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OAR Box 1846 

Prepped by Ollie Stewart 

Document Number: 

81) IV-A-3 

Docket Number: 

A-90-07 

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INDUSTRIAL KPNOVUCS INCJORPORATED 

2067 Massachusetts Avenua Cambridge Massachusetts 02140 Tstophpne: 817/354-0074 Teiecopta: si 7/354-0463 

MEMORANDUM 

6 November 1992 

9 8111 1 ts 

UJ MAY 2 61994 \3 

EPA AIR DOCKET 

TO: 

FROM: 

Jim DeMocker 

Office of Policy Analysis and Review 

Office of Air and Radiation 

U.S. Environmental Protection Agency 

Bob Unsworth, Jim Neumann, and W. Eric Browne 

Industrial Economics, Incorporated 

SUBJECT: Review of Existing Value of Life Estimates: Valuation Document 

INTRODUCTION 

This memorandum summarizes our review of existing estimates for the value of a statistical 

life. This memorandum is intended to serve as an initial step in generating value of life estimates 

for application to the dean Air Act Section 812 analysis. Additional research will be performed 

and tbe conclusions modified in response to comments received. The goals of this effort are: (1) 

to summarize existing benefit estimates which may be appropriate for placing values on the types 

of mortality risks generally attributed to air pollution; (2) to identify factors that could cause these 

existing estimates to be biased; and, (3) where possible, to identify quantitative estimates of the 

magnitude of these biases. 

Summary of Rsaritt 

We reviewed three existing surveys of the value of life literature: Viscusi (1992), Miller 

(1990), and Fisher et aL (1989). Each of these surveys evaluates three types;, of value of life 

estimates: wage-risk studies, which estimate the additional compensation individuals demand in the 

labor market for taking riskier jobs; contingent valuation studies, in which individuals are asked to 

state their willingness-to-pay to avoid additional increments of statistical mortality risk; and 

consumer behavior studies, which examine market situations other than the labor market that involve 

a risk-dollar tradeoff (e.g., the market for smoke detectors). Our analysis and conclusions are based 

primarily on a review of tiiese summaries. Note that no effort has been made to obtain or analyze 

primary data from the underlying studies. 

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We base most of our conclusions and recommendations on the results of Viscusi. This 

survey represents the most recent effort to summarize tbe value of life literature and proposes a 

range of broadly applicable values rather than a point estimate. Based on an analysis of Viscusi's 

results, we conclude that the value of a statistical life can be roughly characterized by a lognormal 

distribution. We use Viscusi's survey results to determine the parameters of this distribution. The 

26 estimates he finds most applicable to policy analysis have a mean value of $4.8 million, a 

geometric mean of $3.6 million, a median of $3.8 million, a standard deviation of $3.2 million, and 

a geometric standard deviation of $23 million (1990 dollars). The geometric mean and geometric 

standard deviation are sufficient to characterize our suggested lognormal distribution. These results 

are summarized in Exhibit 1. 

The underlying valuation studies used to construct this proposed range reflect a variety of 

risks to human health other than those posed by air pollution. Most are based on risk-dollar 

tradeoffs observed in the labor market Since the characteristics and incidence of mortality risk 

considered in these studies may differ significantly from those posed by air pollution, these existing 

studies may provide a biased estimate of the true willingness-to-pay to control mortality risks 

associated with air pollution. Based on a review of the literature, we have identified three major 

sources of bias that should be considered in assigning a distribution to the value of a statistical life 

for use in the Section 812 study risk perception, age, and income. We recommend that the mortality 

risk benefit distribution given above be tested for sensitivity to tiiese biases. We propose 

quantitative methods to conduct sensitivity tests for differences in age and income, and provide an 

illustrative calculation based on a hypothetical mortality risk scenario. These proposed adjustment 

methods are sufficiently uncertain, however, that we do not propose their use in adjusting the 

primary benefits estimate without further refinement 

Neff Steps. 

This memorandum provides an important starting point for valuing mortality risk reduction 

for the Section 812 analysis. We suggest that our proposed methodology, including the primary 

value of life estimate and quantitative sensitivity analyses, be applied to the actual mortality risk 

estimates generated as part of the Section 812 study. The results of this application should then be 

critically assessed to determine if additional research or refinement of adjustment methods is called 

for. 

Outline of the Memorandum 

The remainder of this memorandum is organized into three parts. First, we summarize 

issues raised in the recent literature regarding the value of a statistical life. Second; we summarize 

the results of three recent surveys of this literature, and based on this literature review, propose an 

estimate of the value of hfe, expressed as a probability distribution. Third, we present a discussion 

of biases that may result from the application of these values to estimate the economic benefits of 

reductions in air pollution induced mortality risks and present an illustrative sensitivity analysis 

showing the potential impact of these biases. 

MX5TOAL KENOMICS NCORPCRATK) 

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Exhibit 1 

cn 

cn 

01 

o *. 

I 

o 

cn 

I 

o *. 

cn 

t) 

s 

o 

o 

Observed Distribution of Estimates 

Derived from Viscusi (1992) 

Mean Value: $4.8 million 

Standard Deviation: $3.2 million 

Geometric Mean: $3.6 million 

« 

Geom. Std. Dev.: $2.3 million 

n= 26 (5 CV, 21 labor market) 

. , , , , 

7-8 8-9 9-10 10-1111-12 12-13 13-14 

"TJ 

Range of Estimates (million 1990$) 
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RISK-DOLLAR TRADEOFF ESTIMATION ISSUES 

ADDRESSED IN EXISTING SURVEYS OF THE LITERATURE 

Most studies that estimate the value of a statistical life acknowledge that the difficulties in 

measuring a risk-dollar tradeoff are fonnidable. The estimation of the value of a life involves 

inference about individuals' implicit tradeoff of mortality risk for monetary compensation. Analysts 

encounter uncertainties not only in isolating the amount of compensation a person receives for 

assuming mortality risk, but also in estimating the actual and perceived increment in mortality risk 

that is implied by the transaction.1 This section provides a discussion of these issues and 

uncertainties. In addition, we describe how these issues are addressed in three recent surveys of the 

value of life literature (Fisher et aL 1989, Miller 1990, and Viscusi 1992). 

Three methods are used to estimate the value of a statistical life: (1) those based on 

analyses of tabor market data (Le, wage risk studies); (2) those based on analyses of product 

markets and co^&umer behavior, and (3) those based on direct questioning of individuals to 

determine their willingness to pay to avoid mortality risks (i.e., contingent valuation studies). Some 

of the factors that introduce uncertainty into these value of life estimates are specific to wage-risk 

studies. Others involve risk estimation assumptions or difficulties in contingent valuation. Finally, 

bias may be introduced by limiting the value of life estimate to an individual's value of own life, 

without considering that people are willing to pay to reduce risks posed to family, friends, and other 

persons (Le., altruism). 

ftiVF ffimjpe to WapsRisk Studio 

Most value of life studies reported in the literature apply a wage-risk framework. These 

studies estimate the additional compensation an individual receives to accept a riskier job. There 

are three issues to consider when evaluating wage-risk studies. First, it is imperative that the study 

differentiate between job-related risks, other unpleasant job characteristics, and risks associated with 

lifestyle in order to obtain an unbiased wage-risk estimate. Isolation of job-related risk is one 

criteria used to evaluate studies in the three literature surveys we reviewed 

1

 Some analysts have chosen to account for these inherent biases through quantitative 

adjustment. For example, Miller (1990) divides labor market estimates based on National Institute 

of Occupational Safety and Health (NIOSH) occupational risk data by a factor of three to adjust 

for differences in estimates based on NIOSH and U.S. Bureau of Labor Statistics (BLS) data. 

Viscusi (1992), however, argues that there is greater random measurement error associated with the 

BLS data, which may explain these differences. Viscusi further argues that systematic differences 

in the reporting of the two sets of data imply it is incorrect to transform NIOSH data into BLS data 

through the use of a constant multiplicative scale factor (Viscusi, 1992, p.57). Given the lack of 

consensus on adjustment factors for these types of potential biases, we conclude that using 

adjustment factors of the type MiHer advocates is less defensible than applying a broad range of 

values to incorporate the uncertainty inherent in the underlying estimation procedures into the 

Section 812 analysis. 

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Second, wage-risk studies assume a perfect labor market; this approach will not produce 

accurate wage-risk estimates under conditions of an imperfect market in which workers are not free 

to move between jobs or in which only union members have sufficient market power to receive 

higher wages Cor higher risk jobs. All three surveys consider this second factor, but do not adjust 

for iL 

Third, most wage-risk studies rely on wage data for manual labor to obtain a significant risk 

coefficient. Gegax et al. (198S) argue that lack of variation in the risks associated with white-collar 

jobs could cause estimates of non-manual workers' risk premiums to be less robust Using 

contingent valuation methods, Gegax et ai obtain a value of life for white-collar workers similar to 

that obtained by the bulk of wage-risk studies based on manual laborers' data. Because of this 

similarity, Fisher et al. (1989) do not adjust wage-risk estimates for a manuai/noo-manual labor 

factor. Although he does not address this issue directly, Viscusi (1992) proposes that any bias which 

may be created by this factor will be eliminated through adjustment of the results based oo 

comparison of the income of the sample group relative to that of the general population. Although 

it is likely that some degree of bias is introduced by these three factors, the overall direction and 

magnitude of the bias is unknown. 

Pidf F^rimatinn AMimppona 

Both wage-risk and contingent value methods assume that members of the study population 

understand the nature of the risk being faced or considered. Thus, the degree of risk 

communication is one factor that must be considered. If a labor market study is to obtain an 

unbiased wage-risk premium, workers' perception of risk levels across jobs must match actual risk 

levels. Otherwise, workers' risk compensation requirements will not properly reflect relative risk 

levels. Fisher et al. (1989) believe this potential bias to be small, citing a study by Viscusi and 

O'Connor (1984) that found chemical workers' risk perceptions to be similar to objective measures 

of on-the-job risk.1 In contrast Miller (1990) cites a study by Lichtenstein et al. (1978), which 

found that workers underestimate the risk of on-the-job injuries by about 20 percent Miller uses 

this estimate as a basis to adjust value of life estimates computed from actual risk data upwards. 

Problems in risk communication can also be a potential source of bias in contingent valuation 

surveys. Viscusi and Magat (1987) found evidence that respondents tend to misunderstand lowprobability risks. If a respondent to a contingent valuation survey cannot differentiate between 

changes in the relative degree of risk (e.&, an increased risk of 1 death per 1,000,000 exposed 

population versus 1 death per 100,000 exposed population), the resulting value of life estimate may 

be distorted by as much as an order of magnitude. Fisher etal, Miller, and Viscusi all consider the 

use of extensive risk characterization and consistency checks in contingent valuation surveys as a 

qualitative criteria for the degree of credibility assigned to the reported estimates. 

3

 It is possible that workers in the chemicals industry are more well informed about the 

magnitude and nature of the risks they face. Note that non-fatal, non-cancer occupational risks for 

SIC 28 are slightly higher than the average for all industry (57 versus 37 annual incidents per 10,000 

workers) (U.S. Department of Labor 1991). 

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In addition to errors associated with poor communication of risk, the baseline level of risk 

in the sample populations is a potential source of bias in all value of life studies. Blomquist (1981) 

found that people at a higher level of baseline risk place greater value on the same degree of risk 

reduction. If this is the case, a study based on a sample of individuals exposed to a smaller baseline 

risk will produce a lower value of lite estimate than a study based on a sample of individuals exposed 

to higher levels of baseline risk. Fisher et al appear to ascribe to this theory. They point out that 

their survey includes studies that consider risks between 1 and 10 annual deaths per 10,000 exposed 

population. Fisher et al. state that their selected range for the statistical value of life is probably not 

applicable for evaluating the benefits of reducing risks with baseline levels well outside this range, 

especially categories of risk that are much larger. Miller, on the other hand, found no relationship 

between the value of risk reduction and the baseline level of risk. Although current value of life 

estimates may contain some systematic bias related to baseline risk level, there is insufficient 

information in the literature to adjust for this bias. 

Issues related to economic valuation could affect the magnitude of the value of life estimates 

reported in the literature. For example, Miller (1990) considers the inconsistent treatment of taxes 

in the literature. Many labor market studies analyze before-tax wages, while other market-based and 

contingent value studies analyze expenditures of after-tax dollars. After-tax wages are considered 

by most economists to be the appropriate measure, i.e., that individuals derive no utility from 

marginal taxes paid. Miller multiplies estimates based on before-tax wage rates by an adjustment 

factor of 1.35. Fisher et al. (1989) consider the use of wage rates as opposed to total compensation. 

They conclude that, while wage rates ignore the effect of taxes on take-home pay, the use of wage 

differentials and a sample of individuals in similar tax brackets ensures that any upward bias 

introduced by this factor is small. A third factor involves ex post benefit accounting. Ex post benefit 

accounting takes into account worker's compensation and other benefits that might affect worker 

job choice. Viscusi (1992) notes that several studies include a worker's compensation measure as 

supplementary compensation for job risks to account for the role that this factor may have as a job 

choice criteria. For example, life insurance provided as part of a compensation package could 

reflect a risk premium. Incorporation of this factor into all of the value of life estimates reported 

in the literature would require efforts beyond the scope of this report (i.e., such accounting would 

require analysis of the primary data from these studies). 

A particularly difficult question concerns the extent to which current value of life estimates 

include compensation for non-fatal risks. Fisher et al. observe that most- studies do not treat nonfatal risks as part ofthe wage-risk premium. Although workers' compensation probably covers some 

portion of non-fatal risk, some error in the estimation of fatal risk may still result from this factor. 

Miller states that 55 to 80 percent of tbe wagcrisk premiums paid in five studies he surveyed were 

to reduce non-fatal risks, He goes on to propose and apply an adjustment facton-for this effect 

Miller, however, did not consider the effect of workers compensation, health insurance, or life 

insurance as benefits. Viscusi includes fatality risk, workers' compensation, and/or the implicit value 

of injury as categories in his summary iable, but docs not attempt to adjust for these factors. 

Treatment of non-fatal risks in each study serves as a qualitative criteria in Viscusi's selection of 

estimates for use in developing his recommended range for the statistical value of a life. The overall 

direction and magnitude of bias introduced by these factors is unknown. 

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Altruism 

A final factor to consider when estimating the statistical value of a life is the presence of 

altruism. The existing literature focuses on individual risk tradeoffs, but there is substantial evidence 

that people are willing to pay to reduce risks posed to others (i.e., people lose utility when someone 

else is put at risk of dying). In a study that included willingness to pay to reduce others' risk of 

illness from insecticides, Viscusi, Magat, and Forrest (1988) found evidence of significant altruistic 

values. In addition, Jones-Lee et al. (1985) added to a mean willingness-to-pay value to reduce 

one's own risk an adjustment to take account of people's concern for tbe safety of others. The 

Jones-Lee value was 500,000 (about $650,000 at the 1985 exchange rate of $1.30/), added to the 

initial estimate of 1.5 million (about $2.0 million) for the statistical value of life. However, 

Bergstrom (1982) argues that an altruistic add-on may not apply in all circumstances. Viscusi (1992) 

advocates further study in this area before attempting to inflate value of life estimates to reflect 

altruism. 

VALUE OF LIFE ESTIMATES 

Significant estimation uncertainties are present in existing value of life estimates. We 

propose to account for these uncertainties through consideration of a broad range of values reported 

in the literature. Note that these uncertainties apply to all applications of the value of life literature 

for policy purposes; that is, they are not specific to the air pollution case of specific interest here. 

We examined three recent surveys of the value of life literature: Viscusi (1992); Fisher et 

al. (1989); and Miller (1990). Exhibit 2 summarizes the results of these three surveys. We describe 

the methodologies used in and results obtained from each of these surveys below. 

VJscuafi992) 

Viscusi's survey of the literature concerned with values of risks to life and health is part of 

a larger effort examining public and private responsibilities for risk reduction. Viscusi examined 39 

wage-risk, consumer market, and contingent valuation estimates of the value of a statistical life. He 

concludes that economists have been most successful in using labor market data to assess fatal riskdollar tradeoffs! In discussing the quality of the estimates he reports, Viscusi lists four criteria that 

he finds important in detenmning the value of life for policy applications, 

• Use of appropriate risk measures. Use of actuarial data to determine the 

risk levels faced by workers making a risk-dollar tradeoff employment 

decision win bias the value of statistical life downward. This occurs because 

these actuarial data are not limited to occupational risks, but included types 

of fatality risk faced by the individual. This overly broad risk measure biases 

the value of statistical life estimate downward, but by an unknown amount 

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Ettibtt.2 

SUMMARY OF RECENT VALUBOIMJPB SURVEYS 

Survey Author and 

FUbttcatioo Date 

Viscusi (1992) 

Fisher. Chestnut, 

aad Viotette (1989) 

-

o 

I 

o 

o 

o 

UJ 

Miller (1990) 

Number aad Type off 

39 

from 1974 to 1991 (26 

wage-mil studies, 7 

consumer market 

studies, 6 amtinfent 

value ttudles) 

21 studies published 

from 1974 to 1988 (15 

wage-risk ttudles, 4 

consumer market 

studies, 2 contingent 

valuation studies) 

67 studies published 

from 1973 to 1990 (37 

studies, 15 

studies, and IS 

coatingenMahistioa 

studies) 

:ef Reported 

of 

Value af Liu 

(modottan) 

$70,000 to $16.2 

raiUian (originally 

repotted in 1990 

dottats) 

SSaOjQOO lo $10.1 

million (or $450,000 to 

$8.5 «ullio« as 

originally reported 

1986doBars) 

$40,000 to $167.7 

milium (or $36,000 to 

$15.1 nWoa as 

originally reported 

1988duJUrs) 

(1990 dollars) 

Most maaoaabla estimates of the value 

of life am dustend in tbe $3 to $7 

million 

The meat defeasible empirical results 

indicate a range of estimates from $1.9 

to $10.1 ailton. 

• Concludes that market studies other than 

risk studies am not appropriate Cor polity 

application. 

• Concludes that structural models do not yield 

robust estimates. 

• Places less emphasis on 'exploratory" pilot-scale 

contingent valuation studies. 

£ 

S 

The snggtsird value of a statistical life 

for use in oast-benefit analysis and 

legal damage cases is ia the range 

(ram $1.7 mflHoa to $3.1 minion, with 

a central tifdemy of $24 saillion. 

• Concludes ttwt wage-risk estimates below $1.9 

million result from biases in die measured risk 

variable and thus should not be used for policy 

purposes. 

• Concludes dial results from consumer market 

studies reflect potentially significant downward 

• States that most estimates reported in the 

literature understate the value per statistical life 

appropriate for environmental policy analysis. 

• Adjusts studies fon use of beforc-tax earnings; 

error in risk perception; error In specification of 

risk variables; exclusion of non-fatal injury risks; 

age of sample population; and applies n 

staodardued 23 percent discount rate. 

• Excludes 211 studies from consideration based 

on concerns over study quality. 

Note: Ail values converted to 1990 dolars using the CPl deflator. 

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Model type. Labor market studies that are primarily designed to determine 

the value of a life year, and the implicit discount rate persons apply to this 

value, are less reliable for estimating the value of a statistical life, Although 

diese studies are useful in determining the appropriate discount rate, Viscusi 

argues that greater emphasis should be placed on studies using conventional 

wage-risk estimation procedures, because the complexity of the underlying 

structural models used to estimate discount rates leads to less robust 

estimates of the value of a statistical life. 

Two of the existing pilot-scale contingent valuation surveys aie 

based on much smaller samples (u=30 and 36) than the other four 

contingent value estimates. Viscusi considers these two estimates (one of 

$0.1 million and one of $15.6 million) to be less reliable than the four largescale survey estimates, 

l_f« of appropriate wilHi>gn««B fo p^v proades. Viscusi finds that all seven 

estimates from consumer market studies fail to provide an unbiased estimate 

of the dollar side of the risk-dollar tradeoff, as observed in consumer 

preferences for safety. Fisher et al. agree with this assessment, citing similar 

limitations that cause consumer market studies to produce estimates of the 

value of a statistical life that are likely to be biased downward. 

Viscusi concludes that labor market studies with carefully constructed risk variables, and 

contingent value studies with relatively large sample sizes, are most suitable for policy applications. 

Applying his expert judgement, he finds that most reasonable estimates of the value of life are 

clustered in the $3 million to $7 million range (1990 dollars). However, Viscusi cautions that these 

estimates are based on samples of workers "who generally have lower incomes than die individuals 

being protected by broadly-based risk regulations" (pp 73-74). Based on his earlier work (Viscusi 

and Evans 1990), he concludes that the value of a statistical life is positively correlated with income. 

He also states that "recognition of the income elasticity of the value of life will lead to the use of 

different values of life depending on the population being protected" (pp. 74). To illustrate this 

conclusion, Viscusi uses the empirically derived estimate of income elasticity of one from Viscusi 

and Evans (1990) to show how die results of each study could be adjusted for application to airline 

travelers, who in general have higher income levels than the general population. 

Viscusi concludes that a major gap in the application of value of life estimates for policy 

purposes is the lack of an appropriate schedule of estimates applicable for different populations at 

risk. For example, he cites the importance of distinguishing groups that incur risks voluntarily, have 

high risk tolerances, or accept compensation to bear risks from those groups who bear risks 

involuntarily, who have a high risk-aversion, or who are not compensated for bearing a health risk. 

Viscusi does not, however, suggest a framework for making these types of adjustments. 

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Flstier. Chestnut and Violate f198fl 

Fisher et al (1989) examined 21 studies of willingness to pay for reductions in risk. They 

conclude the most defensible estimates lie in a range from S1.9 million to $10.1 million (1990 

dollars, or $1.6 to $8.5 million as originally reported 1986 dollars). This range includes all of the 

estimates judged to be reasonable and reliable by these authors. Fisher et al. go on to express 

greater confidence in the low end of this range. They determined their recommended range by 

excluding: results of early wage-risk studies that may exhibit biases in the measured risk variable; a 

study of police officers' wage-risk tradeoff that they believe traces a labor supply curve rather than 

showing wage differentials; and consumer market studies that reflect potentially significant 

downward biases. In addition, the estimates measure an individual's value to reduce bis or her own 

risk, and do not account for the valuation of others (family, friends, or strangers) to reduce that 

person's risk. As a result, it is likely that the low end of this range is lower than society's willingness 

to pay to reduce fatal risks of this type. 

Fisher et aL conclude that their recommended range for the value of life provides a basis 

for "evaluating policies or regulations expected to affect risks of fatal injury in the work place" (pp. 

96-97). However, they also believe that this range understates the value of a statistical life 

appropriate for environmental policy assessment In addition, they suggest that this recommended 

range is most appropriate for valuing reductions in annual risks of death that are between 1 and 10 

per 10,000 exposed persons. They also suggest that an adjustment for tbe age of affected persons 

is appropriate, and thus that a more appropriate measure would consider die years of life saved. 

This adjustment, however, requires information on tbe impact of policies on the life tables of 

exposed individuals, in order to calculate tbe years of life potentially saved by the policy. They 

conclude that such information is rarely available or reliable. 

MjHer (19901 

Miller (1990) examined 67 estimates of the value of life. His goal was to narrow the range 

of credible willingness to pay values by weeding out studies with serious flaws and adjusting for 

sources of inconsistency. Miller judged 47 of the 67 estimates to be "reasonably sound*. Unlike 

Viscusi and Fisher et al, Miller concludes that the consumer market estimates of value oi life are 

appropriate for application in cast-benefit analysis. 

Adjustments to the 47 estimates not discarded included correction for systematic bias related 

to: age of population under study; income; the accuracy of risk perception; and the baseline level 

of risk. For fTfrppfr, Miller standardized the value of life to reflect the valuation of a 38 year old 

person with 39 yean of remaining life expectancy. This adjustment involved multiplying the value 

of life estimate by the ratio of discounted life years remaining at age 38 to discounted life years 

remaining at the sample mean age. Miller also adjusted for risk irnsperception in wage-risk studies 

by multiplying the results by 1233. The precise derivation of this value is not described, but it relies 

on data from a Lichtenstein et al. (1978) study of risk perception and a procedure described in 

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Blomquist (1981).3 In addition, Miller re-estimated some results using standardized values for travel 

time (60 percent of the wage rate per person or 120 percent per vehicle4) and the real discount rate 

(2 J percent). 

After these adjustments, Miller calculates the mean value of the 47 sound estimates to be 

$2.4 million (1990 dollars, or $12 million in the originally reported 1988 dollars). He calculates the 

standard deviation of the adjusted estimates to be $0.72 million (1990 dollars, or 0.65 million in 1988 

dollars), but concludes that the values are too uniformly spread to be normally distributed (few are 

within 0 i standard deviations of the mean). Miller states his conclusions in the form of the mean 

value and a range of ± 30 percent of the mean (i.e., $1.7 to $3.1 million), 

RECOMMENDATIONS 

Of the three survey papers we reviewed, we believe that the Viscusi and Fisher et al. studies 

represent the best starting points for value of life estimates for two primary reasons. First, Miller's 

results incorporate estimates from consumer behavior studies, which both Fisher et al. and Viscusi 

argue forcefully are not appropriate for environmental policy purposes. Second, Miller's results are 

dependent on adjustments made to wage-risk data. These adjustments, described earlier, are the 

subject of debate among economists in the field. We believe that their inclusion in our analysis 

would make our results less defensible. 

We further suggest using the Viscusi survey rather than the Fisher et aL review, Although 

the Fisher et aL review has been used by EPA in the past as the basis for a value of life (Deck 

1989), the more recent Viscusi review includes studies published since the Fisher et aL survey was 

completed In addition, Viscusi includes more recent versions of studies that Fisher et al. judged 

to be sound. Three value of life estimates from two studies are included by Fisher et al. but not by 

Viscusi - Gegax et aL (1985) and V.K. Smith (1976)/ Viscusi's more recent survey, soon to be 

published in the Journal of Economic Literature, includes these two studies. After consultation with 

Viscusi, we have added the Gegax et al. contingent value estimate and the V.K. Smith wage-risk 

estimate to our analysis. Viscusi rejects the other Gegax estimates, which was based on a labor 

market model, because the authors did not consider die full range of mortality risks in constructing 

their risk variable. 

i

 Lichtenstein found that individuals underestimate their risk of on-the-job injuries by. about 20 

percent, the risk of injury in motor vehicle crashes by about 40 percent, and the risk of fire-related 

injuries by about 55 percent 

4

 Values derived from Deacon and Sonstelie (1985), Winston (1985), Chui and McFarland 

(1985), and Miller (1989). 

' As cited in Fisher et al. (1989). 

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We applied the four criteria Viscusi suggests (described above) to limit our review to the 26 

estimates he considered applicable to policy analysis.6 The distribution of these 26 estimates is 

given in Exhibit 1. Eleven of die estimates are in Viscusi's recommended range of $3 million to $7 

million, and the mean of all 26 studies is $4.8 million. The geometric mean is $3,6 million. The five 

estimates based on large scale contingent valuation surveys are all below the mean value, ranging 

from $12 million to $34 million. Labor market based estimates demonstrate a wider range, from 

$0.6 million to $13.5 million, Fisher et al.'s recommended range of $2.0 million to $10.4 million 

includes 18 of die 26 values we selected from Viscusi. Frve of the 26 values are below $2.0 million, 

and one is above $10.4 million. 

For the purposes of the Section 812 study, we need to determine the shape of the 

distribution implied by the costing value of life estimates aad the parameters of that distribution. 

We were unable to analyze data from the underlying studies to gain insights into the distribution 

of individual risk-dollar trade-offs. Therefore, we rely on a comparison of the shape of simulated 

distributions to the observed distribution of authors' best estimates from these studies. Exhibits 3, 

4, and 5 present three simulated candidate distributions. Exhibit 3 is a lognormal distribution 

defined by a geometric mean of $3.6 million and a geometric standard d^-viation of $2.3 million 

calculated from the sound studies.7 Exhibits 4 and 5 are triangular distributions with most likely 

values (Le., peaks) corresponding to the median, $34 million, of the set of 26 sound studies*. The 

distribution in Exhibit 4 shows a range of values, or base of the triangle, corresponding to the range 

recommended by Fisher et aL Exhibit 5 shows a range of values corresponding to tbe range of the 

estimates in the 26 sound studies. 

Comparing these three simulated distributions with the observed distribution illustrated in 

Exhibit 1, we conclude that the lognormal distribution in Exhibit 3 appears to most closely reflect 

the actual distribution of estimates. Both of the simulated triangular distributions appear to have 

too much probability in the right tail. In addition, the expected values associated with the two 

simulated triangular distributions are $0,7 and $0.9 million higher, respectively, than the mean of 

the 26 sound estimates. 

To further confirm our hypothesis that a lognormal distribution can be used to represent the 

value of life, we conducted a statistical goodncss-of-fit test comparing the observed with the 

hypothesized lognormal distribution. Using a Kolmogorov-Smimoff test, we found we could not 

reject the null hypothesis of a lognormal distribution.' Based on this visual and statistical evidence, 

we conclude a lognormal distribution such as that simulated in Exhibit 3 will provide a good 

approximation of the range of value of life estimates found in the literature. 

R-98% 

' A list of these 26 estimates can be found in Exhibit A-1 at the end of this memorandum. 

Exhibit A-2 lists the estimates that were dropped from the analysis. 

7

 Note that the ©RISK software package that will be used in the Section 812 Partition Model 

uses the arithmetic mean and standaid deviation to simulate a lognormal distribution. 

' Triangular distributions are often used as approximations to normal and lognormal 

distributions for modeling purposes. 

* We tested the log-transformed data for goodness-of-fit to a normal distribution. See Exhibit 

A-3 for the data used in this test and more' detailed results. 

12 

r^CUSTTUALeOONCWGI^CDRPOR^ 

301 652 7530 04-06-94 04:25PM P013 312 
Expected 

Result55 

4.80717 

20% ' 

o 

CD 

CO 

o 4-06 o 

- o 4 : 2 5P

M PO 

P 

R 

O 

B 

A 

B 

I 

L 

1 

T 

Y 

16% 

12% 

8% 

4% 

0% 

Exhibit 3 

DISTRIBUTION OF VALUE OF LIFE ESTIMATES 

Simulated Lognormal Distribution 

jt..... . 

Mean Value: $4.8 million 

Standard Deviation: $3.2 million 

a 

ID 

5 

rv) 

tn 

1.75 3.5 5.25 7 8.75 10.5 12.25 

Value in Millions of Dollars 
ID 

ID 

Expected 

Resutt= 

5.454908 

Exhibit 4 

DISTRIBUTION OF VALUE OF LIFE ESTIMATES 

Simulated Triangular Distribution 

O) 

Ul 

tv) 

~) 

Ul 

o 

* » • 

I 

o 

o> 

I 

Ul 

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P 

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O 

B 

A 

B 

I 

L 

I 

T 

Y 

20% 

16% 

12% 

8% 

4% 

0% 

70 

i 

8 

Most Likely Value: $3.8 million 

Range of Values: $2.0 to $10.4 million 

£ 

3.5 5.25 7 8.75 

Value in Millions of Dollars 

i —— 

10.5 12.25 

s 

14 

TJ 
w 

a 

CD 

Expected 

Result5.732292 

i 

o 

CT) 

I 

ID 

•TJ 

s 

ro 

P 

R 

O 

B 

A 

B 

I 

L 

I 

T 

Y 

20% 

16% 

12% 

8% 

4% 

0% 

Exhibits 

DISTRIBUTION OF VALUE OF LIFE ESTIMATES 

Triangular Distribution 

. . . — . ...i . 

Most Likely Value: $3.8 million 

Range of Values: $0.0 to $13.5 million 

Value in Millions of Dollars 

TJ 

05 
P.17 

APR 06 '94 04:13PM ABT ASSOC. BETHESDA P.17/21 

SENsrnvrrY ANALYSES FOR TOE VALUE OP LIFE ESTIMATE 

In developing the Section 812 analysis it is important to consider differences in the nature 

of air pollution risk as opposed to the risks faced by persons whose risk-dollar tradeoff decisions 

have been addressed in the literature. For example, premature mortality risks from air pollution 

are experienced on an involuntary basis and are generally uncompensated, while job-related risks 

are assumed by individuals who presumably have some choice as to occupation and are compensated 

for taking a riskier job. In addition, the demographics of the population at risk from air pollution, 

particularly in terms of age and income status, may differ from the demographics of individuals 

surveyed in the literature. As a result, the benefits transfer process may introduce bias into the 

analysis. The value of life range proposed above reflects measurement uncertainty in the estimation 

methods, but does not account for differences in willingness to pay to reduce air pollution mortality 

risks as opposed to other types of mortality risk. 

We suggest conducting sensitivity analyses of results of calculations using the recommended 

value of life range. There are three major sources of bias that should be considered in these 

sensitivity analyses: risk perception, age, and income. Our conclusions are summarized in Exhibit 6, 

along with a list of sources that discuss the estimated direction and magnitude of these biases. 

In the remainder of this section we discuss the direction and potential magnitude of bias 

introduced by these three factors. Based on this review, we propose a detailed framework for 

conducting sensitivity analyses for age and income to test for the effect of these sources of bias. 

• 

Risk Perception 

The value that people place on mortality risk reduction depends on the nature of the risk. 

However, there is general agreement in the literature that current value of life estimates do not 

account for a number of important factors that affect risk perception. It seems clear that the nature 

of air pollution induced health risks are different than job-related risks. Because marry value of life 

estimates axe based on risk-dollar tradeoffs observed in the labor market, this difference should be 

considered when attempting to transfer existing value of life estimates to environmental policy 

analyses. 

16 

^a5TWALE0>O^^^JCDRP0RA7H) 

R-98% 301 652 7530 04-06-94 04:25PM P017 »12 
» 

I 

ID 

00 

J? 

BihnVii 6 

DIRECTION AND MAGNITUDE OF BIAS TO VALUE OP UPE RANGE 

PROPOSED FOR USE IN THE SECTION 8t2 STUDY 

DcmipUoa 

of Ban 

Degree sod type of risk as perceived by 

the exposed population: 

• Voluntary vs. involuntary risks 

• Controllable vs. iracoairoUable 

risks 

• Ordinary vs. catastrophic risks 

• Old vs. new risks 

Age of exposed population 

Income level of exposed population 

i 

i 

ID 

s 

of Bias 

Causes underestimate of value of fife 

Unclear 

Unclear 

Unclear 

Depends on age of affected population. 

Leads to overestimate if affected 

population is older or younger than 

population sampled by vakje-of-Ufe 

studies. 

Causes underestimate of value of lire in 

cases where average income of 

population eaposed to air pollution risk 

is greater than that of persons surveyed 

(latter value hi about $22,000). 

Methods for Adjusting for Bias 

Unknown 

Unknown 

Unknown 

Unknown 

(1) Adjust using ratio of 

discounted life years remaining. 

(2) Use empirical estimates from 

Jones-Lee et aL (1985) data. 

Workers' implicit value of risk of 

job-related injuries has Income 

elasticity of approiimaiely 1.0 * 

Reported income elasticities range 

from 0L25 to 0.44 witii a best 

estimate of 03 * 

Sources 

Beggs (1984); LUai (1980); Fisher 

et al. (1989); Weinstein and 

Quinn (1983) 

£ 

? 

s 

Chestnut and Rowe (1988); 

Jones-Lee et al. (1985); Cropper 

and Sussman (1990); Moore and 

Viscusi (1988); Miller (1990) 

Viscusi and Evans (1990); 

Viscusi (1992) 

Jones-Lee etaL (1985) 

The income elasticity of the value of statistical life expresses aa individual's rate of change in the willingness to pay to reduce mortality risks for 

given rate of change in income (e.&, an elasticity of 0 3 implies the value of statistical life increases three percent for a 10 percent change in 

income). 

m 

ro 

u 

ro 17 

^J 
P.19 

PPR 06 '9 4 04:14PM ABT ASSOC. BCTTCSDA 

Much work has been done to describe the important dimensions in which the nature of risks 

are perceived as different from one another. Litai (1980) conducted a review of literature in this 

area, including the work of Starr (1969), Lawrence (1967), Rowe (1977), Otway (1977), and 

Fischhoff et al. (1978). Based on this review, Litai concludes that the following eight dimensions 

represented a comprehensive list of the factors affecting human risk perception: (1) 

voluntary/involuntary; (2) ordinary/catastrophic; (3) delayed/immediate; (4) natural/man-made; (5) 

old/new, (6) controllable/ uncontrollable; (7) necessary/unnecessary; and (8) occasional/continuous. 

Transfer of value of life estimates between these categories could indicate the potential for 

introduced bias. Note that there dearly are other dimensions of risk perception (eg., 

compensated/uncompensated), which might not be fully encompassed by Litai's non-economic 

categorization approach.10 

Of these eight categories, several may vary between health risks due to air pollution and jobrelated health risks. The category that best captures the difference between job-related and air 

pollution-induced health risks is voluntary/involuntary. In general, job-related risks are considered 

to be voluntary, whereas risks due to air pollution are not.11 Viscusi states that polides affecting 

people who incur health risks in job-related situations should be treated differently than polides 

affecting people who incur health risks involuntarily. Fisher et al. note that "psychologists have 

shown that people are less willing to accept 'Involuntary* risks, such as nudear-power aeddems and 

air pollution exposure" (p. 97). These findings indicate that labor market-based value of life 

estimates may understate the true willingness to pay to reduce mortality risks associated with air 

pollution. 

Other categories of risk perception may also be relevant to this analysis, ioduding 

controuable/uncontroUable, ordinary/catastrophic, and old/new. It is likely that some individuals view 

aii pollution risks as uncontrollable and job-related risks as controllable. Weinstein and Quinn 

(1983) state that "uncontrollable risks are less acceptable because they deprive us of the emotional 

comfort afforded by an unrealistically rosy out-look" (p. 9). The ordinary/catastrophic category of 

risk perception defines different attitudes towards the perceived severity of risk. For example, 

fatalities that are expected (e.g., due to old age) are preferred to violent, unexpected deaths (eg,, 

airplane crash). Some types of air pollution risks may be viewed as catastrophic, for example those 

due to accidental chemical releases, but job-related risks due to such occurrences as mine cave-ins 

may also be viewed as catastrophic The old/new category is based on the observation that persons 

will tolerate a higher level of risk for a familiar hazard such as wood smoke than they would accept 

for a new, unknown source of risk, such as that posed by radon. However, it is not dear that air 

pollution health risks are "new" compared to job-related health risks. 

R-98% 

10

 Litai condudes that there are several other dimensions of risk perception mentioned in the 

literature which are incorporated in the eight categories of risk perception listed above. Litai notes 

that Fischhoff et aL (1978) and Otway (1977) considered the "dread" factor in some detail. These 

analysts found that dread (unexplained, instinctive fear) was most strongly associated with 

catastrophic; involuntary, and immediate death. Another factor considered in the literature is 

reversibility of effects. Litai assumed reversibility of effects to be incorporated in the "controllability" 

category. Therefore, we do not consider these dimensions of risk perception separately. 

11

 This hypothesis is not universally accepted, since some analysts suggest that job choice is not 

entirely voluntary. In tha case, estimates of risk premiums would be underestimated. Although 

many ofthe factors that could limit job choice (e.g., education, experience, marital status, race, sex) 

are controlled for in wage-risk studies, other factors, such as geographic limitations on labor 

mobility, have not always been controlled for in such studies. 

1 8

 NDU5TNAirja0NCW^ 

301 652 7530 04-06-94 04:25PM P019 K12 
P.20 

APR 06 '94 04:14PM ABT ASSOC. BGTCSDA P.20/21 

There is other evidence in the literature that existing value of life estimates underestimate 

the value of life appropriate for environmental risks, because they do not account for differences 

in risk perception. Fisher et al. state that the estimates dted in their report "would be expected to 

understate the value per statistical life appropriate for environmental policy assessment" at least 

partly because they did not incorporate the effects of differences in risk perception. Beggs* (1984) 

survey of willingness to pay to avoid the risk of job-related and air poDution-induced cancers 

provides additional support for a similar directional adjustment Therefore, we conclude that the 

transfer of existing labor-market based value of life estimates to a study of air pollution risks is likely 

to introduce a downward bias into the results. 

Few attempts have been made in the literature to correct for these sources of bias. Litai 

(1980) constructs a model to estimate "risk conversion factors" for individual categories of risk 

perception, but his estimates are best described as ratios of observed risks, Litai's factors do not 

control for compensated risks, and thus are not applicable to this effort At this time we cannot 

recommend a quantitative adjustment factor to serve as the basis of sensitivity tests for differences 

in risk perception. 

AJB 

Several authors have attempted to address potential differences in tbe value of life due to 

differences in the average age of the affected populadon or the average age at which an effect is 

experienced (Cropper and Sussman 1990, Moore and Viscusi 1988). In the case of mortality risks, 

h is assumed that a young person has the opportunity to experience a greater loss in total lifetime 

utility than an older person. This intuitively attractive hypothesis may be confounded by the finding 

that older persons, who as a group tend to avoid health risks assodated with drinking, smoking, and 

reckless driving, reveal a greater demand for reducing mortality risks and hence have a greater 

implidt value of a life year (Ehrlich and Chuma 1990). Considering both remaining years of life and 

the value of a life year, Jones-Lee et al. (1985) find that the value of a life follows a consistent 

"invcrted-U" life-cycle, peaking in the region of mean age. Data from Jones-Lee et aL, illustrated 

in Exhibit 7, support this condusion. Theoretical work by Shepard and Zeckhauser (1982) also 

support an inverted U-shaped life-cycle. Therefore, if the age distribution of persons affected by 

air pollution-induced risks does not match the age distribution of individuals considered in the 

existing value of life estimates, the act of transferring these estimates may introduce bias.into the 

analysis. 

There is some evidence that TSP-induced mortality is greater for persons over 65 years of 

age (Chestnut and Rowe 1988).U ln general, considering the age of persons most likely to 

experience air poDution-induced mortality risks, the appropriate value of life for air pollution risks 

is probably lower than the mean value used in other policy contexts. Preliminary results from the 

Section 812 study indicate TSP will account for the majority of estimated air pollution-induced 

mortality. Therefore, the direction of the adjustment for age will probably be downward. 

13

 An exhaustive search to determine the age distribution of individuals expected to experience 

human health effects for other categories of pollutants was beyond the scope of this analysis, but 

such research will be required prior to applying age adjustment factors for mortality endpoints for 

purposes of the Section 812 study. 

19 

. MlJSTRlALB0CKy\\lCSt«)RPORATTO 

R-98% 301 652 7530 04-06-94 04:25PM P020 812 
CO 

- J 

5? Exhibit 7 

1.3 

301 O) 

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(0 

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51 

(d 

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0 

0 

* 3 

(0 

rr 

f 1.2 

1.1 

0.9^ 

0.8 

0.7 

Ratio of Age Group Mean Value of Life 

to Overall Mean Value of Life 

Source: 

Jones-Lee 

(1985) 

8 

ID 

TJ 

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8 

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8 u 

<24 25-34 35-44 45-54 

Age group of respondents 

55-64 >65 

TJ 

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