683 estimates along with the willingness to pay and standard errors (reported in $/μr). The willingness to 

684 pay for micro-risks are either directly extracted from the underlying studies (when the information was 

reported in the papers) or calculated by dividing the VSL estimates by 10-6 685 when the WTP estimates are 

686 not reported.

687 All estimates were recorded in the currency and dollar year presented in the study. If the dollar 

688 year was not noted or could not be gleaned from other information in the study then we assumed that it 

 

23 While we set a start date of 1974 for inclusion in our data set, only studies published after 1988 met our selection 

criteria. 

24

 For the most part, all possible estimates were calculated or recorded for each study. We did not, however, record 

or calculate estimates for various levels of confidence respondents had in their responses, passing/failing quizzes 

about risk, and various forms of scenario rejection. We felt that these estimates were designed mainly to test the 

validity of the survey instrument and not to produce central estimates of mortality risk valuations per se. 

25 Later we discuss in detail the various issues associated with using multiple estimates and how this can be 

addressed econometrically. 

26

 In general we opted for the estimate(s) that were the most inclusive of all the data in the study. Alternatively, we 

could select more estimates from each study – for example, by including estimates by age group – if this was 

determined to be an important dimension to the analysis. 
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34

689 was the year prior to the release or publication of the paper. All estimates are for individuals; when it 

690 was clear that an estimate reflected a household willingness to pay, we divided those estimates by the 

691 average household size for the country and year when the study was conducted. We then converted all 

692 estimates to U.S. dollars using the Purchasing Power Parity Index for the dollar year of the estimates. 

693 Next, all estimates were converted to 2009 dollars using the Consumer Price Index (CPI) and adjusted for 

694 income growth over time assuming an income elasticity of 0.5. 

695 In addition to the willingness to pay estimates and standard errors (when available), we 

696 quantified and recorded as much information as we could for each study. Our data set includes whether 

697 or not the study was published in a peer-reviewed journal, the year it was conducted and published or 

698 released, the country where the study was conducted, sample characteristics, risk reduction information 

699 (e.g., magnitude, type of risk), scope tests, public versus private risk reductions, etc. See Table 2 for a 

700 description of many of the variables in our data set. Much of this information is only available for a 

701 subset of studies, particularly information on the demographic characteristics of the sample. 

702 Twenty-two studies were published in journals, with 13 published in the Journal of Risk and 

703 Uncertainty. Six of the remaining studies are unpublished reports or working papers and five are book 

704 chapters. We identified nine different sources of mortality risk represented in the studies, including 

705 automobile accidents, air pollution, drinking water, hazardous waste sites, and food. The studies were 

706 predominantly conducted in the U.S. and Europe. Other countries represented in the data include 

707 Canada, Japan, Taiwan, and New Zealand. 

708 Most of the studies are contingent valuation studies where the choice question involves stating a 

709 response (e.g., yes/no to a dichotomous choice question, open-ended response) to a scenario with a fixed 

710 set of attributes. Several studies are choice experiments in which respondents choose one option from 

711 several in which the attributes, including the magnitude of the risk reductions and the cost, vary across 

712 the options. 
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The average sample size for the estimates is 814 observations with a range of 13 to over 2,000.27 713 

714 Most studies were conducted with a self-administered mode via web-TV or a centralized computer 

715 facility. The second most common mode is an in-person survey. Other modes represented in the data 

716 include mail, telephone, and a combination of the two. A scope test was performed or calculated for 

717 about half of the estimates, and of those about 90 percent passed a weak form of the test (i.e., willingness 

718 to pay estimates exhibited a statistically significant increase with the size of the risk reduction, but was 

719 not necessarily proportional). Fifteen percent passed a strong form of the scope test (i.e., willingness to 

720 pay was proportional or nearly proportional to the size of the risk reduction). 

721 4.2 Hedonic wage studies

722 In their recommendations to EPA, the SAB-EEAC and the Meta-Analysis workgroup clearly 

723 stated that both revealed hedonic wage and stated preference studies should be considered when 

724 deriving estimates of mortality risk values (USEPA 2006, 2007). Both groups also recommended that the 

725 two segments of the literature be analyzed separately. In this section we focus on the hedonic wage 

726 literature.

727 Hedonic pricing models use statistical methods to measure the contribution of a good’s 

728 characteristics to its price. As applied to the labor market, hedonic wage studies (also known as 

729 compensating wage studies) are based on the premise that heterogeneous goods and services can be 

730 viewed as ‚bundles‛ of attributes and are differentiated from each other by the quantity and quality of 

731 these attributes. Fatal and nonfatal risks are among the many attributes that differ across jobs. All else 

732 equal, we would expect riskier jobs to pay higher wages. Therefore, it should be possible to estimate the 

733 value associated with reduced occupational fatality risk using data on wage and risk differentials among 

 

27

 This is the sample size for the recorded estimates. Most studies used a subset of the data when recording different 

estimates (e.g., males only, younger respondents only). All studies meet the criteria of a minimum sample size of 100 

respondents. 
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36

734 jobs, controlling for other factors that might influence the wage. A standard regression equation in the 

735 hedonic wage literature is 

736

lnw p u i i i i X β , 

where 

wi

is the wage for individual i, Xi737 is a vector of explanatory variables including various 

characteristics for the individual and her job, 

pi

738 is the probability of dying on the job, and 

β

and are 

739 parameters to be estimated. If the prevailing wages are the result of a market equilibrium in which 

740 individuals have sorted themselves among jobs to optimize their individual-level trade offs between 

wages and risks, then the slope of the hedonic wage function with respect to the risk variable, 

/ w p i i

741 , 

742 will equal the individuals’ marginal willingness to swap wages for risks.

743 4.2.1 Data sources

744 Some of the principal differences between hedonic wage studies arise from the data sources used 

745 to characterize workers and the job risks they face (Bellavance et al. 2009). Since no large data sets exist 

746 that contain both worker and risk information, researchers must match observations from various 

747 sources, which requires judgments on how best to combine data that are often reported at different levels 

748 of aggregation. Most hedonic wage studies conducted in the U.S. rely on one of two datasets for 

749 information on wages, other job characteristics, and worker characteristics: the Panel Study of Income 

750 Dynamics (PSID) and the Current Population Survey (CPS). Until recently, most studies had relied on 

751 two primary sources of risk characteristics: the Bureau of Labor Statistics (BLS) Survey of Working 

752 Conditions and the National Institute of Occupational Safety and Health (NIOSH) National Traumatic 

753 Occupational Fatality Survey. The BLS data are reported as annual counts of deaths by three-digit 

754 occupation or industry while the NIOSH data provide rates of death, averaged over five years, by one755 digit occupation or industry by state. Users of these data necessarily consider risks by broad industry 
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37

756 classifications (assigning all occupations within an industry the same risk) or by broad occupational 

757 classification (ignoring potential differences within an occupation across industries). 

758 A number of recent studies, however, have turned to the Bureau of Labor Statistics’ Census of 

759 Fatal Occupational Injuries (CFOI) as the source for workplace risk characteristics. The CFOI data are 

760 considered the most comprehensive data on workplace fatalities available (Viscusi 2004), compiling 

761 detailed information since 1992 from all states and the District of Columbia. Not only are the counts of 

762 these fatal events reported by 3-digit occupation and 4-digit industry classifications, but the 

763 circumstances of the fatal events as well as other characteristics of the workers involved (e.g., age, gender, 

race) also are recorded.28 764 To ensure the veracity and completeness of the reported data, multiple sources 

765 are consulted and cross-referenced, including death certificates, workers’ compensation reports and 

766 Federal and State administration reports. To form a complete dataset for estimation, these data still must 

767 be paired with worker samples drawn from another source (often the Current Population Survey) and 

768 fatality rates still must be constructed by the researcher using estimates of the number of workers, as with 

769 the other BLS data. 

770 4.2.2 Estimation issues

771 Recently, EPA funded a study to examine the hedonic wage methodology and to provide a 

772 quantitative assessment of the robustness of the resulting value estimates for mortality risk reductions. 

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

774 Black and Kniesner (2003). These studies examined the roles of the functional form of the estimating 

775 equation, measurement error, and unobservable characteristics using various commonly used data sets. 

776 Their findings highlighted a number of potential problems with previous hedonic wage studies. First, 

777 they found that estimates of the value of risk reductions can be very sensitive to seemingly minor changes 

778 in the specification of the regression equation. In fact, many specifications lead to negative estimates, 

 

28 More information on the CFOI data is available at: http://www.bls.gov/iif/oshfat1.htm.
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38

779 which would suggest that people would be willing to accept lower wages for jobs with higher risks. They 

780 were unable to alleviate this problem using more flexible functional forms, so they concluded that this 

781 instability is not due to equation mis-specification. Instead, they found strong evidence that the job risk 

782 estimates contain considerable measurement error. 

783 Black and Kniesner (2003) examined both the BLS SWC and NIOSH data sets (the CFOI dataset 

784 had not been widely used by that time). Their results indicate that, while both datasets have advantages 

785 and disadvantages, they both also are subject to considerable measurement error. They identified three 

786 sources of measurement error in the two data sets:

787 sampling variation within industry and occupation cells given the small size of some of the cells 

788 (in recognition of this problem, BLS and NIOSH suppress data when the number of fatalities is 

789 low),

790 heterogeneity in job risks and non-random assignment of those risks within occupations (e.g., late 

791 night convenience store clerks tend to be male and older), and

792 industry and occupation are not measured accurately, especially at the three-digit level.

793 Moreover, they found that the measurement error is correlated with covariates commonly used in the 

794 wage equations and is likely correlated with the regression error as well. They concluded that studies 

795 that do not control for measurement error suffer from attenuation bias, resulting in under-estimates of 

796 mortality risk values. They also concluded that the NIOSH data produce results most consistent with 

797 economic theory.

798 4.2.3 Recent meta-analyses of hedonic wage studies

799 In addition to the methodological assessment conducted by Black and others, several meta800 analyses of the hedonic wage literature have been conducted in recent years. We focus here on four 

801 recent studies, three of which were reviewed by the Meta-analysis workgroup convened by EPA. The 

802 fourth was published after their deliberations.
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39

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

804 included in their meta-regressions were of three types: (1) those which may influence wage/risk tradeoffs 

805 (e.g., mean hourly earnings), (2) those describing the sample, and (3) methodological choices of the 

806 original researchers (e.g., if a risk-squared term was included in the estimating equation). 

807 The authors used weighted least squares where the weights were the number of estimates 

808 provided by the study. This ensured that each study was weighted equally, regardless of the number of 

809 observations drawn from it. Four meta-regression models were estimated, each using log(VSL) as the 

810 dependent variable. All four models indicated a positive and significant relationship between the mean 

811 risk and VSL. The authors used the meta-analysis results to ‚predict‛ the VSL as if the original studies 

812 had all followed a set of ‚best practice‛ assumptions. The predicted values range from $1.78 million to 

813 $15.4 million (2009 dollars). Those assuming the use of National Institute for Occupational Safety and 

814 Health (NIOSH) data are higher than those assuming use of Bureau of Labor Statistics (BLS) data. The 

815 authors concluded that the evidence best supports an estimate of $2.69 million at the average 

816 occupational risk level of 0.5 per 10,000 (2009 dollars).

817 While this study provides a comprehensive overview of the hedonic wage literature, it includes 

818 studies using older (and possibly unreliable) occupational risk data. In addition, the authors excluded 

819 estimates in original studies that were statistically insignificant or negative. 

820 Viscusi and Aldy (2003) conducted a review of more than 60 hedonic wage studies of values for 

821 mortality risk reductions across 10 countries (including 52 from the U.S.), examining a number of 

822 econometric issues, the effects of unionization on risk premiums, and the effects of age and income on 

823 VSL estimates. No studies were eliminated from the sample, and no attempt was made to modify the 

824 original VSL estimates. Point estimates extracted from each study were those based on the ‚whole 

825 sample‛ and the original authors’ preferred model specification. Viscusi and Aldy generated summary 

826 VSL estimates by using the estimated coefficients from the meta-analysis to predict the natural logarithm 
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40

827 of VSL for each original study, then study-specific predicted-VSLs were averaged to produce an overall 

828 mean estimate. Predicted U.S. mean values were constructed based on regression samples using all 

829 countries, but with averaging across U.S. studies only. The predicted values in the study for the U.S. 

830 range from $6.85 million to $9.47 million (2009 dollars), and the median predicted values were generally 

831 very close to the means. 

832 Kochi et al. (2006) used an empirical Bayes estimation method to generate predicted VSL 

833 estimates based on previous hedonic and stated preference studies. Here we focus on the analysis and 

834 results for the hedonic wage data. Using selection criteria similar to those from Viscusi (1992), the 

835 analysis included 162 VSL estimates from 31 hedonic wage studies. All possible VSL estimates and 

836 associated standard errors for each included study were re-estimated based on information provided in 

837 each original study. Estimates without standard errors were not included. The homogeneous subsetting 

838 method described earlier also was applied to the hedonic wage estimates (the hedonic and stated 

839 preference data were analyzed together), resulting in 42 VSL estimates from hedonic wage studies with a 

840 mean of $11.96 million and a standard error of $0.62 million (2009 dollars). Because of the subsetting 

841 technique employed to pool the estimates, Kochi et al. could not explicitly account for study design and 

842 population characteristics in their analysis. 

843 Bellavance et al. (2009) is the most recent meta-analysis of the hedonic wage literature. The 

844 authors’ principle objective was to better understand the variability in VSL estimates from hedonic wage 

845 studies, which is described as ranging from $0.5 to $50 million. Thirty-nine VSL estimates from 37 

846 studies were assembled based on those used in prior meta-analyses and further searches of several 

847 economics databases. The resulting dataset contains sixteen studies from the U.S., seven from Canada, 

848 and three or fewer from each of several other countries. The earliest study is from 1974 and the most 

849 recent is Viscusi (2004).
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41

850 The authors draw only one VSL estimate from each study. Standard errors were recorded or 

851 computed for 32 of the 39 estimates. Criteria were established to chose the specification within each 

852 study, including: (1) no interaction terms between the probability of death and other explanatory 

853 variables (in order to more easily compute the standard error), (2) similarity of specification to other 

854 included studies, (3) larger samples with characteristics most similar to other studies, and (4) the 

855 recommendations of authors of prior meta-analyses. Bellavance et al. acknowledged that the source for 

856 U.S. risk data varies and has evolved over time from early BLS surveys to NIOSH to BLS’ Census of Fatal 

857 Occupational Injuries (CFOI). However, their analysis did not control for the data source other than for 

858 the use of Society of Actuaries (SOA) data, which was found to have a significant impact on the estimated 

859 VSL. Sensitivity analyses were conducted with and without studies using SOA risk data. 

860 Using a mixed effects model (random intercept with fixed effects for study characteristics), the 

861 authors regressed the VSL estimates on average income, probability of death, and several study design 

862 variables. The mean weighted average VSL is approximately $7.23 million (2009 dollars). Other key 

863 findings include that the VSL is significantly higher for studies that treat risk as endogenous, and there is 

864 some evidence that the VSL declines with the baseline risk.

865 4.2.4 A new meta-analysis of hedonic wage studies

866 Using Appendix 1 from Bellevance et al. as a starting point, we constructed a new data set of 

867 hedonic wage studies, augmenting the information contained therein with data from Kochi et al. (2006)

868 and Viscusi and Aldy (2003). We also conducted a full text search in JSTOR for ‚Census of Fatal 

869 Occupational Injuries‛ and ‚CFOI‛ in order to develop a comprehensive list of studies using these data. 

870 A total of 14 CFOI studies were reviewed, with those actually using the CFOI data in an original, hedonic 

871 wage analysis retained for further assessment. These seven studies were further augmented with an 

872 unpublished manuscript using the CFOI data, for a total of eight additional studies.
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42

873 Additional searches were conducted in JSTOR for studies published in 2000 or later using the key 

874 words ‚hedonic wage‛ and ‚compensating wage.‛ We also conducted a search in the Social Science 

875 Citations Index for studies citing Viscusi (2004), a paper that derives mortality risk valuation estimates 

876 controlling for occupation and industry using the CFOI data. 

877 In constructing our data set, we generally employed the same selection criteria used in Bellavance 

878 et al. (2009), with some exceptions based on our own judgment and to ensure consistency with the criteria 

879 used for the stated preference data set. First, we limited our data to those studies with a sample size of 

880 100 or more. We also retained only those studies conducted in a high-income country as defined by the 

881 World Bank. Third, we omitted studies that rely on Society of Actuaries data as the source of risk 

882 information as these data are thought to reflect broader risks than those experienced on the job (Viscusi 

883 1992, Kochi et al. 2006). We further limited our data by excluding those studies that focus on extremely 

884 dangerous jobs (e.g., police officers), since the risk preferences of individuals who take these jobs may 

885 differ substantially from those of the general public. We do, however, apply the other selection criteria 

886 employed by Bellavance et al., including retaining only those studies using a model specification similar 

887 to that given near the beginning of this section, excluding studies based on specific causes of death, 

888 excluding studies using the same samples as other studies, and excluding studies failing to report enough 

889 information to calculate the value of mortality risk reductions and/or the average probability of death. 

890 Applying all of these criteria resulted in the selection of 37 studies.

891 For each of our selected studies we recorded the following key variables: year of publication, the 

892 country in which the sample was drawn, sample size, average income, average annual probability of 

893 death, source of risk information, the estimated coefficient on the risk variable, whether the sample was 

894 exclusively male, manufacturing, blue collar and white, as well as whether the regression controlled for 

895 nonfatal risks, union status, and worker compensation. We calculated VMRs for each study by deriving 

the VSL and dividing these estimates by 106 896 . As with our stated preference data, all estimates are 
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43

897 reported in 2009 dollars after adjusting for inflation using CPI and accounting for income growth over 

898 time assuming an income elasticity of 0.5. 

899 Similar to the stated preference data, we capture only one specification per study in our database, 

following the criteria established by Bellavance et al. 29 900 Because the hedonic studies are more 

901 homogeneous in their design than the stated preference studies, we are able to be more selective in which 

902 specifications to include. Although one motivation here is to minimize the influence of each individual 

903 study, it does not necessarily rid us entirely of the problem of overlapping subsamples as many of the 

904 studies draw their samples from the same source. 

Table 4 lists key characteristics for our selected studies.30 905 A total of 24 studies out of 37 were 

906 conducted in the U.S. with 3 using NIOSH data, 13 using BLS data and 8 using CFOI data as the source of 

907 occupational risk. Seven of these twenty-four studies rely on the Panel Study of Income Dynamics (PSID) 

908 as a source for worker characteristics with another 11 using CPS data. Twenty-six studies included 

909 women in their samples and 7 focused on blue collar workers only. Three studies restricted their samples 

910 to union members only. Average sample size across studies was 17,741, and the average income was 

911 $40,508 per year (2009 dollars). The mean probability of occupational death across studies was 0.00014.

912 5 Income Elasticity Considerations

913 EPA first attempted to address the income elasticity of VSL issue in its analysis of The Benefits and 

914 Costs of the Clean Air Act, 1990 to 2010 (US EPA, 1999), which made a distinction between application of 

915 income adjustments for longitudinal changes in income over time and cross-sectional income differences 

916 for benefit transfer. The report applied a range of VSL income elasticities in a sensitivity analysis to 

917 project the value of reduced mortality risks in the year 2010. 

 

29 Note that some hedonic studies report results for multiple non-overlapping subsamples (e.g., male vs. female, 

union vs. non-union) within the study. Rather than capture these multiple observations, we have elected to 

implement the selection criteria used by Bellavance et al.

30 Information reported in the table was adapted from Bellavance et al. (2009).
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44

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

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

920 review of the White Paper concluded: ‚With regard to population characteristics, the Committee believes 

921 that it is appropriate to adjust the value of the projected statistical lives saved in future years to reflect 

922 higher incomes in those years, but not for cross-sectional differences in income, because of the sensitivity 

of making such distinctions.‛31 923 The SAB-EEAC recommended that any appropriate adjustments for 

924 income growth should be part of the Agency’s main analysis. 

925 Based on a review of the empirical literature on the cross-sectional income elasticity of VSL 

926 literature originally developed for use in The Benefits and Costs of the Clean Air Act, 1990 to 2010 report, 

927 EPA analyses have typically applied a range of estimates with a low end of 0.08, a central value of 0.4, 

928 and a high end of 1.0. Many analyses characterize this range with a triangular distribution with a 

929 resulting mean estimate of approximately 0.48. Income elasticity is then typically paired with projections 

930 of growth in real US GDP per capita. 

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

932 of hedonic wage studies. The results in Mrozek and Taylor (2002) suggest income elasticities ranging 

933 from 0.37 to 0.49, although the authors note that these results should be interpreted with caution because 

934 of measurement error in the income variable and the functional form used by many hedonic wage studies 

935 included in their meta-analysis. As described earlier in this paper, more recent work from Viscusi and 

936 Aldy (2003) estimates the income elasticity of the VSL in the range of 0.5 to 0.6, slightly higher than the 

937 mean value used in many EPA analyses. None of the 95 percent confidence bounds on the Viscusi and 

938 Aldy estimates include a VSL income elasticity as high as 1.0. The Bellevance et al. (2009) meta-analysis, 

 

31

 ‚An SAB Report on EPA’s White Paper Valuing the Benefits of Fatal Cancer Risk Reduction,‛ US EPA, 2000, page 7. A

2007 SAB review also noted the empirical difficulties of accounting for differences in real income and wealth across 

populations due, in part, to ‚uncertainty about the value(s) of income elasticity and very little empirical evidence 

concerning the relationship between wealth and mortality valuation.‛ US EPA 2007, page D-7.
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45

939 also described earlier, predicts somewhat higher elasticity estimates ranging from 0.84 to 1.08 depending 

940 upon the model.

941 Some recent theoretical research has examined the relationship between the income elasticity of 

942 the VSL and the coefficient of relative risk aversion and noted that these two quantities should be very 

943 close in magnitude. This can be seen most easily in a simple two-period model. Let ‚lifetime‛ utility be 

the expected discounted sum of utility in both periods:

U u1 p u2

, where

t

944

u

is utility in period 

t ,

945

p

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

that 

t

946

u

depends on income in period 

t

and takes the standard ‚constant relative risk aversion‛ (CRRA) 

form:

1

1

t t

947

u y

, where is the coefficient of relative risk aversion. The VSL is the marginal rate 

948 of substitution between the individual’s first period income and her probability of survival to the second 

period, i.e., 

1

1

1 1 2

949

VSL U P U y y y

, and so the income elasticity of the VSL is

950

VSL dy1y1 VSL

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

951 for self-defensive expenditures that could increase the individual’s survival probability. Using that 

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

953 when

0 1

, and at least as large as when

1. 

954 Empirical estimates of the coefficient of relative risk aversion span a wide range—from around 

955 0.5 to 1 at the lower end (e.g., Shepard and Zeckhauser 1984, Eeckhoudt and Hammit 2001, Chetty 2006) 

956 to 10 or more at the high end (e.g., Kocherlakota 1990)—but most estimated or assumed values for 

957 seem to fall in the range of 1 to 3. For example, Hall and Jones (2008) and Hall (2010) estimated to be 

958 around 2, based on the recent trend of income growth and the more rapid growth in health care 

959 expenditures in the United States. Szpiro (1986), Feldstein and Ranguelova (2001), Barro (2006), and 

960 Layard et al. (2008), among others, also estimate or use values of in this range. And in the 
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46

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

962 Arrow 2007; Nordhaus 2008; Dasgupta 2008; Weitzman 2009, 2010a,b). 

963 The theoretical considerations combined with (most of) the empirical estimates of relative risk 

964 aversion cited above are at odds with the early estimates of the income elasticity of the VSL in the 

965 neighborhood of 0.5 cited above. In a more recent study, Kneisner et al. (2009) applied a quantile 

966 regression approach to a dataset assembled from the Panel Study of Income Dynamics (PSID) and the 

967 Census of Fatal Occupational Injuries (CFOI). Their preferred regression model produced estimates of 

968 the income elasticity of the VSL between 1.23, for the lowest quantile, to 2.24, for the highest quantile. 

969 Kneisner et al. note that ‚Our estimates of a large income elasticity of VSL are consistent with the simple 

970 theoretical models that have been developed *by Kaplow (2005)+,‛ and ‚With recent estimates of the 

971 coefficient of relative risk aversion being around 2 based on the labor supply analysis of Chetty (2006) 

972 and the consumption analysis of Kneisner and Ziliak (2002), one would expect the VSL to be income 

973 elastic, which is what the results above indicate.‛

974 Based on theoretical considerations such as those examined by Kaplow (2005) and the new 

975 empirical results of Kneisner et al. (2009), EPA believes that its recommended estimate of the income 

976 elasticity of the VSL appears to be on the low end of the range of estimates and may need to be updated 

977 to a higher value or range of values. 

978

979 6 Methods for Combining Data

980 The values for mortality risk reductions estimated in the stated preference and hedonic wage 

981 studies described above constitute a current empirical summary of the literature, which can be used to 

982 inform the revision of EPA’s mortality risk valuation guidance. These studies could be combined or 

983 synthesized in a number of ways, from a simple point estimate to range, distribution, or systematically 

984 combined in a more rigorous meta-analysis. Our objective in this section is to outline analytical options 
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985 that can be implemented in the longer term for updating the estimate or range of estimates used by EPA 

986 in our guidance on valuing morality risk reductions. We begin with meta-analysis methods, including 

987 methods similar to those used in our current guidance and extending to more rigorous application of 

988 meta-regression techniques. This is followed by the structural benefit transfer approach, which involves 

989 calibrating a direct or indirect utility function so that it is consistent with summary estimates of values for 

990 health risk. Our goal is to provide enough information on the analytical options and key issues to receive 

991 clear recommendations from the SAB-EEAC on an approach to implement for updating our guidance and 

992 on future research directions. 

993 6.1 Meta-analysis

994 There are several options for obtaining simple summary statistics or ranges from the existing 

995 data. We outline these options and key issues in order of increasing complexity. 

996 6.1.1 Parametric distribution

997 EPA’s current guidance took one best estimate from each of five stated preference and twenty998 one hedonic wage studies and then fit a parametric distribution to the values. The resulting mean and 

999 distribution has become EPA’s default estimate for valuing mortality risk reductions. To replicate this 

1000 approach we could use the databases of SP and HW studies discussed above and then separately 

1001 characterize the resulting distributions in a curve-fitting exercise. Based on these distributions we could 

1002 define a range of default values for the value of mortality risk for EPA policies. Key choices and 

1003 principles are:

1004 Use all “independent estimates” from the studies rather than one estimate per study. Because many studies 

1005 provide estimates for different subpopulations or other treatments, we can often include multiple 

1006 study estimates without gross violations of independence. An alternative is to rely upon a single 

1007 estimate per study, which has been done for several meta-analysis. 
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1008 Update all study estimates to a common year, including the effect of real income (GDP per capita) growth over 

1009 time and the estimates income elasticity of the VSL. The review of the literature in the prior section 

1010 already includes this update.

1011 Limit SP study estimates to those that are non-cancer and non-latent. In so doing, we will produce a ‚base 

1012 value‛ that should be more consistent with estimates stemming from the hedonic wage literature. 

1013 We will attempt to address any systematic difference in value between reduced cancer risks and 

1014 other types of risk separately. In part, this is simply recognizing that EPA policies affect both cancer 

1015 and non-cancer mortality risks and different values for each may be appropriate. Similarly, EPA 

1016 policies address risk reductions varying from the near-immediate to those delayed over many years, 

1017 a benefit-transfer aspect that we address by discounting over estimated latency periods. Including 

1018 latent risks in this simple aggregation would double-count the effects of timing on value. 

1019 Include public-risk studies or rely only on private-risk SP studies. Most EPA regulations result in public 

1020 risk reductions. To avoid under-counting benefits, we would want to err toward inclusion, basing 

1021 guidance on the full set of relevant studies including those that incorporate altruism even if we 

1022 cannot distinguish whether it is paternalistic or non-paternalistic. On the other hand, to avoid 

1023 double-counting of benefits we would want to use only those studies that capture private willingness 

1024 to pay for mortality risk reduction. Clear recommendations from the EEAC on this issue in particular 

1025 would be very helpful.

1026 6.1.2 Classical econometrics

1027 A second approach to combining the information from multiple studies—to determine the 

1028 characteristics of the studies that influence the value estimates or to generate a benefit transfer function—

1029 is to perform a meta-regression using classical econometrics. Two issues arise when considering this 

1030 approach. First, the analyst must decide which observations to include in the analysis. Some previous 

1031 meta-regression studies have used all relevant observations in the analysis (e.g., Nelson and Kennedy 
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1032 2008, Braathen et al. 2009, Mrozek and Taylor 2002). This approach incorporates all available 

1033 information, but runs the risk of including estimates from overlapping samples (and therefore non1034 independent observations). For example, the same individual(s) may be represented multiple times in 

1035 the data when a paper reports multiple estimates using different modeling assumptions. Restricting the 

1036 data to non-overlapping samples is a non-trivial exercise because choosing the most appropriate 

1037 estimate(s) from each study involves subjective judgment. In addition, small sample size problems—

1038 already a hurdle in meta-analysis—are exacerbated when the sample is limited in this way. The stated 

1039 preference and hedonic wage meta-analysis datasets described in Section 4 draw independent samples 

1040 based on procedures outlined above. However, a very strict interpretation of the requirement for non1041 overlapping subsamples for the hedonic wage studies could result in just a handful of estimates for use in 

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

1043 Second, there are econometric issues to consider when analyzing these data. Nelson and 

1044 Kennedy (2008) discuss ‚factual‛ versus ‚methodological heterogeneity.‛ Factual heterogeneity arises 

1045 because of real differences in what the primary studies are measuring. For example, the wtp for auto risks 

1046 may factually differ from that for cancer risks. Similarly, the wtp for occupational risks for male blue1047 collar workers may factually differ from that estimated for a more inclusive sample. Methodological 

1048 heterogeneity arises because of different study design choices, such as the use of different models to 

1049 estimate willingness to pay. When these sources of heterogeneity are unobserved, errors may be 

1050 correlated. It also is likely that estimates produced by different surveys and designed by different 

1051 authors have different variances, making heteroskedasticity a concern. Classical econometrics provides 

1052 several approaches for dealing with correlated errors and heteroskedasticity. A fixed effects model 

1053 assumes that the unobserved heterogeneity among studies can be captured with an intercept shift. By 

1054 including a dummy variable for all but one of the studies, the intercept shift is estimated directly. This 

1055 approach can result in low degrees of freedom if each study contributes a small number of estimates. An 
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1056 alternative approach that does not require a new independent variable for each study is the random 

1057 effects model. Using the ‚composite error‛ exposition of the random effects model, the estimating 

1058 equation is

,

ij ij ij

1059

y x β

where 

ij y

is WTP estimate j from study i, 

ij

1060

x

is the row of data for that estimate, and 

β

is a vector of 

coefficients. The error term 

ij

1061 has the following structure

ij i ij u

, where 

2

0,

u

u N

and 

2

1062

N 0, .

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

1064 within studies, and , which can vary within and across studies. 

1065 If heteroskedasticity also is a concern, there will be two potential violations of the classical 

1066 assumption of spherical errors. In this setting, coefficient estimates will be consistent but inefficient and 

1067 standard error estimates may be inconsistent. One solution to this problem is to estimate the model in the 

1068 traditional way but calculate standard errors that are robust to heteroskedasticity. White standard errors 

1069 are robust to heteroskedasticity (Greene 1997 p 503-505), and there is a class of robust standard errors that 

1070 imposes the panel structure on the calculation and is thus robust to correlation within clusters as well. 

1071 Statistical packages such as Stata and SAS are able to produce ‚cluster-robust‛ standard errors. 

1072 A second way to address heteroskedasticity is via weighted least squares, where the weights are 

1073 inversely proportional to the variance of the willingness to pay estimate. However, since a number of the 

1074 studies in our meta-analysis datasets do not provide standard errors of the estimates, we can use the 

1075 number of estimates drawn from a single study (assuming we draw multiple estimates per study) as a 

1076 proxy for variance. The rationale for this proxy is that studies reporting a large number of estimates are 

1077 more likely to report all possible willingness to pay estimates based on different characteristics of the 

1078 sample, versions of the survey, etc., and these estimates may be less precise than those from a study that 
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1079 presents a few, select estimates. Mrozek and Taylor (2002) used this approach, as discussed above. This 

1080 insures that each study is given equal weight, as opposed to each estimate. The sample size for each 

1081 estimate also could be used to generate weights. Observations that arise from larger samples should be 

1082 more precise, all else equal. However, sample sizes are not available for all observations in our meta1083 analysis datasets. Mrozek and Taylor (2002) used the level of significance of the VSL estimate to create a 

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

1 1

,

ij ij ij

i i

y x

n n

1085

where 

ni

is the number of estimates or sample size from the i

th 1086 study. This technique provides more 

1087 efficient estimates than unweighted estimation of the analogous model.

1088 Considering the data issues common to meta-analyses of willingness to pay estimates for 

1089 mortality risk reductions, we propose two classical approaches meant to address both heteroskedasticity 

1090 and correlated errors arising from unobserved study heterogeneity when multiple estimates are drawn 

1091 from each study. Weighted least squares estimation, as discussed above, can correct for 

1092 heteroskedasticity. However, relevant statistics may not be reported to construct the ideal weights. If 

1093 weighted least squares is used, we suggest testing for heteroskedasticity and using standard errors that 

1094 are robust to clustering. Alternatively, one could estimate a study-level panel model to account for 

1095 unobserved heterogeneity and calculate standard errors that are robust to heteroskedasticity. Since many 

1096 studies provide just a few estimates, a fixed effects model may not be feasible while a random effects 

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

1098 alternatives.

1099 6.1.3 Bayesian estimation

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

1101 estimate a meta-regression of values for reductions in mortality risks while addressing heteroskedasticity 
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1102 and correlated errors. However, if we use data sets with non-overlapping estimates—as has been 

1103 recommended by the Meta-analysis workgroup, and as is reflected in the summary of stated preference 

1104 and hedonic wage estimates in Tables 3 and 4—our data selection criteria leave us with relatively small 

1105 samples for meta-regression. The combination of small sample size and non-spherical errors presents a 

1106 particular problem for classical approaches to estimation. Specification tests, including those for 

1107 heteroskedasticity, and calculations of robust standard errors rely on asymptotic relationships and 

1108 therefore may not be reliable when the sample size is small (Moeltner and Woodward 2009). Bayesian 

1109 estimation has desirable small sample properties and can more easily accommodate general error 

1110 structures.

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

1112 used to estimate a meta-regression model to improve value estimates and provide richer inference into 

1113 the results. Koop (2003 p 124-129) presented a Bayesian pooled regression model with an error structure 

1114 general enough to be robust to correlated errors and heteroskedasticity even when the form of 

1115 heteroskedasticity is unknown. Moeltner and Woodward (2009) use this model to estimate a meta1116 regression of wetland valuation estimates from a sample of just 12 values from 9 studies. They use Gibbs 

1117 sampling to estimate the model

2

 with 0, , and ,

2 2

1118

y N IG j j j j j j x β ,

where 

j y

is WTP reported in study j , 

j

1119

x

is a row vector of population and other characteristics 

associated with study j , βis a vector of regression coefficients, 

j

1120 is a zero mean regression error with 

variance 

2

j

1121 , and IG denotes the inverse-gamma distribution. This approach allows the authors to 

estimate study-specific variances by estimating a single parameter ν and drawing 

j

1122 in a data 

1123 augmentation step. Moeltner and Woodward (2009) showed that Bayesian estimation can be used to 
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1124 conduct meta-regression on small heteroskedastic samples and produce consistent and efficient 

1125 parameter estimates.

1126 A Bayesian analogue to the study-level panel model is also developed by Koop (2003 p 149-157). 

1127 Bayesian estimation of a study-level panel model with a non-hierarchical prior is analogous to the fixed 

1128 effects model in classical econometrics because the unobserved heterogeneity between studies is 

1129 attributed to a constant (intercept shift) for each study. If the number of studies is large relative to the 

1130 number of estimates from each study then, just as would be the case under classical assumptions, the 

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

1132 hierarchical prior which places more structure on the unobserved heterogeneity by assuming the study1133 level effects can be drawn from a distribution, thus only the parameters of that distribution, and not the 

1134 individual effects themselves, need to be estimated. Bayesian estimation of a panel model with a 

1135 hierarchical prior is analogous to the classical random effects panel model. In both cases the error 

1136 structure imposed on the model is general enough to be robust to non-spherical errors due to correlation 

1137 within studies and heteroskedasticity. 

1138 6.2 Structural benefit transfer

1139 Thus far we have discussed meta-analysis, including classical and Bayesian approaches to 

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

1141 meta-regression, the form of the estimating equation, and therefore the transfer function, typically would 

1142 be based on a combination of statistical tests and qualitative theorizing about the important variables to 

1143 include in the model. The resulting function can be viewed as a low-order Taylor series approximation to 

1144 the ‚true‛ preference function within the range of the data used to estimate it. 

1145 In contrast to the meta-regression approach, structural benefit-transfer (also known as preference 

1146 calibration) involves first specifying a direct or indirect utility function for a representative individual, 

1147 then deriving analytical expressions for observable economic outcomes from the utility function (Smith et 
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54

1148 al. 2002, 2006). Such observable outcomes could include labor-leisure tradeoffs, demand for related 

1149 market commodities, equilibrium wage schedules for jobs with differing risk or other characteristics, 

1150 responses to stated preference survey questions, etc. The parameters of the utility function are calibrated 

1151 using data on such outcomes, and the calibrated model then can be used to predict willingness to pay or 

1152 accept for any policy changes that can be described by variations in one or more of the parameters that 

1153 appear in the calibrated preference function. 

1154 The key advantages of the structural benefit transfer approach are that it provides a means of 

1155 combining estimates from separate studies that use different benefit concepts (e.g., marginal or non1156 marginal willingness to pay or accept, consumer surplus, compensating or equivalent variation, etc.), and 

1157 it assures the economic consistency of transfers (Smith et al. 2002, 2006). In this context ‚economic 

1158 consistency‛ means, for example, that estimated willingness to pay will never exceed income, that value 

1159 estimates will always be responsive to scope (the size of the postulated change in quantity or quality), 

1160 that WTP and WTA will always stand in the proper relationship to each other, and so forth. The way that 

1161 such consistency is achieved is through the ex ante imposition of a specific form for the utility function, 

1162 from which all subsequent value estimates and behavioral responses are then derived. One way to think 

1163 about the contrast between meta-regression and structural benefit transfer is that the former uses 

1164 relatively more data and fewer theoretical assumptions, while the latter uses relatively fewer data (or 

1165 more highly aggregated data) and stronger theoretical assumptions. Therefore, the meta-regression 

1166 approach may give more accurate value estimates within the range of the data used to estimate the 

1167 function, while the structural benefit transfer approach may be more accurate in out-of-sample transfers. 

1168 Thus, the choice of one approach over the other may depend in part on whether the policy case(s) to be 

1169 examined fall largely within or largely outside of the range of data available for a meta-regression 

1170 transfer function.
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1171 6.2.1 Static preference functions

1172 A simplistic example may help clarify the structural benefit transfer approach. Here we follow 

1173 Smith et al. (2003, 2006) and use a static model of the tradeoff between income and survival. (In the next 

1174 sub-section we will consider a more general dynamic life-cycle model.) Assume that utility conditional 

1175 on survival is proportional to the log of scaled income, so expected utility is 

U p aY ln

, where p is the 

1176 individual’s survival probability. Using this functional form, the marginal willingness to pay for an 

1177 increase in the probability of survival is 

wtp U p U Y Y aY p / / / ln /

. Next suppose that, 

1178 based on a comprehensive review of the hedonic wage literature, wtp is estimated to be $8/μr (i.e., the 

1179 VSL is $8,000,000) for individuals with average annual income 35,000 $/yr and average annual survival 

1180 probability p = 0.984. This allows calibration of the single unknown parameter of the utility function: 

1181

ln / ln a pVSL Y Y

= 214.5, which gives a function that can be transferred to individuals with different 

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

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

1184 form, wtp is inversely proportional to the baseline survival probability (and therefore increases with the 

1185 background mortality risk) and is (nearly) proportional to income.

1186 We also can use the calibrated utility function to calculate willingness to pay for changes in 

1187 mortality risks of any magnitude, rather than relying on the first-order approximation represented by the 

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

WTP Y p aY p p a exp ln / /

. Note that 

1189 for large enough

p

’s the marginal approximation may exceed total income while the actual WTP

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

 

32 Letting 

p

go to its maximum value 

1 p

gives 

1

1 1/ p WTP Y aY

, which is necessarily less than Y. Also 

note that, in this model, 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).
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56

1191 approach: it can produce more realistic predictions of WTP well outside of the range of data used to 

1192 estimate marginal willingness to pay. (Additional numerical examples are provided in Appendix A.)

1193 Another advantage of the structural approach is that it can help to account for potential 

1194 behavioral responses. We can illustrate this by extending the simple model given above. Again 

1195 following the hedonic wage literature, suppose that wages, W, are an increasing function of job-related 

mortality risk, m. Specifically, suppose that 

W W m 0

1196 . Total income is comprised of wages plus 

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

0 0

1197

U p m a y W m ln

, where 

0

1198

p

is the background (non-job related) survival probability. Now suppose that after careful examination 

1199 of the hedonic wage literature we estimate that, for a sample of individuals of prime working age (say, 

around 40 years old), y = 5,000 $/yr, W = 30,000 $/yr, 

0

1200

p

= 0.99, m = 0.006, and 

wtp W m /

= $8/μr. So, 

for example, if = 0.5, then 

1 W m m /

6

8 / 10 / 2 / 0.006 8

1201

6.67 10

and 

W W m 0

= 

9

1202

8.6 10

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

1203 calibrate and simultaneously.) Now recall the standard assumption underlying the hedonic wage 

1204 literature that the individual has chosen her job-risk level optimally, and assume she is able to adjust that 

level to re-optimize her expected utility after a policy intervention changes 

0

1205

p

by some amount 

p

. To 

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

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

1208 and (2) the first-order condition for maximized expected utility with respect to job-risk with the policy 

1209 and a reduction in income equal to WTP. 

1210 Results from some simple numerical experiments with this model are given in Appendix A. The 

1211 main lesson from these examples is that if individuals are able to adjust their job risk level, then WTP

1212 generally will be higher and the total number of ‚statistical lives saved‛ will be lower than otherwise 
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57

1213 predicted under the assumption of no behavioral response. The numerical examples in Appendix A are 

1214 not intended to represent any specific real-world case; nevertheless, they clearly illustrate that the 

1215 structural benefit transfer approach is able to capture these effects.

1216 6.2.2 Life-cycle preference functions

1217 The structural benefit transfer function illustrated above was based on the simplifying 

1218 assumption that the representative individual looks ahead only one period at a time—that is, utility 

1219 depends only on the probability of survival to the next period and expected consumption in the next 

1220 period. A more realistic framework would account for expectations of survival and consumption in all 

1221 future periods. This brings us to the life-cycle consumption modeling approach. A life-cycle 

1222 consumption model represents consumption-versus-saving (and possibly other) choices by an individual 

1223 over the course of her lifetime. Life-cycle models are inherently dynamic, with age-specific mortality 

1224 probabilities included as key parameters. Individuals are assumed to maximize the expected present 

1225 value of discounted utility, where the expectation is conditional on the probabilities of living to all 

1226 possible future ages (e.g., Yaari 1964, Shepard and Zeckhauser 1984, Rosen 1988, Cropper and Sussman 

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

1228 USEPA 2007 p. 14-16). 

1229 A life-cycle consumption modeling framework could be used as the basis for a generalized 

1230 structural benefit transfer function. Such a transfer function would allow calculation of willingness to 

1231 pay for any marginal or non-marginal changes in the individual’s mortality profile (i.e., ‚survival curve‛) 

1232 at any point in the life cycle. As emphasized by Hammit (2007 p. 232), ‚the survival curve and how it 

1233 shifts are the fundamental concepts; the number of life-years saved and lives saved in a specified time 

1234 period are the alternative and partial summary measures of the shift.‛ The life-cycle consumption 

1235 framework is tailor-made to account for shifts in the survival curve, and it can easily account for the age 
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58

1236 and lifetime income profile of the individual and the latency and cessation lag characteristics of the 

1237 policy. 

1238 As in any structural benefit transfer application, it may be necessary to calibrate the parameters 

1239 of a life-cycle consumption model using only a few aggregate data—for example, summary statistics on 

1240 labor-leisure tradeoffs, average rates of saving over a representative individual’s life span, average 

1241 market wage differentials for more versus less risky jobs, summary results from stated preference surveys 

1242 on risk tradeoffs, etc. Thus, like other structural-benefit transfer functions, one based on the life-cycle 

1243 consumption framework would necessarily sacrifice statistical sophistication for theoretical consistency, 

1244 so many of the advantages and disadvantages of structural benefit-transfer functions discussed by Smith 

1245 et al. (2002, 2006) will apply to life-cycle models as well. 

1246 An important potential advantage of using a life-cycle consumption framework for structural 

1247 benefit transfers is that it could help to avoid the transfer errors that may arise from using a single VSL 

1248 point estimate for all varieties of mortality risk reductions. As shown in Appendix A, the life-cycle 

1249 framework allows calculation of the marginal willingness to pay at any age a for risk reductions at any 

later age b, wtpa b,1250 . VSL estimates from hedonic wage studies may be most plausibly interpreted as the 

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

age, e.g., 

wtp40,40

1252 . It may be inaccurate to use such estimates to calculate the willingness to pay for, say, a 

1253 20 year-old who will experience mortality risk reductions at ages 55 through the end of life. In contrast, a 

schedule of 

wtpa b,

1254 estimates based on a calibrated life-cycle consumption model would give a ready 

1255 means of calculating total willingness to pay for any exogenous shift in the survival curve for individuals 

1256 of any age. Furthermore, this approach can properly account for all latency and cessation lag effects 

1257 associated with the specific pattern of mortality risk changes caused by the policy, without the need for 

1258 possibly inaccurate transfers of a VSL point estimate to earlier and later ages and across individuals with 

1259 different levels of wealth and income. 
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1260 Implementing such a structural life-cycle benefit transfer function would be challenging. 

1261 Estimating or calibrating such a model would require specifying or solving for the life-cycle pattern of 

1262 consumption, and specifying a functional form for the utility function as well as calibrating or estimating 

1263 its parameters. Any structural benefit transfer approach—whether based on a life-cycle consumption 

1264 framework or something else—would represent a significant departure from the traditional point 

1265 estimate transfer approach typically used for mortality risk valuations, mainly based on the VSL. To 

1266 accelerate the development of such an approach, we recommend conducting additional case studies 

1267 applying existing structural benefit transfer functions (e.g., Smith et al. 2002, 2003, 2006) to a wider range 

1268 of illustrative policy scenarios, and additional research aimed at expanding and refining the calibration of 

1269 existing benefit transfer functions or developing new ones for potential use in future policy analyses. The 

1270 scholarly research on structural benefit transfer methods is still in an early stage, so we are especially 

1271 interested in EEAC recommendations in this area. 

1272 7 Conclusions

1273 EPA continually strives to improve the quality of its economic analyses of proposed 

1274 environmental policies. This is especially important in the area of human health valuation, in particular 

1275 the value of mortality risk reductions, since such a large fraction of the (monetized) benefits of EPA rules 

1276 are based on this category of impacts. This white paper represents the latest round of literature review 

1277 and study by EPA’s National Center for Environmental Economics on this topic, submitted to the SAB1278 EEAC for feedback. Advice from the committee will be carefully considered as EPA updates its 

1279 Guidelines for Preparing Economic Analyses.

1280 7.1 Addressing key issues: terminology, altruism, cancer valuation

1281 EPA plans to change its metric and terminology for mortality risk valuation in benefit-cost 

1282 analysis to better reflect the risk-dollar tradeoffs faced by individuals as evaluated in the economics 
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1283 literature, and risk reductions provided by environmental policies. As detailed in section 3.1.2 of this 

1284 white paper, for valuation purposes we will report changes in risk reductions valued in terms of the 

1285 value of mortality risk (VMR), scaled to micro-risk reductions. This is consistent with recent suggestions 

1286 in the economics literature and is aimed at reducing confusion about how mortality risks are evaluated in 

1287 benefit-cost analysis. 

1288 A second key issue for EPA is the valuation of cancer risk reductions and how these risks are 

1289 valued systematically differently from the more immediate risks typically considered in WTP studies. 

1290 Our review of the cancer literature, while not conclusive, suggests a ‚cancer differential‛ of roughly 50% 

1291 over immediate accidental or ‚generic‛ risk valuation estimates. We recommend including a differential 

1292 of this general magnitude as part of Agency benefits analyses for reduced cancer risks. Specific guidance 

1293 on the application of this differential will be developed by the Agency at a later date.

1294 7.2 Longer term analytical directions

1295 In the longer term, EPA plans to perform analysis to better and more rigorously synthesize the 

1296 existing mortality risk valuation literature. Two key directions include meta-analysis and structural 

1297 benefit-transfer.

1298 7.2.1 Meta-analysis

1299 Section 5.1 described simplified approaches to aggregating the existing empirical valuation data, 

1300 along with some key issues to consider in this process. These include whether to (i) use multiple 

1301 estimates from studies, (ii) update all studies to a common year accounting for real income growth, and 

1302 (iii) limit SP studies to avoid double-counting the effects of cancer risks and latency or cessation lag. The 

1303 suggested approach evaluates the RP and SP studies separately, from which EPA would develop a range 

1304 of default values for the value of mortality risk (VMR). 
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1305 Alternatively, a new addition to the discussion of mortality risk meta-analysis with the SAB1306 EEAC is the potential for Bayesian meta-regression, and we are particularly interested in the SAB-EEAC 

1307 comments on the potential advantages and disadvantages of this approach. Another key question to 

1308 consider is how the results of any meta-regression would be used to inform guidance, and the merits of 

1309 developing a statistical benefit-transfer function from these results.

1310 7.2.2 Structural Benefit Transfer

1311 An alternative to meta-regression and other largely statistical approaches to synthesizing 

1312 literature results for policy, is to impose more structure on the benefit-transfer problem and then calibrate 

1313 a preference function based on a specified utility function and data on observable outcomes. This is a 

1314 relatively new approach that has been developed and demonstrated in only a few previous studies. We 

1315 recommended conducting additional scoping studies and further research to develop structural benefit 

1316 transfer functions, possibly based on a life-cycle consumption framework, suitable for application in 

1317 benefit-cost analyses of future EPA policies. 

1318 7.3 Other research directions

1319 We see three other areas where more research would be valuable in developing guidance for 

1320 mortality risk valuation, and we welcome SAB-EEAC comment on these (as requested in the 

1321 accompanying charge questions).

1322 First, additional applied research on the altruistic components of WTP for public risk reductions 

1323 would be a valuable contribution, potentially allowing EPA to rigorously include theoretically1324 appropriate altruistic values and better reflect the public value of environmental policies. We 

1325 acknowledge that this is a difficult task. The economics literature on the proper treatment of altruism in 

1326 benefit-cost analysis is well-developed, enumerating the conditions under which it is appropriate to 

1327 include altruistic values in evaluating the benefits of public programs. EPA programs are inherently 
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1328 public and ideally should include paternalistic altruism. However, while the empirical literature has 

1329 been able to capture some altruistic values for public risk reductions, it has not generally been able to 

1330 distinguish among types of altruism sufficiently well for the values to be included neatly in applied 

1331 analysis. 

1332 Second, more and more research reflects the general understanding that value of reducing 

1333 mortality risks is not ‚one-size-fits-all.‛ Rather, these values are heterogeneous, or ‚individuated,‛ and 

1334 depend upon a wide array of individual and risk characteristics. More detailed research in this area also 

1335 will provide data needed for developing more general and more accurate benefit-transfer functions.

1336 Third and finally, most of the valuation literature, and many theoretical frameworks, have 

1337 treated mortality and morbidity risks separately, focusing on just one of these endpoints at a time. 

1338 However, some recent work also suggests that changes in health risks may be best framed as changes in 

1339 health risk profiles that include both mortality and morbidity. Individuals may value different 

1340 combinations of changes in risk or illness and risk of death in complex ways. Systematic empirical work 

1341 to evaluate these relationships could lead to much more robust and complete benefits analysis. 
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1342 References

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1680 Yaari ME. 1964. On the consumer’s lifetime allocation process. International Economic Review 5(3):304-317.

1681 Zhang J, Adamowicz W, Krupnick A, Dupont D. 2009. The role of altruism in the valuation of community 

1682 drinking water risks. Working Paper. 
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Tables and figures

Table 1: Cancer Valuation Literature Summary

Study Timing Treatment of 

Morbidity

Dread Risk context and 

characteristics

Affected 

Pop.

Other health 

effects

Findings / Notes

Hammitt & 

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 fatality

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‛ designation 

effect persists after 

controlling for other risk 

characteristics. 
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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)

Premium for public 

programs

Any premium for 

reduced children’s risk is 

modest (small for cancer 

risks, larger for other 

causes).

Adamowicz et al. 

(2008)

CVM and CE

Risks described 

as community 

deaths over a 35-

year time period 

for microbials 

and carcinogens

Symptoms 

described for 

microbial illness 

and for bladder 

cancer

Not addressed Risk reductions are 

strictly public

Describes tradeoffs 

between reduced 

microbials in DW and 

reduced carcinogens 

Households 

(Canada)

Microbial illness

Microbial fatality

Bladder cancer

- fatal

- nonfatal

Modest cancer 

‚discount‛ (for 

mortality)

Cancer VSL = 

.85*Microbial VSL

Cancer illness = 20-50% 

of cancer mortality

Cameron & 

DeShazo (2008)

Choice experiment

Illness profile 

over specific, 

varying times 

Results support 

lower values for 

longer latency.

No implicit 

Health states 

defined as:

- Current health

- Sickness

- Remission years

- Lost life-years

Illness characterized 

Not addressed Intervention is 

generally a screening 

and treatment 

program to prevent 

the given risk profile.

For auto accidents it is 

a safety program.

Adults 12 major common 

risks, including:

Heart disease, 

heart attack, 

stroke, respiratory 

disease, diabetes, 

Alzheimer’s

Difficult to draw general 

conclusions.

Heart attacks & heart 

disease risks valued 

similarly to some cancers 

(and more than others). 
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76

discount rate 

estimated.

by length and 

severity (pain, 

disability)

Cancer (5 types)

Auto accidents

Tsuge et al. (2005)

Choice experiment

Latency periods 

of 0, 5, 10 years

Implied discount 

rate = 20% 

Unclear, but does 

not appear to be 

detailed. 

Focus is on 

mortality.

Subjective 

perceptions of 

voluntariness, 

controllability, 

dread(pain), 

dread(fear), 

severity, 

exposure

-- Adults 

(Japan) Accidents

Generalized 

cancer

Heart disease

Non-specific

Unique formulation of 

‚quantity-based‛ VSL 

distinguishing WTP for 

opportunities for risk 

reduction 

Depends on model 

specifications, but 

perhaps 20% differential 

over ‚general‛ risks; 

reduced cancer risks 

preferred to reduced 

heart attack risk; 

Hammitt & Liu 

(2004)

CVM

Latent: 20 years 

to onset of 

symptoms

Acute: symptoms 

‚within a few 

months‛

Implied discount 

rates of 1.5% 

(with up to 3% 

plausible)

brief description of 

symptoms

progressive severity 

over time from mild 

to bedridden and 

unable to care for 

themselves

lasting 2-3 years 

before mortality

Not addressed 

directly

All symptoms held the 

same except for 

‚cancer‛ designation: 

Lung cancer v. 

bronchitis (from 

pollution from 

factories)

Liver cancer v. liver 

failure (from drinking 

water contaminants)

Adults 

(Taiwan)

Liver (failure v. 

cancer)

Lung (bronchitis 

v. cancer)

~30% differential for 

cancer relative to 

identical non-cancer 

degenerative disease 

(marginal significance)

Environmental context.

No ‚trauma‛ or 

‚accident‛ alternative for 

comparison. 

Philips et al. (1989) No No No No Adults 

(U.K.)

Motor vehicles

Heart disease

Fatal & Nonfatal

Mean estimates higher 

for cancer; median 

estimates are not

The following two studies are risk-risk studies

Van Houtven et al. 

(2008)

Latency periods 

of 5, 15, 25-year 

periods specified

Symptoms 

described for three 

types of cancer; 

Not treated 

separately

Organ-specific cancer 

risks vs. auto-accident 

risks.

Adults Fatal cancer 

(stomach, liver, 

brain);

Significant cancer 

differential (3x over auto 

accidents at 5-year 
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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 nonfatal lymphoma and 

nerve disease

Respondents told not 

to consider out of 

pocket medical costs

Adults Fatal lymphoma,

non-fatal 

lymphoma; 

fatal auto 

accidents

nerve disease

No evidence of 

differential for cancer 

fatality (ratio of fatal 

cancer: fatal auto is 1:1.) 

Ratio of non-fatal cancer 

to auto is ~.58. 

The following studies examine cancer only (without comparison to other risks)

Carson & Mitchell 

(2006)

Open-ended CVM

Not in survey; 

VSL estimates 

assume 25 years

No No Public/social decision

Cancer risks from 

THM in drinking 

water

Adults 

(Household?

)

No Cancer VSL depends 

upon assumptions about 

latency and discount 

rate. Also sensitive to 

risk reduction.

Assuming 0.4/100,000 

reduction, 25-yr latency, 

results range from

$3.4m at 3% to

$8.8m at 7%

Alberini et al. 

(2010)

0, 2, 5, 10 years

Employed a zero 

discount rate for 

estimation based 

on prior work

Extent unclear Unclear Cancer risks from 

hazardous waste in 

Italy

Adults Fatal Cancer (type 

unspecified)

New estimates of the 

cancer VSL using data 

from 2008 survey in 

Milan

Cancer VSL of ~$5.6m
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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 nonAdults No Hedonic property with $6.0m Value of statistical 
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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 

million
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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)

PUBLIC 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 conducted

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 reduction
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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 reduction
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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) 0.48
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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 for 5 years and then dies; estimate is chosen because it most 

closely matches many EPA policy scenarios (Table 3 in paper)

(8) based on corrected mean for the smallest risk reduction (Table 19.2 in paper) (note: We could also obtain other independent estimates for 

different risk reductions)

(9) from a model with co-variates for the smaller risk reduction using dots for a visual aid (Table 3 in paper)

(10) based on the full sample

(11) based on median (mean not reported) for the smallest risk reduction (Table 5 and 7 in paper)

(12) based on model of WTP for reductions in risk to self, which is based on median WTP, one year latency and cancer set to 0.5 and affected 

organs set to 0.25 (options are brain, bladder, liver and lymphocytes) (Table 2 in paper)

(13) based on latent lung cancer from model with full set of co-variates (Table 3 in paper)

(14) based on private risk reduction (there is also an estimate for a public risk reduction, but they are not independent)
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(15) only estimate in paper; reflects the idea that wtp is independent of the source of risk; CE asks about cancer, accidents, heart disease, over 

different latency periods

(16) based on pooled model (Table 5 in paper)

(17) based on smaller risk reduction with no latency from wave 2 (where smaller risk reduction was presented first (Table 7 in paper)

(18) based on standard estimates (Table 2 in paper)

(19) based on mean estimate for risk reduction provided through an air bag (assumed to be a private risk reduction) using the maximum WTP 

results (Table 2 in paper)

(20) based on WTP for vaccine at age 60 (Table 3 in paper)

(21) based on WTP for a safer car (Table 3 in paper)

(22) based on WTP for private reductions in risk from environmental causes (Table 10 in paper)

(23) based on WTP for private cancer risk reductions assuming no treatment or purchase of bottled water (Table 9 in paper)
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Table 4: Hedonic Wage dataset

Study Country Sample

Sample 

Size

Sample 

Characteristics

Risk Variable

Mean 

Risk

Nonfatal 

Risk 

Included 

(1=Yes)

Workers' 

Comp 

Included? 

(1=Yes)

WTP

UnionWhiteMaleManual/Mfg

(2009$) SE

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 3.47
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Study Country Sample

Sample 

Size

Sample 

Characteristics

Risk Variable

Mean 

Risk

Nonfatal 

Risk 

Included 

(1=Yes)

Workers' 

Comp 

Included? 

(1=Yes)

WTP

(2009$) SE

UnionWhiteMaleManual/MfgBlue 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 1.34
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Study Country Sample

Sample 

Size

Sample 

Characteristics

Risk Variable

Mean 

Risk

Nonfatal 

Risk 

Included 

(1=Yes)

Workers' 

Comp 

Included? 

(1=Yes)

WTP

(2009$) SE

UnionWhiteMaleManual/MfgBlue 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 8.82
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Study Country Sample

Sample 

Size

Sample 

Characteristics

Risk Variable

Mean 

Risk

Nonfatal 

Risk 

Included 

(1=Yes)

Workers' 

Comp 

Included? 

(1=Yes)

WTP

(2009$) SE

UnionWhiteMaleManual/MfgBlue 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 4.895E-05 1 0 6.16 1.89
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Appendix A

This appendix gives some illustrative numerical examples using the simple static (single-period) 

structural benefit transfer function from Section 5.2.1, and a more formal exposition of the life-cycle 

modeling framework discussed in Section 5.2.2. Table B1 shows willingness to pay values for a range of 

mortality risk reductions using the static model in Section 5.2.1. The first three columns in the table show 

the difference between the marginal approximation and the exact WTP [$] for a range of changes in 

baseline risks 

p

[

1

yr

]. The final six columns in the table show WTP [$] and 

**

m

[yr-1] (explained 

below) for a range of 

p

’s and three possible values of , accounting for the behavioral response 

described in Section 5.2.1. To determine the maximum willingness to pay for an exogenous change in 

background mortality risks, we must solve the two-equation system comprised of the equality between 

expected utility with and without the policy, 

* * ** **

0 0 0 0 p m a y W m p p m a y W m WTP ln ln , 

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., 

** 1   ** 

0 0 0 m p p m y W m WTP a y W m WTP / ln 0 , 

where 

**

m

is the job-risk level that the individual would choose if her baseline survival probability were 

increased by 

p

and if she were charged the amount WTP for this change. The level of m that she would 

actually choose after the policy is implemented would depend on the actual cost of the policy to her. 

The main lesson from these examples is that—when preferences for consumption and risk are not 

separable, as in this example—if individuals are able to freely adjust their job risk level, then WTP

generally will be higher and the total number of ‚statistical lives saved‛ will be lower than otherwise 

predicted under the assumption of no behavioral response. In fact, if = 1 and if each individual were 
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charged their maximum WTP for the change, then the individuals’ behavioral responses would fully 

offset the changes in their baseline mortality risk. In this extreme case, WTP would exactly equal 

wtp p

and, if each individual had to pay this full amount to fund the policy, then the number of ‚lives 

saved‛ would be zero. If the full costs of the policy were less than the aggregate WTP, then both the net 

social benefits and the number of statistical lives saved would be positive, though the latter still would be 

less than 

p N

. If the full costs of the policy were greater than the aggregate WTP, then of course the 

net social benefits would be negative, but also note that the number of statistical lives ‚saved‛ would be 

negative as well—that is, even though environmental risks were reduced, the policy would increase

overall mortality rates since people’s behavioral responses to the increased costs would involve shifting 

to jobs with higher mortality risks. The numerical results in Table B1 are not necessarily intended to be 

realistic, especially considering that they involve mortality risk reductions that are much larger than 

those we would typically expect from most environmental regulations, but they nevertheless highlight 

the importance of calculating benefits and costs simultaneously for non-marginal policies when 

behavioral adjustments are expected.

Next, a brief exposition of a generalized life-cycle (multi-period) model may help to describe the 

potential usefulness of this framework as a basis for structural benefit transfers of mortality risk 

reductions. Suppose that the value function for a representative individual is given by 

,

, ,

T

t a

a t t a t

t a

V u c h t s e

, where 

, , t t u c h t

is utility in period t (assumed here to depend on 

consumption 

t

c

, health status 

t

h

, and possibly age t), 

s

is the probability of surviving to the beginning 

of age 

1

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

,

t

a t a

s s

, 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 

,

/

/

a a b

a b

b a a

dc V s

wtp

ds V c

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

at some future age t = b, 

1

, ,

, , , ,

b T

t a t a

a t t a t t t a t

t a t b

V u c h t s e u c h t s e

, then re-write second term 

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

1

, ,

, ,

b

t a b a

a t t a t b a b

t a

V u c h t s e V s e

, which means 

, 1

b a a

b a b

b

V

V s e

s

.

33

 Thus, the marginal 

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

, 1

,

, , /

b a

b a b

a b

a a a

V s e

wtp

u c h a c

.

34

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

discounted by the survival probability and the pure rate of time preference between ages a and b, and 

then monetized by the marginal utility of consumption at age a. 

Developing a usable structural benefit-transfer function based on a lifecycle framework would be 

challenging. Estimating or calibrating such a model would require specifying or solving for the life-cycle 

pattern of consumption, calibrating or estimating the pure rate of time preference, and specifying a 

 

33 Throughout this section we treat the path of consumption over the life cycle as exogenous; that is, we ignore any 

behavioral responses to changes in mortality risks that would adjust the levels of consumption in future periods. 

This simplification will be strictly valid only under some special conditions—namely, that that the individual can 

never be a net borrower (Cropper and Sussman 1990, USEPA 2007 p D-15)—but it should provide a close 

approximation for small changes in exogenous mortality risks. More specifically, we would expect it to provide a 

close lower bound on willingness to pay in most cases of interest—a lower bound because it assumes that the 

individual is constrained to maintain the same consumption path after the change, and a close approximation 

because we would expected any adjustments in future consumption levels to be very small for reasonably small 

changes in mortality risks.

34 Direct inspection of this equation suggests some simple comparative static results: (1)

wtpa b,

decreases with the 

latency period 

b a

because all elements of the numerator— Vb 1, 

ab, 1 s

, and 

b a

e —decrease and the denominator 

does not change. (2) 

wtpa a,

could increase or decrease with a because, while 

V

a 1

and 

aa, 1 s

decrease with a, the 

denominator could decrease or increase with a depending on the pattern of consumption and health status over the 

life cycle (USEPA 2007 p D-16). If the pattern of consumption were perfectly flat over the life cycle, and if utility 

depended only on consumption and not health status or age per se, then 

wtpa a,

would unambiguously decrease with 

age. However, observed consumption patterns generally are not flat; consumption typically is low in the early 

(adult) years, high in middle age, and lower again in later years, which, all else equal, would tend to increase then 

decrease 

wtpa a,

.
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functional form for the period utility function 

, , t t u c h t

and calibrating or estimating its parameters. 

The simplest reasonable implementation of such an approach might proceed as follows:

1.) Specify the lifetime pattern of consumption for a ‚representative‛ individual as the pattern of 

average consumption levels for a random sample of individuals of various ages from the population 

of interest. Alternatively, multiple representative life-cycle consumption patterns could be generated 

based on average consumption levels for sub-samples of the population, e.g., by gender, race, 

geographic region, etc., as appropriate for the exposed sub-population relevant for the policy to be 

examined.

2.) Set 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: 

1 1 / 1 t t u c d

. 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 pay for well-specified mortality risk changes from the revealed or stated 

preference literature to calibrate d, or

b. use at least two valid estimates of marginal willingness to pay from the RP or SP literature to 

calibrate and d simultaneously. 

Such a calibrated life-cycle model then could be used to calculate 

wtpa b,

for all combinations of a and b

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

pattern of mortality risk changes that are projected for one or more policies under consideration. More 

sophisticated versions of this approach could specify 

t

u

as a function of age and/or health status, which 

might facilitate a link to the QALY literature. 
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Table A1. Maximum willingness to pay for a range of changes in survival probabilities, 

p

, based on a 

marginal approximation (

wtp p

) and direct calculation (

WTP

), with and without a behavioral 

response. Baseline job risk is m = 0.006. Estimates of the adjusted job risk with a behavioral response (

**

m

) assume that the individual’s income is simultaneously reduced by WTP (that is, expected utility 

without the policy is equal to that with the policy combined with the charge WTP).

No behavioral 

response

With behavioral response

0.33 0.67 1

p [yr1

]

wtp p

[$]

WTP

[$]

WTP

[$]

**

m [yr1

]

WTP

[$]

**

m [yr1

]

WTP

[$]

**

m [yr1

]

0.000005 40.0 25.0 40.0 0.0060034 400 0.0060040 40.0 0.0060050

0.00005 400.0 397.7 399.2 0.0060337 399.6 0.0060404 400.0 0.0060500

0.0005 4,000.0 3,778.1 3,926.6 0.0063399 3,956.7 0.0064062 4,000.0 0.0065000

0.005 40,000.0 23,773.6 33,977.6 0.0096250 36,431.3 0.0102351 40,000.0 0.0110000
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