## JOINT CENTE R

AEI

- BROOKINGS JOINT CENTER FOR REGULATOR Y STUDIES



## The Value of a Statistical Life: A Critical Review of Market Estimates throughout the World

W. Kip Viscusi and Joseph E. Aldy

Related Publication 03

- 2

January 2003

Mr. Vis cusi is John F. Cogan Jr. Professor of Law and Economics at Harvard Law School. He can be contacted by phone at (617) 496

- 0019 or by email at: kip@law.harvard.edu. Mr. Viscusi’s research is supported by the Sheldon Seevak Research Fund; the Harvard Olin C enter for Law, Business, and Economics; and the Environmental Protection Agency. Mr. Aldy is a Researcher at the Department of Economics, Harvard University. Mr. Aldy’s research is supported by the Environmental Protection Agency STAR Fellowship program. The authors thank James Hammitt, Randall Lutter, and Robert Smith for helpful comments on an earlier draft of this paper.Executive Summary

A substantial literature over the past th irty years has evaluated tradeoffs between money and fatality risks. These values in turn serve as estimates of the value of a statistical life. This article reviews more than 60 studies of mortalit y risk premiums from ten countries and approximately 40 studies that present estimates of injury risk premiums. This critical review examines a variety of econometric issues, the role of unionization in risk premiums, and the effects of age on the va lue of a statistical life. Our meta-analysis indicates an income elasticity of the value of a statistical life from about 0.5 to 0.6. The paper also presents a detail ed discussion of policy appli cations of these value of a statistical life estimates and related issues, including risk-risk analysis.1

The Value of a Statistical Life: A Critical Review of Market Estimates throughout the World

W. Kip Viscusi and Joseph E. Aldy

Introduction Individuals make decisions everyday th at reflect how they value health and mortality risks, such as driving an autom obile, smoking a cigarette, and eating a mediumrare hamburger. Many of these choices involve market decisions, such as the purchase of a hazardous product or working on a risky job. Because increases in health risks are undesirable, there must be some other aspect of the activity that ma kes it attractive. Using evidence on market choices that involve implicit tradeoffs between risk and money, economists have developed estimates of th e value of a statistical life (VSL). This article provides a comprehensive review a nd evaluation of the dozens of such studies throughout the world that have b een based on market decisions. 1 These VSL estimates in turn provide governments with a reference point for assessing the benefits of risk reduction efforts. The long history of government risk policies ranges from the draining of swamps n ear ancient Rome to suppress malaria to the limits on air pollution in developed countri es over the past 30 years (McNeill 1976, OECD 2001). All such policy choices ultimate ly involve a balancing of additional risk

reduction and incremental costs. The proper value of the risk reduction bene fits for government policy is society’s willingness to pay for the benefits. In the ca se of mortality risk reduction, the benefit is

1 Past reviews of this literature include Smith (197 9), Miller (1990), and Viscusi (1992, 1993, 2000). Several researchers have conducted meta-analyses of this literature, including Liu, Hammitt, and Liu (1997), Miller (2000), Bowland and Beghin (2001), and Mrozek and Ta ylor (2002). See Hammitt (2002) and Krupnick (2002) for co mmentaries on the Mrozek and Taylor paper.2

the value of the reduced probability of death that is experienced by the affected population, not the value of the lives that have been saved ex post. The economic literature has focused on willingness-to-pay (willingness-to-accept) measures of mortality risk since Schelling’s (1968) discus sion of the economics of life saving. Most of this literature has concentrated on valuing mortality risk by estimating compensating differentials for on-the-job risk exposure in labor markets. While the early studies assessed such compensating differentials in the United States, much of the more recent work has attempted to estimate risk-money tradeoffs for other developed and some developing countries. In addition, economists ha ve also investigated price-risk (pricesafety) tradeoffs in product markets, such as for automobiles and fire alarms.

Use of the economic research on the va lue of mortality and injury risks in government policy evaluation has been a key be nefit component of policy evaluations for a wide range of health, safety, and enviro nmental policies. The policy use of risk valuations, however, has raised new questio ns about the appropriateness of these applications. How should policymakers r econcile the broad range of VSL estimates in

the literature? Should the va lue of a statistical life vary by income? Should the VSL vary by the age distribution of the affected population? What other factors may influence the transfer of mortality risk valuation estimat es from journal articles to policy evaluation

in different contexts? We begin our assessment of this literatu re with an overview of the hedonic wage methodology in Section 1. This approach mo tivates the discussion of the data and

econometric issues associated with estimati ng a VSL. Although there continue to be controversies regarding how best to isolat e statistically the risk-money tradeoffs, the3

methodologies used in the various studies typically follow a common strategy of estimating the locus of market equilibria regarding money-risk tradeoffs rather than isolating either market supply curves or market demand curves.

Section 2 examines the extensive literat ure based on estimates using U.S. labor market data, which typically show a VSL in the range of $4 million to $9 million. These values are similar to those generated by U.S. product market and housing market studies, which are reviewed in Section 3. A parallel l iterature reviewed in Section 4 examines the implicit value of the risk of nonfatal injuries. These nonfatal risks are of interest in their own right and as a control for hazards other th an mortality risks that could influence the

VSL estimates. Researchers subsequently have extended such analyses to other countries.

Section 5 indicates that not withstanding the quite differe nt labor market conditions throughout the world, the general order of ma gnitude of these foreign VSL estimates

tends to be similar to that in the United States. International estimates tend to be a bit lower than in the United States, as one would expect given the positive income elasticity with respect to the value of risks to one’s life. A potentially fundamental concern with respect to use of VSL estimates in different contexts is how these values vary with income. While the income elasticity should be positive on theoretical grounds, extr apolating these values across different contexts requires an empirical estimate of this elasticity. Our meta-analyses of VSL estimates throughout the world in Section 6 impl y point estimates of the income elasticity in the range of 0.50 to 0.60. The meta-analy sis also provides a characterization of the uncertainty around the measures of central tendency for the valu e of a statistical life, i.e.,4

95 percent confidence intervals for the predicted VSLs. Heterogeneity in VSL estimates based on union status (Section 7) and age (S ection 8) indicate that the VSL not only varies by income but also across these importa nt labor market dimensions. The existence of such heterogeneity provide s a cautionary note for policy. While policymakers have relied on VSL estimates to an increasing degree in their benefit assessments, as Section 9 indicates, matching these values to the per tinent population at risk is often problematic, particularly for people at the extr eme ends of the age distribution.

1. Estimating the value of a stat istical life from labor markets 1.1 The hedonic wage methodology More than two centuries ago, Adam Smith (1776) noted in The Wealth of Nations that: “The wages of labour vary with the ease or hardship, the cleanline ss or dirtiness, the

honourableness or dishonourableness of the employment” (p. 112). Finding empirical evidence of such compensating differentials, however, has been problematic. Because of the positive income elasticity of the demand fo r safety, the most attractive jobs in society tend to be the highest paid. To disentangle the wage-risk tr adeoff from the other factors that affect wages, economists have relied on statistical models that control both for differences in worker productivity as well as different quality components of the job. The primary approach has been hedonic wage and hedonic price models that examine the equilibrium risk choices and either the wage le vels or price levels associated with these

choices. 2 Market outcomes reflect the joint influence of labor demand and labor supply,

2 For more extensive discussion of hedonic analysis, see Griliches (1971), Rosen (1974, 1986), Thaler and Rosen (1975), Smith (1979), and Viscusi (1979).5

but hedonic models do not examine the underlying economic structure that gives rise to these outcomes. For concreteness, we focus on the hedonic wage case.

The firm’s demand for labor decreases with the total cost of employing a worker. The cost of a worker may include the worker’s wage; training; benef its such as health insurance, vacation, child care; and the costs of providing a safe working environment.

Because worker costs increase with the level of safety, for any given level of profits the firm must pay workers less as the safety leve l rises. Figure 1 de picts two firms with wage-risk offer curves (isoprofit curves) with wage as an increasi ng function of risk, OC 1 for firm 1 and OC 2 for firm 2. For any given level of risk, workers prefer the wage-risk

combination from the market offer curve wi th the highest wage level. The outer envelope of these offer curves is the market opportunities locus w(p). The worker’s supply of labor is in part a function of the work er’s preferences over wages and risk. The labor supply is best charac terized subject to several mild restrictions on preferences. Consider a von Neumann-Morg enstern expected utili ty model with statedependent util ity functions. 3 Let U(w) represent the utility of a healt hy worker at wage w and let V(w) represent the utility of an inju red worker at wage w. Typically, workers’ compensation after an injury is a function of the worker’s wage. We assume that the relationship between workers’ compensation and the wage is subsumed into the functional form of V(w). Further, assume that workers prefer to be healthy than injured [U(w) > V(w)] and that the marginal utility of income is positive [U'(w) > 0, V'(w) > 0]. 4 Workers choose from potential wage-r isk combinations along some market opportunities locus w(p) to maximize expected utility. In Figure 1, the tangency between

3 For a discussion of irrational behavior in the presence of mortality risk inconsistent with expected utility theory, refer to Viscusi 1998. 4 Individual risk neutrality or risk aversion, i.e., U'', V'' ≤ 0 is required to ensure a global maximum.6

the constant expected utility locus EU 1 and firm 1’s offer curve OC 1 represents worker 1’s optimal job risk choice. Likewise, wo rker 2 maximizes expected utility at the tangency between EU 2 and OC 2 . All wage-risk combinations associated with a given worker’s constant expected utility locus must satisfy ) ( ) ( ) 1 ( w pV w U p Z +

− = . The wage-risk tradeoff along this curve is given by

0 ) ( ' ) ( ' ) 1 ( ) ( ) ( > +

− − = − = w pV w U p w V w U Z Z dp dw

w p

,

so that the required wage rate is increasing in the risk level. The wage-risk tradeoff consequently equals the difference in the uti lity levels in the two states divided by the expected marginal utility of income. Actual labor market decisions by work ers can be depicted by the wage-risk combinations at the tangencies of the offer curves and expected utility loci at points (p 1 ,

w 1 ) and (p 2 , w 2 ). All that is observable using marketdata are these points of tangency. Expanding beyond our two worker example, obser vations of a large set of workers can show the locus of these workers’ wage-risk tradeoffs, depicted by the curve w(p) in Figure 1. Hedonic wage analyses trace out poi nts on this w(p) curve that workers find acceptable. The observed labor market decisions (p i , w i ) reflect the joint influence of supply and demand on the market equilibrium. The estimated tradeoff between wage and risk,

∂ w/ ∂ p, is a local measure of the wage-risk trad eoff for marginal changes in risk. This estimated slope corresponds to both the worker’s marginal willingness to accept risk and the worker’s marginal willingness to pay for more safety and the firm’s marginal cost of more safety as well as the firm’s marginal cost reduction from an incremental increase in7

risk. For the worker and firm associat ed with a given labor market decision (p i , w i ),

∂ w i / ∂ p i reflects both the marginal supply price and the marginal demand price of risk. Econometric models that estimate a linear w(p) curve are estimating an average tradeoff

rate across different levels of risk. The estimated wage-risk tradeoff curve w(p) does not imply how a particular worker must be compensated for non-marginal changes in risk. Consider workers 1 and 2 in Figure 1. Worker 2 has revealed a willingness to accept risk p 2 at wage w 2 (p 2 ) along

EU 2 . A change in the risk exposure to worker 1 from p 1 to p 2 would require a higher wage compensation to keep worker w 1 on the expected utility locus (EU 1 ), implying that

w 1 (p 2 ) > w 2 (p 2 ) (or alternatively, that ∂ w 1 / ∂ p 2 > ∂ w 2 / ∂ p 2 ). With large changes in risk, a worker’s wage-risk tradeoff will not be the sa me because the relevant tradeoff must be made along the worker’s expected utility lo cus, not the estimated market wage-risk

tradeoff. 1.2 Econometrics and data issues in hedonic labor market analysis Most researchers estimate the wage-ri sk relationship in labor markets by specifying a wage equation along the lines of the following:

i i i i i i i i i i H p WC q q p X H w ε β γ γ γ β β α + ′ + + + + ′ + ′ + = 3 3 2 1 2 1 where w i is the worker i’s wage rate, α is a constant term, H is a vector of personal characteristic variables for worker i, X is a vector of job characteristic variables for worker i, p i is the fatality risk associ ated with worker i’s job, q i is the nonfatal injury risk associated with worker i’s job, WC i is the workers’ compensation benefits payable for a job injury suffered by worker i, and ε i is the random error reflecting unmeasured factors8

influencing worker i’s wage rate. The terms α , β 1 , β 2 , β 3 , γ 1 , γ 2 , and γ 3 represent parameters estimated through regression analysis. The personal characteristic variables represented by H i often include a variety of human capital measures, such as education and job experience, as well as other individual measures, such as age and union status. The job characteristic variables represented by X often include indicators for blue-collar jobs , white-collar jobs, management positions, the worker’s industry, and measures of physical ex ertion associated with the job. These two sets of variables reflect both workers’ preferen ces over jobs as well as firms’ offer curves

for labor. Some studies intera ct personal characteristics H i with the fatality risk p i to capture how the returns to risk may vary with these characteristics, such as age and union

status.

1.2.1 Risk data. An ideal measure of on-the-job fatality and injury risk would reflect both the worker’s perception of such risk and the firm’s perception of the risk. Because the market opportunity locus reflects both wo rkers’ preferences over income and risk and firms’ preferences over costs and safety, information on both sets of beliefs would be necessary to appropriately ch aracterize the risk premium. However, very few studies have compiled workers’ subjective preferen ces regarding risks (V iscusi 1979, Viscusi and O’Connor 1984, Gerking et al. 1988, a nd Liu and Hammitt 1999) and there is no available research on firms’ risk perceptions . If individuals’ and fi rms’ subjective risk perceptions closely reflect objective measures of fatality risk, then such objective risk data could be used instead as a pr oxy for unobserved subjective risk data. 5 The standard

5 Gaba and Viscusi (1998) compared qualitative and quantitative subjective measures of on-the-job accident risk. They find that for a given level of quantitative risk, a college-educated individual is more likely to report that risk as “dangerous” than an indivi dual with less than college education. For example, for those workers who report their quantitative risk as comparable to an annual injury risk of less than 1 in9

approach in the literature is to use industry-specif ic or occupation-specific risk measures reflecting an average of at leas t several years of obs ervations for fatalities, which tend to be relatively rare events. 6 Measures of job-related fatality and inju ry risk have included self-reported risks based on worker surveys and objective risk measures derived from actuarial tables, workers’ compensation records, and surveys and censuses of death certificates. The choice of the measure of fatality risk can si gnificantly influence the magnitude of the risk premium estimated through regression analysis. The nature of the risk measures also raise questions about possible errors in esti mation and the need to correct the econometric specification to address them. Several early papers on compensating di fferentials used the University of Michigan Survey of Working Conditions and Quality of Employment Survey data that include several qualitative measures of on-th e-job risk. These measures utilize direct surveys of workers and their perceptions of their work environment. For example, Hamermesh (1978), Viscusi (1979, 1980), and Fairris (1989) estimated the hedonic wage equation with a dichotomous measure of injury risk based on a worker’s perception of whether his or her job is “dangerous.” 7 The survey asked workers if their job exposed them to physical dangers or unhealthy conditions. These studies estimated statistically significant coefficients on this “risk” variable in some of the specifications. Duncan and

20, half of the college-educated described their job risk as “dangerous” while only 19 percent of the lessthan-college educated reported their job risk as su ch. This differences in the “danger” cutoff biases estimates of risk premiums in wages, and this bias has implications distinct from typical measurement error. Gaba and Viscusi find that subjective quantita tive measures of risk yielded wage premiums more consistent with estimates based on objective risk meas ures (BLS). Analysis of the qualitative risk measure (a dichotomous 0-1 “is the job dangerous?” variable) produced a much larger risk premium. 6 Averaging over a period of 5 to 10 years would likely remove any potential distortions associated with catastrophic accidents in any particular year. 7 Viscusi (1979, 1980) includes the danger variable in some regressions, although his research focused on compensating differentials based on BLS measures of injury and fatality risk discussed below.10

Holmlund (1983) undertook a similar analysis of compensating differentials with a “danger” variable in a study of male workers in Sweden. Several papers on the U.S. labor mark et from the 1970s and early 1980s used actuarial data (Thaler and Rosen 1975, Brown 1980, Leigh 1981, Arnould and Nichols 1983). These studies all employed a job-relate d risk measure based on data collected by the Society of Actuaries for 1967. The Society of Actuaries data set provides fatality risk data for 37 occupations. Across these 37 occupations, the annual risk averaged approximately 1 in 1,000. This fatality risk exceeds averages from other data sets by nearly an order of magnitude. To the extent that these data reflect workers in extremely high risk jobs, the estimated wage-risk tradeo ffs will suffer from a selection bias. As a result, one would expect th ese estimates to be lower than found in more broadly representative samples, which has in fact proven to be the case. Another difficulty is that the Society of Actuaries data do not di stinguish fatalities caused by the job but rather reflect the overall fa tality rates of people within a particular job category. For example, one of the highe st risk occupations based on these actuarial ratings is actors, who typically face few risks other than unfavorable reviews.

Several studies of U.S. and Canadian labor markets have used workers’ compensation records to construct risk m easures (Butler 1983, Dillingham 1985, Leigh 1991, Martinello and Meng 1992, Meng 1991, Cous ineau et al. 1992, Lanoie et al. 1995). Only three studies have used workers’ compensation data to evaluate compensating differentials in U.S. labor markets, whic h may reflect the decentralized nature and

differences in information collection associated with state (not Fede ral) management of11

U.S. workers’ compensation programs. 8 In contrast, researchers in Canada can obtain workers’ compensation-based risk data from Labour Canada (the labor ministry for the Federal government) and the Quebec government. For analyses of the United States, the majo rity of the mortality risk studies have used data collected by the U.S. Department of Labor Bureau of Labor Statistics (BLS). About 80 percent of the U.S. nonfatal injury risk studies summarized below used BLS injury risk data. The BLS has compiled indust ry-specific fatality and injury risk data since the late 1960s. Through the early 1990s, BLS collected its data via a survey of industries, and reported the data at a fairly a ggregated level, such as at the 2-digit and 3- digit Standard Industrial Classification (SIC) code level. The aggregation and sampling strategy have elicited some concerns about measurement error in the construction of the mortality risk variable (s ee Moore and Viscusi 1988a). Concerns about the BLS fatality risk data led the National Institute of Occupational Safety and Health (NIOSH) to collect information on fatal occupational injuries through its National Traumatic Occ upational Fatalities su rveillance system (NTOF) since 1980. NIOSH compiles these da ta from death certificates managed by U.S. vital statistics reporting units (NIOSH 200 0). These data are reported at the 1-digit SIC code level by state. Because NIOS H compiles data from a census of death certificates, it circumvents some of the c oncerns about sampling in the pre-1990s BLS approach. Some have raised concerns, howev er, about the accuracy of reported cause of death in death certificates (Dorman and Hagstrom 1998).

8 Leigh’s (1991) analysis with risk data derived from workers’ compensation records in 11 states appears to be the only U.S. study to aggregate such data from more than one state.12

Comparing the BLS and NIOSH fatality risk data over time provides some interesting contrasts. The or iginal NIOSH data set for the fatality census averaged over 1980 – 1985 has a mean fatality risk nearly 50 percent higher than a roughly comparable BLS data set averaged over 1972 – 1982. 9 Moreover, the BLS data had greater variation (a standard deviation 95 per cent greater than its mean) th an the NTOF data, although the NIOSH data also had substantial variation (s tandard deviation 23 percent greater than its mean) (Moore and Viscusi 1988a). Since 1992, the BLS has collected fatal occupational injury data through the Census of Fatal Occupational Injuries (C FOI). The BLS compiles information about workplace fatality including wo rker characteristics and occupation, circumstances of the event, and possible equipment involved. The BLS draws on multiple sources such as death certificates, workers’ compensation r ecords, and other Federal and state agency reports. The BLS reports these fatality data by industry at the 4-di git SIC level. In contrast to the earlier comparisons of BLS a nd NIOSH data, more recent years’ data on fatality risk collected through the CFOI now show that the BLS measure includes approximately 1,000 more fatalities per year than the NIOSH measure (NIOSH 2000).

Table 1 illustrates the recent national rates of job-related fatalities at the one-digit industry level for the four-year period in wh ich both NIOSH and CFOI data are publicly available. In every instance the BLS measure shows a higher risk mo rtality rate, which in some cases, such as wholesale trade, is quite substantial.

The risk variables used in several ofthe non-U.S. studies were based on jobrelated accident and mortality data collected by foreign governments. For example, the

9 Averaging fatality risk data over several years can re duce the distortion of a catastrophic event in one year in one industry on the measure of an industry’s risk.13

data sets used in Shanmugam (1996/7, 1997, 2000, 2001) were from the Office of the Chief Inspector of Factories in Madras. Several of the United Kingdom studies employ data provided by the Office of Populatio n Censuses and Surveys (Marin and Psacharopoulos 1982, Sandy and Elliott 1996, Arabsheibani and Marin 2000) while others used unpublished data from the U.K. Health and Safety Ex ecutive (Siebert and Wei 1994). In their study of the South Korean labor mark et, Kim and Fishback (1999)

obtained their accident data from the Ministry of Labor. Few of these studies indicate whether the mortality risk data were derived from samples or censuses of job-related

deaths. While the large number of studies of la bor markets around the world evaluated the compensating differential for an on-the-j ob death and/or on-the-job injury, very few attempted to account for the risk of occupati onal disease. Lott and Manning (2000) used

an alternative data set to estimate the risk premium for jobs with higher cancer risk associated with occupational exposure to various chemicals (see Section 2). 1.2.2 Wages and related data. Labor market studies of the value of risks to life and

health match these risk measures to data se ts on characteristics of wages, workers, and employment. Some researchers survey workers directly to collect this information, such as Gegax et al. (1991) for the United States, Lanoie et al. (1995) for Canada, Shanmugam (1996/7) for India, and Liu and Hammitt (1999) for Taiwan, among others. For the United States, researchers have also used the University of Michigan’s Survey of Working Conditions (SWC), the Quality of Em ployment Survey (QES), the Bureau of Labor Statistics’ Current Population Survey (CPS), the Panel Study of Income Dynamics (PSID), and decennial census data. Simila r types of surveys undertaken in other14

countries have also provided the data n ecessary to undertake hedonic labor market analysis, such as the General Household Su rvey in the United Kingdom (e.g., Siebert and Wei 1994 and Arabsheibani and Marin 2000). The dependent variable in virtually all labor market analyses has been a measure of the hourly wage. With some data sets, researchers have had to construct the wage measure from weekly or annual labor earnings da ta. For some data sets, a worker’s aftertax wage rate is provided, which can put wa ge and workers’ compensation benefits in comparable terms. While many studies have included pre-tax wage s as the dependent variable, this would not likely bias the results significantly so long as workers’ income

levels and tax rates do not differ substantiall y. If the regression model includes workers’ compensation benefits, then both the wage an d these benefits shoul d be expressed in comparable terms (both in after-tax or both in pre-tax terms) to en sure proper evaluation of the benefits’ impacts on wages. 10 Typically, researchers match a given year’s survey data on wages and worker and employment characteristics with risk data for that year, or preferably, the average over a recent set of years. Some researchers have restricted their samples to subsets of the surveyed working population. For example, it is common to limit th e analysis to fulltime workers, and many have focused only on ma le, blue-collar workers. Restricting the sample in this manner partially addresses the measurement problem with industry-level

risk values common to most risk datasets by including only those workers for whom the risk data are most pertinent.

10 Most hedonic wage-risk studies ha ve not accounted for labor taxes in their construction of the wage variable or in their interpretation of the value of a statistical life. Exceptions include several papers that have focused on the effects of workers’ compensation on the compensating differential for occupational risk (e.g., Moore and Viscusi 1990a). This reflects the more common use of pre-tax wages in the broader labor market analysis literature.15

1.2.3 Wage vs. log(wage). Most researchers have estimated the wage equation using linear and semi-logarithmic specifications. Choosing a preferred functional form from these two specifications cannot be determined on theoretic grounds (see Rosen 1974). To identify the specification with greatest ex planatory power, Moore and Viscusi (1988a) employed a flexible functional form given by the Box-Cox transformation. The Box-Cox

transformation modifies the de pendent variable such that the estimated regression model

takes the form:

i i i i i i i i i i H p WC q q p X H w ε β γ γ γ β β α λ λ + ′ + + + + ′ + ′ + = − 3 3 2 1 2 1 1

.

This approach presumes that a λ exists such that this model is normally distributed, homoskedastic, and linear in the regressors. Note that the case where λ Æ 0 represents the semi-logarithmic fu nctional form and the case where λ Æ 1 represents the

linear functional form. The flexible form under the Box-Cox transf ormation can test the appropriateness of these two restrictions on the form of the mode l. Using maximum likelihood methods, Moore and Viscusi’s estimate for λ equaled approximately 0.3 for

their data. While this value is more consiste nt with a semi-logarithmic form than a linear form, the authors reject both specifications ba sed on a likelihood ratio test. The estimated

value of a statistical life ba sed on the Box-Cox transforme d regression model, however, differed only slightly from the log(wage) spec ification. Shanmugam (1996/7) replicated this flexible form evaluation with his evaluation of compensating differentials in India.

His maximum likelihood estimate for λ equaled approximately 0.2. While Shanmugam rejected the semi-logarithmic and linear m odels, he found that the semi-logarithmic16

functional form also generated results closer to t hose found with the unre stricted flexible

form. 11 1.2.4 Errors in variables problem with risk measures. Every compensating differential study employs a less than perfect measure of an y particular worker’s job-related fatality risk. The majority of these studies have used fatality risk measures from the BLS averaged across the entire industry. Such an approach, however, suffers from measurement error. As noted above, some researchers have found that the pre-1992 BLS data sets (and NIOSH data sets to a lesser extent) suffer from incomplete reporting. The industry averages constructed by the BLS do not exactly reflect realized industry averages. Further, applying industry aver ages to individuals may result in errors associated with matching workers to industries due to response error in worker surveys. Mellow and Sider (1983) evaluated several surveys that asked workers and their employers to identify the workers’ industry and occupation (among other questions). In their assessment of the January 1977 Current Population Survey, 84 percent of workers and their employers agreed on industry affiliation at the thre e-digit SIC code level while only 58 percent agreed on the three-digit occupational status. Merging a worker

characteristics data set with a risk meas ure data set based on industry affiliation (or occupation status) can result in a mismatch of worker char acteristics and industry risk. Mellow and Sider’s statistical analysis of the 16 percent “mismatched” workers by industry affiliation showed that the erro rs in matching reduced the compensating differential for injury risk by about 50 percent in their samples.

11 In the product market context, Atkinson and Halvorsen (1990), Dreyfus and Viscusi (1995), and Gayer, Hamilton, and Viscusi (2000) employ Box-Cox transformations to evaluate their respective hedonic price models (the first two focused on automobile prices and the third on housing prices).17

Even with a perfect industry measure of fatality risk and appropriate matching of workers and their industry, measurement error still exists si nce some workers bear risk that differs from their industry’s average. For example, different occupations within an industry may pose different levels of risk. This measurement error can be characterized

as:

i

i i p p η + = * , where p i reflects the observed industry average fatality risk, p i * reflects the unobserved (to the econometrician) fatality risk associated with worker i’s job, and η i reflects the deviation of that job’s risk from the indus try average. Random measurement error will

result in a downward bias on coefficient estim ates, and the least squares estimate of the coefficient on fatality risk in th is example would be inconsistent:

1 2 2 2

, 1 ˆ γ σ σ σ γ

η        

+ →

 p p p OLS

where the signal-noise ratio determines the extent of the downward bias towards zero.

In addition to the downward effect on the risk coefficient, applying industry-level

risk data to individual obser vations may also induce some correlation in the residuals among individuals within industries. R obust (White) standard errors would not appropriately correct for this correlation and result in inappropriately small standard errors. Hersch (1998) and Viscusi and Hers ch (2001) employ robust standard errors correcting for within-group (w ithin-industry) correlation.

1.2.5 Omitted variables bias and endogeneity. Failing to capture all of the determinants of a worker’s wage in a hedonic wage equa tion may result in bias ed results if the

unobserved variables are correlated with observe d variables. Dangerous jobs are often18

unpleasant in other respects. Omission of non-p ecuniary characteristics of a job may bias the estimated risk premium if an omitted variab le is correlated with risk. For example, one may find a correlation between injury risk and physical ex ertion required for a job or

risk and environmental factors such as noise , heat, or odor. While some studies have attempted to control for th ese unobservables by including industry or occupation dummy variables (see below), a model may still suffer from omitted variables bias. Several studies have explored how omitti ng injury risk affects the estimation of mortality risk. Viscusi (1981) found that omitting injury risk re sulted in a positive bias in the mortality risk measure for union affiliated workers. Cousineau et al. (1992) also found that omitting injury risk may cause a positive bias in the estimation of the coefficient on mortality risk. The high corr elation (collinearity) between injury and mortality risks, however, can make joint es timation difficult. Some studies have attempted to estimate regression equations with both types of risk and have found nonsignificant coefficients on at least one of the measures, including Smith (1976), Leigh (1981), Dillingham and Smith (1984), and Kniesner and Leeth (1991). While including injury risk in a regre ssion model could address concern about one omitted variable, other possible influences on wages that could be correlated with mortality risk may not be easily measured. Several papers ha ve investigated this bias. Garen (1988) notes that “individuals may systematically differ in unobserved characteristics which affect their productivity and earnings in dangerous jobs and so these

unobservables will affect their choice of job risk” (p. 9). One example Garen offers is “coolheadedness,” which may make a worker more productive under the stresses of a dangerous job but may not be re levant in a safe job. In this case, an econometrician19

would prefer to include both the mortality risk variable and the interaction or the mortality risk variable with a variable m easuring coolheadedness as regressors in the hedonic labor market model. Failing to includ e this interaction term results in biased least squares estimation. Garen attempts to address this concern with an instrumental variables technique, although s ubsequent researchers such as Hwang et al. (1992) have noted the difficulty in identifying appropriate instruments for his procedure. Employing this instrumental variables technique, Gare n found a mortality ri sk premium about double what the standard least squares model produced. The significant increase in the risk pr emium associated with a method to account for unobserved productivity is consistent with the theoretical and si mulation findings in Hwang et al. (1992). They estimate that for plausible parameter estimates, models that fail to account for heterogeneity in unobserved productivity may bias estimates of the risk premium by about 50 percent and could result in incorrectly (n egative) signing of the risk

variable. With the ex ception of some non-union samples in several studies (e.g., Dorsey 1983 and Dickens 1984), the empiri cal literature presents very little eviden ce of this wrong signing. Siebert and Wei (1994) have also found that accounting for the endogeneity of risk can increase the risk premium compared to a standard least squares approach. Recent theoretical research, how ever, has also illustrated the potential for over-estimating the risk premium by failing to control for unobser vables (Shogren and Stamland 2002). They note that workers with th e ability to avoid inju ry select into risky jobs while those less able to avoid injury (“cl umsy” workers) select into less-risky jobs. They argue that risk premiums could be overe stimated by a factor of four with plausible parameter estimates in their simulations. Whet her there will be such biases hinges on the20

monitorability of individual’ s safety-related productivity. If these differences are monitorable, as in Viscusi and Hersch ( 2001), there will be a separating compensating differential equilibrium for work ers of different riskiness. Viscusi and Hersch (2001) note that differences in work ers’ preferences over risk can affect the shape of their indifference curves and workers’ safety behavior and, by affecting firms’ cost to suppl y safety, can influence firms’ offer curves. They evaluated the wage-risk (injury) tradeoff of workers with a data set that includes measures of risk preferences (e.g., smoking status) and measures of workers’ prior accident history. While smokers work, on average, in industries with higher injury risk than non-smokers, smokers also are more likely to have a work -related injury controlling for industry risk. Smokers also are more prone to have had a recent non-work-related acci dent. As a result,

Viscusi and Hersch find that nonsmokers rece ive a greater risk pr emium in their wages than do smokers because the safety effect flattens smokers’ offer curves enough to offset smokers’ preferences for greater wa ges at higher risk levels. To address potential omitted variable bias arising from differences in worker characteristics, employing a panel data set could allow one to difference out or dummy out individual-specific unobservables, so l ong as these are constant throughout the time period covered by the panel. Unfortunately, very few data sets exist that follow a set of workers over a period of several years. Br own (1980) used the National Longitudinal Study Young Men’s sample over 1966 – 1973 (exc luding 1972) with the Society of Actuaries mortality risk data. While he reporte d results that were not consistent with the theory of compensating differentials fo r a variety of nonpecuniary aspects of employment, he did estimate a positive and statistically significant coefficient on the21

mortality risk variable. Brown noted that his estimate of the risk premium was nearly

three times the size of the estimate in Th aler and Rosen (1975), which first used the Society of Actuaries mortality risk data. 1.2.6 Compensating differentials for risk or inter-industry wage differentials. Several recent papers have claimed that estimates of risk premiums in this kind of wage regression analysis actually re flect industry wage premiums because the fatality risk variables typically reflect i ndustry-level risk (Leigh 1995, Dorman and Hagstrom 1998). Both Leigh and Dorman and Hagstrom eval uate the proposition that risk premiums simply reflect industry premiums by comp aring compensating differential models without dummy variables for industry affiliation of each worker with models that include such dummy variables. Their claim that industry premiums mask as risk premiums in these wage regressions suffers from several deficiencies . First, a large number of studies have included industry dummy variables in their statistical analyses and found significant compensating differentials for risk. For ex ample, the first wage-risk tradeoff study by Smith (1974) employed six industry dummies and yielded a statis tically significant compensating differential for risk. Vi scusi (1978a) included 25 industry dummy variables in his analysis based on the Survey of Working Conditions danger variable (0, 1 variable reflecting a worker’s subjective perception of on-the-j ob risk), although he excluded the dummy variables from the analysis based on the industry-level BLS risk

data. 12 In both sets of analyses, danger and the BLS risk measure were statistically significant and generated very similar estimat es of the risk premium. Freeman and

12 Viscusi (1978a) excluded the dummy variables out of concern of inducing multicollinearity between an industry-level risk measure and industry dummy variables. Refer to the discussion below on multicollinearity.22

Medoff (1981) found a statisti cally significant risk premiu m in their analyses that included 20 industry dummy variables and the BLS injury rate measure. In their

evaluation of the U.K. labor market with an occupational mortality risk variable, Marin and Psacharopoulos (1982) found a statistically signifi cant risk coefficient while their SIC code dummies were insigni ficant. Dickens (1984) estimat ed regression models with the BLS fatality risk measure and 20 industr y dummy variables (1- and 2-digit SIC code industries). For the union sample, he found a positive and statistically significant coefficient on risk. Leigh and Folsum ( 1984) included 2-digit SI C code industry dummy variables in their wage regressions, and they found statistically signifi cant coefficients on mortality risk in all eight mortality risk models reported. Dillingham (1985) estimated regression models with industr y dummy variables (at the 1-digit SIC code level) and without. In both cases, he found statistically significant and positive coefficients on his measure of mortality risk. Moreover, the coe fficients were virtually identical (0.0023 vs. 0.0022), although the standard error was high er for the model with industry dummy variables (perhaps related to risk-industry dummy variable collinearity). Cousineau et al. (1992) included 29 industry variables in thei r evaluation of the Canadian labor market that estimated statistically significant coeffici ents on both injury and mortality risks. Lott and Manning (2000) included 13 industry dummy variables in their evaluation of longterm cancer risks in U.S. labor markets, and found a statistically significant risk premium based on industry-level meas ures of carcinogen exposure. Second, inserting industry dummy variable s into the regressi on equation induces multicollinearity with the risk variable. Prev ious researchers such as Viscusi (1979) have

noted this as well. Hamermesh and Wolfe (1990) employed dumm y variables for five23

major industries in their analysis of injury risk on wages. They note that a finer breakdown by industry could be us ed. A complete set of dummy variables at the 3-digit SIC code level, however, would completely e liminate all variation in the injury risk variable, which is measured at the 3- digit SIC code level (p. S183). While multicollinearity does not affect the consis tency of the parameter estimates, it will

increase standard errors. This induced multicollinearity is also evid ent in the Dorman and Hagstrom results for the models using NIOSH fatality risk data. 13 Dorman and Hagstrom interact the NIOSH fatality risk measure by a dummy va riable for union status (and for non-union status in the second set of regressions). C ontrary to their hypothe sis, including industry dummy variables does not reduce the coefficient in the un ion-risk interaction models. Inducing multicollinearity does depress the t-statistics slightly, although not enough to render the coefficients statistically insigni ficant. The models with the non-union-risk

interaction reflect the induced multicollinear ity, as the t-statistics fall below levels typically associated with stat istical significance moving from the standard model to the industry dummy model. While the coeffici ents in these indus try dummy-augmented

models fall from their levels in the standard models, they are not statistically different from the standard models’ coefficients. Based on the NIOSH fatality risk data, the Dorman and Hagstrom results appear to illu strate that including collinear regressors

13 We focus our discussion here on their NIOSH data-based results for several reasons. First, we believe that the NIOSH data are superior to the 1980s BLS fa tality risk data as discussed above. Second, the regression models based on non-NIOSH data in Dorman and Hagstrom have insignificant risk coefficients for all specifications – without industry dummy variable s, with industry dummy variables, and with other industry characteristics. While we are not certain wh y they did not find significan t risk coefficients with the BLS risk data as previous researchers had, it seem s moot to argue that a coefficient on a risk variable actually represents an industry effect if that coefficient is not significant.24

(industry variables) can increase standard errors but not significantly affect the magnitudes of the parameter estimates.

2. The value of a statistical life ba sed on U.S. labor market studies

The value of a statistical life should not be considered a universal constant or some “right number” that researchers aim to infer from market evidence. Rather, the VSL reflects the wage-risk tradeoffs that refl ect the preferences of workers in a given sample. Moreover, transferring the estimates of a value of a statistical life to non-labor market contexts, as is the case in benefit-cost analyses of environmental health policies for example, should recognize that different populations have different preferences over

risks and different values on lif e-saving. If peopl e face continuous sa fety choices in a variety of contexts, however, the same i ndividual should exhibit the same risk-money tradeoff across different contexts, provided the character of the risks is the same.

Researchers have undertaken more than 30 stud ies of compensating differentials for risk in the U.S. labor market. Some studies have evaluated the wage-risk tradeoff for the entire labor force, while othe rs have focused on subsamples such as specific occupations (e.g., police officers in Low and McPheters 1983 ), specific states (e.g., South Carolina in Butler 1983), blue-collar workers only (e.g ., Dorman and Hagstrom 1998 and Fairris 1989), males only (e.g., Berger and Gabrie l 1991), and union members only (e.g., Dillingham and Smith 1984). These hedonic labor market studies also vary in terms of their choice of mortality risk variable, whic h can significantly influence the estimation of a value of a statistical life (for comparis on of NIOSH and BLS data, refer to Moore and Viscusi 1988a and Dorman and Hagstrom 1998).25

Table 2 summarizes the estimated VSLs for the U.S. labor market from the literature over the past three decades. 14 Because some studies provided multiple estimates, in these instances we provide illustrative results based on the principal specification in the analysis. Table 2 provides a sense of the magnitude and range of U.S.

labor market VSLs and illustrates the influe nce of factors such as income and the magnitude of risk exposure as well as specif ication issues such as including nonfatal injury risk and worker’s compensation. 15 Viscusi (1993) reported that most surv eyed studies fall within a $3.8 - $9.0 million range, when converted into year 2000 dollars. 16, 17 While we include more papers from the United States as well as fi ndings from other countries, the general conclusion remains unchanged. Half of the studies of the U.S. labor market reveal a value of a statistical life range from $5 million to $12 million. Estimates below the $5 million value tend to come from studies that used the Society of Actuaries data, which

14 We selected papers for inclusion in this literature review with a modest set of criteria. First, a study should be written in English. Second, a study should be published in either an academic journal or a book. Third, a study should provide enough information to calculate a value of a statistical life. In several cases, information provided in more recent papers (such as per capita incomes report ed for some studies in Viscusi 1993 and Mrozek and Taylor 2002) has been used with reported coefficien t estimates to calculate the value of a statistical life for a study. Our aim is to characterize as best as possible the universe of wagerisk studies in the literature, so we have not attempted to purge this assessment of so-called “low quality” studies or to modify the value of a statistical life estimates from such studies. For some studies, we have presented a range of the value of a statistical life esti mates and for others we have presented an illustrative point estimate. In the case of the latter, we have focused on the reported results for the whole sample (as opposed to union-only, blue-collar only, managerial-only, etc. samples) based on the econometric specification preferred by th e studies’ authors. 15 While these estimates have been adjusted to constant year dollars (2000 US$), they have not been adjusted for differences in the samples’ income levels. The per capita income data provided in Table 2 coupled with income elasticity estimates in Section 6 can be used to modify the values of a statistical life in Table 2 so that they reflect a common income level. 16 In this paper, we present all VSLs in terms of 2 000 US$. All domestic values are converted using the CPI-U deflator series (Council of Economic Advisers 2002 Table B60). International conversions are made using purchasing power parity exchange rates from the Penn World Table 6.0 (see Summers and Heston 1991, Aten et al. 2001, and Internet: http://pwt.econ.upenn.edu ) and then converted to year 2000 dollars with the CPI-U deflator series. 17 Viscusi (1993) actually reports $3 – $7 million in December 1990 US$. This has served as a reference range in several subsequent value of a statistical life st udies. Note that we have updated this range to 2000 US$.26

tends to reflect workers who have self-selected themselves into jobs that are an order of magnitude riskier than the average. Ma ny of the studies yielding estimates beyond $12

million used structural methods that did not estimate the wage-risk tradeoff directly or

were derived from studies in which the author s reported unstable estimates of the value of

a statistical life. Our median estimated VSL from Table 2 is about $7 million, which is in line with the estimates from the studies that we regard as most reliable. In terms of methodology, we are more confident in the re sults presented in Viscusi (1978a, 1979), which include the most extensive set of non-pe cuniary characteristics variables to explain workers’ wages, and the results presented in Moore and Viscusi (1988a), which include the NIOSH mortality risk data in lieu of the pre-1992 BLS mortality risk data. A salient research issue of policy importance is the effect of income levels on the wage-risk tradeoff. For example, Hamermesh (1999) notes that as wage inequality has increased over the last several decades, so ha ve on-the-job mortality risks diverged. He notes that workplace safety is highly income-elastic. This result is related to the findings in Viscusi (1978b) that the valu e of a statistical life is increasing in worker wealth. Similarly, Viscusi and Evans (1990) have estim ated the income elasticity of the value of statistical job injury risks to be 0.6 to 1.0. The effect of income on the wage-risk tradeoff

is evident in a historical evaluation of em ployment risks as well. Kim and Fishback (1993) estimated compensating differentials for mortality risk in the railroad industry over the period 1893 – 1909 and found implicit valu es of statistical life on the order of $150,000 in today’s dollars. 18 Our meta-analysis below examines the role of income differences in generating the variation in VSL estimates.

18 Also refer to Fishback and Kantor (1992) for a historical evaluation of compensating differentials for occupational risk in the late 19th century.27

While most hedonic labor market studies focus on the risk of accidental death or accidental injury, several papers have attemp ted to explore the effect of occupational disease. Lott and Manning (2000) evalua ted the effect of carcinogen exposure on workers’ wages within the context of changi ng employer liability laws. In lieu of the standard mortality risk measures, the aut hors employ the Hickey and Kearney carcinogen index, which represents worker carcinogen exposure at the 2-digit SIC code level. 19 They find that workers’ wages reflect a ri sk premium for carcinogen exposure. Lott and Manning convert their results into a value of a statistical life assuming that the index is a proportional representation of the actual probability of ge tting occupational-related cancer, that 10 – 20 percent of all cancer deat hs result from occ upational exposures, and that the probability of a worker getting cancer ranges from 0.04 to 0.08 percent per year. We have modified their reported VSL range to account for a latency period. 20 Based on these assumptions, the authors estimate that the value of a statistical life based on occupational cancer would range from $1.5 – $3.0 million. Assuming that occupational cancers, however, comprise a smaller fractio n of all cancer deaths would increase the implicit VSL. 21

19 Smith (1983) also used the Hickey and Kearney carcinogen exposure index to complement his assessment of compensating differentials for injury risk in U.S. labor markets. He found that the index is significantly positively correlated with wages im plying a risk premium for workers’ operating in environments exposing them to more carcinogens. Further, Smith included a measure of total suspended particulates (TSP) based on the workers’ locations and found a statistically significant and positive correlation between TSP and workers’ wages. Since TSP has been linked with various respiratory diseases, this could illustrate another premium for workers’ bearing long-term risks on the job. 20 The values we report reflect an assumed latency period of 10 years and a real discount rate of 3 percent. Note that the VSL estimates in parentheses in Table 2 represent the values repo rted by Lott and Manning. Employing a real discount rate of 7 percent, consistent with U.S. Office of Management and Budget (1992) guidance, over a 10-year period effectively reduces the VSL reported by Lott and Manning in half. 21 Meng (1991) attempted to account for occupational disease by including a variable that reflected the rate of heart attacks and industrial disease. However, very modest information about the basis for this variable is provided. It is difficult to discern whether the variable captures long-term work-related risks or simply a selection effect that contaminates the data like the Society of Actuaries data set.28

Several early papers in the literature did not find statistically significant compensating differentials for on-the-job mo rtality risk. For example, Leigh (1981) estimated a risk premium for injuries but not for fatalities. Dorsey (1983) likewise did not find a mortality-based ri sk premium. The Leigh study coupled the Society of Actuaries mortality data with BLS injury data. The combination of greater measurement error in the data and the high correlation between injury risks and mortality risks probably led to the insignifican ce of the mortality risk vari able. The Dorsey study uses industry-level averages, instead of worker-specific values, as its unit of observ ation. This averaging across industry for wages and relate d explanatory variable s may have reduced the variation necessary to discern the effects of job-specific influences on wage, such as job risk. More recent papers by Leigh (1995) and Dorman and Hagstrom (1998) also do not find compensating differentials in many m odel specifications. As discussed above, we do not find their inter-industry wage different ial discussion compelling. Nevertheless,

Table 2 includes their results based on the NIOSH data with industry dummy variables. 22 Some of these analyses of U.S. labor markets investigated the potential heterogeneity in the risk preferences of workers in the labor force in which there is worker sorting by level of risk. The empiri cal issue is whether the wage-risk tradeoff takes a linear or concave shape. A linear fo rm would imply that an incremental increase of risk in the labor market requires a propor tional increase in the wage differential. A concave form, however, would imply a less than proportional increase in the wage differential, perhaps reflecti ng sorting by workers based on their risk preferences.

22 The authors also report estimates using the less reliable pre-1992 BLS risk data.29

To evaluate the shape of this tradeo ff, one can modify the wage equation regression model to incl ude both mortality risk and the sq uare of mortality risk. If the latter term is not significant, then the wage -risk tradeoff is linear for the range of risks and wages covered by the study’s sa mple. If the squared term is significant and negative, then the wage-risk tradeoff takes a concave form. Viscusi (1981), Olson (1981), Dorsey and Walzer (1983), and Leigh and Folsum ( 1984) all found evidence that the risk-wage

tradeoff curve is concave. 23 All four studies include regr ession models with a quadratic representation of mortality risk. Figure 2 illustrates how the value of a statis tical life varies with mortality risk for a sample of six regression models from th ese four papers. Viscusi (1981; linear) and Leigh and Folsum (L&F 1984; linear) repres ent regression models where the dependent variable is the hourly wage while the other four lines represent re gression models with the logarithm of the wage as the dependent variable. All si x models include measures of nonfatal injury risks (probability of a lost-w orkday accident and, in some cases, duration of lost-workday accident). The slopes of th e risk-VSL lines in this figure are similar within the wage-specification type where the wa ge-based models appear to have a steeper tradeoff than do the logarithm of wage-based models (with the exception of the Dorsey and Walzer model, although this may reflect th e fact that the sample in their study faced mortality risks 2 to 3 times smaller on average than the samples in the other studies). Based on these models, populations of individuals who select into jobs with very minor risks (e.g., on the order of 1 in 100,000) have implicit values of st atistical life ranging from $12 to $22 million. Increasing the risk ten -fold, to levels that are close to the mean

23 Siebert and Wei (1998) found a concave wage-risk relationship with a risk and risk-squared specification for their analysis of the Hong Kong labor market. Meng and Smith (1990, 1999) also found the same relationship in their assessments of the Canadian labor market.30

mortality risks in these studi es, modestly reduces the VSL into the range of $10 to $18 million. Figure 2 illustrates that very high risks result in small values of statistical lives, although caution should be exercised when considering extrapolations beyond the samples’ ranges.

3. Evidence of the value of a statistical lif e from U.S. housing and product markets Housing and product market decisions also reflect individual tradeoffs between mortality risk and money. The main me thodological difference is that economists typically estimate a hedonic price equation rather than a hedonic wage equation. The underlying theory is essentially the same, as comparison of Rosen ( 1974) with the wage equation analysis above will indicate. Table 3 presents the results from ten studies that evalua ted the price-risk tradeoffs for seatbelt use, cigarette smoking, home fi re detectors, automobile safety, bicycle helmets, and housing price responses to hazardous waste site risks. 24 The studies in general find an implicit value of a statistic al life on the same orde r of magnitude as the labor market studies, although they tend to be a little lower. The lower estimates may reflect several characteristics of these studies that distinguish them from the labor market st udies. First, some product decisions do not provide a continuum of price-ri sk opportunities (unlike the la bor market that does offer a fairly continuous array of wage-risk employme nt options) but rather a discrete safety decision. For example, Dardis’ (1980) eval uation of smoke detector s represents such a

24 All these studies evaluate risk-income tradeoffs in th e United States. In our survey of the literature, we found only one study focusing on behavior outside of the United States. Ghosh, Lees, and Seal (1975) study the tradeoff between highway speeds and mortality risk in the United Kingdom. They derive a value of a statistical life estimate of $0.9 million.31

discrete choice. In such a case, the cons umer’s decision to purchase a smoke detector reveals only the lower bound on the willingness to pay for the reduced risk. Similarly, the study by Jenkins, Owens, and Wiggins ( 2001) examines the purchase of bicycle helmets. It is interesting, however, that th eir results show VSLs increasing over the first half of the life cycle. Second, the types of products considered in some studies may induce selection based on risk preferences. For example, the low estimated VSL for cigarette smokers found by Ippolito and Ippolito (1984) presumab ly reflects the non-random character of the smoking population. Their research focu ses on cigarette smokers, and they estimate a VSL lower than from most product market studi es. The lower VSL is consistent with the findings in Hersch and Viscusi (1990) and Viscusi and Hersch (2001) who find that individuals who engage in ris ky behaviors, such as cigare tte smoking and driving without seatbelts, have lower implicit values for inju ry than do those who do not engage in such

behavior. Third, several studies are based on infe rred, instead of observed, price-risk

tradeoffs. Consider the seat belt and child seat studies by Blomqui st (1979) and Carlin and Sandy (1991). In these studies, drivers’ or occupants’ safety is traded off with the time to secure a seat belt or a child seat. The authors assume a given time cost – for example, Blomquist assumes that it takes 8 seconds to secure a seat belt. Then this time is monetized at the individual’s wage rate . Unlike labor market studies where the monetary value of the attribute in question (j ob wage) is observed, these studies do not

observe the actual time drivers take to buckle their seat belts. Moreover, they do not account for other aspects of seat belt use, su ch as the costs of discomfort of wearing a32

seatbelt, which would increase the implicit valua tion of a statistical li fe derived by this methodology. The studies focused on automobile pur chases and home purchases do not suffer from the need to infer the monetary component of the price-risk tradeoff. For example, Atkinson and Halvorsen (1990) and Dreyfus and Viscusi (1995) evaluate the risk-price tradeoff for automobiles. They construct hedonic price models very similar to the hedonic wage models used in labor market an alyses. Both studies include car purchase price (annual average for a given model) as the dependent variable and an array of automobile attributes as explanatory variables, such as vehicle size, power, reliability, fuel economy, and safety (fatal accident rate). Just as in the labor market hedonic studies, the coefficient on the safety variable in thes e automobile price hedonic studies reveals the price-risk tradeoff. Automobile purchases s hould be less likely to suffer the selection bias of the cigarette smoking study or the discre teness in decision of the fire alarm study. Gayer, Hamilton, and Viscusi (2000) eval uate the tradeoff between housing prices

and cancer risk associated with hazardous wa ste sites. The auth ors develop a housing hedonic price model, similar in form to the labor market hedonic studies. The dependent variable is the price of a hous e sold over a five-year period in the gr eater Grand Rapids, MI area, and explanatory variables include house characteristics such as number of bedrooms and bathrooms, neighborhood characteri stics, property tax rates, measures of proximity to a Superfund hazardous waste site, and calculated cancer ri sk associated with exposure from the nearest hazardous site. The VSL interpretation from this study is analogous to that of Lott and Manning (2000) . The hedonic price model generates the value of avoiding a statistical cancer case, wh ich may not necessarily reflect the value of33

a statistical life to the extent that some cancers are treatab le. If housing decisions are made based on the expectation that cancers as sociated with hazardous waste site exposure are terminal, then this price-risk tradeo ff can be considered comparable to a VSL. 25

4. The value of a statistical life base d on non-U.S. labor market studies While about 25 wage-risk studies of the U.S. labor market were published in the 1970s and 1980s, only three studies on non-U.S. la bor markets appeared in the literature during this period. We have identified anot her 19 labor market hedonic studies in both developed and developing countries outside of the U.S. context published since 1990. The studies presented in Table 4 include ev aluations of wage-risk tradeoffs in labor markets in Australia, Austria, Canada, Japan, and the United Kingdom. More recent work in developing countries has focused on As ia, including analyses of labor markets in Hong Kong, India, South Korea, and Taiwan. Marin and Psacharopoulos (1982) undert ook the first hedonic labor market analysis of job risks outside of the United Stat es in their study of the U.K. labor market. Based on wage and risk data from the 1970s, they found a value of a statistical life of about $3.5 million. Arabsheibani and Marin (2000) sought to replicate the earlier Marin and Psacharopoulos analysis for the Un ited Kingdom. By employing a similar methodology and more recent wage and risk data from the same sources as in the original study, the authors evaluated the stability of VSL estimates over time. They found,

consistent with other studies of the U.K. la bor market during the 1980s, a higher value of

a statistical life than did Marin and Psachar opoulos. While the evaluation of the whole

25 We have discounted the reported VSLs assuming that homeowners perceive a 10-year latency period and use a 3 percent discount rate in making their housing decisions.34

U.K. labor force yielded a relatively large VSL of about $18 million, regression analyses of subsamples resulted in VSLs ranging up to $68 million (in this case, for non-manual workers). While this result qualitatively confor ms to the U.S. findings of lower VSLs for workers in higher risk jobs (see Figure 2) , the magnitude of the U.K. compensating differentials seems implausibly large. The results from several of the studies of the United Kingdom reveal compensating differentials on the order of 10 percent of total worker wage income. One regression result (with a VSL of $63 million) from Sandy and Elliott (1996) implies a compensating differential for mortality risk comprising nearly 20 percent of worker wages. These risk premia are substantially larger than the compensating differentials evident in other developed countries’ labor ma rkets, even those countries with higher per capita incomes. Moreover, risk levels cannot account for the hi gh wage share of compensating differentials as the mortality risk is lower than in many U.S. studies. The large U.K. compensating differentials may re flect correlation between the risk measure and other unobservables that yield substantial returns to the worker. After the United States, no country has been the focus of more hedonic labor market analyses of wage-risk tradeoffs than Canada. The Canadian studies appear to produce compensating differentials more in line with the U.S. experience than with the

evidence from the U.K. labor market. With the exception of the Lanoie, Pedro, and LaTour (1995), most Canadian labor mark et VSLs fall within the range of $3 – $6 million. The Lanoie et al. findings of a VSL on the order of $18 million – $20 million may reflect their data collection methodology. They surveyed about 200 workers in the Montreal area and solicited workers’ perceptions of risk with a risk information ladder35

similar to that in Gegax et al. (1991), which suffered from using a truncated job risk scale that omitted most job risks in the U.S. economy. Analyses by Lanoie et al. with industry risk measures provided by the Quebec Compen sation Board did not yield statistically significant risk coefficients, while the perc eived risk measures generated these large VSLs. This result contrasts with the findings of Cousineau, Lacroix, and Girard (1992) who found a statistically significant compensa ting differential for ri sk using mortality risk data from the same source on a sample of more than 30,000 Quebec workers. With the exception of some U.K. studies , the compensating differentials estimated in developed country analyses tend to find ri sk premiums ranging between 1 – 2 percent of labor income. These results are broadly co nsistent with the findings in the Duncan and Holmlund (1983) that used Swedish workers’ pe rceptions of danger in lieu of measured industry mortality risks. The authors estimat ed a statistically significant and positive compensating wage differential for dangerous jobs on the order of about 2 percent of wages. Swedish workers’ perceptions of danger yield comparable compensating

differentials to measured indus try mortality risk in both U. S. and European studies (see Viscusi 1979 for an example from the U.S. labor market).

Researchers have also evaluated the VSL in several of the newly industrialized countries of Asia, including Hong Kong, Sout h Korea, and Taiwan. Note that these countries have on-the-job mortal ity risks three to five times greater than the average in Australia, the United States, and the United Kingdom. Fu rther, the average worker earnings are two to four times lower than la bor earnings in developed countries. Kim and Fishback (1999) examined the S outh Korean labor ma rket over the 1984 – 1990 period. Unlike many of the studies in developed countries, which employ worker-36

level data, their unit of observation is at the in dustry level. Kim and Fishback estimate a VSL of approximately $0.5 million. They not e that the estimated VSL is about 94 times the average annual earnings of workers. Si ebert and Wei (1998) estimate a VSL for the Hong Kong workforce that is larger than the Ko rean estimate by about a factor of three. The ratio of VSL to average annual earn ings for Hong Kong is about 150. These estimates are of the same order of magnitude as the ratio of VSL to annual earnings

evident in the U.S. labor market. Liu, Hammitt, and Liu (1997) and Li u and Hammitt (1999) estimated the wagerisk tradeoff in Taiwan. The Liu, Hammitt, and Liu study focuses on all non-agricultural workers while Liu and Hammitt base their analysis on in-person surveys of petrochemical workers. In the former case, the authors use 3-di git industry level ri sk data, while the latter paper uses workers’ ri sk perceptions derived from a survey instrument similar to that in Gegax et al. (1991). Workers’ risk perceptions in the petr ochemical industry yield a mortality risk rate about 35 percent greater than the rate published by the Taiwan Labor Insurance Agency, the data source for the Liu, Hammitt, and Liu study. 26 While petrochemical workers face higher average mort ality risk (perceived and measured) than the average for all non-agricultural worker s in Taiwan, the higher wages and income associated with petrochemical workers in 199 5 relative to the broa der workforce in the early to mid 1980s probably explains why Li u and Hammitt estimated a VSL about twice what Liu, Hammitt, and Liu found. Estimates for the Indian labor market yiel d a value of a statisti cal life greater than the VSLs in other developing countries despite the fact that per capit a income in India is

26 The difference between the mean subjective mortality risk and the objective mortality risk reported by the Taiwan Labor Insurance Agency is statistically significant at the 1 percent level.37

an order of magnitude smaller than in th ese countries. Shanmugam (1996/1997, 1997, 2000, 2001) assessed the wage-risk tradeoff in a variety of studies using survey data of manufacturing workers in Madras, India in 1990. The VSL estimates from these studies range by nearly a fact or of four, even though they reflec t the same wage and risk data, illustrating how a variety of econometric sp ecifications can produ ce in some cases a range of results.

5. The implicit value of a statistical in jury: U.S. and international estimates Complementing the research on the returns to bearing fatal risks in the workplace, a significant number of studies have evaluated the risk premium associated with bearing nonfatal job risks. The hedonic labor market studies of nonfatal risk employ the same econometric approach as used for mortality ri sk. As discussed above, some studies that attempt to estimate jointly the effects of fata l and nonfatal risks on workers’ wages do not find significant effect s of risk on wages for at least one of the risk m easures. Fatal risk is highly correlated with nonfatal ri sk, so joint estimation may resu lt in large standard errors due to collinearity. Omitting one of these variables when estimating the other could result in an upwardly biased estimate of the return to that type of risk. Table 5 summarizes 31 studies from the U.S. labor market (Table 5a) and 7

studies of labor markets outsi de of the United States (Table 5b) that have found statistically significant influen ces of nonfatal job risk on wa ges. These studies employ

three different measures of nonfat al job risks: the ove rall injury rate, th e rate of injuries severe enough to result in a lost workday, a nd the rate of total lost workdays. Studies using different measures of nonfatal job ri sks will generate different risk premiums38

because the return to the frequency of injuries (the injury rate) will usually differ from the return to the severity of injuries (lost wor kdays rate). In two st udies with specialized data, Butler (1983) constructed an inju ry rate from South Carolina workers’ compensation claims, restricting his risk meas ure to only the more se rious work accidents and French and Kendall (1992) and French (199 0) constructed an injury rate for railroad workers based on data collected by the Fe deral Railroad Administration. As an

alternative to these ob jective measures of risk, Viscus i and O’Connor (1984) and Hersch and Viscusi (1990) used workers’ own assessments of risk with risk scales based on the BLS injury rate and the BLS lost workday acci dent rate, respectively. These authors estimated comparable wage-risk tradeoffs base d on subjective risk pe rception as the other studies based on objectively meas ured industry-level risk. These value of statistical injury studies yield a wide range of estimates, reflecting

both the differences in the risk measures us ed as well as whether mortality risk is

included in the results. While several studie s have very high values of injury, such as McLean, Wendling, and Neergaard (1978), Leigh and Folsum (1984), and Biddle and Zarkin (1988), most studies have estimates in the range of $20,000 – $70,000 per injury. The value of statistical injury appears to vary with workers’ preferences over risk, consistent with some of the findings based on the mortality risk literature. As a proxy for risk attitudes, several studies have used information about workers’ behavior outside of the workplace, such as smoking status and seat belt use, to identify the effect of risk preferences on wage-risk tradeoffs. Hersch and Viscusi (1990), Hersch and Pickton (1995), and Viscusi and Hersch (2001) all f ound that smokers have lower injury risk premiums than do non-smokers. Hersch and Visc usi as well as Hers ch and Pickton also39

found that individuals who do not wear seatbelts have lower in jury risk premiums than do individuals who regular ly wear seatbelts. The study by Hersch (1998) is of partic ular interest because it used genderspecific risk measures. Many previous studies had focused on male samples only because estimates using industry-based measur es often failed to yield significant risk premiums for women. Resear chers hypothesized that women di d not work in risky jobs that would pose health and sa fety risks. The estimates by Hersch indicate that the nonfatal injury risk for women is over two-thir ds the size of that for men and that the wage-injury risk tradeoff rates are similar for men and women. The evidence outside of the United States, while based on a smaller set of studies, also indicates significant injury risk premiums. For example, the Cousineau et al. (1992)

result falls within the U.S. range of about $20,000 – $70,000. However, several other Canadian labor market studies provide some es timates that are lower, such as Martinello and Meng (1992) and Meng and Smith (1999). Th e value of statistical injury estimates for India are much smaller, likely reflecting the effect of per capita income on wage-risk tradeoffs. The low values of statistical inju ry are somewhat surprising given that these same studies generated fairly large values of statistical life.

6. The effects of income on th e value of a statistical life

The review of the VSLs above shows th at developing countries tend to have

lower values of statistical life than do deve loped countries. A vari ety of factors could account for such an outcome, such as cu ltural influences on ri sk preferences and40

variations in labor market institutions. Th e dominant cause, however, is most likely that developing countries are poorer , and safety is a normal good, as shown in Viscusi (1978a). The value of a statis tical life should increase with per capita income. To assess the relationship between the value of a statistical life and income, we first review several meta-analyses of the wage-risk literature. Second, we provide our estimates of the income elasticity of the value of a statistic al life based on the meta-analysis approaches employed in four previous studies with a data set we constructed from our review of the papers presented in Tables 2 and 4. Third, we report income elasticities for a number of specifications in our preferre d meta-analytic approach. Since wage-risk studies employ a measure of income (usually a function of hourly or weekly labor earni ngs) as the dependent variable, an individual study cannot estimate the effect of income on the premium for bearing mortality risk. The injury risk study of Viscusi and Evans (1990) used experimental data coupled with market evidence to estimate income elasticities of injury risk valu ations from 0.6 to 1.0. A meta-analysis of existing VSL studies can facilitate the calcula tion of the income elasticity for the value of a statistical life. The type of meta-analysis used in the VSL literature attempts to evaluate the VSL (the constructed dependent variab le) as a function of a number of studies’ characteristics (such as mean income of th e sample population, mean mortality risk, and econometric specification). The published meta-analyses on the value of a statistical life l iterature vary in terms of their sample construc tion, explanatory variables, an d regression technique. Liu, Hammitt, and Liu (1997) sampled 17 wage-risk studies surveyed in Viscusi (1993) and regressed VSL on income and mean risk. The Liu et al. sample comprised primarily41

U.S. wage-risk studies. They reported a stat istically insignificant income elasticity of 0.53. Miller (2000) developed an internati onal sample including more than 60 wage-risk, product-risk, and contingent valuation studies. Miller employed a rela tively small set of explanatory variables, including income. For five models, Miller estimated statistically significant income elasticities ranging from 0.85 to 0.96. Bowland and Beghin (2001) conducted a meta-analysis with a set of 33 wa ge-risk and contingent valuation studies surveyed in Viscusi (1993) and Desvousges et al. (1995). They matched the data on these studies with a variety of country-specifi c data on demographics, human capital, etc. Bowland and Beghin employed robust regression with Huber weights to address concerns about the non-normality in the residuals of their data. Bowland and Beghin reported statistically significant income elas ticities of 1.7 and 2.3. In contrast to the previous three papers, Mrozek and Taylor (2002) constructed a sample of about 200 observations reflecting multiple VSL estimates from 33 wage-risk studies (eight of which evaluated non-U.S. labor markets). They employed the most extensive set of control variables, including those characterizing a study’s sample, risk measure, specification, and earnings. For two models, Mrozek and Taylor impute stat istically significant estimates of 0.46 and 0.49 for the income elasticity for the value of a statistical life. To further explore the relationship betw een income and WTP, we have conducted a meta-analysis based on the U.S. and intern ational VSLs reported in this paper. Our sample includes the VSLs for 49 st udies presented in Tables 2 and 4. 27 Each study yields one observation. Refer to the appendix for a description of the expl anatory variables and their summary statistics.

27 Studies for which we do not have an income measure were omitted.42

We replicated the results from the four previous meta-analysis studies with our wage-risk study sample (see Table 6). For the Li u et al. (1997) model, we replicated their econometric specification exactly . Miller (2000) reported a number of specifications. Only model 3 of Miller’s meta-analysis employed per capita incomes converted to US dollars on a purchasing power pa rity (PPP) basis. Because we constructed all VSLs and annual incomes based on a PPP basis, we rep licated his model 3. Note that dummy variables for contingent valuation surveys and wage-risk studies are unnecessary since our data set comprises only wage-risk stud ies. Bowland and Be ghin (2001) reported results for linear, log-linear, and trans-log specifications. While they presented very

limited information about most of their control variables, we have attempted to replicate

their set of controls. We do not have inform ation on the average age of the sample used in the VSL studies, and we have omitted this va riable from our specif ication. We have proxied for percent of sample in union-aff iliated jobs by accounting for whether the VSL study includes union membership as a control and whether the VSL is union-based. Our studies do not provide average educational atta inment, so we have proxied these values with national annual averag e educational attainment fo r the over-25 population from Barro and Lee (1996). We replicated the robu st regressions with Huber weights. Our analyses with log-linear and trans-log spec ifications, however, yi elded insignificant coefficients on income. We only present th e results from the linear robust regression model with our data. Mrozek and Taylor ( 2002) reported results fr om four specification

models. We have focused on their model 2 sinc e model 1 yields virtua lly identical results and models 3 and 4 are U.S.-specific. We have included all the control variables that43

Mrozek and Taylor report, with the exception of a dummy variable for white collar-based VSLs. Our sample does not incl ude any white collar-based VSLs. Three of the four specifi cations yield statistically significant coefficients on the relevant income variable. We found a comparable point estimate with much narrower

bounds than Liu et al. with th eir specification, perhaps reflecting our larger sample, as their sample is essentially a subset of our sa mple. We found a smaller coefficient on the

income variable than Mill er with his specification, although a very comparable coefficient on the Society of Actuaries risk data dummy variable (e quivalent to Miller’s variable label “risk beyond workplace” with our data). For comparison with Bowland and Beghin’s choice of using “marginal willin gness to pay” as thei r dependent variable (apparently equivalent to the VSL expressed in terms of hourly wage instead of annual labor income), we modified our dependent variable accordingly. Imputing the income elasticity with the linear income coefficient in this model requires the sample means of VSL ($3,350 per hour worked, assuming 2000 hours worked per year and $6.7 million VSL) and income ($26,006). With 23 expl anatory variables a nd only 41 observations, the Mrozek and Taylor specifi cation yields very few precise coefficient estimates. While the reported income elasticities from these four studies va ry by a factor of 3, the imputed elasticity point estimates with our data set cover a mu ch smaller range (see Table 7). With these studies’ specifications , we found income elasticities from about 0.5 to 0.6. The 95 percent confidence interval upper bounds fall below 1.0 for two of the three statistically significant income elasticit ies estimated by the specifications outlined in these four studies. The apparently large variation in income elasticities in this44

literature apparently reflects authors’ choice s of studies for inclusion more so than choices over control variables, regression techniques, etc. To augment the replications of previ ously published meta-analysis specifications, we evaluated a large number of specifications. Based on the existing literature, we focused on two regression techniques, ordinary least squares and robust regression with Huber weights. We have varied the control variables from as few as 3 to as many as 18, recognizing that coefficient estimates’ precision will decline with the length of the righthand side of the regression equations given our sample size. We chose to include explanatory variables of the following types: income and mean risk (common to all specifications), type of risk measure, and specification variables.

The estimated coefficient on the income variable is rather stable across both regression techniques and for a wide variation in the number of control variables (see Table 8). For the OLS specifications, the income elasticity varies from 0.49 to 0.60. The 95 percent confidence intervals never range below 0.2 and ne ver exceed 0.95. For the robust regression specifications, the income elasticity varies from 0.46 to 0.48. The 95 percent confidence intervals never fa ll below 0.15 and never exceed 0.78. 28 The income coefficients in all specifica tions are statistically significant at the 1 percent level. Based on the approximately 50 wage-risk studies from 10 countries, we can conclude from these results that the income elasticity for the value of a statistical life is

28 We also estimated a regression with the Mrozek and Taylor set of control variables, with an important exception of replacing the hourly earning s variable with the natural logarithm of annual income. With an OLS specification, we estimated an income elasticity of 0.76 with a 95 percent confidence interval of 0.20 – 1.32 (n=41). In the robust regression with Huber weights specification, we estimated again a point estimate for the income elasticity of 0.76, but with a much tighter 95 percent confidence interval of 0.73 – 0.79 (n=38). The income variable was statistically si gnificant at the 5 percent level in the OLS regression and significant at the 1 percent level in the robust regression. The iterative weighting process in robust regression with this much larger set of control va riables effectively eliminat ed several low-VSL studies relative to specification 6 in Table 8, which may have resulted in the larger elasticity.45

less than 1.0. Across a number of specificati ons with our data, our point estimates of the income elasticity range betw een about 0.5 and 0.6. No te that in none of our specifications did the income elasticity ’s 95 percent confidence interval upper bound

exceed 1.0. Current practice by regulatory agencies is effectively in line with these findings. The U.S. EPA (1999) accounted for income growth into the 22nd cen tury in monetizing the long-term mortality risk reduction benefits from stratospheri c ozone protection. 29 In a regulatory context, the U.S. EPA (2000b) also accounted for income growth over a thirtyyear period in monetizing the mortality risk reduction benefits from reduced particulate matter pollution associated with the diesel sulf ur standard for heavy- duty trucks. In both these cases, the U.S. EPA employed an income elasticity of 0.4 and conducted sensitivity analyses with a low-end elasticity of 0.1 and a hi gh-end elasticity of 1.0. If our results of the income elasticity apply over time, the point estimate chosen by the EPA is reasonable, although more narrow bounds may be appropr iate for the sensitivity analysis. The meta-analysis regressions can also serve to characterize some of the uncertainty in value of a stat istical life estimates. We constructed the mean predicted VSL values presented in the last two rows of Table 8 by first using the estimated coefficients from the meta-analysis regressi ons to predict the natural logarithm of VSL for each study. Then we converted each pred icted log(VSL) to a predicted VSL. We averaged these over all studies that were incl uded in each regressi on model’s sample to produce the average values reported in the ta ble. We constructed the average 95 percentconfidence intervals by first estimating the prediction error for each study from the metaanalysis regressions. We th en used this prediction error to construct study-specific 95

29 The Science Advisory Board (2000) has supported EPA’s adjustment of the VSL for income growth.46

percent confidence intervals. The valu es for the lower and upper bounds of these confidence intervals were then averaged over all the studies in the regression sample. The U.S. specific results are based on regressi on samples that include non-U.S. studies; only the averaging is U.S.-specific. 30 The mean predicted VSLs from the meta -analysis regression models for the whole sample vary from $5.0 to $6.2 million, and from $5.5 to $7.6 million for the U.S. sample. An assessment of median predicted VSLs produced very similar results. For most regression models, the 95 per cent confidence interv al upper bound is double or more than the 95 percent confidence interval lower bound. Note that the small number of degrees of freedom in specifications 3 and 6 yielde d very large bounds around the measure of central tendency. While this analysis can ch aracterize some of the uncertainty around the value of a statistical life, several caveats are in order. First, the description of uncertainty presumes that the proper VSL meta-analysis model has been specified. Otherwise, the bounds around the predicted means are not valid. Sec ond, this assessmen t of uncertainty regards the value of a statistical life construc ted from a sample of wage-risk studies of prime-aged workers. Policy a pplications of these VSLs in benefits transfer should consider appropriate modificati ons to the VSL point estimate and the distribution around

it.

30 We also calculated the median predicted VSL values for the full and U.S. samples. For the full sample, the median predicted VSL never exceeded the mean predicted VSL in any of the six regression models by more than 14 percent, and the mean predicted VSL ne ver exceeded the median predicted VSL by more than 15 percent. For the U.S. sample, the median predicted VSL exceeded the mean predicted VSL in all six regressions, but never by more than 7 percent.47

7. The effects of union affiliation on the value of a statistical life

Since the U.S. and international evid ence from labor markets and other product markets demonstrate a significant wage-risk tradeoff, numerous researchers have explored several factors that may influence the compensating differential for risk. The relationship between union affiliation and the wage-risk tradeoff has received substantial

attention in the literature. Most studies of the U.S. labor market find that union affiliation is positively correlated with a grea ter wage-risk tradeoff while the international

evidence is much more mixed. Workers in union jobs may enjoy an addi tional premium for b earing risk greater than those in nonunion jobs for several reasons . First, if firms face an upward sloping labor supply curve, then the absence of coll ective bargaining may re sult in inefficiently low level of workplace safety. Viscusi (1980) shows that if the marginal worker’s valuation of workplace safety differs from th e average worker’s valuation, then the firm would provide a suboptimal level of safety. If the marginal worker is willing to accept less of a decrease in wage for an incrementa l improvement in safety than the average worker, then workplace safety would be too lo w. If the marginal worker tends to be younger and less experienced while the average worker tends to be older and wealthier, then the average worker with greater wealth and family obligations may have a greater preference for workplace safety than the margin al worker. In light of this inefficiently low provision of safety, unions may bargain over workplace safety in addition to wages

and other benefits on behalf of the inframarginal workers who may place greater value on risk reduction than the marginal worker.48

A second, and not entirely unrelated phenomenon, is that workplace safety may be a quasi-public good and suffer the comm on under-provision associated with such goods due to free-riding (Dillingham and Smith 1984). If a firm provides some level of workplace safety (e.g., a fire extinguishing system), then one worker’s consumption of this safety does not preclude another worker from enjoying the same consumption. Since safety is quasi-public, a worker lacks the incentive to truthfully reveal his or her preference for safety, especially since an in crease in safety would likely correspond to a decline in the wage (or some other benefit). Collective action can overcome such freeriding. In this case, collective bargaini ng by a union with a firm could reflect all workers’ true preferences for safety, and result in higher a ggregate demand for safety by workers than what would be expected in a non-union setting. This higher demand would translate into greater compensating differentials for job-related injury and fatality risk. Third, if some workers lack adequate information about th e safety at their workplace, then they may underestimate the actual risks th ey face. Workers underestimating their on-the-job risk would dema nd lower wages than if they held correct perceptions of risk. Unions potentially could provide workers with more accurate information about their on-the-job risks (V iscusi 1979, Olson 1981). Unions can take advantage of economies of scale in providi ng information not avai lable to unorganized non-union workers (Dillingham and Smith 1984) . Unions may also negotiate for mechanisms that increase worker exposure to safety information. For example, Olson noted that a 1976 BLS survey showed that 36 percent of all workers covered by a collective bargaining agreement worked in es tablishments that sponsored joint firmworker safety committees.49

To evaluate the extent to which these factors influence compensating differentials for on-the-job risk, researchers have taken two estimation approaches (see Table 9). First, some have split their samples into union and non-union subsamples and estimated the wage regressions separately for each subs ample. Second, others have included an interaction term, risk variable x union dummy variable, in the wage regression model. In our review of papers evalua ting union effects, only Olson (1981) assessed the union-risk premium with both the separate sample regression approach and the risk-union interaction approach. Both approaches yi eld substantial differences in compensating

differentials for union a nd non-union members. Regardless of estimation strategy, most assessments of the U.S. labor market found higher risk premiums for union workers th an for non-union workers (see Table 9a).

Of the ten U.S. labor market value of life stud ies we reviewed that evaluated the role of unions in risk premiums, nine found uni on workers enjoyed greater compensating differentials for bearing risk than nonunion wo rkers. In contrast to accepted theory, several of these papers found that non-union workers had insi gnificant or statistically significant negative compensating differentials for risk. 31

Table 9b summarizes the rather mixed e ffects of unionization on premiums for

nonfatal risks in the U.S. labor market. In th e studies that controlled for fatal risks, the compensating differential for injury ri sk for nonunion workers often exceeded the differential for union workers, even in the same studies where the union fatality risk premium was greater (e.g., Olson 1981, Dors ey 1983, Dorsey and Walzer 1984). Olson

31 For example, Dorsey (1983) estimated a statistically significant negative coefficient on the fatality risk variable and a statistically significant positive coeffi cient on the union x risk interaction variable. This combination (with the union x risk coefficient greater in magnitude than the fatality risk coefficient) results in a positive compensating differential for union workers and a negative differential for non-union workers.50

found that union workers enjoyed a greater positive premium than nonunion workers for injury incidence but a negative premium for inju ry duration (number of lost workdays), in

contrast to nonunion worker s’ positive premium. In regressions that did not include a variable for fatality risk in the estimation model, the findings reflected the results for fatality risk discussed above. Hamermesh and Wolfe (1990) found that the extra co mpensating differential for union workers reflected injury incidence, while injury dur ation was insignificant, similar to Olson. While Freeman and Medoff (1981) could not di scern between the sta tistically significant injury risk premiums for union and non-union workers, Smith (1983), Biddle and Zarkin (1988), Fairris (1992), and Hersch and Pi ckton (1995) all found greater compensating

differentials for nonfatal risks for union than for nonunion workers. While the majority of the U.S. research illustrates greater risk premiums for union workers, the research on labor markets in other countries often reveals a more ambiguous union impact on risk premiums. Marin a nd Psacharopoulos (1982) conducted the first analysis of compensating differentials for ri sk in the U.K. labor market, and found that union affiliation had an insignificant impact on the risk premium. In an attempt to replicate this initial study, Arabsheibani and Marin (2000) al so could not find any evidence supporting a union-risk premium base d on membership or union strength. In contrast, Siebert and Wei (1994) found higher union risk premiums when accounting for potential endogeneity of risk. Subsequent research by Sandy and Elliott (1996) countered this finding with analysis indicating larg er compensating differentials for risk for

nonunion members. These four researchers coll aborated in a follow-up study, Sandy et51

al. (2001), which concluded with a qualifie d claim that nonunion workers enjoy greater risk premiums. For the Canadian labor market, several analyses have found little support for a positive impact of union affiliation on compensating differentials for risk. In a series of analyses with union x fatality risk interaction terms, Me ng (1989, 1991), and Martinello and Meng (1992) found no significant effect for accident risk, while Meng and Smith (1990) found a negative statistica lly significant coefficient th at when combined with the fatality risk coefficient would translat e into no compensating differential for union members (in contrast to the positive risk premium for non-union members). In contrast, Cousineau et al. (1992) found for a large Qu ebec sample that union members received larger premiums for both fatality risk and injury incidence, but a smaller premium for injury duration, than nonunion members. Furt her, Lanoie et al. ( 1995) found significant positive compensating differentials for perceived risk for the union sub-sample from their survey of Montreal work establishments. Finally, the few analyses of developing country labor markets have also found

mixed effects of union affiliation on a worker’s risk premium. In his analysis of the Indian labor market, Shanmugam (1996-7) incl uded a union x fatality risk interaction term, and found that union members alone enjo y a compensating differential for risk. For the South Korean labor market, Kim and Fish back (1999) could not statistically discern compensating differentials for risk between union and non-union workers.52

8. The effects of age on the value of a statistical life Evaluating wage-risk tradeoffs in labor markets to estimate the value of a statistical life raises the important question of whether life expectancy affects the value of a statistical life. Age affects the duration of life at risk and also may be correlated with

other variables that a ffect one’s willingness to bear risk, which are not age effects per se but rather reflect changing preferences over th e life cycle. Numerous analyses have shown that the magnitude of the VSL is a de creasing function of age, whereas the value of any particular year of life may increase with age (Rosen 1988). 32 Wholly apart from life expectancy effects, accounting for the effect of age in the utility function in terms of deteriorating health and quality of lif e would have generated similar results. 33 Using this framework, Rosen undertook seve ral simulations based on his previous empirical work (Thaler and Rosen 1975). He es timated that the value of a statistical lifeyear, which is equal to the expected consum er surplus for another year, for the averageaged individual in the sample ranges from about $31,000 to $130,000, based on discount rates ranging from 0 to 12 percent. Usin g data on life expe ctancy by age, Rosen

calculated the value of a statistical life for comparable individuals who varied from 36 years to 48 years of age. The 48-year old’s VSL is 10 percent less th an the 36-year old’s

VSL.

Several researchers have unde rtaken direct empirical esti mates of the effect of age

on the return to risk in hedonic labor market analysis. A simple approach to estimating

32 Rosen’s research yields results similar to the Jone s-Lee (1976), Jones-Lee et al. (1985), and Shepard and Zeckhauser (1982, 1984) finding that the value of a sta tistical life takes an inverted-U shape with respect to age. Also refer to Garber and Phelps (1997) for an assessment of quality-adjusted life-years (QALYs) in the cost-effectiveness literature. Jenkins et al. (2001) provide some evidence that the value of a statistical life is increasing over childhood through the pre-retirement years. 33 Modifying utility functions in this way would be analogous to constructing QALY measures, common to valuations based on health status in the health economics literature. The QALYs are usually based on stated preference methods (see Cutler and Richardson 1997).53

the effect requires interacting the mortality risk and age variables in the regression model. While some researchers did not identify signific ant coefficients to this interaction (Meng and Smith 1990 and Shanmugam 1996/7, 2001), several others found statistically significant and negative estimate s broadly consistent with th e theory (see Table 10). Research by Thaler and Rosen (1975), Visc usi (1979), Arnould and Nichols (1983), and Moore and Viscusi (1988b) yielded the negativ e relationship between age and the return

to risk. Within the context of a local housi ng market, Portney (1981) found that the value

of a statistical life based on trading off mortality risk associated with local air pollution exposure and housing prices declines significan tly with age: an individual under the age of 45 has a VSL 20 times gr eater than an individual over the age of 65. Dillingham, Miller, and Levy (1996) employe d a modified approach by focusing on the willingness to pay to avoid a fully impa ired worklife, where death is the extreme case of impairment. The authors construct a risk variable that reflects injury frequency, severity, and probability of fatality. They assume that a worklife shortened by a fatal injury is equivalent to a worklife shortene d by a permanently disabling injury. Their “value of remaining worklife” ranges from $3.1 - $4.7 million for the whole sample, although it decreases with age. For example, they estimate that a 50-year old values remaining worklife at half the value held by a 30-year old. Some researchers have proposed a valu e per discounted e xpected life-year approach (Moore and Viscusi 1988b) . In lieu of a value of a statistical life, one could adjust the VSL measure for the life expectan cy of individuals by es sentially annuitizing the estimated VSL. Based on actuarial tables, one could estimate the life expectancy for the average-aged individual in a study and th en develop estimates of the life-year value54

(either by assuming a discount rate, or as in several studies, estimating a discount rate based on revealed preference procedures – se e below). Then this life-year could be applied to other situations where life expectancy would differ from the average in the study in question. This a pproach provides an “age-adju sted” or “life expectancyadjusted” VSL alternative to the standard VSL. While the life-year approach does

address the concern that values of a statisti cal life should vary with life expectancy, they assume that the marginal value of another year is constant across the age spectrum and across time for a given individual. 34 Accounting for the effects of age on the value of a statistical life through a lifeyear approach requires the discounting of futu re consumer surplus (since, on the margin, the compensating differential should equal th e present discounted va lue of a worker’s expected consumer surplus). A variety of pa pers have imputed workers’ or consumers’ implicit rates of discount (Moore and Viscusi 1988b, 1990a, 1990b, 1990c, Viscusi and Moore 1989, Dreyfus and Viscusi 1995). Wh ile the Moore and Viscusi (1988b) and Dreyfus and Viscusi papers estimate implicit discount rates and marg inal discounted lifeyears based on reduced form models, the other three papers develop st ructural models to

estimate discount rates. Also note that all of these models are based on data from labor markets, except for the Dreyfus and Viscusi’s automobile hedonic study. Rational individuals can implicitly discount their health capital at a different rate than what they face in markets (e.g., real interest rate for a home mortgage) since he alth status is a nontraded commodity (one cannot “save” good health at age 25 fo r consumption at age 75).

34 Based on Rosen’s life cycle model, one would expect that the marginal value of another year is greater for an elderly person than for a middle-aged person but that the value of all future years declines with age for a given individual. Accounting for health status may counter the effect of increasing marginal values for a one-year life extension for an elderly person. If health status is decreasing in age, then it may be ambiguous whether the marginal value of another year increases with age.55

Despite this possibility, these models estimate discount rates that are broadly consistent

with the real rates of inte rest typical workers and consumers face (see Table 11).

9. The application of the value of a stat istical life to public policy decisions

At least in the countr ies with a high level of development, governments recommend or require economic analyses of proposed regulations and public policies. 35 Regulatory agencies in the United States, th e United Kingdom, and Canada, have been most prominent in their use of VSL estimates to value the benefits of proposed environmental, health, and safety rules. In some cases, regulatory agencies have

modified the VSL to account for distinctive ch aracteristics of the risk and the affected population. In the United Stat es, some environmental laws preclude the promulgation of regulations based on benefit-cost analysis. In these cases, analysts have turned to riskrisk analysis – based in part on an application of the value of a statistical life – to provide some guidance about whether a proposed policy is in fact risk reducing. 9.1 The use of VSLs in government decision-making around the world

9.1.1 United States. Over the past twenty years in the United States, executive orders by Presidents Carter, Reagan, and Clinton have mandated economic impact analyses of all significant Federal regulations (E.O. 12044, E.O. 12291 and E.O. 12866). Beginning with the Reagan Administration, these ex ecutive orders vested with the Office of Management and Budget (OMB) the responsib ility for overseeing and coordinating the review of regulatory impact analyses. OMB has published guidelines for all Federal agencies, such as its report with respect to the use of “best practices” in these analyses

35 For example, refer to the guidance to improve regul atory decision-making provided by the OECD (1995) to its member countries.56

(U.S. OMB 1996). The guidance recommends the use of a value of a statistical life to

monetize the benefits associated with rules that change th e population’s mortality risk. While OMB does not recommend a specific VSL or set of VSLs, it does provide a discussion of the issues agencies should consider when choosing a VSL based on the current state of knowledge. Until the 1980s the dominant policy approach to valuing the benefits of reduced risks of death was based on various human capit al measures, such as the present value of lost earnings and medical expenses. These values are lower than the VSL amounts. Typical of this approach was the 1982 analysis by OSHA of its proposed hazard communication regulation. OSHA valued lives saved based on the cost of death, which was the human capital value, because in its view life was too sacred to value. After OMB rejected the regulation, clai ming that the costs exceeded the benefits, OSHA appealed the decision to then Vice-President Bush. W. Kip Viscusi was asked to settle the economic dispute between the two agenci es. By valuing life properly using a VSL, the estimated benefits exceeded the costs. The regulat ion was approved the day after his analysis reached the Reagan White House. 36 Thus, the historical impetus for the adoption of the VSL methodology was that these values boosted assessed benef its by roughly an order of magnitude, improving the attractiveness of agencies’ regulatory efforts. The flexibility provided to U.S. agencies in choosing a VSL appropriate to the population affected by their specific rules has resulted in significant variations in the selected VSL both across agencies and thr ough time (see Table 12 and Adler and Posner 2000). In addition, some regulatory impact an alyses have included a range of benefits reflecting different assumptions about the VS L, often reflecting the age profile of the

36 For a review of the substance of this analysis, see Viscusi (1992a).57

affected population by using a VSL adjusted by the number of life-years saved (e.g., the FDA rule restricting tobacco sales to childre n, 61 FR 44396, and the EPA rule regulating the sulfur content of gasoline, 65 FR 6698). The U.S. Environmental Protection Agency (EPA), responsible for more costly Federal ru le-makings than any other U.S. agency, has developed economic guidelines for its regula tory impact analyses (U.S. EPA 2000a). The EPA guidelines recommend a VSL of $6.2 million (2000US$), reflecting the arithmetic mean of 26 studies reviewed in Viscusi (1992a). In contrast, the U.S. Federal Aviation Administration (1998) recommends a value of a statistical life of $3 million in its 2002 economic analyses of regulations. 37 This comparatively low value of life may reflect in part an anchoring effect. The U.S. Department of Transportation was a leader in valuing mortality risk reductions, but began doing so in an era in which the present value of lost earnings was the dominant approach. The agency has slowly increased the value att ached to reduced risks of death, but it has continued to lag behind the estimates in the literature. 38 9.1.2 United Kingdom. In the United Kingdom, the Cabi net Office has lik ewise provided guidance for economic analyses for the government’s regulatory and policy-making agencies (U.K. Cabinet Office 2000, H.M. Treasury 1997). While the guidance does not specify the value of a statistical life to be used by agencies, it does recommend careful consideration of the challenges in applying va lues estimated in the economic literature to potentially different risk and population contexts of the policy or regulation.

37 Refer to Table E-1 at Internet: http://www.api.faa.gov/economic/EXECSUMM.PDF and http://www.api.faa.gov/economic/742SECT2.PDF

. 38 The low VSL used by the agency also reflects a political dimension as well. In the early 1990s when Viscusi prepared the report that was subsequently published as Viscusi (1993) for the Federal Aviation Administration, that branch of the agency favored a higher value of life than was later mandated for use throughout the department.58

The U.K. Department of the Environm ent, Transport, and Regions (DETR; formerly Department of Transport) has em ployed a willingness-to-pay based value of preventing a fatality since 1988 in its regulator y and policy analyses (Chilton et al. 1999). The value of preventing a fatality se lected in 1988, $1.2 million (£500,000 in 1987 prices), is still used by the Department. This value reflects contingent valuation-based estimates of individuals’ willingness-to-pay for risk reduction. The U.K. Health and Safety Executive uses the DETR value of preventing a fatality as a starting point for its regulatory impact analyses. The HSE has employed a value of preventing a fatality

double the DETR value for cancer-related fatal ities, concluding that individuals’ dread of the disease significantly outweighs the affect s of latency on willingness-to-pay (Andrews and McCrea 1999). 39 Whereas U.S. agencies rely on market-b ased VSL estimates, in the U.K. the emphasis is on contingent valu ation estimates. This diffe rence in approach no doubt stems in part from the different character of the empirical evidence in the two countries.

There have been dozens of studies of U.S. wa ge-risk tradeoffs, most of which have been in a reasonable range. There have been fa r fewer such analyses for the U.K., and the resulting empirical estimates have been much more unstable.

9.1.3 Canada. In Canada, the Privy Council Office published guidelines for benefit-cost analysis in 1995. While these guidelines do not specify one or a set of values of a statistical life, they do note the need for se rious consideration of the value of life,

39 Note that the Science Advisory Board to the U. S. Environmental Protecti on Agency considered the effects of latency and dread within the context of cancer-related mortality. The SAB (2000) concluded that the literature does not currently support a modification of the value of a statistical life to reflect dread. In contrast, the SAB did recommend that economic anal yses account for latency by discounting future mortality to the present time consistent with the approach to other categories of benefits and costs.59

determinants of the appropria te VSL, and possible appro aches to presenting useful information for policymakers and the public. The value of a statistical life is left to the discretion of agencies promulgating regulat ions, again much like the U.S. and U.K. approaches. Transport Canada reviewed the economic analyses for 145 transportation-related projects over 1982 – 1993 (Blanc hard 1996). The VSL used in these analyses ranged from $400,000 to $3.2 million. A recent analys is of a Canadian pr oposed rule on tobacco products information used a range of the valu e of a statistical lif e of $1.7 - $5.7 million, 40 with higher values for individuals under ag e 65 (Hara Associates 2000). A comparable range and age-based VSL differential was em ployed in an evalua tion of a Canadian proposal for cleaner vehicles in fuels as well (Lang et al. 1995). 9.1.4 Multinational organizations. The value of a statistic al life has also received

attention in multinational contexts. The In tergovernmental Panel on Climate Change (IPCC), established by the United Nations Environment Programme and the World Health Organization in 1988 to provide technical support to pa rticipants in global climate change negotiations, discussed issues regardin g the value of a statis tical life in its 1995 and 2001 assessments of the economic and social dimensions of climate change (IPCC 1996, 2001). Moreover, the European Commi ssion (EC) began in 2000 a process to prepare guidance for benefits analysis to impr ove benefit-cost analys is procedures within

the EC. The EC effort has focused a subs tantial amount of time and resources on the

value of a statistical li fe question (EC 2000).

40 The conversion to U.S. dollars for the Hara A ssociates analysis was based on the annual market exchange rate reported by the Federal Reserve (refer to Internet: http://www.federalreserve.gov/releases/g5a/current/ ) because the Penn World Table does not provide conversions for the most recent years.60

9.2 Issues Pertaining to Benefits Transfers The vast majority of the studies reviewed in this pa per cover prime-aged workers

who have chosen to bear the risk of accident al, immediate death. Many of the studies based their quantitative analyses on samples from the 1970s and 1980s. With the exception of occupational safe ty policies, most government regulations affect mortality risks with different qualitative characteristics or affect popul ations with characteristics that differ from those of the samples in these studies. The demographic characteristics of specific groups and the population at large likely differ today (and will differ in the future) from what they were 20 to 30 year s ago. The risk-money tradeoffs of those affected by government policy may differ from those values estimated in hedonic market

studies. For example, many environmental regulat ions address carcinogen exposure. Reduced cancer-related mortality presents se veral issues that merit consideration when employing a VSL. First, individuals may be willing to pay more to avoid dying of cancer

than to avoid an instantaneous accidental de ath. Revesz (1999) hypothesizes that this “dread” effect of cancer mortality should result in an upward revision to the VSL. This reasoning apparently underl ies the higher VSL used by the UK Health and Safety

Executive for cancer-related fatalities. Th e EPA’s Science Advisory Board (2000) recommended against any “dread”-related modifi cation to the value of a statistical life on the grounds that the current literatu re did not support any such change. 41 In particular, contingent valuation estimates of cancer mort ality risks have produced values similar to

41 While Revesz suggests other adjustments to the value of a statistical life based on the qualitative characteristics of the risk, such as involuntariness of the risk, the Science Advisory Board (2000) noted that the existing literature does not justify adjustments for these effects.61

those observed for accidental deaths. 42 The market-based evidence for cancer risks

discussed above is similar to the results for accident risks. Cancer-related mortality also differs si gnificantly from occupational mortality in terms of the timing of the death. The l ong latency period for can cer (and other chronic

health conditions affected by government regulations) sh ould be discounted in the benefits analysis (Revesz 1999, Science Advisory Board 2000). Given the rough similarity of the implicit rates of discount discussed in Section 8 to current market interest rates, a benefit-co st analysis could employ one common discount rate for all categories of benefits and costs. Several researchers have que stioned the discounting of be nefits of reducing future risks to life when evaluating public pol icies. Heinzerling (1998, 1999, 2000) has criticized the discounting of statistical lives on moral grounds. She claims that a

statistical life cannot be dis cerned from an actual life, which society would not attempt to price. This concern pertains to both curre nt and future risk reductions and is not a discounting argument per se. While Heinzerli ng expresses significant concerns with the concept of statistical lives and in their discounting, individuals make private risk-income, risk-time, and risk-r isk tradeoffs every day , as evidenced by the literature surveyed in this paper, as well as by simple casual observation. 43 Further, as the studies presented in Table 11 illustrate, individua ls value risks in the futu re less than they value commensurate risks they face today. Both Re vesz and Heinzerling raise concerns about

42 See Magat, Viscusi, and Huber (1996). 43 This discussion implicitly acknowledges an important aspect of most occupational, safety, and environmental health risks: these risks are relatively sma ll. In cases of certain, or near-certain death, the empirical economic evidence and this argument are not relevant (see our discussion in Section 1).62

discounting statistical lives in future genera tions (also see Arrow et al. 1996 for a survey of intergenerational discounting). Failure to discount creates potentially fundamental paradoxes (see Keeler and Cretin 1983). Suppose that the cost structur e for reducing risks to life is unchanged over time. Then it is always desirable to defer a ny life saving policy and invest the money that would have been spent on risk reduction. I ndeed, continual postponement of a life saving effort is always desirable if future benefits are never discounted but the money spent on these policies continues to grow at the rate of interest. Similarly, suppose that future life saving benefits are not discounted. If, however,

one converts the cost allocations to a terminal value rather than discounting the benefits back to a present value, the effect will be id entical in terms of whether the policy passes a

benefit-cost test. What the di scounting critics generally fail to grasp is that what is being discounted are not lives but rather society’s willingness to pay for these future risks to

life. The differences in the age of the populat ion in labor market studies and of the population affected by a regulation should also affect the value of a statistical life. While fewer studies have focused on the effects of age on the return to risk, those that have tend

to find that the value of a statistical life dec lines with age, consistent with the theoretical

work. Since these labor hedonic studies in clude samples where age usually ranges no higher than about 60 years, it may be diffi cult to extrapolate th ese results for older populations. This is a significant issue in be nefits transfer, since many environment and public health policies (as opposed to worker safety programs) deliver benefits to the elderly. For example, recent air qual ity regulations promulgated by the U.S.63

Environmental Protection Agency dispropor tionately benefit older individuals as illustrated by the average increase in life expectancy of less than 15 years (U.S. EPA 1999, Science Advisory Board 1999a). In resp onse to this, the EPA’s Science Advisory Board (SAB) has questioned the appropriate ness of EPA’s choice of a VSL for this population. The SAB notes that it “question[s] the applic ation of a WTP estimate for prime-aged individuals to a population of ol der individuals and people who are in poor health” (p. 6). The SAB (1999b) has recommen ded that the EPA revise its VSL in light

of this concern. Several agencies already employ age-adjusted VSLs. As noted above, the economic analysis of a Canadian tobacco regulation employed a smaller VSL for

individuals older than 65. The U.S. Food and Drug Administration regularly employs the value of statistical life-years, instead of VSLs, as a way to monetize the health benefits of their proposed rules. The U.S. Environm ental Protection Agency has reluctantly conducted benefit-cost analyses with the value of statistic al life-years approach. The clear findings in the th eory and existing empiri cal evidence support such age adjustments. Future empirical research should further refine age-specific estimates of the value of a statistical life for use in regulatory analyses. 9.3 The role of risk-risk analysis

While the value of a statistical life can be used to monetize the benefits for risk policy evaluation, most laws do not require th at agencies undertake such balancing and some laws in the United States actually preclude the considera tion of benefit-cost analysis in setting standards. For example, the courts have interpreted the Clean Air Act such that the U.S. Environmental Protection Agency cannot base ambient air quality64

standards on benefit-co st analysis or an assessment of the costs. 44 Even if a benefit-cost test cannot be applied, policies that on bala nce harm individual health presumably should not be adopted. Several forms of risk-risk analysis can account for these various risk effects of policies in an effort to ascertain whether risk regulations on balance are risk reducing. While risk-risk anal ysis cannot determine if a polic y improves societal welfare, it can identify the policies that clearly do not im prove societal welfare because they result in a net increase in mortality risk. Four types of risk-risk tradeoffs could influence the net effect of a policy or regulation on a population’s risk exposure. First, a policy may reduce risks of one type while increasing risks of another type. For example, the U.S. Food and Drug Administration considered banning saccharin, th e artificial sweetener, in response to an animal study finding that it may be a poten tial human carcinogen. However, banning saccharin would likely increase the risks associated with obesity. In this case, the U.S. Congress allowed the use of saccharin in f oods subject to a warning label on products containing the sweetener (Viscusi 1994b). Second, policies to reduce risks may create incentives for individuals to undertake

less individual effort to redu ce their exposure to risks (moral hazard). These behavioral responses will offset some of the risk re duction of the policy, and could potentially increase net risks. For example, Peltzma n (1975) described how drivers responded to mandated safety devices in automobiles by ch anging their driving behavior. Drivers in

44 For example, the 1997 final rule for the national ambient air quality standard for ozone introduced the section on the regulatory impact analysis with the fo llowing: “As discussed in Unit IV of this preamble, the Clean Air Act and judicial decisions make clear that the economic and technological feasibility of attaining ambient standards are not to be considered in setting NAAQS, although such factors may be considered in the development of State plans to implement the standards. Accordingly, although, as described below, a Regulatory Impact Analysis (RIA) has been prepared, ne ither the RIA nor the associ ated contractor reports have been considered in issuing this final rule” (62 FR 38856).65

“safer cars” drove more recklessly than be fore. The empirical evidence showed that while the safety measures reduced fatalitie s among automobile occupants, these gains have been offset at least in part by increases in pedestrian deaths and nonfatal accidents. Third, risk-reduction policies may result in regulatory expenditures that directly increase fatalities. For example, policies to remove asbestos from buildings may increase asbestos exposure by workers and use of excavation equipment at Superfund hazardous waste sites may result in construction-related injuries and fatalities (Graham and Wiener 1995). Viscusi and Zeckhauser (1994) illustra te through an input-output analysis the total direct and indirect injury and fatality risks associated with expenditures by industry. Regulations that require a reallocation of reso urces to industries with higher risks, for example towards construction to build new wast ewater treatment facilities or to install pollution control technologies would result in an offsetting increase in mortality risk. Fourth, the costs of risk -reduction policies decrease inco me available to finance other health and safety expenditures. W ildavsky (1980, 1988) noted that the costs of risk-reduction policies reduce national income, some of which would otherwise be used to promote health and safety. This argum ent focuses on the correlation between income and health, evident in both international cross-sectional data and U.S. time-series data (Viscusi 1983, 1994b, Graham et al. 1992, Lutter and Morrall 1994; see Smith et al. 1994 for a critique of the international evidence). 45 These analyses illustrate that wealthier countries have lower mortality rates asso ciated with greater health and safety investments. Graham et al. (1992) extende d the previous analyses on the mortalityincome relationship by focusing on the effect of permanent income. They conclude that:

45 This relationship is also revealed within a cross-section of the U.S. population. Viscusi (1978b) found that work-related risk exposure decreases with worker wealth.66

“If government regulation reduces the level (o r the rate of growth) of permanent income, it is likely to cause smaller health investment s and an eventual decline in health status compared to what would have occurred wit hout the economic burdens of regulation” (p. 336). 46 Keeney (1990, 1994, 1997) formalized Wildavsky’s proposition and found that some expensive regulations aimed at reduci ng mortality risks actually increase mortality risks by reducing national income. Keeney’s model yields various estimates for the induced-expenditure associated with an additi onal fatality that de pend on the distribution of the burden of the policy costs. Based on the mortality-income relationships estimated by Kitawaga and Hauser (1973) an d Frerichs et al. (1984), Keeney estimates that between $13.6 million and $15.2 million of expenditure s would induce a fatality, assuming costs are borne proportional to income. 47, 48 This research inspired a legal opinion of an OSHA regulation in the early 1990s. 49 U.S. Federal Appeals Court Judge Steven F. Williams wrote that regulations that do not pass a risk-risk analysis would be counterproductive. The U.S. Office of Management and Budget then suggested to OSHA that it consider risk-risk analysis in conducting its regulatory impact analyses. While the research on the income-mortality relationship influenced several policy discussions in the early 1990s in the United St ates, the results from these studies point

46 Portney and Stavins (1994) question whether the income losses from regulations would reduce the population’s health status. They claim that the nonlinear relationship between income and health and the modest impact of most regulations on the economy would not likely have a significant effect on health status. While individual regulations may involve small costs as a share of the economy, it is important to note that environmental regulations alone cost about 1 – 2 percent of U.S. economic output (U.S. OMB 2001). 47 We have updated the reported values in Keeney (1990) to 2000 U.S. dollars using the CPI-U deflator. 48 The Keeney estimates are near the high end of 11 studies cited in Lutter and Morrall (1994) on the income gains necessary to avert one fatality. They are very similar to Lutter and Morrall’s estimated range of $11.4 million to $15.2 million for the United States. 49 Refer to UAW v. OSHA , United States Court of Appeals for the District of Columbia Circuit, 89-1559.67

towards a peculiar inconsistency. For the st udies with expenditure-induced fatalities on the order of $5 million per fatality, the expenditure associated with a loss of one life is on par or perhaps below what individuals are willing to pay to reduce the risk of one fatality in the population based on the labor market he donic studies (Viscusi 1994b). Moreover, the mortality-income studies also suffer severa l other potential problems. Some of these do not appropriately account for the simulta neity in the data – higher incomes allow

individuals to invest more in health, but poor health ofte n draws down an individual’s income (Chapman and Hariharan 1994). 50 Some of these studies also may suffer from omitted variable bias resulting in misiden tifying the relationship between income and

health. As an alternative to deriving the income-mortality relationship from aggregate data, Viscusi (1994a) illustrates how to gene rate an estimate for the expenditure-induced fatality rate based on the value of a statistical life and the marginal propensity to spend on

health. Viscusi shows that

health on spend to propensity marginal life l statistica a of value lost life l statistica per e expenditur marginal = . This approach requires an estim ate of the value of a statisti cal life and an estimate of the marginal propensity to spend on health. The literature surveyed in previous sections provides estimates for the numerator. For the marginal propensity to spend on health, Viscusi estimated this based on an analys is of 24 OECD count ries over the 1960 – 1989 period and a time-series analysis for the Unit ed States over the same period (Viscusi

50 A recent paper by Gerdtham and Johannesson (2002) attempts to address this problem by controlling for initial health status in regressions of mortality risk on income (with other relevant controls) for a study focusing on Sweden in the 1980s and 1990s. They find that an income loss ranging from $7.5 – $10.8 million would induce an expected fatality in Sweden. The range reflects variation in the progressivity of the burden of the regulation.68

1992b, 1994a, 1994b). Over an array of specifi cations for both data sets, the marginal propensity to spend on health ranged from 0.08 to 0.12. This implies that for every dollar increase in national income, an additional 8 to 12 cents are spent on health care. Assuming a marginal propensity to spend on h ealth of 0.1 and a VSL of about $6 million, the marginal expenditure per statistical life lost would be about $60 million. 51 Lutter, Morrall, and Viscusi (1999) extended Viscusi’s (1994a) model to account for the effect of income to influence risky behaviors (such as smoki ng, drinking, and poor diet) as well as the consumpti on of health care. Their statis tical analyses illustrate that higher incomes promote better health habits, including reduced excessive drinking and cigarette smoking and increased exercise. Incl uding the effects of income on risky health behavior reduces the estimated marginal expe nditure per statistical life lost from the Viscusi (1994a) by more than a factor of 3 to $17 million. Lutter et al. note that policies

that increase national income would reduce on e fatality for every $17 million increase. The authors also note that since many regula tions have costs per life saved of $100 million or more, the expenditures may be wasteful and counterproductive. 52 If a regulation directly reduces mo rtality risk with regulatory-induced expenditures yielding a high cost per life saved ratio, then the indirect increase in mortality risk may exceed the dir ect decrease in risk resulting in an aggregate increase in

51 Viscusi (1994a, 1994b) selected a VSL estimate of $5 million (in 1992 US$) because it represented the midpoint of the basic range for VS Ls of $3 million - $7 million in Viscusi 1993. In 2000 US$, the midpoint would be $6.1 million. 52 Refer to Morrall (1986) and Tengs et al. (1995) for lists of regulations’ cost-effectiveness for the United States. Tengs et al. found that for 124 environmental regulations (primarily toxin control), the median cost per life-year saved is $3.3 million. About 15 percent of the environmental regulations exceeded $100 million per life-year saved . Converting these life-year values to statistical life values would result in a significant number of regulations with incredibly exorbitant cost-effectiveness measures. Life-saving regulations in other sectors of the economy (e.g., health care, transportation) had much lower costs per lifeyear saved. Refer to Ramsberg and Sjoberg (1997) fo r an evaluation of the cost -effectiveness of lifesaving interventions in Sweden.69

societal mortality risk. The ex isting literature varies in terms of a preferred value for the amount of induced expenditures associated with an additional mortality. However, some regulations would clearly not pass a risk-risk analysis with any plausible value for an induced-expenditure mortality. For example, the 1986 OSHA regulation limiting asbestos occupational exposure cost about $250 million per normalized life saved, and the 1987 OSHA regulation limiting formaldehyde occupational exposure cost about $290 billion per normalized life saved (V iscusi, Hakes, and Carlin 1997).

While the risk-risk literature has focu sed on mortality risks, many environment and safety regulations provide other kinds of benefits, such as reduced morbidity and injury as well as non-human health relate d effects such as improved visibility and ecosystem health (Lutter and Morrall 1994, Po rtney and Stavins 1994). A regulation that primarily delivers non-mortality benefits coul d fail a risk-risk anal ysis but still pass a benefit-cost analysis. One approach could be to convert the morbidity effects into mortality risk equivalents. Alternatively one could fo cus on policies whose primary intent is to reduce mortality risks. Recogni zing this criticism, Hahn, Lutter, and Viscusi (2000) conducted risk-risk analysis on a number of major environment, health, and safety regulations over the 1986 – 1998 period whose pr imary benefits were reduced mortality risk (see Table 13). 53 Their analysis focuses on 24 re gulations promulgated by the U.S. Environmental Protection Agency (EPA), U.S. Department of Housing and Urban Development (HUD), U.S. Department of La bor (OSHA), and U.S. Consumer Products Safety Commission (CPSC). Thirteen of 24 regulations designed primarily to reduce mortality risks actually increased mortality ri sks based on the Lutter et al. work finding

53 Hahn, Lutter, and Viscusi only considered regulations with reduced mortality risk benefits comprising at least 90 percent of total monetized benefits.70

that $15 million of expenditures induces a fatali ty. Ten of these thirteen rules failing a risk-risk analysis had at least ten times more expenditure-induced fatalities than lives

saved. 54

10. Conclusion For nearly thirty years, economists have attempted to infer individuals’ preferences over mortality and morbidity risk and income in labor and product markets.

The substantial literature that has developed over that time has confirmed Adam Smith’s intuition about compensating differentials fo r occupational hazards in a significant and growing number of countries. In addition to evaluating various international labor markets, the literature has expanded to addre ss a variety of econometric issues, morbidity risk premiums, and factors influencing mortality risk premiums such as union affiliation and age. While the tradeoff estimates may vary sign ificantly across studies, the value of a statistical life for prime-aged workers has a median value of about $7 million in the United States. Our meta-analysis characterizes some of the uncertainty in estimates of the value of a statistical life, and finds th at 95 percent confiden ce interval upper bounds can exceed the lower bounds by a factor of two or more. Other developed countries appear to have comparable VSLs, although some studies of the United Kingdom have found much larger risk premiums . Consistent with the fact that safety is a normal good, developing countries labor market s also have significant, but sm aller, values of statistical life. Overall, our point estimates of the inco me elasticity of the value of a statistical life

54 Note that the construction of discounted statistical lives saved reflects both an accounting for life-years saved and discounting for latency.71

range from 0.5 to 0.6. Union members in U.S. labor markets appear to enjoy greater risk premiums than non-members, while the eviden ce in other developed countries is rather mixed. The theoretical and empirical literature indicates that the value of a statistical life decreases with age.

The estimates of the value of a statistical life can continue to serve as a critical input in benefit-cost analyses of proposed regulations and policies. Refining VSLs for the specific characteristics of the affected population at risk remains an important priority for the research community and the government agencies conducting these economic analyses. Improving the applica tion of VSLs in this way can result in more informed government interventions to address market fa ilures related to envir onmental, health, and safety mortality risks.72

References Adler, M.D. and E.A. Posner. (2000). “Implementing Cost-Benefit Analysis When Preferences Are Distorted,” Journal of Legal Studies 29, 1105-1148. Andrews, R.M. and P. McCrea. (1999). “ UK Health and Safety Executive Approach to Exposure Limit Setting.” In Proceedings of the OECD Workshop on the Integration of Socio-Econom ic Analysis in Chemical Risk Management Decision Making , London, January 7-9, 1998. Paris: Organization of Economic Cooperation and Development, pp. 193-202. Arabsheibani, G.R. and A. Marin. (2000). “Stability of Estimate s of the Compensation for Danger,” Journal of Risk and Uncertainty 20(3), 247-269. Arnould, R.J. and L.M. Nichols. (1983) . “Wage-Risk Premiums and Workers' Compensation: A Refinement of Estimate s of Compensating Wage Differential,” Journal of Political Economy 91(2), 332-340. Arrow, K.J., W.R. Cline, K.-G. Maler, M. Munasinghe, J.E. Stiglitz, and R. Squitieri. (1996). “Intertemporal Equity and Discountin g.” In J.P. Bruce, H. Lee, and E. Haites (eds.), Climate Change 1995: Economic and Social Dimensions. Cambridge, England: Cambridge University Press, pp. 125-144. Aten, B., R. Summers, a nd A. Heston. (2001). The Penn World Table Mark 6

. Philadelphia, PA: The Center for Internat ional Comparisons at the University of Pennsylvania. Internet: http://pwt.econ.upenn.edu

. Atkinson, S.E. and R. Halvorsen. (1990). “The Valuation of Risks to Life: Evidence from the Market for Automobiles,” Review of Economics and Statistics 72(1), 133-136. Barro, R.J. and J.W. Lee. (1996). “Int ernational Measures of Schooling Years and Schooling Quality,” American Economic Review 86(2), 218-223. Berger, M.C. and P.E. Gabriel. (1991). “Risk Aversion and the Earnings of U.S. Immigrants and Natives,” Applied Economics 23, 311-318. Biddle, J.E. and G.A. Zarkin. (1988). “W orker Preference and Ma rket Compensation for Job Risk,” Review of Economics and Statistics 70(4), 660-667. Blanchard, G. (1996). Highway Benefit-Cost Analysis: A Review of Evidence. Transport Canada, Economic Analysis, Special In frastructure Project. Report no. TP12790E. Ottawa, Ontario. Blomquist, G. (1979). “Value of Life Saving: Implications of Consumption Activity,” Journal of Political Economy 87(3), 540-558.73

Bowland, B.J. and J.C. Beghin. (2001). “R obust Estimates of Value of a Statistical Life for Developing Economies,” Journal of Policy Modeling 23, 385-396. Brown, C. (1980). “Equalizing Diffe rences in the Labor Market,” Quarterly Journal of Economics 94(1), 113-134. Bureau of Labor Statistics. (n.d.). Census of Fatal Occupational Injuries . Washington, DC: Department of Labor. Internet: http://www.bls.gov/iif/oshcfoi1.htm

. Butler, R.J. (1983). “Wage and Injury Rate Responses to Shifting Levels of Workers' Compensation.” In J.D. Worrall (ed.), Safety and the Workforce: Incentives and Disincentives in Workers' Compensation . Ithaca, NY: ILR Press, pp. 61-86. Carlin, P.S. and R. Sandy. (1991). “Estim ating the Implicit Value of a Young Child's Life,” Southern Economic Journal 58(1), 186-202. Chapman, K.S. and G. Hariharan. (1994). “Controlling for Causality in the Link from Income to Mortality,” Journal of Risk and Uncertainty 8(1), 85-94. Chilton, S., J. Covey, L. Hopkins, M. J ones-Lee, G. Loomes, N. Pidgeon, and A. Spencer. (1999). “Annex: New Research Results on the Valuation of Preventing Fatal Road Accident Casualties.” In Health Costs Due to Road Traffic-related Air Pollution: Economic Evaluation , Prepared for the WHO Ministerial Conference on Environment and Health, London, June 1999. Bern, Switzerland: Federal Department of Environment, Transport, Energy and Communications, Bureau for Transport Statistics. Council of Economic Advisers. (2002). Economic Report of the President . Washington, DC: Government Printing Office. Cousineau, J-M., R. Lacroix, and A-M. Gira rd. (1992). “Occupational Hazard and Wage Compensating Differentials,” Review of Economics and Statistics 74(1), 166-169. Cutler, D.M. and E. Richardson. (1997). “M easuring the Health of the U.S. Population,” Brookings Papers on Economic Activity, Microeconomics vol. 1997, 217-271. Dardis, R. (1980). “The Value of Life: New Evidence from the Marketplace,” American Economic Review 70(5), 1077-1082. Desvousges, W.H., F.R. Johnson, H.S. Banzhof, R.R. Russell, E.E. Fries, K.J. Dietz, and S.C. Helms. (1995). Assessing the Environmental Externality Costs for Electricity Generation . Research Triangle Pa rk, NC: Triangle Economic Research.74

Dickens, W.T. (1984). “Differences Be tween Risk Premiums in Union and Nonunion Wages and the Case for Occupational Safety Regulation,” American Economic Review 74(2), 320-323. Dillingham, A.E. (1985). “The Influence of Risk Variable Definition on Value-of-Life Estimates,” Economic Inquiry 23(2), 277-294. Dillingham, A.E., T. Miller, and D.T. Levy. (1996). “A More General and Unified Measure for Valuing Lab our Market Risk,” Applied Economics 28, 537-542. Dillingham, A.E. and R.S. Smith. (1984). “Union Effects on the Valuation of Fatal Risk.” In Dennis, B.O. (ed.), Proceedings of the Industrial Relations Research Association 36th Annual Meeting , San Francisco, CA, December 28 – 30, 1983. Madison, WI: Industrial Relations Re search Association, pp. 270-277. Dorman, P. and P. Hagstrom. (1998). “Wage Compensation for Dangerous Work Revisited,” Industrial and Labor Relations Review 52(1), 116-135. Dorsey, S. (1983). “Employment Hazards and Fringe Benefits: Further Tests for Compensating Differentials.” In J.D. Worrall (ed.), Safety and the Workforce: Incentives and Disincentives in Workers' Compensation . Ithaca, NY: ILR Press, pp. 87-102. Dorsey S. and N. Walzer. (1983). “Worke rs' Compensation, Job Hazards, and Wages,” Industrial and Labor Relations Review 36(4), 642-654. Dreyfus, M.K. and W.K. Viscusi. (1995). “Rates of Time Preference and Consumer Valuations of Automobile Safety and Fuel Efficiency,” Journal of Law and Economics 38(1), 79-105. Duncan, G.J. and B. Holmlund. (1983). “W as Adam Smith Right After All? Another Test of the Theory of Compensating Wage Differentials,” Journal of Labor Economics 1(4), 366-379. European Commission. (2000). Workshop on the Value of Re ducing the Risk of IllHealth or a Fatal Illness . Proceedings, November 13, 2000, Brussels, Belgium. Internet: http://europa.eu.int/comm/environment/e nveco/others/procee dings_of_the_works hop.pdf

. Fairris, D. (1989). “Compensating Wage Differentials in the Union and Nonunion Sectors,” Industrial Relations 28(3), 356-372. Fairris, D. (1992). “Compensating Pa yments and Hazardous Work in Union and Nonunion Settings,” Journal of Labor Research 13(2), 205-221.75

Fishback, P.V. and S.E. Kantor. (1992). “`Square Deal’ or Raw Deal? Market Compensation for Workplace Disamenities, 1884-1903,” Journal of Economic History 52(4), 826-848. Freeman, R.B. and J.L. Medoff. (1981). “The Impact of the Percentage Organized on Union and Nonunion Wages,” Review of Economics and Statistics 63(4), 561- 572. French, M.T. (1990). “Estimating the Full Cost of Workplace Injuries,” American Journal of Public Health 80(9), 1118-1119. French, M.T. and D.L. Kendall. (1992). “The Value of Job Safety for Railroad Workers,” Journal of Risk and Uncertainty 5(2), 175-185. Frerichs, R.R., J.M. Chapman, P. Nourjah, and E.F. Maes. (1984). Cardiovascular Diseases in Los Angeles, 1979 – 1981 . Los Angeles: American Heart Association – Greater Los Angeles Affiliate, Inc. Gaba, A. and W.K. Viscusi. (1998). “Di fferences in Subjective Risk Thresholds: Worker Groups as an Example,” Management Science 44(6), 801-811. Garbacz, C. (1989). “Smoke Detector Effec tiveness and the Value of Saving a Life,” Economics Letters 31, 281-286. Garber, A.M. and C.E. Phelps. (1997). “Economic Foundations of Cost-Effectiveness Analysis,” Journal of Health Economics 16, 1-31. Garen, J. (1988). “Compensating Wage Differentials and th e Endogeneity of Job Riskiness,” Review of Economics and Statistics 70(1), 9-16. Gayer, T., J.T. Hamilton, and W.K. Viscusi. (2000). “Private Values of Risk Tradeoffs at Superfund Sites: Housing Market Evidence on Learning About Risk,” Review of Economics and Statistics 82(3), 439-451. Gegax, D., S. Gerking, and W. Schulze. (1991). “Perceived Risk and the Marginal Value of Safety,” Review of Economics and Statistics 73(4), 589-596. Gerdtham, U. and M. Johannesson. (2002). “Do Life-Saving Regulations Save Lives?” Journal of Risk and Uncertainty 24(3), 231-249. Gerking, S., M. de Haan, and W. Schulze. (1988). “The Marginal Value of Job Safety: A Contingent Valuation Study,” Journal of Risk and Uncertainty 1(2), 185-199. Ghosh, D., D. Lees, and W. Seal. (1975) . “Optimal Motorway Speed and Some Valuations of Time and Life,” Manchester School Economics and Social Studies 43(2), 134-143.76

Graham, J.D., B.-H. Chang, and J.S. Evans. (1992). “Poorer is Riskier,” Risk Analysis 12(3): 333-337. Graham, J.D. and J.B. Wiener. (1995). Risks vs. Risks: Tradeoffs in Protecting Health and the Environment . Cambridge, MA: Harvard University Press. Griliches, Z. (ed.). (1971). Price Indexes and Quality Change . Cambridge: Harvard University Press. Hahn, R.W., R.W. Lutter, and W.K. Viscusi. (2000). Do Federal Regulations Reduce Mortality? Washington, DC: AEI-Brookings Jo int Center for Regulatory Studies. Hamermesh, D.S. (1978). “Economic Aspects of Job Satisfaction.” In O. Ashenfelter and W. Oates (eds.), Essays in Labor Market Analysis . New York: John Wiley and Sons, pp. 53-72. Hamermesh, D.S. (1999). “Changing Inequality in Markets for Workplace Amenities,” Quarterly Journal of Economics 114(4), 1085-1123. Hamermesh, D.S. and J.R. Wolfe. (1990). “Compensating Wage Differentials and the Duration of Wage Loss,” Journal of Labor Economics 8(1), S175-S197.Hammitt, J.K. (2002). “Commentary on: What Determines the Value of Life? A MetaAnalysis,” Journal of Policy An alysis and Management 21(2), 271-273. Hara Associates Inc. (2000). Benefit/Cost Analysis of Proposed Tobacco Products Information Regulations . Prepared for Health Canada and Consulting and Audit Canada. Ottawa, Ontario. June 5, 2000. Heinzerling, L. (1998). “Regulator y Costs of Mythic Proportions,” Yale Law Journal 107, 1981-2070. Heinzerling, L. (1999). “Discounting Life,” Yale Law Journal 108, 1911-1915. Heinzerling, L. (2000). “The Rights of Statistical People,” Harvard Environmental Law Review 24, 189-207. Hersch, J. (1998). “Compensating Differentia ls for Gender-Specific Job Injury Risks,” American Economic Review 88(3), 598-627. Hersch, J. and T. S. Pickton. (1995). “R isk-Taking Activities and Heterogeneity of JobRisk Tradeoffs,” Journal of Risk and Uncertainty 11(3), 205-217. Hersch, J. and W.K. Viscusi. (1990). “Cig arette Smoking, Seatbelt Use, and Differences in Wage-Risk Tradeoffs,” Journal of Human Resources 25(2), 202-227.77

Herzog Jr., H.W. and A.M. Schlottmann. (1990). “Valuing Risk in the Workplace: Market Price, Willingness to Pay, and the Optimal Provision of Safety,” Review of Economics and Statistics 72(3), 463-470. H.M. Treasury. (1997). “The Green Book”: Appraisal and Evaluation in Central Government, Treasury Guidance . London: Her Majesty’ s Stationary Office Hwang, H.-S., W.R. Reed, and C. Hubbard. (1 992). “Compensating Wage Differentials and Unobserved Productivity,” Journal of Political Economy 100(4), 835-858. Intergovernmental Panel on Climate Change (IPCC) (1996). Climate Change 1995: Economic and Social Dimensions of Climate Change . Cambridge: Cambridge University Press. Intergovernmental Panel on Climate Change (IPCC) (2001). Climate Change 2001: Mitigation . Cambridge: Cambridge University Press. Ippolito, P.M. and R.A. Ippolito. (1984). “Measuring the Value of Life Saving from Consumer Reactions to New Information,” Journal of Public Economics 25, 53- 81. Jenkins, R.R., N. Owens, and L.B. Wiggins. (2001). “Valuing Reduced Risks to Children: The Case of Bicycle Safety Helmets,” Contemporary Economic Policy 19(4), 397-408. Jones-Lee, M.W. (1976). The Value of Life: An Economic Analysis . Chicago: University of Chicago Press. Jones-Lee, M.W., M. Hammerton, and P.R. Phillips. (1985). “The Value of Safety: Results of a National Sample Survey,” Economic Journal 95, 49-72. Keeler, E.B. and S. Cretin. (1983). “Discounting of Life-Saving and Other Nonmonetary Effects,” Management Science 29(3), 300-306. Keeney, R.L. (1990). “Mortality Ri sks Induced by Economic Expenditures,” Risk Analysis 10(1), 147-159. Keeney, R.L. (1994). “Mortality Risk s Induced by the Costs of Regulation,” Journal of Risk and Uncertainty 8(1), 95-110. Keeney, R.L. (1997). “Estimating Fatal ities Induced by the Economic Costs of Regulation.” Journal of Risk and Uncertainty 14(1), 5-24.78

Kim, S-W. and P.V. Fishback. (1993). “Institutional Change, Compensating Differentials, and Accident Risk in American Railroading, 1892-1945,” Journal of Economic History 53(4), 796-823. Kim, S-W. and P.V. Fishback. (1999). “The Impact of Institutional Change on Compensating Wage Differentials for A ccident Risk: South Korea, 1984-1990,” Journal of Risk and Uncertainty 18(3), 231-248. Kitawaga, E.M. and P.M. Hauser. (1973). Differential Mortality in the United States of America: A Study in Socioeconomic Epidemiology . Cambridge, MA: Harvard University Press. Kniesner, T.J. and J.D. Leeth. (1991). “Compensating Wage Differentials for Fatal Injury Risk in Australia, Ja pan, and the United States,” Journal of Risk and Uncertainty 4(1), 75-90. Krupnick, A. (2002). “Commentary on: What Determines the Value of Life? A MetaAnalysis,” Journal of Policy Analysis and Management 21(2), 275-282. Lang, C., G. Yarwood, F. Lalonde, and R. Bloxam. (1995). Environmental and Health Benefits of Cleane r Vehicles and Fuels . Prepared for Canadian Council of Ministers of the Environment, Task Fo rce on Cleaner Vehicles and Fuels. October 5, 1995. Lanoie, P., C. Pedro, and R. Latour. ( 1995). “The Value of a Statistical Life: A Comparison of Two Approaches,” Journal of Risk and Uncertainty 10, 235-257. Leigh, J.P. (1981). “Compensating Wages for Occupational Injuries and Diseases,” Social Science Quarterly 62(4), 772-778. Leigh, J.P. (1987). “Gender, Firm Size, Indus try, and Estimates of the Value of Life,” Journal of Health Economics 1, 331-344. Leigh, J.P. (1991). “No Evidence of Compen sating Wages for Occupa tional Fatalities,” Industrial Relations 30(3), 382-395. Leigh, J.P. (1995). “Compensating Wages, Va lue of a Statistical Life, and Inter-Industry Differentials,” Journal of Environmental Economics and Management 28(1), 83- 97. Leigh, J.P. and R.N. Folsom. (1984). “Estim ates of the Value of Accident Avoidance at the Job Depend on the Concavity of the Equalizing Differences Curve,” Quarterly Review of Economics and Business 24(1), 56-66. Liu, J-T., J. Hammitt, and J-L. Liu. ( 1997). “Estimating Hedonic Wage Function and Value of Life in a Developing Country,” Economics Letters 57, 353-358.79

Liu, J-T. and J.K. Hammitt. (1999). “Perceiv ed Risk and Value of Workplace Safety in a Developing Country,” Journal of Risk Research 2(3), 263-275. Lott, J.R. and R.L. Manning. (2000). “Have Changing Liability Rules Compensated Workers Twice for Occupational Hazards? Earnings Premiums and Cancer Risks,” Journal of Legal Studies 29, 99-130. Low, S.A. and L.R. McPheters. (1983). “W age Differentials and the Risk of Death: An Empirical Analysis,” Economic Inquiry 21, 271-280. Lutter, R. and J.F. Morrall. (1994). “Health-H ealth Analysis: A New Way to Evaluate Health and Safety Regulation,” Journal of Risk and Uncertainty 8(1), 43-66. Lutter, R., J.F. Morrall, and W.K. Viscusi. (1999). “The Cost-Per-Life-Saved Cutoff for Safety-Enhancing Regulations,” Economic Inquiry 37(4), 599-608. Magat, Wesley, W. Kip Viscusi, and Joel H uber. (1996). “A Reference Lottery Metric for Valuing Health,” Management Science 42(8), 1118-1130. Marin, A. and H. Psacharopoulos. (1982). “T he Reward for Risk in the Labor Market: Evidence from the United Kingdom and a R econciliation with Other Studies,” Journal of Political Economy 90(4), 827-853. Marsh, Suzanne M. and Larry A. Layne. (2001). Fatal Injuries to Civilian Workers in the United States, 1980 - 1995 . DHHS/NIOSH pub. no. 2001-129s. July. Washington, DC: Department of Health and Human Services. Martinello, F. and R. Meng. (1992). “Workplace Risks and the Value of Hazard Avoidance,” Canadian Journal of Economics 25(2), 333-345. McLean, R.A., W.R. Wendling, and P.R. N eergaard. (1978). “Compensating Wage Differentials for Hazardous Work: An Empirical Analysis,” Quarterly Review of Economics and Business 18(3), 97-107. McNeill, W.H. (1976). Plagues and Peoples . Garden City, NY: Anchor Press. Mellow, W. and H. Sider. (1983). “Accur acy of Response in Labor Market Surveys: Evidence and Implications,” Journal of Labor Economics 1(4), 331-344. Meng, R. (1989). “Compensating Differen ces in the Canadian Labour Market,” Canadian Journal of Economics 22(2), 413-424. Meng, R. (1991). “Compensating Wages for Long-Term Job Hazards in Canadian Industry,” Economics Letters 36(3), 331-336.80

Meng, R.A. and D.A. Smith. (1990). “The Valuation of Risk of Death in Public Sector Decision-Making,” Canadian Public Policy - Analyse de Politiques 16(2), 137- 144. Meng, R. and D.A. Smith. (1999). “The Impact of Workers' Compensation on Wage Premiums for Job Hazards,” Applied Economics 31(9), 1101-1108. Miller, P., C. Mulvey, and K. Norris. (1997) . “Compensating Differentials for Risk of Death in Australia,” Economic Record 73(223), 363-372. Miller, T.R. (1990). “The Plausible Range for the Value of Life – Red Herrings Among the Mackerel,” Journal of Forensic Economics 3(3), 17-39. Miller, T.R. (2000). “Variations between C ountries in Values of Statistical Life,” Journal of Transport Economics and Policy 34(2), 169-188. Moore, M.J. and W.K. Viscusi. (1988a). “Doubling the Estimated Value of Life: Results Using New Occupational Fatality Data,” Journal of Policy Analysis and Management 7(3), 476-490. Moore, M.J. and W.K. Viscusi. (1988b). “The Quantity-Adjusted Value of Life,” Economic Inquiry 26, 369-388. Moore, M.J. and W.K. Viscusi. (1990a). Compensation Mechanisms for Job Risks

. Princeton: Princeton University Press. Moore, M.J. and W.K. Viscusi. (1990b). “Discounting Environmental Health Risks: New Evidence and Policy Implications,” Journal of Environmental Economics and Management 18, S51-S62. Moore, M.J. and W.K. Viscusi. (1990c). “Models for Estimating Discount Rates for Long-Term Health Risks Using Labor Market Data,” Journal of Risk and Uncertainty 3, 381-401. Morrall, J. (1986). “A Re view of the Record,” Regulation (Nov/Dec), 25-34.Mrozek, J.R. and L.O. Taylor. (2002). “What Determines the Value of Life? A MetaAnalysis,” Journal of Policy Analysis and Management 21(2), 253-270. National Institute for Occupational Safe ty and Health (NIOSH). (2000). Worker Health Chartbook, 2000 . Report no. 2000-127. U.S. Department of Health and Human Services. Internet: http://www.cdc.gov/niosh/pdfs/2000-127.pdf

. Organization for Economic Cooperation and Development (OECD). (1995). Recommendation of the Council of the OE CD on Improving the Quality of Government Regulation . Report OCDE/GD(95)95. Paris: OECD.81

Organization for Economic Cooperation and Development (OECD). (2001). OECD Environmental Outlook . Paris: OECD. Olson, C.A. (1981). “An Analysis of Wage Differentials Received by Workers on Dangerous Jobs,” Journal of Human Resources 16(2), 167-185. Peltzman, S. (1975). “The Effects of Automobile Regulation,” Journal of Political Economy 83(4), 677-726. Privy Council Office, Canada. (1995). Benefit/Cost Analysis Guide for Regulatory Programs . Ottawa, Ontario. Internet: http://www.pco-bcp.gc.ca/raoics-s rdc/ProcGuides/cbgcntents_e.htm

. Portney, P.R. (1981). “Housing Prices, Health Effects, and Valuing Reductions in Risk of Death,” Journal of Environmenta l Economics and Management 8, 72-78. Portney, P.R. and R.N. Stavins. (1994). “Regulatory Review of Environmental Policy: The Potential Role of Health-Health Analysis,” Journal of Risk and Uncertainty 8(1), 111-122. Ramsberg, J.A.L. and L. Sjoberg. (1997). “The Cost-Effectiveness of Lifesaving Interventions in Sweden,” Risk Analysis 17(4), 467-478. Revesz, Richard L. (1999). “Environmenta l Regulation, Cost-Ben efit Analysis, and the Discounting of Human Lives,” Columbia Law Review 99, 941-1017. Rosen, S. (1974). “Hedonic Prices and Imp licit Markets: Product Di fferentiation in Pure Competition,” Journal of Political Economy 82, 34-55. Rosen, S. (1986). “The Theory of Equalizi ng Differences.” In O. Ashenfelter and R. Layard (eds.), Handbook of Labor Economics . Amsterdam: North-Holland, pp. 641-692. Rosen, S. (1988). “The Value of Changes in Life Expectancy,” Journal of Risk and Uncertainty 1, 285-304. Sandy, R. and R.F. Elliott. (1996). “Unions and Risk: Their Impact on the Level of Compensation for Fatal Risk,” Economica 63(250), 291-309. Sandy, R., R.F. Elliott, W.S. Siebert, and X. Wei. (2001). “Measurement Error and the Effects of Unions on the Compensating Di fferentials for Fatal Workplace Risks,” Journal of Risk and Uncertainty 23(1), 33-56.82

Schelling, T.C. (1968). “The Life You Save May Be Your Own.” In S.B. Chase (ed.), Problems in Public Expenditure and Analysis . Washington, DC: Brookings Institution, pp. 127-162. Science Advisory Board. (1999a). Advisory Letter to Administrator Browner Regarding the Clean Air Act Amendments Sectio n 812 Prospective Study of Costs and Benefits . October 29, 1999. Internet: http://www.epa.gov/sab/coua0002.pdf

. Science Advisory Board. (1999b). Final Advisory Letter to Administrator Browner Regarding the Clean Air Act Amendments Section 812 Prospective Study of Costs and Benefits . November 19, 1999. Internet: http://www.epa.gov/sab/coua0003.pdf

. Science Advisory Board. (2000). SAB Report on EPA’s Whit e Paper “Valuing the Benefits of Fatal Cancer Risk Reduction.” Transmitted to the EPA by letter to Administrator Browner. Ju ly 27, 2000. Internet: http://www.epa.gov/sab/eeacf013.pdf

. Shanmugam, K.R. (1996/7). “The Value of Life: Estimates from Indian Labour Market,” Indian Economic Journal 44(4), 105-114. Shanmugam, K.R. (1997). “Value of Li fe and Injury: Estimating Using Flexible Functional Form,” Indian Journal of Applied Economics 6(3), 125-136. Shanmugam, K.R. (2000). “Valuations of Life and Injury Risks,” Environmental and Resource Economics 16, 379-389. Shanmugam, K.R. (2001). “Self Selecti on Bias in the Estimates of Compensating Differentials for Job Risks in India,” Journal of Risk and Uncertainty 22(3), 263- 275. Shepard, D.S. and R.J. Zeckhauser. (1982) . “Life-Cycle Consumption and Willingnessto-Pay for Increased Survival.” In M.W. Jones-Lee (ed.), The Value of Life and Safety . Amsterdam: North Holland. Shepard, D.S. and R.J. Zeckhauser. (1984). “Survival Versus Consumption,” Management Science 30(4), 423-439. Shogren, J.S. and T. Stamland. (2002). “Skill and the Value of Life,” Journal of Political Economy 110(5), 1168-1173. Siebert, W.S. and X. Wei. (1994). “Com pensating Wage Differentials for Workplace Accidents: Evidence for Union a nd Nonunion Workers in the UK,” Journal of Risk and Uncertainty 9(1), 61-76.83

Siebert, W.S. and X. Wei. (1998). “Wag e Compensation for Job Risks: The Case of Hong Kong,” Asian Economic Journal 12(2), 171-181. Smith, A. (1776). The Wealth of Nations . Chicago: University of Chicago Press. 1976 edition. Smith, R.S. (1974). “The F easibility of an `Injury Tax’ Approach to Occupational Safety,” Law and Contemporary Problems 38(4), 730-744. Smith, R.S. (1976). The Occupational Safety and Health Act: Its Goals and Its Achievements . Washington, DC: American Enterprise Institute. Smith, R.S. (1979). “Compensating Wage Diffe rentials and Public Policy: A Review,” Industrial and Labor Relations Review 32(3), 339-352. Smith, V.K. (1983). “The Role of Site and Job Characteristics in Hedonic Wage Models,” Journal of Urban Economics 13, 296-321. Smith, V.K., D.J. Epp, and K.A. Schwabe. (1994). “Cross-Country Analyses Don’t Estimate Health-Health Responses,” Journal of Risk and Uncertainty 8(1), 67-84. Smith, V.K. and C.C.S. Gilbert. (1984). “The Implicit Valuation of Risks to Life: A Comparative Analysis,” Economics Letters 16, 393-399. Smith, V.K. and C.C.S. Gilbert. (1985). “The Valuation of Environmental Risks Using Hedonic Wage Models.” In M. David and T. Smeeding (eds.), Horizontal Equity, Uncertainty, and Economic Well-Being . Chicago: University of Chicago Press. pp. 359-385. Summers, R. and A. Heston. (1991). “T he Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950 – 1988,” Quarterly Journal of Economics 106, 327-368. Tengs, T.O., M.E. Adams, J.S. Pliskin, D.G. Safran, J.E. Siegel, M.C. Weinstein, and J.D. Graham. (1995). “Five-Hundred Li fe-Saving Interventions and Their CostEffectiveness,” Risk Analysis 15(3), 369-390. Thaler, R. and S. Rosen. (1975). “The Valu e of Saving a Life: Evidence from the Labor Market.” In N.E. Terleckyj (ed.), Household Production and Consumption . New York: Columbia University Press, pp. 265-300. U.K. Cabinet Office. (2000). Good Policy Making: A Guide to Regulatory Impact Assessment . London: Cabinet Office Regulat ory Impact Unit. Internet: http://www.cabinet-office.gov.uk/regu lation/2000/riaguide/default.htm

.84

U.S. Environmental Protection Agency. (1999). The Benefits and Costs of the Clean Air Act 1990 to 2010 . Report 410-R-99-001. Washi ngton, DC: Office of Air and Radiation, USEPA. Internet: http://www.epa.gov/oar/sect812/copy99.html

. U.S. Environmental Protection Agency. (2000a). Guidelines for Preparing Economic Analyses . Report 240-R-00-003. Washington, DC: Office of the Administrator, USEPA. Internet: http://yosemite1.epa.gov/ee/e pa/eed.nsf/pages/guidelines

. U.S. Environmental Protection Agency. (2000b). Regulatory Impact Analysis: HeavyDuty Engine and Vehicle Standards and Highway Diesel Fuel Sulfur Control Requirements . Report 420-R-00-026. Washi ngton, DC: Office of Air and Radiation, USEPA. U.S. Federal Aviation Administration. (1998). Economic Values for Evaluation of Federal Aviation Administration Investment and Regulatory Program . Report no. FAA-APO-98-8. Washington, DC: Department of Tr ansportation. June. Internet: http://www.api.faa.gov/economic/TOC.PDF

. U.S. Office of Management and Budget. (1992). Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs . Circular A-94. Washington, DC: The White House. Internet: http://www.whitehouse.gov/omb/circulars/a094/a094.pdf

. U.S. Office of Management and Budget. (1996). Economic Analysis of Federal Regulations Under Executive Order 12866 . Washington, DC: The White House. Internet: http://www.whitehouse.gov/omb/inforeg/riaguide.html

. U.S. Office of Management and Budget. (2001). Making Sense of Regulation: 2001 Report to Congress on the Costs and Benefits of Regulations and Unfunded Mandates on State, Local, and Tribal Entities . Washington, DC: The White House. Internet: http://www.whitehouse.gov/omb/inforeg/costbenefitreport.pdf

. Viscusi, W.K. (1978a). “Labor Market Valuations of Life and Limb: Empirical Evidence and Policy Implications,” Public Policy 26(3), 359-386. Viscusi, W.K. (1978b). “Wealth Effects a nd Earnings Premiums for Job Hazards,” Review of Economics and Statistics 60(3), 408-416. Viscusi, W.K. (1979). Employment Hazards: An Investi gation of Market Performance

. Cambridge, MA: Harvard University Press. Viscusi, W.K. (1980). “Union, Labor Market Structure, and the Welf are Implications of the Quality of Work,” Journal of Labor Research 1(1), 175-192.85

Viscusi, W.K. (1981). “Occupational Safety and Health Regulation: Its Impact and Policy Alternatives.” In J.P. Crecine (ed.), Research in Public Policy Analysis and Management . Greenwich, CT: JAI Press, vol. 2, 281-299. Viscusi, W.K. (1983). Risk by Choice: Regulating Hea lth and Safety in the Workplace

. Cambridge, MA: Harvard University Press. Viscusi, W.K. (1992a). Fatal Tradeoffs: Public and Priv ate Responsibilities for Risk

. New York: Oxford University Press. Viscusi, W.K. (1992b). Wealth, Health Investments, and the Value of Life . Report prepared for the U.S. Office of Management and Budget, Washington, DC. Viscusi, W.K. (1993). “The Value of Risks to Life and Health,” Journal of Economic Literature 31, 1912-1946. Viscusi, W.K. (1994a). “Mortality Effect s of Regulatory Costs and Policy Evaluation Criteria,” RAND Journal of Economics 25(1), 94-109. Viscusi, W.K. (1994b). “Risk-Risk Analysis,” Journal of Risk and Uncertainty 8(1), 5- 17. Viscusi, W.K. (1998). Rational Risk Policy . New York: Oxford University Press. Viscusi, W.K. (2000). “The Value of Life in Legal Contexts: Survey and Critique,” American Law and Economics Review 2(1), 195-222. Viscusi, W.K. and W. Evans. (1990). “Utility Functions that are Dependent on One’s Health Status: Estimates and Economic Implications,” American Economic Review 80, 353-374. Viscusi, W.K., J.K. Hakes, and A. Carlin. (1997). “Measures of Mortality Risks,” Journal of Risk and Uncertainty 14(3), 213-233. Viscusi, W.K. and J. Hersch. (2001). “C igarette Smokers as Job Risk Takers,” Review of Economics and Statistics 83(2), 269-280. Viscusi, W. K. and M.J. Moore. (1989). “Rates of Time Preference and Valuations of the Duration of Life,” Journal of Public Economics 38, 297-317. Viscusi, W.K. and C.J. O'Connor. (1984). “Adaptive Responses to Chemical Labeling: Are Workers Bayesian Decision Makers?” American Economic Review 74(5), 942-956. Viscusi, W.K. and R.J. Zeckhauser. (1994) . “The Fatality and Injury Costs of Expenditures,” Journal of Risk and Uncertainty 8(1), 19-41.86

Weiss, P., G. Maier, and S. Gerking. ( 1986). “The Economic Evaluation of Job Safety: A Methodological Survey and Some Estimates for Austria,” Empirica 13(1), 53- 67. White, H. (1980). “A Heteroskedasticity-Cons istent Covariance Matr ix Estimator and a Direct Test for Heteroskedasticity,” Econometrica 48(3), 817-830. Wildavsky, A. (1980). “Richer is Safer,” The Public Interest 60, 23-39. Wildavsky, A. (1988). Searching for Safety . New Brunswick, NJ: Transaction Books.87Figure 1Market Process for Determining CompensatingDifferentialsw1(p2)w2(p2)w1(p1)p1p2WageRiskEU1w(p)OC1OC2OC2OC1w(p)EU2EU1EU288Figure 2The Value of Statistical Life asa Function of Mortality Risk05101520250.01 0.05 0.09 0.13 0.17 0.21 0.25 0.29 0.33 0.37Annual Occupational Mortality Risk per 1,000 WorkersValue ofStatisticalLife(millions,2000 US$)Viscusi (1981; linear)Viscusi (1981; log)L&F (1984; linear)L&F (1984; log)Olson (1981; log)D&W (1983; log)89Table 1. U.S. Occupational Fatality Rates by Industry, 1992– 1995 National AveragesFatality Rate per 100,000WorkersIndustry NIOSH (NTOF) BLS (CFOI)Agriculture, Forestry, &Fisheries17.0 23.9Mining 24.5 26.3Construction 12.8 13.4Manufacturing 3.6 3.8Transportation & Utilities 10.4 10.6Wholesale Trade 3.5 5.4Retail Trade 2.8 3.6Finance, Insurance, &Real Estate1.1 1.5Services 1.5 1.8Sources: Rates constructed byauthors based on Marsh andLayne (2001) and BLS (n.d.).90Table 2. Summary of Labor Market Studies ofthe Value of a Statistical Life, United StatesAuthor (Year) Sample Risk Variable Mean RiskNonfatal RiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Implicit VSL(millions, 2000US$)Smith (1974) Current Population Survey(CPS) 1967, Census ofManufactures 1963, U.S.Census 1960,Employment and Earnings1963Bureau of Labor Statistics(BLS) 1966, 19670.000125 Yes,significantNo $29,029 $9.2Thaler and Rosen (1975) Survey of EconomicOpportunity 1967Society of Actuaries 1967 0.001 No No $34,663 $1.0Smith (1976) CPS 1967, 1973 BLS 1966, 1967, 1970 0.0001 Yes, notsignificantNo $31,027 $5.9Viscusi (1978a, 1979) Survey of WorkingConditions, 1969-1970(SWC)BLS 1969, subjective riskof job (SWC)0.0001 Yes,significantNo $31,842 $5.3Brown (1980) National LongitudinalSurvey of Young Men1966-71, 1973Society of Actuaries 1967 0.002 No No $49,019 $1.9Viscusi (1981) Panel Study of IncomeDynamics (PSID) 1976BLS 1973-1976 0.0001 Yes,significantNo $22,618 $8.3Olson (1981) CPS 1978 BLS 1973 0.0001 Yes,significantNo $36,151 $6.7Arnould and Nichols(1983)U.S. Census 1970 Society of Actuaries 1967 0.001 No Yes NA $0.5, $1.3Butler (1983) S.C. Workers'Compensation Data 1940-69S.C. Workers'Compensation ClaimsData0.00005 No Yes $22,713 $1.391Author (Year) Sample Risk Variable Mean RiskNonfatal RiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Implicit VSL(millions, 2000US$)Low and McPheters(1983)International CityManagement Association1976 (police officerwages)Constructed a riskmeasure from DOJ/FBIpolice officers killed data1972-75 for 72 cities0.0003 No No $33,172 $1.4Dorsey and Walzer (1983) CPS May 1978 BLS 1976 0.000052 Yes,significantYes $21,636 $11.8, $12.3Leigh and Folsom (1984) PSID 1974; Quality ofEmployment Survey(QES) 1977BLS 0.0001 Yes,significantNo $29,038,$36,946$10.1-$13.3Smith and Gilbert (1984,1985)CPS 1978 BLS 1975 NA No No NA $0.9Dillingham and Smith(1984)CPS May 1979 BLS industry data 1976,1979; NY Workers' CompData 19700.000082 Yes,significant insomespecificationsNo $29,707 $4.1-$8.3Dillingham (1985) QES 1977BLS 1976; NY Workers'Compensation data 19700.000008,0.00014No No $26,731 $1.2, $3.2-$6.8Leigh (1987) QES 1977; CPS 1977 BLS NA No No NA $13.3Moore and Viscusi(1988a)PSID 1982 BLS 1972-1982, NIOSHNational TraumaticOccupational Fatality(NTOF) Survey 1980-19850.00005,0.00008No Yes $24,931 $3.2, $9.4Moore and Viscusi(1988b)QES 1977 BLS, discounted expectedlife years lost; subjectiverisk of job (QES)0.00006 No Yes $31,092 $9.792Author (Year) Sample Risk Variable Mean RiskNonfatal RiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Implicit VSL(millions, 2000US$)Garen (1988) PSID 1981-1982 BLS 1980, 1981 0.000108 Yes,significantNo $29,865 $17.3Viscusi and Moore (1989) PSID 1982 NIOSH NTOF Survey,Structural Markov Model0.0001 No No $24,611 $10.0Herzog and Schlottman(1990)U.S. Census 1970 BLS 1969 0.000097 No No $48,364 $11.7Moore and Viscusi(1990b)PSID 1982 NIOSH NTOF Survey,Structural Life CycleModel0.0001 No No $24,611 $20.8Moore and Viscusi(1990c)PSID 1982 NIOSH NTOF Survey,Structural Integrated LifeCycle Model0.0001 Yes Yes $24,611 $20.8Kniesner and Leeth (1991) CPS 1978 NIOSH NTOF Survey1980-19850.0004 Yes,significant insomespecificationsYes $33,627 $0.7Gegax, Gerking, andSchulze (1991)Authors' mail survey 1984 Workers' assessed fatalityrisk at work 19840.0009 No No $41,391 $2.1Leigh (1991) QES 1972-3, QES 1977,PSID 1974, 1981,Longitudinal QES 1973-1977, CPS January 1977BLS 1979, Workers'Compensation data from11 states 1977-19800.000134 No No $32,961 $7.1-$15.3Berger and Gabriel (1991) US Census 1980 BLS 1979 0.00008-0.000097No No $46,865,$48,029$8.6, $10.9Leigh (1995) PSID 1981, CPS January1977, QES 1977BLS 1976, 79-81 andNIOSH 1980-850.00011-0.00013No No $29,587 $8.1-$16.893Author (Year) Sample Risk Variable Mean RiskNonfatal RiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Implicit VSL(millions, 2000US$)Dorman and Hagstrom(1998)PSID 1982 BLS 1979-1981, 1983,1985, 1986; NIOSHNTOF 1980-19880.000123-0.0001639Yes Yes $32,243 $8.7-$20.3Lott and Manning (2000) CPS March 1971 andMarch 1985Hickey-Kearneycarcinogenic exposure1972-1974, NIOSHNational OccupationalExposure Survey 1981-1983NA No No $30,245 $1.5, $3.0 ($2.0,$4.0)†† Lott and Manning (2000) estimate represents the value of avoiding a statistical fatal cancer case with an assumed latency period of 10 years (discounted at 3percent). The reported values from their paper without discounting of this latency period are presented in parentheses.94Table 3. Summary of Value of a Statistical Life Studies Based on Tradeoffs Outside the Labor Market, United StatesAuthor (Year) Nature of Risk, YearComponent of the MonetaryTradeoffAverage IncomeLevel (2000 US$)Implicit VSL (millions,2000 US$)Blomquist (1979) Automobile death risks, 1972 Estimated disutility of seat belts $38,395 $1.0Dardis (1980) Fire fatality risks without smokedetectors, 1974-1979Purchase price and maintenancecosts of smoke detectorsNA $0.77Portney (1981) Mortality effects of air pollution,1978Property values in AlleghenyCounty, PANA $1.03Ippolito and Ippolito (1984) Cigarette smoking risks, 1980 Estimates monetary equivalent ofeffect of risk informationNA $0.90Garbacz (1989) Fire fatality risks without smokedetectors, 1968-1985Purchase price of smoke detectors NA $2.56Atkinson and Halvorson (1990) Automobile accidentrisks, 1989 Prices ofnew automobiles NA $5.13Carlin and Sandy (1991) Fatality risks with use ofchildren's car seats, 1985Purchase price of car seats plustime to buckle children, 10 Indianacities$24,737 $0.84Dreyfus and Viscusi (1995) Automobile safety, 1988 Prices of automobiles NA $3.8-$5.4Gayer, Hamilton, and Viscusi (2000) Superfund sites' cancer risks,1988 - 1993Property values in Greater GrandRapids, MINA $3.2-$3.7 ($4.3-$5.0)†Jenkins, Owens, and Wiggins (2001) Bicycle-related fatal head injuryrisks, 1997Purchase price of bicycle helmets NA $1.4-$2.9 (5-9 year olds)$1.2-$2.8 (10-14 year olds)$2.1-$4.3 (20-59 year olds)† Gayer et al. (2000) estimate represents the value of avoidinga statistical cancer case with an assumed latency period of 10years (discounted at 3 percent). Thereported values from their paper without discounting of this latency period are presented in parentheses.95Table 4. Summary of Labor Market Studies ofthe Value of a Statistical Life, InternationalAuthor (Year) Country SampleRisk Variable Mean RiskNonfatalRiskIncluded?Workers'CompIncluded?Average IncomeLevel(2000 US$)Implicit VSL(millions, 2000US$)Marin andPsacharopoulos(1982)UK General HouseholdSurvey 1975OPCS OccupationalMortality Decennial Survey1970-720.0001 No No $14,472 $4.2Weiss, Maier, andGerking (1986)Austria Austrian MicrocensusFile of Central Bureau ofStatistics 1981Austrian Social InsuranceData on job-relatedaccidents 1977 - 1984NA Yes No $12,011 $3.9, $6.5Meng (1989) Canada National Survey of ClassStructure and LabourProcess 1981Labour Canada and QuebecOccupational Health andSafety Board 19810.00019 No No $43,840 $3.9-$4.7Meng and Smith(1990)Canada National Election Study1984Labour Canada and QuebecOccupational Health andSafety Board 1981-830.00012 No No $29,646 $6.5-$10.3Kniesner and Leeth(1991)Japan Two-digit manufacturingdata 1986 (Japan)Yearbook of LaborStatistics (Japan)0.00003 Yes No $44,863 $9.7Kniesner and Leeth(1991)Australia Two-digit manufacturingdata 1984-85 (Australia,by state)Industrial Accidents,Australia Bureau ofStatistics 1984 - 19860.0001 Yes Yes $23,307 $4.2Cousineau, Lacroix,and Girard (1992)Canada Labor, Canada Survey1979Quebec CompensationBoard0.00001 Yes No $29,665 $4.6Martinello andMeng (1992)Canada Labour Market ActivitySurvey 1986Labour Canada andStatistics Canada 19860.00025 Yes No $25,387 $2.2-$6.896Author (Year) Country SampleRisk Variable Mean RiskNonfatalRiskIncluded?Workers'CompIncluded?Average IncomeLevel(2000 US$)Implicit VSL(millions, 2000US$)Kim and Fishback(1993)SouthKoreaMinistry of Labor'sReport on Monthly LaborSurvey and Survey onBasic Statistics for theWage StructuresMinistry of Labor'sAnalysis for IndustrialAccidents0.000485 Yes Yes $8,125 $0.8Siebert and Wei(1994)UK General HouseholdSurvey 1983Health and SafetyExecutive (HSE) 1986-880.000038 Yes No $12,810 $9.4-$11.5Lanoie, Pedro, andLatour (1995)Canada Authors' in-personsurvey 1990Quebec Workers'Compensation Board 1981-19850.000126 Yes No $40,739 $19.6-$21.7Sandy and Elliott(1996)UK Social Change andEconomic Life InitiativeSurvey (SCELI) 1986OPCS OccupationalMortality Tables DecennialSupplement 1979/80-1982/30.000045 No No $16,143 $5.2-$69.4Shanmugam(1996/7)India Author's survey of bluecollar manufacturingworkers, Madras, India1990Administrative Report ofFactories Act 1987-19900.000104 No No $778 $1.2, $1.5Liu, Hammitt, andLiu (1997)Taiwan Taiwan Labor ForceSurvey 1982-1986Taiwan Labor InsuranceAgency 1982-19860.000225-0.000382No No $5,007 - $6,088 $0.2-$0.9Miller, Mulvey, andNorris (1997)Australia Australian Census ofPopulation and Housing1991Worksafe Australia,National OccupationalHealth and SafetyCommission 1992-930.000068 No No $27,177 $11.3-$19.1Siebert and Wei(1998)Hong Kong Hong Kong Census 1991 Labour Department 0.000139 No No $11,668 $1.7Liu and Hammitt(1999)Taiwan Authors' survey ofpetrochemical workers1995Workers' assessed fatalityrisk at work 19950.000513 Yes No $18,483 $0.797Author (Year) Country SampleRisk Variable Mean RiskNonfatalRiskIncluded?Workers'CompIncluded?Average IncomeLevel(2000 US$)Implicit VSL(millions, 2000US$)Meng and Smith(1999)Canada Labour Market ActivitySurvey 1986Ontario Workers'Compensation Board0.00018 Yes Yes $19,962 $5.1-$5.3Arabsheibani andMarin (2000)UK General HouseholdSurvey (1980s)OPCS OccupationalMortality Decennial Survey1979-830.00005 Yes No $20,163 $19.9Shanmugam (2000) India Author's survey of bluecollar manufacturingworkers, Madras, India1990Administrative Report ofFactories Act 1987-19900.000104 Yes No $778 $1.0, $1.4Shanmugam (2001) India Author's survey of bluecollar manufacturingworkers, Madras, India1990Administrative Report ofFactories Act 1987-19900.000104 Yes No $778 $4.1Sandy, Elliott,Siebert, and Wei(2001)UK SCELI 1986 OPCS 79/80 - 82/3, HSE1986 - 880.000038, 0.000045 No No $16,143 $5.7, $74.198Table 5a. Summary of Labor Market Studies of the Value of Statistical Injury, United StatesAuthor(Year)Sample Risk VariableMeanInjury RiskFatal RiskIncluded?Workers'CompIncluded?Average IncomeLevel(2000 US$)Implicit Value of a Statistical Injury(2000 US$)Smith (1974) Current Population Survey(CPS) 1967, Census ofManufactures 1963, U.S.Census 1960, Employmentand Earnings 1963Bureau of LaborStatistics (BLS)1966, 1967NA Yes,significantNo $29,029 -$30,934Smith (1976) CPS 1967, 1973 BLS 1966, 1967,1970NA Yes,significantNo $31,027 nonfatal injurycoefficient not significantViscusi(1978a, 1979)Survey of WorkingConditions, 1969-1970(SWC)BLS non-fatal injuryrate 1969 (preOSHA)0.032 Yes,significantNo $31,842 $25,693-$49,442Viscusi(1978b)SWC 1969-1970 BLS non-fatal injuryrate 1969 (preOSHA)0.032 No No $32,675 $61,537-$63,241McLean,Wendling,andNeergaard(1978)Wisconsin Census 1970 Wisconsin Workers'Compensationaccident data 19700.05 No No $34,414 $141,659Viscusi(1981)Panel Study of IncomeDynamics (PSID) 1976BLS non-fatal injuryrate 19760.032 Yes,significantNo $22,618 $59,238Olson (1981) CPS 1978 BLS total lostworkday accidentrate 19730.035 Yes,significantNo $36,151 $24,009-$32,30499Author(Year)Sample Risk VariableMeanInjury RiskFatal RiskIncluded?Workers'CompIncluded?Average IncomeLevel(2000 US$)Implicit Value of a Statistical Injury(2000 US$)Freeman andMedoff(1981)CPS May 1973 - 1975 BLS mean lostworkdays per worker1972 - 19740.701 No No NA Not reported -- can't calculate (positiveand statistically significant)Leigh (1981) PSID 1974, QES 1977 BLS injury rates1974NA Yes, notsignificantNo NA Not reported -- can't calculate (positiveand statistically significant)Butler (1983) S.C. Workers'Compensation Data 1940-69S.C. Workers'CompensationClaims Data.061(claimsrate)No Yes $22,713 $936/day or $16,848 for an 18-day injuryDorsey andWalzer(1983)CPS May 1978 BLS nonfatal lostworkday injuryincidence rate 19760.03 Yes, somespecificationsYes $21,636 $60,581, $69,235Smith (1983) CPS 1978 BLS Work InjuryRate0.078 No No $32,488 $35,485Dorsey(1983)Employers' Expendituresfor EmployeeCompensation survey 1977,BLS May 1978, BLS May1979BLS 0.036 Yes, notsignificantYes, in somespecifications$33,019 $102,360Leigh andFolsom(1984)PSID 1974; Quality ofEmployment Survey (QES)1977BLS nonfatal injuryrate0.074,0.066Yes No $29,038, $36,946 $99,431-$114,663Viscusi andO'Connor(1984)Author's chemical workersurvey, 1982Workers' assessedinjury and illnessrate0.1 No No $37,642 $17,707-$22,773100Author(Year)Sample Risk VariableMeanInjury RiskFatal RiskIncluded?Workers'CompIncluded?Average IncomeLevel(2000 US$)Implicit Value of a Statistical Injury(2000 US$)Dickens(1984)CPS May 1977 BLS industry data1977NA Yes No NA Not reported -- can't calculateViscusi andMoore (1987)QES 1977 BLS lost workdayinjury rate, BLS totalinjury rate0.038,0.097No Yes $43,503 $70,650 lostworkday accident; $27,950for nonpecuniary loss-lost workdayaccident; $45,400 per accidentBiddle andZarkin (1988)QES 1977 BLS nonfatal lostworkday injuryincident rate, 19770.037 No No $42,170 $168,603 (willingness to accept),$155,582 (willingness to pay)Garen (1988) PSID 1981-1982 BLS nonfatal injuryrate, 1980-1981NA Yes No $29,865 $26,953Moore andViscusi(1988b)QES 1977 BLS annualincidence rate of lostworkday cases 1973-19760.047 Yes,significantYes $31,092 $36,818, $48,349Hersch andViscusi(1990)Authors' survey in Eugene,OR, 1987Workers' assessedinjury rate usingBLS lost workdayincidence rate scale0.059 No No (one state) $21,897 $72,429 (whole sample); $39,468(smokers); $118,277 (seat belt users)Viscusi andEvans (1990)Viscusi and O'Connorchemical worker surveyUtility functionestimates usingassessed injury andillness rate0.1 No No $37,802 $23,781 (marginal risk change); $37,030(certain injury)Hamermeshand Wolfe(1990)PSID 1981 BLS 1980, 1981 incidence:0.0476;duration:0.1571No Yes NA Not reported -- can't calculate (positiveand statistically significant)101Author(Year)Sample Risk VariableMeanInjury RiskFatal RiskIncluded?Workers'CompIncluded?Average IncomeLevel(2000 US$)Implicit Value of a Statistical Injury(2000 US$)Kniesner andLeeth (1991)CPS 1978 BLS lost workdayinjury rate0.055 Yes Yes $33,627 $60,624French andKendall(1992)CPS 1980 (railroad industryonly)Federal RailroadAdministrationInjury Rate0.048 No No $46,284 $48,928Fairris (1992) SWC 1969-1970 BLS 1969 industryinjury frequency rate0.032 No No $33,850 $49,290Hersch andPickton(1995)National MedicalExpenditure Survey 1987BLS total lostworkdays per workerper year 19870.702†No No $26,345 $120,709 (whole sample); $155,453(nonsmoker-seat belt users); $83,186(smoker-nonseat belt users)Dillingham,Miller, andLevy (1996)QES 1977 constructed a riskmeasureNA Yes No $24,267 $155,435-$242,671 WTP to avoid oneyear of worklife impairmentDorman andHagstrom(1998)PSID 1982 BLS 1981 0.052 Yes Yes $32,243 Nonfatal injury coefficient not significantHersch(1998)CPS March 1994 BLS 1993 (numberof cases of daysaway from work)0.029wholesample;0.022femalesNo No $28,004 $22,810-$33,723 (females); $12,146-$36,192 (males)102Author(Year)Sample Risk VariableMeanInjury RiskFatal RiskIncluded?Workers'CompIncluded?Average IncomeLevel(2000 US$)Implicit Value of a Statistical Injury(2000 US$)Viscusi andHersch(2001)National MedicalExpenditure Survey 1987BLS 1987 injury rateand lost workdaysrateinjury rate:0.042nonsmoker;0.49smokerNo No $31,651(nonsmokers);$28,316 (smokers)$47,476-$59,144 (nonsmokers); $20,755-$31,028 (smokers)† Note that the measure used in the Hersch and Pickton study – probability of losing 1 workday due to injury per worker per year – differs from the measure usedin most other studies – probability of a lost workday injury per worker per year.103Table 5b. Summary of Labor Market Studies ofthe Value of Statistical Injury, InternationalAuthor (Year) Country Sample Risk VariableMean InjuryRiskFatal RiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Implicit Value of aStatistical Injury(2000 US$)Cousineau,Lacroix, andGirard (1992)Canada Labor, Canada Survey1979Quebec CompensationBoardNA Yes No $29,665 $38,104Martinello andMeng (1992)Canada Labour Market ActivitySurvey 1986Labour Canada andStatistics Canada 19860.063 Yes No $25,387 $10,815-$14,456 for injury;$161,210-$191,027 forsevere injurySiebert and Wei(1994)UK General HouseholdSurvey 1983Health and SafetyExecutive (HSE) 1986-88data0.0143 Yes No $12,810 coefficient on injury risk notsignificant in allspecificationsLanoie, Pedro,and Latour(1995)Canada Authors' in-personsurvey 1990Quebec Workers'Compensation Board1981-19850.099 Yes No $40,739 $8,148Liu andHammitt (1999)Taiwan Authors’ survey ofpetrochemical workers1999Workers’ assessed injuryrisk at work 19950.0109 Yes No $18,483 $49,717Meng andSmith (1999)Canada Labour Market ActivitySurvey 1986Ontario Workers'Compensation Board3.01 --workdayslost perworkerYes Yes $19,962 $423 per work day lostShanmugam(2000)India Author's survey of bluecollar manufacturingworkers, Madras, India1990Administrative Report ofFactories Act 1987-19900.0729 Yes No $778 $150-$560Shanmugam(2001)India Author's survey of bluecollar manufacturingworkers, Madras, India1990Administrative Report ofFactories Act 1987-19900.0729 Yes No $778 $350104

Table 6. Replication of Published Me ta-Analyses with Viscusi-Aldy Data

Variable Viscusi-Aldy Version of Liu

et al. (1997) Equation 2 (1) Viscusi-Aldy Version of Miller (2000) Model 3 (2) Viscusi-AldyVersion of BowlandBeghin (2001) Linear Model (3) Viscusi-Aldy Version of Mrozek-Taylor

(2002) Model 2 (4) Dependent

Variable log(VSL) log(VSL) VSL (Expressed in Per Hour Terms) log(VSL) log(Income) 0.51* (0.15) 0.53* (0.17) - -

Income

- - 0.078** (0.031) - Hourly Wage

- - - 0.040 (0.026)

Mean Risk -0.015* (0.0057) - -19.34** (8.56) -0.16*** (0.075)

Mean Risk Squared - - - 0.0019 (0.0015)

Union x Mean Risk - - - 0.22*** (0.11) Dillingham Risk - - - -0.32 (0.58) Society of Actuaries Risk - -1.29* (0.28) - -

BLS Risk

- - 1445.18** (591.47) -

NIOSH Risk

- - - 0.27 (0.40)

Education Level - - -157.14 (192.32) - Unemployment Rate - - - 0.045 (0.048)

U.S. National Data - - - 0.31 (0.82)

Non-U.S. Study - - - -0.0048 (0.81)

Union VSL

- - 2995.05* (1086.09) -0.42 (0.90) Union Dummy Variable - - 1000.76 (638.37) 0.43 (0.40)105

Variable Viscusi-Aldy Version of Liu

et al. (1997) Equation 2 (1) Viscusi-Aldy Version of Miller (2000) Model 3 (2) Viscusi-AldyVersion of BowlandBeghin (2001) Linear Model (3) Viscusi-Aldy Version of Mrozek-Taylor

(2002) Model 2 (4) Dependent

Variable log(VSL) log(VSL) VSL (Expressed in Per Hour Terms) log(VSL)

Male Only Sample - - -588.20 (600.82) -

Blue Collar Sample - - -812.78 (644.54) -0.68 (0.49) Quadratic Risk

- - - 0.54 (0.33) Morbidity Variable Included - - - 0.11 (0.32)

log(Dependent Variable) - - - -0.24 (0.36) Regional Dummy Variable - - -757.70 (601.16) 0.16 (0.35)

Urban Dummy Variable - - -65.91 (804.50) 0.12 (0.41)

Workers’ Compensation - - - 0.10 (0.45) Wage in After Tax Terms - - - -0.29 (0.50) Industry Dummy Variable - - - 0.081 (0.27)

Occupation Dummy Variable - - - 0.0039 (0.20)

No Occupation Dummy Variable - 0.48 (0.33) - -

Job Characteristics Dummy Variable - - - -0.021 (0.51)

Constant 10.56* (1.49) 9.80* (1.78) 1935.54 (1506.92) 15.68* (1.39)106

Variable Viscusi-Aldy Version of Liu

et al. (1997) Equation 2 (1) Viscusi-Aldy Version of Miller (2000) Model 3 (2) Viscusi-AldyVersion of BowlandBeghin (2001) Linear Model (3) Viscusi-Aldy Version of Mrozek-Taylor

(2002) Model 2 (4) Dependent

Variable log(VSL) log(VSL) VSL (Expressed in Per Hour Terms) log(VSL)

R 2 0.37 0.27 - 0.83

n 46 49 45 41 Specifications (1), (2), and (4) estim ated with ordinary least squares. Specification (3) estimated with robust regression with Huber weights. Robust (White) standard errors are presented in parentheses for specifications (1), (2), and (4). Asymptotic standard errors presented in parentheses for specification (3). * Indicates statistical signi ficance at 1 percent level. ** Indicates statistical signi ficance at 5 percent level. *** Indicates statistical signi ficance at 10 percent level.107

Table 7. Income Elasticity of Willingness-to-Pay to Reduce Mortality Risk Paper (Model) Reported Elasticity in Authors’ Papers Viscusi-Aldy Version Liu et al. (1997) (Equation 2) 0.53 0.51* (0.21 – 0.80) Miller (2000) (Model 3) 0.89* 0.53* (0.20 – 0.86) Mrozek and Taylor (2002) (Model 2) 0.46** 0.52 (-0.18 – 1.22) Bowland and Beghin (2001) (Linear Model) 1.66* 0.61** (0.11 – 1.10) * Indicates elasticity is based on coefficient that is statistically significant at 1 percent level. ** Indicates elasticity is based on coefficient that is statisti cally significant at 5 percent level. Ranges in parentheses represent the 95 per cent confidence interval around the point estimate for the income elasticity.108

Table 8. Regression Models fo r Viscusi-Aldy Meta-Analysis Variable (1) (2) (3) (4) (5) (6) Regression Technique OLS OLS OLS Robust with Huber weights Robust with Huber weights Robust with Huber weights log(Income) 0.51* (0.15) 0.49* (0.13) 0.60* (0.16) 0.48* (0.12) 0.46* (0.11) 0.47* (0.15) Mean Risk -0.015** (0.0057) -0.053* (0.011) -0.045* (0.015) -0.029* (0.0061) -0.090* (0.018) -0.11* (0.029) Mean Risk Squared - 0.00022* (0.000052) 0.00016* (0.000055) - 0.00065* (0.00019) 0.0010** (0.00035) Society of Actuaries Risk - - 0.50 (0.87) - - dropped

NIOSH Risk - - 0.50 (0.41) - - 0.56 (0.41) Subjective - - -0.69 (0.78) - - -0.16 (0.98) Union Dummy Variable - - 0.44 (0.32) - - 0.50 (0.30) Male Only Sample - - 0.24 (0.36) - - 0.36 (0.34) Blue Collar Sample - - -0.016 (0.31) - - -0.23 (0.33) Quadratic Risk - - 0.092 (0.27) - - 0.20 (0.34) Morbidity Variable Included - - 0.55*** (0.30) - - 0.62** (0.30) log(Dependent Variable) - - 0.17 (0.31) - - 0.13 (0.41) Regional Dummy Variable - - -0.16 (0.25) - - 0.16 (0.31) Urban Dummy Variable - - 0.38 (0.29) - - 0.087 (0.39) Workers’ Compensation - - -0.57 (0.33) - - -0.28 (0.38) Industry Dummy Variable - - -0.46 (0.27) - - -0.37 (0.28) Occupation Dummy Variable - - -0.45 (0.31) - - -0.24 (0.33) Constant 10.56* (1.49) 11.22* (1.30) 9.58* (1.82) 11.05* (1.23) 11.83* (1.12) 11.22* (1.68)

R 2 0.37 0.55 0.72 - - -

n 46 46 46 45 45 44 Income Elasticity (95% Confidence Interval) 0.51 (0.21 – 0.80) 0.49 (0.23 – 0.75) 0.60 (0.27 – 0.94) 0.48 (0.23 – 0.73) 0.46 (0.24 – 0.69) 0.47 (0.15 – 0.78) Mean Predicted VSL, Full Sample (millions 2000 US$) (95% Confidence Interval) 5.0 (3.4 – 7.4) 5.4 (3.7 – 7.8) 5.9 (2.7 – 13.9) 5.5 (4.1 – 7.5) 5.9 (4.4 – 8.1) 6.2 (2.5 – 15.7)

Mean Predicted VSL, U.S. Sample (millions 2000 US$) (95% 5.5 (3.8 – 8.1) 5.8 (4.1 – 8.3) 6.9 (3.1 – 16.2) 6.1 (4.6 – 8.2) 6.3 (4.8 – 8.4) 7.6 (3.0 – 19.4)109

Variable (1) (2) (3) (4) (5) (6) Regression Technique OLS OLS OLS Robust with Huber weights Robust with Huber weights Robust with Huber weights Confidence Interval) Dependent variable: log(VSL) Robust (White) standard errors presented in parentheses for specifications 1 – 3. Asymptotic standard errors presented in parentheses for specifications 4 – 6. * Indicates statistical significance at 1 percent level. ** Indicates statistical signifi cance at 5 percent level. *** Indicates statistical signifi cance at 10 percent level. Note: Estimation with robust standard erro rs clustered by wage data source yiel ds same significance levels, with the exception of Mean Risk in (1) and (3) and Mean Risk Squared in (3), which are all significant at the 2 percent level, and the industry dummy variable in (3) which is significant at the 8 percent level.110Table 9a. Summary of Union Effects in Valueof a Statistical Life Studies, United StatesAuthor (Year) Sample Risk Variable Mean RiskNonfatalRiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Union ImplicitVSL(millions, 2000US$)NonunionImplicit VSL(millions, 2000US$)Specification ofUnion StatusThaler andRosen (1975)Survey of EconomicOpportunity 1967Society of Actuaries19670.001 No No $34,663 $1.7-$1.9 Negative Risk x union interactionViscusi (1980) SWC 1969-1970 BLS 3-digit industrydata for 19690.000118 Yes No $31,842 $5.5-$15.2 Not significant Risk x union interactionOlson (1981) CPS 1978 BLS 1973 0.0001 Yes,significantNo $36,151 $30.6-$44.2 $5.7-$5.8 Risk x union interactionand separate regressionsby union statusDorsey (1983) Employers' Expendituresfor EmployeeCompensation survey1977, BLS May 1978,BLS May 1979BLS 0.000071 Yes,significantYes, in somespecifications$33,019 $9.6 Negative Risk x union interactionDorsey andWalzer (1983)CPS May 1978 BLS 1976 0.000052 Yes,significantYes $21,636 $11.8, $12.3 NegativeSeparate regressions byunion statusDillingham andSmith (1984)CPS May 1979 BLS industry data 1976,1979; NY Workers'Comp Data 19700.000082 Yes,significant insomespecificationsNo $29,707 $6.1, $6.6 $3.1 Separate regressions byunion statusGaren (1988) PSID 1981-1982BLS 1980, 1981 0.000108 Yes,significantNo $29,865 Insufficientinformationprovided tocalculatePositive, butsmaller thanunion VSLRisk x union interactionGegax, Gerking,and Schulze(1991)Authors' mail survey1984Workers' assessedfatality risk at work19840.0009 No No $41,391 $2.7 Not significant Separate regressions byunion status111Author (Year) Sample Risk Variable Mean RiskNonfatalRiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Union ImplicitVSL(millions, 2000US$)NonunionImplicit VSL(millions, 2000US$)Specification ofUnion StatusKim andFishback (1993)Interstate CommerceCommission data 1893 -1909, 1926 - 32, 1934 –45ICC Fatality Data 1890- 19450.0006 -0.0018Yes No NA No statisticaldifferencebetween unionand nonunionmembersRisk x union interactionDorman andHagstrom(1998)PSID 1982 BLS 1979-1981, 1983,1985, 1986; NIOSHNTOF 1980-19880.000123 -0.0001639Yes Yes $32,243 $18.1 $8.7 Riskx union interaction112Table 9b. Summary of Union Effects in Valueof Statistical Injury Studies, United StatesAuthor (Year) Sample Risk VariableMeanRiskFatal RiskIncluded?Workers'CompIncluded?Average IncomeLevel (2000 US$)Union ImplicitValue of aStatistical Injury(2000 US$)Nonunion ImplicitValue of aStatistical Injury(2000 US$)Specification of UnionStatusBiddle and Zarkin(1988)QES 1977 BLS nonfatal lostworkday injuryincident rate, 19770.037 No No $42,170 $319,678 $56,832 Risk x union interactionFreeman andMedoff (1981)CPS May 1973 –1975BLS mean lostworkdays perworker 1972 - 19740.701* No No NA No statisticaldifference betweenunion andnonunion membersSeparate regressions byunion statusSmith (1983) CPS 1978 BLS Work InjuryRate0.078 No No $38,138 (males);$25,672 (females)$74,368 (males);$59,815 (females)$46,528 (males);$25,672 (females)Risk x union interactionFairris (1992) SWC 1969-1970 BLS 1969 industryinjury frequencyrate0.032 No No $33,850 $246,449 Not significant Separate regressions byunion statusHamermesh andWolfe (1990)PSID 1981 BLS 1980, 1981 incidence:0.0476;duration:0.1571No Yes NA Insufficientinformationprovided tocalculatePositive, butsmaller than unionvalue of injuryRisk x union interactionHersch and Pickton(1995)National MedicalExpenditure Survey1987BLS total lostworkdays perworker per year19870.702* No No $26,345 $222,448 $99,478 Risk x union interaction*Lost workdays per 100 full-time workers.113Table 9c. Summary of Union Effects in Value of a Statistical Life Studies, InternationalAuthor (Year) Country Sample Risk Variable Mean RiskNonfatal RiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Union ImplicitVSL(millions, 2000US$)NonunionImplicit VSL(millions,2000 US$)Specification ofUnion StatusMarin andPsacharopoulos(1982)UK General HouseholdSurvey 1975OPCSOccupationalMortalityDecennialSurvey 1970-720.0001 No No $14,472 No statisticaldifferencebetween unionand nonunionmembersRisk x unioninteractionMeng (1989) Canada National Survey ofClass Structure andLabour Process1981Labour Canadaand QuebecOccupationalHealth andSafety Board19810.00019 No No $43,840 No statisticaldifferencebetween unionand nonunionmembersRisk x unioninteractionMeng and Smith(1990)Canada National ElectionStudy 1984Labour Canadaand QuebecOccupationalHealth andSafety Board1981-830.00012 No No $29,646 No statisticaldifferencebetween unionand nonunionmembersRisk x unioninteractionMeng (1991) Canada Labour MarketActivity Survey1986Labour Canadaand Workers'CompensationBoards0.00023 foraccidents,0.00012 fordiseaseNo No $25,387 $1.9 $4.2 Risk x unioninteractionCousineau,Lacroix, andGirard (1992)Canada Labor, CanadaSurvey 1979QuebecCompensationBoard0.00001 Yes No $29,665 $4.4 $2.0Separate regressionsby union statusMartinello andMeng (1992)Canada Labour MarketActivity Survey1986Labour Canadaand StatisticsCanada 19860.00025 Yes No $25,387 No statisticaldifferencebetween unionand nonunionmembersRisk x unioninteraction114Author (Year) Country Sample Risk Variable Mean RiskNonfatal RiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Union ImplicitVSL(millions, 2000US$)NonunionImplicit VSL(millions,2000 US$)Specification ofUnion StatusSiebert and Wei(1994)UK General HouseholdSurvey 1983Health andSafety Executive(HSE) 1986-880.0000379 Yes No $12,810 $11.5 $9.4Separate regressionsby union statusLanoie, Pedro,and Latour(1995)Canada Authors' in-personsurvey 1990QuebecWorkers'CompensationBoard 1981-19850.000126 Yes No $40,739 $19.6, $21.7 NotsignificantSeparate regressionequationsSandy and Elliott(1996)UK Social Change andEconomic LifeInitiative Survey(SCELI) 1986OPCSOccupationalMortality TablesDecennialSupplement1979/80-1982/34.4831E-05 No No $16,143 $69.0 $69.4 Risk x unioninteractionShanmugam(1996)India Author's survey ofblue collarmanufacturingworkers, Madras,India 1990AdministrativeReport ofFactories Act1987-19900.000104 No No $778 $0.6 NotsignificantRisk x unioninteractionKim andFishback (1999)SouthKoreaMinistry of Labor'sReport on MonthlyLabor Survey andSurvey on BasicStatistics for theWage StructuresMinistry ofLabor's Analysisfor IndustrialAccidents0.000485 Yes Yes $8,125 No statisticaldifferencebetween unionand nonunionmembersRisk x unioninteraction115Author (Year) Country Sample Risk Variable Mean RiskNonfatal RiskIncluded?Workers'CompIncluded?AverageIncome Level(2000 US$)Union ImplicitVSL(millions, 2000US$)NonunionImplicit VSL(millions,2000 US$)Specification ofUnion StatusArabsheibaniand Marin(2000)UK General HouseholdSurvey (1980s)OPCSOccupationalMortalityDecennialSurvey 1979-83reported as-0.006Yes No $20,163 No statisticaldifferencebetween unionand nonunionmembersRisk x unioninteractionSandy, Elliott,Siebert, and Wei(2001)UK SCELI 1986 OPCS 79/80 -82/3, HSE 1986- 880.000038,0.000045No No $16,143 $5.7, $44.8 $36.1, $74.1 Risk x unioninteraction116Table 10. Summary of Age-Risk Interaction Effects in Value of a Statistical Life Studies, United StatesAuthor (Year) SampleAverage Ageof SampleRisk Variable Age x Risk Variable CoefficientThaler and Rosen(1975)Survey of EconomicOpportunity 196741.8 Society of Actuaries 1967 Significant (5%), negativeViscusi (1979) Survey of Working Conditions,1969-1970 (SWC)39.7 BLS 1969, subjective risk ofjob (SWC)Significant (1%), negativePortney (1981) Property values in AlleghenyCounty, PA 1978NA Air pollution annual mortalityrate data, EPAVSL by age females (males): lessthan 45: $1.5 (1.0) million; 45-64: $0.3 (0.12) million; over 65:$0.05 (0.05) millionArnould and Nichols(1983)U.S. Census 1970 NA Society of Actuaries 1967 Significant (1%), negativeMoore and Viscusi(1988b)QES 1977 38.1 Expected life years lost (=BLSfatality risk x discountedremaining life)Significant (1%), positive(implies risk premium increaseswith life expectancy, decreaseswith age, ceteris paribus)Meng (1989) National Survey of ClassStructure and Labour Process198139.9 Labour Canada and QuebecOccupational Health andSafety Board 1981Significant (10%), negativeMeng and Smith(1990)National Election Study 1984 NALabour Canada and QuebecOccupational Health andSafety Board 1981-83InsignificantDillingham, Miller,and Levy (1996)QES 1977 36.5 Constructed a risk measureDeclining scale of WTP to avoidimpaired worklife as function ofage117Author (Year) SampleAverage Ageof SampleRisk Variable Age x Risk Variable CoefficientShanmugam (1996/7) Author's survey of blue collarmanufacturing workers,Madras, India 199034.1 Administrative Report ofFactories Act 1987-1990InsignificantShanmugam (2001) Author's survey of blue collarmanufacturing workers,Madras, India 199034.1 Administrative Report ofFactories Act 1987-1990Insignificant118

Table 11. Summary of Imputed Disc ount Rate Studies, United States Year Author (Year) Type of Study Sample Implicit Discount Rate 1988 Moore and Viscusi (1988b) Labor Hedonic with Reduced Form Discounting Model QES 1977 9.6%-12.2%

1989 Viscusi and Moore (1989) Labor Hedonic with Structural Markov Model PSID 1982 10.7%

1990 Moore and Viscusi (1990b) Labor Hedonic with Structural Life Cycle Model PSID 1982 2%

1990 Moore and Viscusi (1990c) Labor Hedonic with Structural Integrated Life Cycle Model PSID 1982 1.0%-14.2%

1995 Dreyfus and Viscusi (1995) Automobile Hedonic 1988 Residential Transportation Energy Consumption Survey 11%-17%119

Table 12. Values of Statistical Life Us ed by U.S. Regulatory Agencies, 1985 – 2000* Year Agency Regulation Value of a Statistical Life (millions, 2000 $) 1985 Federal Aviation Administration Protective Breathing Equipment (50 Federal Register 41452) $1.0**

1985 Environmental Protection Agency Regulation of Fuels and Fuel Additives; Gasoline Lead Content (50 FR 9400) $1.7

1988 Federal Aviation Administration Improved Survival Equipment for Inadvertent Water Landings (53 FR 24890) $1.5**

1988 Environmental Protection Agency Protection of Stratospheric Ozone (53 FR 30566) $4.8

1990 Federal Aviation Administration Proposed Establishment of the Harlingen Airport Radar Service Area, TX (55 FR 32064) $2.0**

1994 Food and Nutrition Service (USDA) National School Lunch Program and School Breakfast Program (59 FR 30218) $1.7, $3.5**

1995 Consumer Product Safety Commission Multiple Tube Mine and Shell Fireworks Devices (60 FR 34922) $5.6**

1996 Food Safety Inspection Service (USDA) Pathogen Reduction; Hazard Analysis and Critical Control Point Systems (61 FR 38806) $1.9

1996 Food and Drug Administration Regulations Restricting the Sale and Distribution of Cigarettes and Smokeless Tobacco to Protect Children and Adolescents (61 FR 44396) $2.7**

1996 Federal Aviation Administration Aircraft Flight Simulator Use in Pilot Training, Testing, and Checking and at Training Centers (61 FR 34508) $3.0**

1996 Environmental Protection Agency Requirements for Lead-Based Paint Activities in Target Housing and Child-Occupied Facilities (61 FR 45778) $6.3

1996 Food and Drug Administration Medical Devices; Current Good Manufacturing Practice Final Rule; Quality System Regulation (61 FR 52602) $5.5**

1997 Environmental Protection Agency National Ambient Air Quality Standards for Ozone (62 FR 38856) $6.3

1999 Environmental Protection Agency Radon in Drinking Water Health Risk Reduction and Cost Analysis (64 FR 9560) $6.3

1999 Environmental Protection Agency Control of Air Pollution from New Motor Vehicles: Tier 2 Motor Vehicle Emissions Standards and Gasoline Sulfur Control Requirements (65 FR 6698) $3.9, $6.3

2000 Consumer Product Safety Commission Portable Bed Rails; Advance Notice of Proposed Rulemaking (65 FR 58968) $5.0** * This table augments a similar presentation of values of a statistical life used in U.S. regulatory analyses in Adler and Posner (2000) by including more regulations and presenting VSLs in constant year dollars. ** The published summaries of the regulatory impact analyses for these rules do not specify the year in which the reported dollars are denominated. We have assumed that the dollar year corresponds to the date of rule publication for purposes of converting all values into 2000 dollars. Note that the CPSC reported a VSL of $5 million in both its 1995 and 2000 regulations; the difference in values reflects our deflating to 2000 dollars.120

Table 13. Evaluation of Risk-Risk Trad eoff for 24 U.S. Regulations, 1986 – 1998

Regulation Year Agency Discounted Statistical Lives Saved Fatalities Induced by Cost of Regulations Net Lives Saved by Regulations Toxicity characteristics to determine hazardous wastes 1990 EPA 0.048 -23 23 Underground storage tanks: technical requirements 1988 EPA 1.1 -22 24

Manufactured home construction and safety standards on wind standards 1994 HUD 1.5 -3.2 4.7

Process safety management of highly hazardous chemicals 1992 DOL 220 -42 260

Regulations restricting the sale and distribution of cigarettes and smokeless tobacco to protect children and adolescents 1996 HHS 4,700 -140 4,900

Medicare and Medicaid programs: hospital conditions of participation; identification of potential organ, tissue, and eye donors; and transplanthospitals' provision of transplantrelated data 1998 HHS 710 9.2 700

Quality mammography standards 1997 HHS 75 1.4 74 Food labeling regulations 1993 HHS 520 10 510 Childproof lighters 1993 CPSC 95 2.9 92 Standard for occupational exposure to benzene 1987 DOL 4.4 1.8 2.6 Occupational exposure to methylene chloride 1997 DOL 12 5.9 6.2 Occupational exposure to 4,4' methylenedianiline 1992 DOL 0.7 0.71 -0.01 Asbestos: manufacture, importation, processing, and distribution in commerce -- prohibitions (total) 1989 EPA 3.9 4.3 -0.41

National primary and secondary water regulations -- phase II: maximum contaminant levels for 38 contaminants 1991 EPA 44 63 -19

Occupational exposure to asbestos 1994 DOL 13 20 -7.1121

Regulation Year Agency Discounted Statistical Lives Saved Fatalities Induced by Cost of Regulations Net Lives Saved by Regulations Hazardous waste management system -- wood preservatives 1990 EPA 0.29 0.83 -0.55

Sewage sludge use and disposal regulations, 40 CFR pt. 503 1993 EPA 0.24 2.6 -2.3

Land disposal restrictions for "third third" scheduled wastes 1990 EPA 2.8 30 -27

Hazardous waste management system: final solvents and dioxins land disposal restrictions rule 1986 EPA 1 12 -11

Occupational exposure to formaldehyde 1987 DOL 0.21 4.8 -4.5 Prohibit the land disposal of the first third of scheduled wastes ("second sixth" proposal) 1988 EPA 2.9 66 -63

Land disposal restrictions -- phase II: universal treatment standards and treatment standards for organic toxicity, characteristic wastes, and newly listed wastes 1994 EPA 0.16 8.3 -8.2

Drinking water regulations, synthetic organic chemicals -- phase V 1992 EPA 0.0061 3.4 -3.4

Solid waste disposal facility criteria, 40 CFR pt. 257 and pt. 258 1991 EPA 0.0049 10 -10

Source: Hahn, Lutter, and Viscusi (2000).122

Appendix Table A. Description of Variables Used in Viscusi-Aldy Meta-Analyses Variable Description Summary Statistic, Viscusi-Aldy data VSL Value of a statistical life (millions, 2000 US$) $6.7 ($5.6) Income Annual labor income (2000 US$) $26,006 ($12,002) Mean Risk Average mortality risk of sample 0.0002 (0.0003) Hourly Wage Hourly wage or hourly equivalent of weekly income (2000 US$) $13.00 ($6.00)

Union VSL VSL for union members only (dummy variable) 4/49 Dillingham Risk VSL based on Dillingha m (1985) constructed New York workers compensation-based fatality risk measure (d.v.) 1/49

Society of Actuaries Risk VSL based on Society of Actuaries 1967 mortality risk data (d.v.) 2/49

BLS Risk VSL based on BLS mortality risk measure (d.v.) 16/49 NIOSH Risk VSL based on NIOSH mortality risk measure (d.v.) 5/49 Subjective VSL based on self-reported m easure of mortality risk (d.v.) 1/49 Education Level Barro-Lee average educational attainment for population > 25 by country (in years) 9.6 (2.0)

Unemployment Rate Annual unemployment rate by year of wage data 7.6 (4.6) U.S. National Data VSL based on national U.S. worker sample (d.v.) 24/49 Non-U.S. Study VSL based on non-US wage-risk study (d.v.) 22/49 Male Onl y Sam p le VSL based on male onl y sam p le ( d.v. ) 21/49 Blue Collar Sample VSL based on blue collar only sample (d.v.) 15/49 Quadratic Risk VSL based on econometric specification quadratic in mortality risk (d.v.) 7/49

Morbidity Variable Included VSL based on study that included an injury risk measure (d.v.) 25/49

log(Dependent Variable) VSL derived from specification with natural logarithm of dependent variable (d.v.) 44/49

Union D.V. VSL based on specificatio n that included dummy variable for union affiliation (d.v.) 32/49

Regional D.V. VSL based on specification with regional dummy variables (d.v.) 24/49

Urban D.V. VSL based on specification with urban/MSA dummy variable (d.v.) 13/49

Workers’ Compensation VSL based on specification w ith workers’ compensation variable (d.v.) 11/49

Wage in After Tax Terms VSL based on specification with income expressed in aftertax terms (d.v.) 10/49

Industry D.V. VSL based on specifica tion with industry dummy variables (d.v.) 21/49

Occupation D.V. VSL based on specification with occupational dummy variables (d.v.) 20/49

No Occupation D.V. Study does not include occupational dummy variables 29/49123

Variable Description Summary Statistic, Viscusi-Aldy data (dummy variable) Job Characteristics D.V. VSL based on specification with variables describing job characteristics (d.v.) 10/49 Means (standard deviations) reported for continuous variables. Share of studies in which variable equals 1 reported for dummy variables. n =49