?/EPA
United States
Environmental Protection
Agency
Office of Policy
Planning and Evaluation
Washington DC. 2CW60
March 1989
EPA-230-06-86-016
Valuing Risks: New Information
on the Willingness to Pay for
Changes in Fatal Risks
by Daniel M. Violette and
Lauraine G. Chestnut
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ACKNOWLEDGEMENT
The authors would like to thank Ann Fisher for supporting this effort and
making significant contributions to the review.
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TABLE OF CONTENTS
Page
1 .0 INTRODUCTION 1
2.0 VALUE-OF-LIFE ESTIMATES FROM LABOR MARKET ANALYSES OF WAGE-
RISK TRADEOFFS 4
2.1 STUDY 1: Marin and Psacharopoulos (1982) 7
2.2 STUDY 2: Dillingham (1985) 11
2.3 STUDY 3: Gegax, Gerking, and Schulze (1985) 13
2.4 STUDY 4: Duncan and Holmlund (1983) 17
3.0 VALUE-OF-LIFE ESTIMATES FROM CONTINGENT VALUATION STUDIES 20
3.1 STUDY 1: Jones-Lee, Hammerton, and Philips (1985) 20
3.2 STUDY 2: Gegax, Gerking, and Schulze (1985) 27
4.0 OVERALL CONCLUSIONS 30
END NOTES 34
BIBLIOGRAPHY 36
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1.0 INTRODUCTION
This report updates the Violette and Chestnut (1983) report which assembled
and reviewed estimates of the willingness to pay for changes in fatal risks.
The 1983 report compiled the available empirical estimates in one reference
source, presented a critical discussion of the estimates, and discussed their
usefulness in environmental policy assessment. Since its publication, several
studies have produced new estimates. Some of these studies directly address
weaknesses pointed out in the earlier review, so the estimates now can be
re-evaluated.
The 1983 review focused on willingness-to-pay (WTP) and willingness-to-accept
compensation (WTA) estimates for valuing changes in risks. Other valuation
approaches have been used including estimates of future earnings that would be
lost due to an increase in deaths or illness, and estimates of medical
expenses associated with an increase in illness and death. Although providing
useful benchmarks, these approaches do not provide estimates of the benefits
to the individual of reducing or preventing health risks because they do not
reflect the change in utility, or well-being, that would result from the
change in risk of illness or death. WTP measures reflect how much of other
goods and services the individual is willing to give up in order to obtain a
reduction or prevent an increase in health risks. Correspondingly, WTA
measures reflect how much a person would have to be paid to accept an increase
in risk. These measures, therefore, give a dollar estimate of the change in
well-being that the individual has or expects to experience. Summing this
measure of individual benefits across all affected individuals can provide the
benefits component of a benefit-cost analysis.
In this report, results of the different studies are compared by reference to
the estimated "value of life." This is not meant to be thought of as an
amount of money that an individual would accept in exchange for his or her
life. Instead, it is a way of comparing valuations for small changes in small
risks that affect a large number of people. For example, say a certain
environmental decision will reduce the risk of death from exposure to a given
toxic substance from 3 out of 10,000 to 1 out of 10,000 for a total population
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of 10,000 people. Implementing the policy would, on average, save two lives.
These are termed statistical lives since the change is in the statistical
risks faced by the population, and there is no way in advance to identify
which two individuals in the population would be saved. If each of the 10,000
individuals is willing to pay $100 for this reduction in the probability of
his or her death, then the total willingness to pay is
($100 per person X 10,000 people) = $1,000,000
and, given that two lives are saved, the value per statistical life is
$500,000.
The 1983 report examined studies that fell into three general categories:
1. Wage-risk studies that use data from the labor market to examine
workers' trade-offs between on-the-job risks and wages.
2. Consumer market studies that examine individuals' purchases of
products that influence safety, such as smoke detectors.
3. Contingent market studies where hypothetical markets are constructed
and survey respondents are questioned about their willingness to pay
for changes in levels of safety.
The previous review did not include the primarily theoretical literature
concerning the relationship between the "value of life" and "human capital,"
as expressed largely by a person's lifetime earnings. This work has focused
on the conceptual basis for determining when a person's human capital can be
viewed as a lower bound to the value of life. Mishan (1982) pointed out that
any hypothesized relationship between a statistical value of life based on WTP
and a human capital figure is essentially an empirical question which cannot
be answered until we have empirical estimates of the "value of life" based on
willingness to pay. This review has therefore focused on empirical
willingness to pay estimates.1
While a substantial literature on the valuation of fatal risks has been
published since the previous report, this update focuses on studies that we
judge to be most important for shedding new light on the valuation of risks.
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The studies emphasized in this update have analyzed new data sets rather, than
re-examining data sets used in previous studies. This is not meant to
minimize the contributions from using different model variations for existing
data sets, which certainly provide valuable information on the robustness of
the results. However, one of the principal criticisms of the earlier work on
the value-of-life estimates was that most of the wage-risk studies used one of
only two sets of data on job risks and, as a result, did not produce
independent estimates. Further, the willingness-to-pay estimates were found
to lie in roughly two groups corresponding to the selection of the risk
variable data set. This makes wage-risk studies that use new and different
data on job risks particularly useful.^
In addition to the new wage-risk valuation studies, several recent risk
valuation studies have used contingent market approaches. These new
contingent market studies represent a considerable advancement over the ones
reviewed in the earlier report. Estimates from the earlier contingent market
studies were viewed as largely unreliable due to various methodological
problems. Two new studies specifically address the criticisms presented in
the earlier review and produce estimates deserving careful consideration.
Six new studies will be emphasized in this report. Each one uses new data on
risks. Four use data from labor markets and base estimates on wage-risk
premiums. The remaining two studies use contingent market survey methods.
Some additional studies are mentioned as their results have some bearing on
the overall conclusions. The studies examined in detail are:
1. Wage-Risk Studies: Marin and Psacharopoulos (1982); Dillingham
(1985); Duncan and Holmlund (1983); and Gegax, Gerking, and Schulze
(1985).3
2. Contingent Market Studies: Jones-Lee, Hammerton, and Philips
(1985) and Gegax, Gerking, and Schulze (1985). Jones-Lee et al. use
a contingent market approach to examine the willingness to pay for
reduced risks in travel, while Gegax et al. examine contingent bids
for a safer workplace.
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2.0 VALUE-OF-LIFE ESTIMATES FROM LABOR MARKET ANALYSES OF WAGE-RISK TRADEOFFS
This section discusses four hedonic wage-risk studies that address specific
criticisms and concerns about the wage-risk literature reviewed earlier in
Violette and Chestnut (1983). One criticism of the previous wage-risk studies
was that they relied on only two available data sets on job risks. The
estimates from these studies clustered into two groups depending on which
measure of risk was selected. Table 1 presents the results of these studies.
The studies that found value-of-life estimates in the lower range used
actuarial risk estimates compiled from insurance data, while those that found
estimates in the higher range used industry-specific job risks compiled by the
U.S. Bureau of Labor Statistics.4
One difference between the two risk measures is that the actuarial risk
measure may incorporate factors other than occupational risks. First used by
Thaler arid Rosen (1975), these data were obtained from a 1967 survey conducted
by the Society of Actuaries. The survey provides data on the death rates
associated with selected occupations. To obtain a measure of occupational
risks from these data on total fatalities, Thaler and Rosen subtracted the
age-adjusted expected deaths for the population from the death rate for each
occupation. The remainder was assumed to represent deaths associated with the
occupation. Constructed in this manner, the risk variable measures the extra
risk to the insurance company of insuring those who are in a particular
occupation.
These actuarial risk data result in an unexpected ranking of the risks
associated with each occupation. For example, elevator operators, bartenders
and waiters were calculated to have higher risks of death than policemen or
firemen. This may be because the risk estimates reflect both true
occupational risks and risks associated with worker characteristics. Rather
than bartending being a particularly risky occupation, it may be that people
attracted to this profession have personal habits or characteristics which
increase their insurable risk independent of their occupation. On the other
hand, people who work as firemen or policemen may be in better physical
condition thereby reducing the incidence of illnesses or accidents leading to
death. To the extent that an occupation's higher death rate is caused by
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Table 1
Labor Market Based Estimates of the Marginal
willingness to Pay for Reductions in Risks
Study
Value Per
Statistical Life
(millions of 1984 dollars)
Mean Risk Level
for the Sample4
All
Estimates1
Judgemental
Best Estimates
LOW RANGE ESTIMATES
(all based on actuarial risk data)
1. Thaler and
Rosen (1975)
a. without ri sk 11.0
interaction terms
b. Wi th risk 1 1 .0
interaction terms
.42
.54
.58
.80
.01
.21
.30
.36
.61
2. Arnould and
Nichols (1983)
11.0
.6
HIGH RANGE ESTIMATES
(all based on BLS industry accident rates)
3. R. SmJ th
(1976)
1.0 and 1 .5
3.47
3.70
3.55
4. V.K. Smith
(1982)
3.0C
1 .36'
to
5.57
3.80
5. W.K. Viscusi
(1978b)
1 .2
1.57
2.40
2.86
3.70
4.25
4.53
4.71
4.20
6. C. Olson
7. R. Smith
(1974)
1 .0
1.0 to 1.5
7.64
8.09
14.20
7.64
8.09
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a Approximate annual deaths per 10,000 workers.
D For different model specifications. Estimates from all specifications are
shown since one outlier can distort the range.
c Assuming .4 percent of all injuries are fatal, as reported by Viscusi
(19785) for the BLS injury statistics.
Assuming the risk premium for fatal injuries ranged from 33 percent to 100
percent of the premium for all risks.
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personal characteristics that are attached to the individual rather than
associated with the job, there will be no positive compensating wage
differential. In fact, if these characteristics are attached to the person,
they could have the opposite effect, i.e., result in lower wages for these
occupations. Having individuals as employees who are more likely to incur
injuries may increase the cost of doing business. This would result in lower
productivity and, therefore, lower wages being offered to these individuals.
Even if the actuarial occupational risk data were entirely accurate, it is
questionable that it would match the perceptions of individuals in the labor
market who are negotiating their wage-risk premiums. The ranking of
occupations by risk implied by the actuarial data does not conform to usual
expectations. One of the assumptions of the hedonic technique is that the
participants have accurate information regarding the risk characteristics of
the job.
In contrast to the actuarial data, the data compiled by the U.S. Bureau of
Labor Statistics have the advantage of reporting only work related fatalities
by industry group. This measure still has problems since job risks are not
likely to be uniform across occupations within the same industry. For
example, clerical workers and heavy equipment operators classified as being in
the same industry will have very different risks of injury. Also, the BLS
on-the-job injury data do not include all long-term illnesses that may be
associated with exposures to harmful substances in the workplace and may
result in premature death. As a result, there is measurement error in both
the actuarial and the BLS industry measures of risk used in earlier studies.
In general, the BLS industry risk measure is viewed as being the more
appropriate. Still, additional research using new risk data sets is needed.
The four studies reviewed below each use a different risk data set.
2.1 STUDY 1; Marin and Psacharopoulos (1982)
Marin and Psacharopoulos (M&P) use data from the labor markets in the United
Kingdom to determine whether compensating wage differentials exist for jobs
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that have higher risks of death. In addition to this primary objective, M&P
examine the influence of different job risk measures on the estimated value of
life.
Data and Estimation Methods
M&P obtained data on job risks classified by 223 occupational groups from
surveys conducted by the Office of Population Censuses and Surveys. The risk
measures were based on detailed records of deaths by occupation registered
over the three-year period 1970 through 1972. This is the first study to use
this data base on job risks and, given the paucity of risk data, its results
are an important contribution to the literature on the value of life as
estimated by wage premiums.
MSP constructed a number of risk variables. The two measures that were given
the greatest attention were termed ACCRISK and GENRISK. The ACCRISK variable
solved a number of the problems associated with both the actuarial risk
measure and the BLS risk measure used in U.S. studies. Their ACCRISK measure
was based on deaths caused by an accident at work. It was constructed by
subtracting the expected on-the-job accidental death rate, given the age
structure of the occupation, from the actual rate of on-the-job accident
fatalities. The influence of personal characteristics that are not job
related is reduced by using a risk measure based only on accidents at work.
Having occupation-specific risk measures also reduces the errors-in-variables
problem present with the BLS industry risk measures. For these reasons, the
ACCRISK variable constructed by M&P is superior to any of the risk variables
used in the studies of the U.S. labor market referenced in Table 1.
The second risk measure, GENRISK, was defined as the extra risk of dying in
each occupational group and was calculated as the actual death rate minus the
death rate that could have been expected given the age and social class
structure of workers in the occupational group. Since GENRISK was calculated
in the same way as Thaler.and Rosen's actuarial risk variable, it is subject
to the same criticisms as their risk measure.
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The empirical model estimated by M&P was a conventional earnings function:
In Y = f(S, EX, EX squared, In WEEKS, RISK, ONION, OCC,
UNIONxRISK) -t- error;
where Y is annual earnings, S is the number of years of schooling, EX is years
of experience in the labor force, WEEKS is the number of weeks worked in the
survey year, RISK is one of the risk measures, UNION is the proportion of the
workers covered by a collective bargaining agreement, and OCC is a measure of
occupational desirability based on the Goldthorpe and Hope (1974) scale.
Results
The M&P results show that earnings in the United Kingdom do, in fact,
compensate for higher work related risk. The difference between estimates
using the ACCRISK and GENRISK risk measures is interesting. The estimated
coefficients on the GENRISK measure were an order of magnitude smaller than
those based on the more appropriate ACCRISK measure. Using the ACCRISK
measure, the estimated value of life ranged from 603,000 British pounds to
681,000 British pounds. Using an approximate exchange rate of 2:1 for this
time period, these estimates roughly translate into a range of $1,206,000 to
$1,362,000 in 1975 dollars.
In an interesting side analysis, M&P construct industry risk measures
comparable to the BLS measure used in many of the U.S. studies. These
industry-based risk measures produced higher estimates of the value of life
than were found when the occupation specific ACCRISK measure was used. The
implied value of life was about 2 million British pounds.
M&P also estimated wage-risk premiums for certain worker subgroups. Three
subgroups were examined: (1) managers and professionals, (2) nonmanual
workers, and (3) manual workers. M&P found the job risk coefficient to be
insignificant in the equation for managers and professional workers. This was
felt to be due to the small variation in the risks across the occupations in
this category. The risk variable coefficient was positive and significant for
the other two worker classifications. The implicit value-of-life estimates
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based on these estimated risk coefficients ranged from 2,259,000 to 2,245,000
British pounds for nonmanual workers and from 619,000 to 686,000 British
pounds for manual workers. The difference in the estimate for these two
worker classifications is large. More weight should probably be given to the
manual work estimates since the standard errors of the estimates for nonmanual
workers were much larger relative to the estimated coefficients.
MSP drew several conclusions from their analyses. In particular, when viewing
the labor force as a whole, the implicit values of life were found to fall
into the 600,000 to 700,000 (British pounds) range. Translating this into
1975 U.S. dollars gives a range of $1,200,000 to $1,400,000. When the sample
was split, the range of values of life for manual workers was similar but the
range for nonmanual workers was approximately three times greater.
Also of interest were the M&P results using the different measures of risk.
When the more conceptually correct measure of risk was employed the resulting
estimates were approximately an order of magnitude greater than when the
actuarial type of risk measure was used. Further, this result held up for
industry risk measures similar to those based on the BLS data in the U.S.
studies, which produced even higher estimates than the occupation-specific
measure of on-the-job accidents. This led M&P to conclude that:
"The reason previous U.S. studies have differed in the value
of life that they estimate is mainly that the high-valued
studies used the more relevant concept of risk, namely
accidents at work."
When converted into 1984 dollars, the results of wage-risk analysis based on
occupation-specific measures of on-the-job accidents by MSP support a value of
life that falls in the upper range of estimates presented in Table 1.
There is one criticism that can be leveled at the earnings function that was
estimated by MSP. In their equation, they use a variable OCC to measure of
occupational desirability. This measure is an index of how people rate the
desirability of different occupations. It is not clear that OCC is truly an
independent variable. In particular, M&P present evidence that job safety and
the amount of required education may be positively related with the OCC
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desirability index. This being the case, a more appropriate estimation
probably would have been two stage least squares.
2.2 STUDY 2: Dillingham (1985)
The recent Dillingham study is similar to the work by M&P in several respects.
Dillingham uses a measure of job risks other than the actuarial risk measure
or the BLS industry measure. This permits an evaluation of the wage-risk
relationship with an independent data set. As in the MSP study, Dillingham
delineates risks both by occupation and industry which reduces measurement
error in the risk variable and allows for an examination of the influence of
different risk measures on the estimated value of life. Finally, Dillingham's
work sheds new light on what was felt to be a key issue in assessing the
empirical estimates of the value of life for policy applications in the
previous Violette and Chestnut'(1983) review. in that review, it was believed
to be likely that the low range of estimates resulted from the use of an
incorrect, or at least deficient, measure of job risks. All of the studies
that produced estimates in the low range used the actuarial type of risk
measure with one important exception — the Dillingham (1979) study. This
study used a different and seemingly more appropriate risk measure and still
came up with a value of life in the low range. This result was pivotal to the
conclusion in the earlier review that the low range estimates, based on the
information then available, could not be ignored when presenting the range of
value of life estimates for policy purposes. However, Dillingham (1985) shows
that the risk measure used in his earlier study was flawed and, when
corrected, his empirical results also fall into the upper range. This leaves
only studies using the questionable actuarial risk measure in the low value of
life range.
Data And Estimation Methods
The data on job related fatalities used by Dillingham were compiled from
records at the New York State Workman's Compensation Board. The data from the
Workman's Compensation Board were detailed enough to allow for the
construction of both occupation and industry risk measures. In all, Dillingham
constructed five risk measures and examined their implications for the
value-of-life estimates. Four of these were based on the Workman's
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Compensation Board data which allowed very detailed industry and occupation
breakdowns. The most disaggregated risk measure consisted of about 13,000
industry/occupation categories, similar to the risk measure used in Dillingham
(1979). The second had about 200 industry/occupation categories. The third
was risk by industry group (similar to the BLS measure) and the fourth was
risk by occupation group. The fifth risk measure was based on data from the
BLS on industry-wide risks to explore the empirical significance of
alternative risk measures.
Dillingham estimated several hedonic wage-risk equations using these risk
measures with data on individual workers from two different sources: (1) the
1977 Quality of Employment Survey conducted by the Survey Research Center at
the University of Michigan, and (2) the 1970 Census in New York State (the
same data used in Dillingham, 1979)..
Results
With the Quality of Employment Survey, Dillingham found a statistically
significant risk coefficient for all but the most disaggregated risk measures.
The implied value of life estimates ranged from $1.4 million to $3.8 million
(1979 dollars), with a mean of $2.4 million. The highest value was obtained
with the BLS risk measure. The author placed less confidence in this result
because it was not stable when industry/occupation dummy variables were added
suggesting that the risk coefficient may reflect some effect other than risk.
Dillingham favored the estimates in the $1 million to $2 million range.
The results obtained with the 1970 Census data for New York suggest a problem
with the more disaggregated risk measures. The risk coefficient for the most
disaggregated risk measure was statistically significant, but the implied
value-of-life estimate was only $340,000 to $380,000 (1979 dollars). This is
in the same range as the Dillingham (1979) results ($140,000 to $450,000)
using a similarly disaggregate risk measure. The value increased with less
disaggregated risk measures. With the major industry/occupation groupings
(about 200 categories), the value-of-life estimate was about $870,000, and
with the occupation groups alone it was $1.1 million to $1.3 million.
Dillingham argues that the more disaggregated risk measures are not
appropriate due to the fairly infrequently occurrence of fatal injuries. He
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suggests that the similarity between the results for the two different worker
samples in this analysis, in terms of the value-of-life estimates associated
with each risk measure, supports the conclusion that the 1979 study results
may have been the result of errors-in-variables bias. It is also of interest
that in contrast to the findings of MSP, the occupation risk measure yielded
higher values than the industry risk measure based on the Workman's
Compensation data for both worker samples.
In addition to producing these new value-of-life estimates, Dillingham draws
a number of conclusions regarding the bimodal distribution of past estimates
shown in Table 1. He states that his analysis significantly alters the
interpretation of the labor market value-of-life estimates. The low value
estimates "are all from studies using the actuarial data from Thaler and Rosen
... the so-called high estimates are based on a variety of risk measures all
of which have one element in common: they reflect the extra risk assumed at
work." If these low estimates are "either ignored or adjusted upward, the
bimodal character of the estimates is eliminated and the mean value of the
labor market estimates is in excess of $1 million (1979 dollars)."
Dillingham's work supports and extends the conclusions of M&P. It provides
furthur evidence that the appropriate range of estimates for the value of life
should exclude the low estimates found by Thaler and Rosen. More
significantly, this study provides an independent set of value-of-life
estimates, .most of which are greater than $1 million in 1979 dollars.
2.3 STUDY 3; Gegax, Gerking, and Schulze (1985)
The work by Gegax, Gerking, and Schulze (GGS) addresses several of the
criticisms that have been directed towards the hedonic wage-risk studies. One
frequently mentioned concern is that workers may not be well informed with
respect to the actual risks of different occupations so that their perceptions
of job risks may be different from the accident rates used in the wage-risk
studies. The result is that occupational rankings based on the workers'
perceptions of risk may not be the same as rankings based on the actual rate
of fatal accidents. GGS address this concern by obtaining information on
workers' perceptions of the relative riskiness of their own occupations and
then using these perceived risks in a wage-risk study. Another concern often
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expressed about hedonic wage-risk studies stems from the restricted sample of
workers used in each study. GGS avoid this second problem by using data for
the workers in a national random sample of U.S. residents.
Data and Estimation Methods
The data used in the GGS study were collected by means of a national mail
survey which was conducted during the summer of 1984. Information was
collected on annual labor earnings, the perceived risk of fatal accidents at
work, the individual's human capital, work environment, and personal
characteristics. To obtain information on perceived risks, an illustration of
a ladder with equally spaced steps labeled from one to ten was provided.
Seven example occupations were placed on the ladder according to their average
levels of job-related risks of death. The examples ranged from jobs such as
school teachers to risky occupations such as lumberjack. The respondent was
then asked to specify the step number which came closest to describing the
risk of accidental death on his or her primary job. GGS argue that this
variable may be a more accurate measure of the individual's self-assessed risk
of death at work than other industry or occupation measures.
GGS used this self-assessed risk measure in a conventional hedonic wage
equation for the entire sample and for several subsamples of workers.
Results
The result for the entire sample is shown in the first line of Table 2. The
coefficient on the risk variable was not significant at conventional levels,
but was of the expected sign. Disregarding the low t-statistic, the estimated
coefficient yields an estimated value 'of life of $.727 million (1983 dollars).
Investigating possible reasons for the lack of statistical significance, GGS
investigate differences in the wage-risk relationship across different
occupational groups. Two concerns are addressed. One concern with the use of
the full national sample is that there may be insufficient variation in the
risk variable to drive the hedonic wage variable. A second concern is that in
jobs where there are extremely low risks of accidents, the marginal value of
reducing risks further may be zero and no wage-risk gradient may exist. To
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Table 2
Hedonic Wage-Risk Results
From Gegax et al. (1985)
Subsample Coefficient
Full Sample .0073
Union-Blue
Collar Workers .0159
Union-Whi te
Collar Workers .0541
All Union
Workers .0176
Mean
t-Statistic Risk Level1
.995 2.6
1.879 4.0
1.611 1 .8
1.852 3.3
Value-of-Life
($ millions)
.727
1 .495
5.981
1 .753
NOTE: The dependent variable for all estimations was the natural logarithm of
the 1983 average wage adjusted for regional price differences. All
non-union specifications yielded insignificant results.
1 deaths per 4,000 workers annually
2 in 1983 dollars
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explore these issues, GG5 segmented the sample into unionized blue-collar
workers, unionized white-collar workers, nonunion blue-collar workers, and
nonunion white-collar workers.
The results of the hedonic estimation for selected subsamples are shown in
Table 2. The statistical significance of the risk variable increased in
subsamples with higher mean risk levels, but the risk variable was not
significant in the nonunion equations. The mean risk variable was
approximately 50 percent higher for the all-union sample (includes both
blue-collar and white-collar workers) than for the nonunion sample, however,
nonunion blue-collar workers still had risk levels considerably higher than
the mean of the full sample. This could indicate a possible market failure
where only union members are able to obtain higher wages for higher risks.
GGS suggest that this may be as much due to unions providing information on
safety risks as it is to the increased bargaining power of the union.
White-collar workers had both the lowest mean risk levels and the lowest
standard deviations. The lower significance of the risk variable may be
because there is insufficient variation in risks across white-collar
occupations or because the marginal value of lowering risks still further is
zero. GGS state that these workers may have positive values of life when
measured at the margin, but the hedonic method may not be able to estimate
these values; alternative techniques such as contingent valuation methods may
be superior for obtaining these estimates. Given these concerns, GGS selected
$1.5 million (1983 dollars) as their judgemental best estimate of the
statistical value of life based on the hedonic wage-risk estimations.
For comparison purposes, the authors also estimated the hedonic wage function
using the BLS fatal injury rate by industry in place of the perceived risk
measure. In this case, statistically significant coefficients were obtained
for the union and all blue-collar samples, similar to the results with the
perceived risk variables, but the implied values per life were considerably
higher at about $6 to $10 million. These values overlap with the highest
results obtained for one of the union samples with the perceived risk measure.
Combined with the results of M&P and Dillingham, this suggests that value-of-
life estimates using the BLS industry injury rates may be overstated, but it
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should be noted that the same magnitude of difference did not occur between
Dillingham's industry and occupation estimates obtained using the Worlcman's
Compensation data.
Viscusi and O'Connor (1984) used an approach similar to GSS to estimate wage
premiums for on-the-job risks of injury (including fatal and non-fatal). They
conducted a survey of workers in the chemical industry and asked them to
estimate their risks of injury relative to other private sector workers in the
U.S. Using this self-perceived risk measure, they found a statistically
significant annual risk premium of $740 to $790 (1982 dollars) per worker for
the blue collar sample. The risk coefficients were not consistently
statistically significant for the full sample (similar to the findings of
GSS). It is not possible to calculate a value per fatal injury from the
information reported by the authors, but the estimated wage premium is quite
comparable to that estimated by Viscusi (1978b) using the BLS injury data.
Results of the 1978 analysis indicated an annual risk premium of about $1000
per worker and a value per fatal injury of about $2.5 to $4 million (1982
dollars).
2.4 STUDY 4; Duncan and Holmlund (1983)
This hedonic wage study uses a unique data set on job characteristics which
provides another independent reference point for estimates of compensating
wage rate differentials. The particular job risk variables used by Duncan and
\
Holmlund (DSH) are only indirect measures of job risks and, as a result, can
not be converted into value-of-life estimates. Still, the analyses and
findings from DSH are supportive of the general hedonic wage method. This is
valuable in itself, given that a new, independent data set is used in the
study. Also, D&H use a different estimation technique which is made possible
by their longitudinal data set.
Data and Estimation Methods
The data used by DSH are from two surveys of workers in Sweden -- one
conducted in 1968 and the second in 1974. The surveys covered a wide array of
personal and job characteristics. The job characteristics were classified
-------
into four broad categories: (1) hours constraints (inflexible hours), (2) hard
physical work (heavy lifting, physically demanding, daily sweating), (3)
stressful work (mentally demanding, hectic), and (4) dangerous work (noise,
smoke, shake, exposure to chemicals). All of the job characteristics were 0-1
dummy variables.
Results
D&H employed an estimation procedure that was made possible by their
longitudinal panel data. The same individuals were interviewed in both 1968
and 1974. The variables were entered in the wage equation in change form,
i.e., the net change in these variables between 1968 and 1974. The hypothesis
being tested is that the change in the wage rate over this time period is a
function of the changes in personal characteristics and job characteristics.
D&H use this wage change formulation to control for the effects of unmeasured
and unchanging characteristics of workers. If important characteristics such
as motivation and intelligence lead to both higher pay and better working
conditions; then, the omission of these worker characteristics will bias the
estimated relationship between wages and working conditions, but will not
necessarily bias the relationship between the change in wages and the change
in working conditions.
D&H estimated wage equations using cross-sectional data for each of the years,
as well as estimating the wage change equation. The cross-sectional
specifications produced many coefficients on the job characteristic variables
that had "wrong" signs. The wage change equation resulted in many more
reasonable coefficients on the job characteristic variables. The index of
dangerous working conditions was associated with a compensating wage
differential using the change equation, but not with the cross-sectional
specification. The same was true for the index of stressful working
conditions.
The index of dangerous working conditions could not be translated into a risk
of death measure which could then be used to calculate a value-of-life
estimate. As a result, this study does not provide us with another
value-of-life estimate. Instead, the importance of these results is
18
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additional evidence they provide that workers do respond to job related
characteristics such as risks, using a data set that is independent of those
used i.n orevious studies.
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3.0 VALUE-OF-LIFE ESTIMATES FROM CONTINGENT VALUATION STUDIES
In the earlier critique of empirical estimates for valuing reductions in
risks, Violette and Chestnut (1983) reviewed the five contingent valuation
studies that were then available. The 1983 review concluded that most of
these studies had not used state-of-the-art techniques, all suffered from
potentially severe shortcomings, and their estimates were not reliable.
However, two recent contingent valuation studies (Jones-Lee et al., 1985; and
Gegax et al., 1985) use state-of-the-art methods and represent important
contributions to the value-of-life literature.
Contingent valuation studies and revealed preference approaches (such as the
hedonic wage method discussed in the previous section) are the two procedures
used to obtain estimates of the willingness to pay for reductions in risks.
Revealed preference approaches attempt to identify instances where individuals
actually trade off risks for income or other goods. The labor market studies
are the most common revealed preference studies. The CV approach uses a
questionnaire format to construct a hypothetical market where the individual
can express his preference for alternative levels of income and safety. Each
procedure has strengths and weaknesses. The revealed preference approach has
the advantage of being based on actual decisions. While this is a strength,
the researcher is limited to using data on actual market situations that may
differ from what is needed for a specific policy analysis in either the type
of risk faced or the particular individuals making the tradeoff. The CV
approach has the advantage that it can be tailored to address the specific
question of interest. It can be applied to a general population sample or to
a subsample of the population, and it can address changes in risks of the
specific magnitudes of interest. The principal disadvantage is that the CV
approach is based on what people say rather than what they do.
3.1 STUDY 1; Jones-Lee, Hammerton, and Philips (1985)
This study is a considerable improvement over the five contingent market
studies reviewed in Violette and Chestnut (1983). The criticisms of these
earlier studies encompassed, among other things, that the samples were
nonrandom or too narrow to provide estimates applicable to public policy
20
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questions; the scenarios and payment mechanisms were not well defined; the
change in risks being valued was not clearly presented; and there was little
checking for "problem" bids or consistency across bids. All of these issues
were addressed by Jones-Lee, Hammerton, and Philips (JHP).
Data and Research Methods
The JHP study examined individuals' WTP and WTA for changes in the risks of
motor vehicle accidents resulting in injuries or fatalies. The work was
funded by the United Kingdom Department of Transport. A final questionnaire
was developed through a process that included extensive pilot testing of the
questions and detailed modification of the survey instrument. The
questionnaire contained questions that fell into three broad classifications:
(1) valuation questions designed to obtain estimates of the values individuals
placed on changes in risks; (2) perception and consistency questions designed
to test the individuals' ability to handle the probability concepts and
stability of responses,- (3) factual questions concerning vehicle ownership,
income, age and other experience/personal data.
Serious doubts about the credibility of valuation responses were expressed by
some members of the U.K. Department of Transport at the beginning of the
research effort. Two particular concerns were stated. The first was that
there would be no way of knowing whether responses to hypothetical valuation
questions were, in fact, related to the individual's true willingness to pay.
Second, there was concern about whether the respondents could understand the
probability concepts presented in the questionnaire and provide reliable
estimates in response to the questionaire scenarios. To the extent possi.ble,
JHP tried to build a system of checks into the questionnaire. Tests for
consistency and perception bias were incorporated to detect cases of
misrepresentation, random guessing in valuation responses, or an inability to
handle the probability concepts. To mitigate risk perception bias, the risks
of each travel mode were presented to the respondent numerically and
pictorially. To test for stability of the•responses, a followup questionaire
was administered to selected participants approximately one month after the
first survey was completed.
-------
JHP obtained 1,103 full responses that, when used with appropriate weights,
were representative of the general population of Great Britain. Acton (1972)
conducted the only other CV study to use a general population sample but this
study was limited by the size of the sample — only 32 complete responses.
The type of risk examined by JHP was one most people regularly face — risks
of death in a motor vehicle accident. The scenarios and payment mechanisms
were realistic and well defined. This makes the results potentially more
applicable to the general population than those of the best previous CV study
(Acton, 1972), which used fatalities following heart attacks, risks that may
not be very high for the average individual (or at least will vary a lot
between high risk and low risk segments of the population). The public-good
(free-rider) problem in the survey questionnaire was mitigated by defining
risks and payments associated with transportation in a private good context —
payments that would specifically reduce risks to yourself. Payment mechanisms
were: (1) an increase in bus fare in return for greater safety, and (2) a
higher price for a new, safer car. The general types of questions are
depicted below:
1. Commercial bus fatalities - You have been given $400 for travel
expenses in a foriegn country and given the name of a coach service
which will take you on your itinerary for exactly the amount on money
you have been given. The risk of being killed on the journey with
this coach firm is 8 in 100,000. You can choose to travel with a
safer coach service if you want to, but the fee will be higher, and
you will have to pay the extra cost yourself.
a) How much extra, if anything, would you be prepared to pay to use a
coach service with a risk of being killed of 4 in 100,000?
b) How much extra, if anything, would you be prepared to pay to use a
coach service with a risk of being killed of 1 in 100,000?
2. Similar questions were asked concerning the willingness-to-pay for
additional safety features in a new car that would reduce the risks of
death to the driver (if you do not drive assume that you do).
Results
The survey was conducted during the summer of 1982 and, using an average
dollar-to-British-pound exchange rate of 1.76, the empirical results from
JHP are presented in Table 3. The average value-of-life estimates ranged from
roughly $2 million to $4 million (1982 dollars). One interesting finding was
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Table 3
Summary of Results of WTP
Prom Jones-Lee et al. (1985)
(1982 U.S. Dollars)
1 )
2)
Type of
Risk
Commercial
bus fatali ty
Automobi le
fatali ty-dri vers
Initial
Level of Risfc
3x1CT5
8x10~5
10X1CT5
10x10~5
Increment
of Risfc
-4x10~5
-7x10~5
-5x10~5
-2x10"5
Mean
• Response
Per Life
2.8x106
2.4X106
2.1X106
3.9x106
Median
Response
Per Life
2.2X106
1 .3x106
.88x106
1 .4x106
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the skewness of the distribution of responses. In all instances, the median
bid was lower than the mean value-of-life and ranged from $.88 to $2.2
million. The difference between the mean and median value-of-life estimates
raises questions concerning which is the most policy relevent. Since the
median represents that value of life that has 50 percent of the estimates
below that number and 50 percent above that number, a democratic voting
process would indicate the the median should be employed. The skewness of the
distribution implies that more than 50 percent of the individuals have values
of life less than the mean value. The use of the mean could have the result
that a minority of individuals with high values of life may be "dragging along
an unwilling majority" (Jones-Lee et al., p.70).
JHP conducted a number of analyses attempting to explain the variation in risk
valuation estimates across individuals. A number of potential explanatory
variables were used in a statistical regression framework. These variables
included income, age, social class, miles driven, car ownership, accident
experience, and other personal data. In general, the explanatory power of
these statistical models was low. Only the age and income were generally
significant and they were not significant in all of the equations. The income
elasticity from those equations where the coefficient on the income variable
was significant was approximately .3. This indicates that changes in the
distribution of income would result in only minor changes in the statistical
value of life.
The results of some, but not all, of the consistency checks employed by
JHP were encouraging. Among the encouraging findings were that 75 percent of
the responses were coherent, i.e., conformed with standard axioms of rational
choice for simple decisions under uncertainty. With respect to the
consistency of responses in multipart valuation questions, only 8 percent of
the responses were higher for smaller reductions in risks (plainly
inconsistent). The stability of responses was examined by re-questioning a
subsample of respondents one month later. No statistically significant
differences in the means was found, but the standard deviation was larger in
the second round of responses. The effect of the order of the questions was
also investigated and found not to be a significant influence on the
estimates. Finally, the respondents were asked whether they found the
24
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questions easy or difficult to understand. The majority found the questions
understandable.
while some of the consistency checks were encouraging, some potential problems
were found. Forty-two to forty-seven percent of the respondents gave the same
WTP estimate for different reductions in risk. While not plainly
inconsistent, the frequency of the same dollar response for different
reductions in risk may indicate that people place a value on reducing risk,
but may not be able to distinguish between one level of risk and another
within the magnitudes of risks used in this questionnaire. On another
question designed to assess the respondents understanding of the uncertainty
concepts, respondents were asked:
"Imagine that you have to face two different risks of being killed:
- in one, your risk of death is 2 in 100,000
- in the other, your risk of death is 20 in 100,000.
You cannot avoid either of these risks but you can choose to have
one reduced. Which would you prefer:
- the risk of 2 in 100,000 reduced to 1 in 100,000
- the risk of 20 in 100,000 reduced to 15 in 100,000"
Approximately 47 percent of the respondents expressed a preference for a
reduction in the risk of 2 in 100,000, i.e., a reduction of 1 in 100,000 being
preferred to a reduction of 5 in 100,000. While this is an apparently
inconsistent answer, eliminating these respondents did not change the mean
value-of-life estimate.
JHP evaluate the various consistency checks and conclude that the balance of
the arguments are strongly in favor of regarding the value-of-life estimates
as a reliable indication of the order of magnitude of the "true" value. They
also compare their estimates to those obtained by Marin and Psacharopoulos
(1982) using occupational data and find the consistency of the estimates
encouraging and state that this consistency confirms the expected hypothesis
that individuals tend to be roughly equally averse to the prospect of dying in
a transport accident and in a accident at work.
-------
The responses to a few other questions are also of interest to the evaluation
of environmental hazards. in one line of questioning, respondents were told
that current annual deaths due to three causes were:
4,000 motor vehicle accidents
11,000 heart disease
16,000 cancer
when asked if one cause could be reduced by 100, which would they select, 76
percent said cancer. The authors interpret this as indicating that death due
to cancer is worse than death due to motor vehicle accidents or heart, disease.
This may be the case, but the interpretation may be confounded by the higher
amount of cancer deaths; people may simply find it more desirable to reduce
the largest cause of death.
In response to another question, respondents indicated that they are willing
to pay additional amounts to reduce risks to others as well as to themselves.
These additional amounts are approximately one-third of their WTP to reduce
thei r own ri sks.
Another contingent valuation study also found evidence that subjects may have
difficulty evaluating changes in very small probabilities of death. Smith et
al. (1985) conducted a contingent valuation study concerning risks of exposure
to hazardous wastes and subsequent risks of premature death 30-years after
exposure. 'The responses varied considerably depending on the risk increment
and the question (either WTP to obtain a reduction in risk or WTP to prevent
an increase). Due to the two-part risk of death and the 30-year time
component, the responses are not directly comparable to those obtained by JHP,
but Smith et al. did calculate some roughly comparable annualized
"value-of-life" estimates based on their findings. For average annual changes
in probabilities of death roughly comparable to those hypothesized by JHP the
estimates are between $1.5 and $7 million (1984 dollars). Although
respondents generally gave rational answers for increments to their posited
initial risk level, those who had larger posited risk levels, closer to
on-the-job risk levels, gave values corresponding to a value-of-life from
$200,000 to $1,000,000. Those with very small initial risk levels gave bids
that implied values two orders of magnitude larger.
26
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3.2 STUDY 2; Gegax, Gerking and Schulze (1985)
In addition to performing a hedonic wage-risk analysis with their survey data,
Gegax, Gerking, and Schulze (GGS) incorporated contingent valuation questions
in their survey. The random sample of U.S. wage earners used by GGS is an
improvement over the samples used in earlier contingent valuation studies.
Data and Estimation Methods
In one-half of the sample, respondents were asked how much of an increase in
annual wages would be required to get them to voluntarily work at the same job
if the risk of job related death were one step higher on the risk ladder than
where they initially placed their current job related risk of death (WTA).
The other half of the survey sample was asked how much of a decrease in wages
they would accept if their job related risk of death were moved one step down
on the ladder (WTP). These questions were based on the same risk measures
used by GGS in their hedonic wage-risk analysis which allows for some
comparability between the two components of the study.
The survey procedures used in this study were substantially improved over the
contingent valuation studies previously reviewed in Violette and Chestnut
(1983). With respect to scenario development and realism, the concept of
on-the-job risks was introduced reasonably well with preliminary questions
about job safety, but the concept of trading off wages against risks is not
introduced before the WTP/WTA questions were asked. The authors did not note
any problems with lower response rates with these particular questions, which
is about the only indication of problems that this mail format allows. Past
studies have seen protest responses to questions of this type. These protests
are in the form of "I couldn't get by with less money", or "I wouldn't take a
job that would increase my risk of accident". GGS offer no indication of
whether or not protest bids posed a problem.
Results
The results of the WTP and WTA questions are shown in Table 4. The WTP
measure gives a mean value of about $2,600,000. The results for the different
27
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Table 4
Contingent Valuation Results
From Gegax et al.(1985)
ALL WORKERS
ALL UNION
UNION WHITE-COLLAR
UNION BLUE-COLLAR
NON-UNION WHITE-COLLAR
NON-UNION BLUE-COLLAR
Mean Risk
Level1
2.6
3.3
1 .8
4.0
1 .6
3.7
Mean
Value Of Life
Based On WTP2
$2,558,000
$2,789,000
$2,030,000
$2,952,000
$2,531 ,000
$2,544,000
Mean
Value Of Life
Based On WTA
$7
$7
$7
$7
$7
$7
,404,000
,384,000
,156,000
,480,000
,436,000
,342,000
1 Number of deaths per 4,000 workers,
2 1983 Dollars
28
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subsamples of workers show that the values are very consistent across the
different worker samples, in contrast to the results of the hedonic wage-risk
analysis. This supports the earlier argument of the authors that white-collar
workers probably place a significant value on reducing or avoiding risks but
that there is insufficient variation in risks to obtain a significant risk
coefficient in a hedonic wage equation.
The WTA estimates are on the order 'of three times greater than the WTP
estimates. Deferring to the substantial body of evidence that has been
accumulated suggesting that the willingness to accept measures of value are
biased upwards, GGS suggest $2,600,000 as a best value-of-life estimate from
this contingent value study (1983 dollars). This can be compared to their
best estimate of $1.5 million from the hedonic wage study.
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4.0 OVERALL CONCLUSIONS
The different value-of-life estimates obtained from the new studies reviewed
in this update are presented in Table 5 in 1984 dollars. In general, the
methods employed in these studies are superior to the earlier work reviewed by
Violette and Chestnut (1983). These new results indicate that a value-of-life
estimate based on the types of risks faced by workers on the job are likely to
exceed $1.6 million (1984 dollars). There is strong evidence that some of the
low value-of-life estimates obtained from early wage-risk studies are the
result of biases in the measured risk variable and should not be included in
the range of empirical estimates.
In the earlier Violette and Chestnut review, potential biases in the value-of-
life estimates from hedonic wage models were discussed. The bias of most
concern was whether potentially important explanatory variables were omitted
from the hedonic wage equations. The issue was whether high job risks may be
correlated with other unpleasant working conditions with the result being that
the risk variable is acting as a proxy for other unpleasant working conditions
rather than capturing a true wage-risk premium. This is the potential bias
most likely to result in overstated values for reductions in risks. The two
contingent valuation studies provide additional information that indicates
that wage premiums are due to job risks. In particular, Gegax et al. (1985)
were able to hold all factors other than job risks constant in their
contingent valuation study and still find a WTP similar to the estimate
obtained from their hedonic model.
Two of the studies have estimated hedonic wage equations using risk data from
sources other than the BLS and then re-estimated the equations using the BL3
data. The results suggest that the BLS data may give higher value-of-life
estimates and may be reflecting job characteristics other than risks alone.
The highest values obtained for manual or blue-collar workers with non-BLS
risk data were about $2.5 million. It is not clear whether the higher results
obtained with the BLS data are due to the data being for industry-wide injury
levels. M&P found very high values using a similar non-BLS industry variable
while Dillingham did not.
30
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Table 5
Estimates from Recent Studies
(millions of 1984 dollars)
Mean Risk
Level for the Range Judgemental Best
Sample3 of Values Estimate
WAGE-RISK STUDIES
1. Marin and Psacharopoulos (1985)
a. manual workers " 2.3-2.6 2.4
b. non-manual workers 6.4 - 6.5 6.4
2. Dillingham (1985) 1.4 - 8.3 1.2 - 5.4 2.1
3. Gegax et al. (1985)
a. total sample 6.5 .8
b. union workers only 8.2 1.6 - 6.2 1.6
CONTINGENT VALUATION STUDIES
4. Jones-Lee Qt al. (1985)c 0.8 - 1.0 2.2 - 4.2 3.0
5. Gegax et al. (1985)
a. WTP 4.2-10 2.1-3.1 2.7
b. WTA 4.2-10 7.5-7.8
a Approximate annual deaths per 10,000 individuals.
" Marin and Psacharopoulos used an age adjusted normalized risk variable wnich
is not directly comparable to the risk levels used in other studies.
However, the average risk of death for the entire sample was 2 in 10,000.
c The estimates came from valuing decrements in risk. The large number of
individuals not responding to questions about their WTA for increased risks
made estimates based on risk increments unreliable.
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Most of the authors placed greater confidence in the hedonic wage results for
manual and blue-collar workers. Higher value of life estimates were sometimes
obtained with the full or white-collar samples, but statistical significance
was weaker. It appears that there may be insufficient variation in risks
across many of these jobs to allow for estimation of a risk premium. The
contingent valuation results support the conclusion that the different results
for blue-collar and white-collar workers are due to different job risk
characteristics rather than due to different risk preferences on the part of
the individuals. This is contrary to what is sometimes argued, which is that
one group may be more risk averse than the other and that this accounts for
the differences in results. The low mean risk levels as well as the small
variation in risks across white-collar jobs may make the application of the
hedonic method unreliable and Gegax et al. suggest that contingent valuation
techniques may be more appropriate for obtaining value-of-life estimates for
this segment of the population.
In summary, this updated review suggests a possible narrowing of the range of
values for on-the-job risks of death to $1.5 to $3 million. The lower-bound
appears more solid than the upper-bound since these new studies fairly
convincingly show that the actuarial risk data are not appropriate. However,
values substantially above $3 million have been obtained with the BLS risk
data or for non-manual worker samples. This review suggests that some upward
bias or greater error may exist in these results, but this has not been firmly
demonstrated. The values of up to $8 million should not be completely
dismissed until further study is made of these potential problems.
This range of $1.5 to $8 million seems fairly well established for on-the-job
risks and may be directly applicable for evaluating policies or regulations
expected to affect risks of fatal injury in the workplace (although long-term
risks due to exposures to hazardous substances may not be fully reflected).
The results of the contingent valuation studies suggest that this range may
also be appropriate for other population groups and for other types of
voluntary risks of fatal accidents of at least a roughly similar magnitude,
but more studies are needed to confirm this.
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Further questions remain concerning whether these value-of-Life estimates are
appropriate for valuing reduced risks from environmental hazards. Arguments
have been made that people place higher values on reducing risks that are
involuntary, perceived as new and/or potentially catastrophic compared with
those that are voluntary, familiar, and tend to affect small numbers when an
"event" occurs (see Violette and Chestnut, 1983). Thus, values for reducing
environmental risks may be higher than values for reducing job and
transportation risks. We have little empirical information on this, so far,
but that which is available seems to indicate that the values presented in
Table 5 should be viewed as a lower bound to the value of life appropriate for
environmental policy assessment.
Another interesting policy issue raised by JHP (1985) concerns whether the
mean or median value-of-Life is most appropriate for policy analysis. Their
study found a highly skewed distribution of value-of-life estimates where a
few individuals had very high values of life. This result was also found by
Loehman (1979) for values individuals placed on changes in morbidity risks.
As far as we know, there has been no research on this question.
33
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ENDNOTES
1. Landefeld and Seskin (1982) develop estimates using the human capital
approach and adjust them to develop an approximation to WTP based on
individuals' preferences. Their starting assumption is that a person's
human capital is a lower bound to their WTP. While this seems likely, it
has not been firmly established. Still, the Landefeld and Seskin
adjustments seem plausible, although they do not fully consider potential
pain and suffering.
2. Authors of two empirical studies, not specifically reviewed in this
update, have drawn the conclusion that the estimated value of life from
wage-risk studies should not be used in the evaluation of public policies.
Smith and Gilbert (1984) estimate an inter-city wage model including both
air pollution levels and on-the-job risks and found very different
value-of-life estimates implied by the coefficients for these two
variables, with a much higher value based on the air pollution
coefficient. They therefore argue that the wage-risk based estimates are
unlikely to be correct for environmental applications. That may be true,
but we are unwilling to place much confidence in their estimate based on
the air pollution coefficient due to the extremely tenuous assumptions
required in its calculation. Dickens (1984) based his negative conclusion
about the usefulness of the wage-risk results on his finding of a negative
and statistically significant coefficient on the risk variable in a
non-unixon sample. His conclusion that this invalidates all wage-risk
results is unwarranted wi thout considerably more analysis of the structure
of his data. Other studies reviewed here suggest that the variation in
risk across a subsample and the role of the unions may be important, and
that risk premiums may not be estimable for all subsamples.
3. Two other wage-risk studies were reviewed, but are not specifically
presented in this paper. They are Low and McPheters (1983) and Graham,
Shakow, and Cyr (1983). The Low and McPheters study was limited to police
officers, a subsample with unusual risk characteristics. They found
significant wage differentials for police officers who work in more
dangerous cities. The Graham, Shakow, and Cyr study used the same
34
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actuarial risk measure employed by Thaler and Rosen (1976). Like other
studies that have employed this risk measure, they derive an estimate for
the value of life that is less than 3.5 million. Ippolito and Ippolito
(1984) conducted another study of potential interest that was not included
in this review because the type of risk involved is very different than in
most other studies. This is a consumer market study looking at cigarette
smoking.
4. The 1983 report also included estimates in the lower range obtained by
Dillingham (1979) using a third risk data set compiled from workers'
compensation data for the state of New York. Based on subsequent analysis
with these data, Dillingham concluded that his 1979 results were
incorrect. We have therefore left these numbers out of Table 1. The new
analysis of this data set reported by Dillingham (1985) is reviewed.
5. Other U.S. studies, including Viscusi (1979), have found evidence of
higher risk premiums for union members than for nonunion workers.
35
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\
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