United States Office of EPA-230-05 83-003
Environmental Protection Policy Analysis June 1983
Agency Washington. DC 20460
Valuing Reductions in Risks:
A Review of the Empirical
Estimates Summary
Environmental Benefits Analysis Series
-------
Energy and Resource Consultants, Inc.
VALUING REDUCTIONS IN RISKS: A REVIEW OF THE EMPIRICIAL ESTIMATES
EPA - 230-05-83-002
Daniel M. Violette and Lauraine G. Chestnut
Correction Note
In this report, one set of estimated "values per statistical life" was calculated from the
findings of V.K. Smith (1983). Smith's analysis did not distinguish between fatal and non-
fatal risks so that some assumptions were required before a value per statistical life
could be inferred. After our report was finalized, Smith found and relayed in personal
communication that we had made an error in calculating a value per statistical life from
the results reported in his paper. We have determined what this calculation should have
been and have reviewed this with Smith. Since it has some bearing on the conclusions of
the report, we would like to supplement the report with this note. The effect on the
conclusions is that the correct number based on the V.K. Smith (1983) results is higher
than we first calculated and is within the range of other wage-risk studies that have
found values per statistical life of several million dollars. This serves to accentuate the
two distinct groupings of results from wage-risk studies, the lower range being $400,000
to $600,000, as typified by the Thaler and Rosen results, and the upper range now being
$3,500,000 to $7,000,000 in 1982 dollars. (We previously reported this range as
$1,000,000 to $7,000,000, the $1,000,000 figure being based on the Smith results.) All of
the results in this upper range are based on studies that have used BLS injury rate data.
Specifically, the report should be corrected to read as follows:
PAGE 2-51, LAST PARAGRAPH:
Change "Comparison of the V.K. Smith results ... $1.* million." to (new sentences are
underlined)
"Comparison of the V.K. Smith results with empirical estimates of the value of a statis-
tical life is difficult because the BLS injury rate he used did not distinguish between fatal
and nonfatal injuries. The total wage premium estimated by V.K. Smith is approximately
$12,400 per injury in 1978 dollars. This represents the premium paid for both fatal and
nonfatal injury risks. If R. Smith (1974) is correct in his hypothesis that the wage
premium reflects only the risk of fatal accidents since nonfatal accidents are covered by
insurance and worker's compensation, then the coefficient on the risk variable could
-------
Energy and Resource Consultants, Inc.
represent only the premium associated with the fatal risks. Viscusi (1978b) reported that
in the BLS injury statistics, fatal injuries are .4 percent of all injuries. Assuming that
fatal and nonfatal injuries occur in equal proportions throughout the sample, we can say
that the injury variable should have been simply .004 times what it was. If this were the
case, the value of life estimate from the V.K. Smith regression would be .0114 (the
coefficient on the risk variable) f .004 x 6.18 (the mean hourly wage) x 2000 working
hours per year x 100 (the risk variable was per 100 workers) = $3,522,600 in 1978
dollars. Olson found the premium paid for risks of fatal injuries to be approximately 3.8
percent of wages and the premium paid for nonfatal injuries to be approximately 7.3
percent of wages, i.e., a ratio of approximately 1:2. Using this ratio, a reasonable value
for a statistical life from the V.K. Smith results would be (.0114 r 3 * .004 x mean hourly
wage x 2000 hours x 100 = $1,174,200 in 1978 dollars. A similar method of apportioning
the risk premium estimated by Viscusi (1978a) shows a ratio between risk premium paid
for fatal and nonfatal accidents of between 1:1 and 1:2.5. Bailey (1979) uses several ad
hoc procedures to determine this ratio. His estimates range from 1:.75 to 1:1.75. Using
these ratios for partitioning the wage-risk premium for all injuries into fatal and nonfatal
risk premiums generally would result in a calculated value for a statistical life between
the above estimates."
PAGE 2-57, TABLE 2.33, STUDY #7:
Change "$73 to $207" to "$173 to 518"
Change "($100)" to "($350)"
Change "$7.3 x 10^ to 20.7 x 105" to "$1.73 x 106 to 5.18 x 106"
Change "(1.0 x 106)" to "(3.5 x 106)"
Similar references to the V.K. Smith results in the conclusions (p. 6-2) and in the
summary version (Tables 2-1 and 2-2 and pp. 6-1 and 6-2) should be corrected accord-
ingly.
PAGE B-6:
The correct citation for the V.K. Smith article is:
Smith, V.K. 'The Role of Site and Job Chracteristics in Hedonic Wage Models."
Journal of Urban Economics 13 (1983): 296-321.
-------
SUMMARY VERSION
of
VALUING REDUCTIONS IN RISKS;
A REVIEW OF THE EMPIRICAL ESTIMATES
Prepared for:
Economic Analysis Division
U.S. Environmental Protection Agency
Prepared by:
Daniel M. Violette
Laura ine G. Chestnut
Energy and Resource Consultants, Inc.
P.O. Drawer 0
Boulder, CO 80306
June, 1983
The information in this document has been funded wholly or in part by the United States
Environmental Protection Agency under Contract #68-01-6596. It has been subject to
the Agency's peer and administrative review, and it has been approved for publication as
an EPA document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
-------
ACKNOWLEDGEMENT
The authors would like to give special thanks to Ann Fisher, the EPA contract manager
for this project. Her analytic and editorial comments on each draft of the report were
extremely beneficial and greatly appreciated by the authors. Other helpful reviewers
were V. Kerry Smith, 3on Harford, Brett Snyder, Jeff Kolb, Robert Raucher, and Philip
G raves.
We cannot list all the authors who sent us copies of papers and responded to our
questions, but we would like to mention Glenn Blomquist and Arona Butcher who were
especially helpful at the beginning of the project.
Responsibility for remaining errors and omissions rests, of course, with the authors.
-------
TABLE OF CONTENTS
CHAPTER PAGE
1.0 INTRODUCTION TO THE SUMMARY VERSION
2.0 RISK VALUATION USING WAGE STUDIES ............................. 2-1
2.1 Hedonic Wage-Risk Studies— Introductory Discussion ................ 2-1
2.2 Summary Review of the Wage-Risk Studies ........................ 2-3
2.3 Summary of Estimates from the Hedonic Wage Studies .............. 2-7
2.4 Methodological Issues in the Wage-Risk Approach:
What Confidence Can Policy Makers Have in the Estimated
Wage-Risk Relationship? ........................................ 2-12
3.0 CONSUMER MARKET STUDIES ....................................... 3-1
4.0 CONTINGENT MARKET APPROACHES ................................
4. 1 Background on Contingent Market Approaches ..................... 4-1
4.2 Summary of Contingent Market Studies ............. . ............. 4-1
4.3 Applications Issues in the Contingent' Market Approaches ...... . ..... 4-7
5.0 OTHER VALUE OF LIFE AND SAFETY ESTIMATION ISSUES ............. 5-1
5.1 Properties of an Individual's Willingness to Pay for Changes
in Morta lity Risks .............................................. 5-1
5.2 The Choice Between Ex Ante or Ex Post Risk Valuations in
Policy Assessment .............................................. 5-2
5.3 The Valuation of Different Risk Types ............................ 5-2
5.3. 1 Risk-Benefit Ratios as Conversion Factors ................. 5-3
5.3.2 Risk Conversion Factors ................................ 5-4
5.3.3 Conclusions Regarding the Valuation of Different
Risk Types ............................................ 5-5
5.4 Measuring and Def in ing Risks to Life and Safety .................... 5-7
5.4.1 Quality of Life Adjustments ............................. 5-7
5.4.2 Externalities and the Potential Usefulness of
Decision Analytic Approaches ............................ 5-9
5.4.3 Valuing Nonfatal Risks ................................ ... 5-10
5.5 Perceptions of Risks ........ . ................................... 5-11
5.5.1 Biased Perceptions of Risks .............. '. ............... 5-11
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TABLE OF CONTENTS
CHAPTER PAGE
5.5.2 Preference Reversal 5-12
5.5.3 Cognitive Dissonance 5-12
6.0 CONCLUSIONS 6-1
6.1 The Value of Life Estimates—Is There a Reasonable Range? 6-1
6.2 Suggestions for Future Research 6-5
BIBLIOGRAPHY B-l
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LIST OF TABLES
PAGE
2-1 Hedonic Wage-Risk Studies Summary Table 2-4
2-2 Estimates of Marginal Willingness to Pay for Reductions in Risks 2-10
3-1 Consumer Market Studies Summary Table 3-2
3-2 Summary of Value of Life Estimates from Consumer Behavior
Studies 3-3
4-1 Contingent Market Studies Summary Table 4-2
4-2 Summary of Value of Life Estimates From Contingent Market Studies 4-5
5-1 Risk Characteristics Used by Litai (1980) 5-6
5-2 Risk Conversion Factors (Litai, I960) 5-7
5-3 Mean Values for Risk Types Accepted by U.S. Soc iety (Lita i, 1980) 5-8
LIST OF FIGURES
2-1 Market Equilibrium 2-2
4-1 CS and ES Consumer Surplus Measures 4-3
5-1 Risk (R) Plotted Relative to Benefit (B) for Various Kinds of
Voluntary and Involuntary Exposure 5-4
5-2 One Possible Assessment of Current Risks and Benefits from y
25 Activities and Technologies 5-10
HI
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CHAPTER 1.0
INTRODUCTION TO THE SUMMARY VERSION
Many of the programs and policies that
are under development by the U. S.
Environmental Protection Agency will
influence the level of health risks faced by
individuals. Executive Order 12291
requires that the potential benefits of a
major regulation be shown to outweigh the
potential costs before it is adopted.
Assessing the benefits and costs of
changes in health risks associated with a
regulatory action poses many difficult
problems.
This document is a summary of a report
reviewing empirical estimates of the
values associated with changes in health
risks.* The primary difference between
the two versions is that this summary does
not contain a detailed technical discussion
of each study reviewed. The emphasis is
on presenting overviews of the research
and the conclusions drawn by the review.
In many cases, only a brief discussion of
the different studies is incorporated
here. Those desiring more detail are
referred to the main report.
Previous reviews have not included both
the range of estimates found by each
study and the rationale for selecting one
estimate as better than another for policy
questions.** The qualifications presented
by study authors, along with their esti-
mates and the context in which they are
estimated, are important for interpreting
the policy usefulness of these numbers.
Most prior reviews give these considera-
tions a cursory treatment and when the
estimates actually appear in policy
assessments, the qualifications tend to
disappear entirely. The result often has
been inappropriate application of the es-
timates and, even where applied properly,
the level of confidence policy makers
should have in the numbers generally has
been left unstated. The purpose of the
main report is to compile the available
empirical estimates and documentation in
one reference source, present a critical
discussion of the estimates, and evaluate
their usefulness in environmental policy
assessment. Many questions are raised for
which adequate empirical studies are not
available, but which point to useful ave-
nues for future research.
The project focused only on willingness-
to-pay (WTP) and willingness-to-accept-
compensation (WTA) estimates for valuing
changes in risks. Other valuation
approaches have been used including es-
timates of future earnings that would be
lost due to an increase in deaths or illness
and estimates of medical expenses asso-
ciated with an increase in illness and
death. Although providing useful bench-
marks, 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 and WTA 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. This, therefore, gives a
dollar measure of the change in well-being
that the individual has or expects to ex-
perience. Summing this measure of indi-
vidual benefits across all affected indivi-
duals can provide one component of a
benefit-cost analysis.
A Review of the Empirical Esti-
* The main report is Valuing Reductions in Risk;
mates. //EPA/230-05-83-002.
** Recent reviews include Bailey (1979), Butcher (1981) and Blomqyist (1982).
*** Butcher (1981) and Bailey (1979) discuss this in more detail.
1-1
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Risks of fatalities, rather than of nonfatal
injuries or illnesses, are emphasized in this
review. This should not be construed as
implying that risks of morbidity are ir-
relevant for environmental policy ques-
tions, because they are very important.
This emphasis merely reflects the fact
that most empirical estimates of the value
of life and safety have used mortality
data. The many facets of morbidity have
not made it conducive to empirical work.
Individuals suffering from an illness differ
in the severity of the symptoms, the
length of the illness, and whether it is an
acute or chronic malady. On the other
hand, mortality tends to be an unequivocal
health measure.
We apologize in advance to any authors
whose work may be relevant but omitted
from this document. Simply reading all of
the potentially relevant reserach work
would have exhausted the project funds.
A common response of reviewers to the
draft version of the report was to list 10
.to 15 potentially relevant articles that we
had not incorporated. Of course, it was
not possible to include all of the helpful
suggestions. We feel that we have in-
cluded the major empirical results, but
work on related theoretic issues was
included on a very selective basis. A
major line of research that was omitted
concerns the relationship between the
"value of life" and human capital as
expressed largely by one's lifetime earn-
ings and activities. Selected contributions
include Usher (1973), Conley (1976),
Jones-Lee (1978 and 1980), Linnerooth
(1979) and Arthur (1981). The focus of
this work has been on identifying when a
person's human capital, based on lifetime
earnings and consumption, can be viewed
as a lower bound to the value placed on
his/her life on purely theoretical
grounds. Mishan (1982) points out that the
conclusions from these models remain un-
validated until we have direct estimates
of the "value of a life." Once the esti-
mates are obtained, these models become
superfluous for policy making. In any
event, since these articles did not present
empirical results and since the large
amount of work on this topic could not be
easily reviewed or condensed, they were
reluctantly excluded from this document.
Throughout this report, the results of the
different studies are compared by refer-
ence to the estimated value of life or
value per life saved. The reader should be
aware that this is not meant to be thought
of as an amount of money that an indivi-
dual would accept in exchange for his or
her life. This is rather a way of compar-
ing valuations for small reductions in risks
that affect a large number of people. For
example, say a certain environmental
policy decision will reduce the risk of
death from exposure to a given toxic sub-
stance from I out of 100,000 to I out of
200,000 for a total of 1,000,000 people.
Each individual's probability of death from
this cause will be reduced frorn 10 x I0~°
to 5 x IO'6, a change of 5 x IO'6. If every
individual is willing to pay $10 for this
reduction in the probability of his or her
death, then the willingness to pay per life
saved is
$107.000005 = $2,000,000
An alternative derivation of this "value of
life" is to look at the number of lives
.saved. The number of deaths out of the
1,000,000 people affected would be re-
duced from 10 to 5. For these five lives
each individual in the group would be will-
ing to pay $10. Thus the total value per
life saved would be:
$10 x 1,000,000/5 = $2,000,000.
The studies reviewed in this report are
grouped into three categories. Chapter 2
covers hedonic wage-risk studies that look
at tradeoffs between on-the-job risks and
wages. Chapter 3 includes consumer mar-
ket studies that examine consumption and
activity choices that people make that
affect their safety. Chapter 4 covers con-
tingent market studies that use surveys
that ask people how much they value in-
creases in safety or improvements in
health. Chapter 5 discusses estimation
issues that are of concern for policy ques-
tions related to environmental health and
safety, but that have not been addressed
in these empirical studies. Chapter 6
summarizes the conclusions of the report
and provides suggestions for future
research.
1-2
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CHAPTER 2.0
RISK VALUATION USING WAGE STUDIES
This section examines empirical estimates
of the value of life and safety that have
been based on observations of transactions
that take place in the labor market.
These studies have found a consistently
positive and statistically significant wage
premium that is attributed to risks of in-
jury on the job.
2.1 Hedonic Wage-Risk Studies - Intro-
ductory Discussion
These studies are based on hedonic price
theory which views a market good as a
bundle of attributes that can occur in
various combinations and quantities. The
price that the consumer is willing to pay
for such a good is a reflection of the sum
of the utility expected to be derived from
the attributes. The labor market can be
viewed from this perspective. The worker
supplies his labor for a job that can be
described by a set of job characteristics,
or attributes, in exchange for a wage.
These job characteristics include such
things as job safety, type of work, location
and physical environment. At the same
time, the employer is willing to offer a
certain wage in exchange for having this
job done. This interaction between the
employers and the workers maps out a set
of market equilibrium wages that are paid
or accepted for specific jobs reflecting
the associated job characteristics. In the
case of risks of accidents and illnesses re-
sulting from work activites, we can expect
a tradeoff between the wage rates that
workers will accept and the risks they
expect to encounter. Also, there is a
tradeoff between the measures an
employer is willing to take to make the
job safer and the wage he must pay to
attract workers. If wages are positively
related to job risks, then the employer can
implement additional safety measures in
return for a lower wage-risk premium re-
quired by workers. In theory, the employ-
er will undertake safety improvements up
to the point where the marginal cost of
increasing job safety equals the marginal
reduction in wage cost resulting from a
lower risk premium being demanded by
workers. The worker's position will be in-
fluenced by his skills in protecting him-
self, his aversion to risk and other socio-
economic characteristics. The employer's
position will be influenced by his produc-
tion technology and the costs and benefits
to him of providing increased safety on
this particular job.
This market equilibrium between workers
and employers establishes the risk pre-
mium paid to workers. It is important to
recognize that the wage-risk studies do
not estimate an individual's wage-risk
indifference (i.e., tradeoff) curve ; instead
the market clearing wage-risk function is
estimated. This market equilibrium, or
hedonic wage-risk function, represents one
point on each worker's indifference
curve. The only data point available is the
wage accepted and the associated level of
risk for each individual Other points on
each worker's indifference curve are not
known. As a result, the hedonic wage-risk
curve must be carefully interpreted.
According to conventional econmic
theory, an individual's wage-risk indif-
ference curve would be convex (see
Curves A and B in Figure 2-1), since most
individuals would require compensation at
an increasing rate to entice them to
accept greater levels of risk. However,
the assumption of convexity for indivi-
dual's wage-risk curves says nothing about
the shape of market clearing hedonic
wage-risk curve. In fact, several authors
have argued that workers who pace a
lower value on incurring risks (i.e., require
a lower wage-risk premium) will, through
the market process, gravitate to the more
risky jobs. If true, this could result in the
concave hedonic wage-risk curve shown in
Figure 2-1.
2-1
-------
Wanes
Workers: Y, Z
(Indifference curves)
W(P)
Source: Butcher 1981
Firms: A, B
(Isoprot'lc curves)
Probability
of Injury
Figure 2.1
Market Equilibrium
Hedonic Estimation Assumptions
The estimation procedure used to identify
the tradeoff between wages and job
characteristics is to take wages as a func-
tion of job characteristics and see how
changes in job risks affect market deter-
mined wages. Market equilibrium will
occur where each worker is maximizing
his utility with the wage-risk tradeoff that
he accepts; therefore, the point at which
he is observed will reflect the marginal
valuation he would put on a marginal
change in risk, holding all else constant.
In order for this marginal valuation of risk
to be reflected in market conditions as has
been described, certain assumptions must
be met. Two of the most problematic are
(I) that the labor market operates freely
and is in equilibrium, and (2) that workers
are aware of the risks associated with dif-
ferent jobs that they might consider.
If the first assumption is violated, the es-
timated valuation can be biased. If, for
example, a universal improvement in safe-
ty equipment has occurred and wage mar-
kets have not yet adjusted, observed risk
premiums may be biased upward because
they are still reflecting the higher level of
risk. Slow adjustments will not introduce
bias if changes in safety have occurred
randomly and in both directions—better
equipment introduced in one place and a
more dangerous procedure in another.
These reviewers are not aware of any
empirical evidence concerning the speed
and nature of these kinds of labor market
adjustments.
Union bargaining power may also push risk
premiums higher than they would be under
competitive equilibrium conditions.
Several authors (Olson, 1981; Thaler and
Rosen, 1975; V. K. Smith, 1982) have
found a positive and statistically signifi-
cant interaction between union member-
ship and wage-risk premiums. Union
members are observed to receive greater
compensation for incurring risk than non-
union workers. A variety of explanations
could account for this, each requiring
empirical verification along some other
avenue. Whatever the correct explana-;.
2-2
-------
tion, it is doubtful whether, based on this
evidence, the EPA would want to conclude
that union workers are more risk averse
than nonunion workers or that the benefits
of protecting union workers are greater
than protecting nonunion workers.
The assumption that workers are aware of
the risks associated with different jobs is
necessary in order for observed wage-risk
premiums to be an accurate reflection of
the amount of compensation that would be
required to induce the individual to accept
such a risk. Misperceptions that are ran-
dom will increase the standard errors of
the estimated wage-risk premiums but the
estimate will be biased only if there is
some systematic pattern in the misper-
ceptions. Very little is known about the
factors that may influence a person's per-
ceptions of risk. Lichtenstein et al. (1978)
found that there was some systematic
error in what people thought to be the
frequency of lethal events. Some empiri-
cal work in the form of surveys concerning
perceived injury rates could be very help-
ful in terms of establishing the validity of
wage-risk studies for quantifying risk
premiums.
2.2 Summary Review of the Wage-Risk
Studies
Eight wage-risk studies were reviewed.
All of them use some variation of the
hedonic framework that was introduced
above. The authors of these studies were
aware of the potential policy applications
of their results, but the focus of these
studies has been on testing whether the
labor market functions as is theorized. In
this sense, they are concerned more with
accurate characterizations of the labor
market than with the applicability of their
estimates to policy questions.
A description and summary of each study
can be found in Table 2-1. Except for
Dillingham (I 979), each study used data on
job risks from one of two sources—the
Bureau of Labor Statistics (BLS) or a sur-
vey conducted by the Society of Actu-
aries. The appropriateness of the two
data sets has been one area of contention
in the wage-risk literature. The BLS data
provide average injury rates by industry.
The use of industry averages introduces
measurement error because job risks are
not uniform across occupations within an
industry. For example, clerical workers
and heavy machinery operators in the
same industry will face very different job
risks. Most studies have attempted to re-
duce potential measurement errors by
including dummy variables to distinguish
beween different occupations within an
industry. For example, R. Smith (1974 and
1976) used dummy variables for eight
occupation classifications: professional
worker, manager, clerical, craftsmen,
operatives, service workers, laborers, and
part-time workers.
The most often cited value-of-life esti-
mates are those obtained by Thaler and
Rosen (1975). They were the first to use
the 1967 occupation survey conducted by
the Society of Actuaries. This survey pro-
vides data on actual deaths associated
with selected hazardous occupations. To
isolate occupational fatalites from these
data on total fatalities, Thaler and Rosen
subtracted the age adjusted expected
deaths for.the population. The remainder
is assumed to represent deaths associated
with the occupation.
Thaler and Rosen claimed that the use of
this occupational risk data is superior to
the BLS injury indices by industry used by
R. Smith (1974). They admitted that some
measurement errors exist in their data set
since the occupational classifications are
still quite broad, but they asserted that
the degree of measurement error in their
risk estimates is perhaps as much as an
order of magnitude smaller than with the
BLS data.
While their occupational risk data have
some desirable attributes, the particular
data set used by Thaler and Rosen con-
tains some potential problems. Lipsey
(1975) pointed out that their risk data
actually measure something other than
occupational risk. The risk they are
measuring is the extra risk to the insur-
ance company of insuring those who are in
a particular occupation. This insurance
risk will encompass both true occupational
risk and risk associated with personal
characteristics. Using Lipsey's example,
people attracted to bartending may have
personal habits or characteristics which
increase their insurable risk independent-
2-3
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I ..Me?-1
I Icdnnir Wane-Risk Studies Summary Table
Sludx
Variables \
Data Sources
Unique Aspects
list imalion Approach
Results
1902 Dollars
Comments
R. Smith (1974)
ho
I
Thaler and Rosen
(1975)
o Three risk variables
were used: risks of
death, permanent im-
pairment, temporary
disability. Injury rates
by industry were ob-
tained from from the
Bureau of Labor Statis-
tics for 1966 and 1967.
o Individuals' data on
wages, union member-
ship, education, worker
class, experience, age,
occupation, past health
problems, geographic
region and other demo-
graphic variables were
obtained from the 1967
Survey of Economic
Opportunity, U.S. Cen-
sus.
o Risks of death for 36
hazardous occupations
were obtained from the
1967 Occupation Survey
conducted by the Soci-
ety of Actuaries.
o Wage data and other
characteristics of indi-
viduals were obtained
from the 1967 Survey
of Economic Opportuni-
ty, U.S. Census.
This was the first study to
use occupational wage
and risk data to try and
estimate a wage-risk
premium. The actual goal
of study wus to estimate
what "injury fine" would
be necessary to encourage
firms to reduce injuries.
The wage-risk relation-
ship was one component
of the model.
Differed from R. Smith
(1974) in that risks by oc-
cupation rather than risks
by industry were used.
Thaler and Rosen claimed
that this reduced meas-
urement error in the risk
data since risks will vary
across different occupa-
tions within an industry.
Two specifications were
examined. Doth regressed
the natural log of wages
as a function of job risks
and other socloeconomic
variables. One equation
incorporated dummy vari-
ables for the following In-
dustry groupsi construc-
tion, manufacturing, per-
sonal services, business
services and wholesale
trade. Both specifica-
tions Incorporated region-
al dummy variables.
Linear and semilog linear
equations were estimated
with wage rates as a
function of job risks and
other characteristics of
the occupation and indi-
vidual. Selected risk/
socio-economic interac-
tion terms were included
in several equations.
The two spec i f ica I ions
showed substantially dif-
ferent results. The addi-
tion of the industry dum-
my variables reduced the
estimated value of a
statistical life from $13.2
million to $7.5 million. In
the equation without the
industry dummy variables,
both fatal and nonfatal
risks were significant var-
iables in explaining
wages. When tlie industry
dummies were included,
the fatal risk variable was
significant and nonfatal
risks were not significant.
Of the eight equations es-
timated by Thaler and
Rosen, four found a risk
variable to be significant
at the 90% confidence in-
terval. Value of life es-
timates ranged from
$390,000 to $746,000 for
the equations without in-
teraction terms. The
equations with interaction
terms found much lower
value of life estimates,
but the precision of the
estimates was also much
lower.
o The large t-vulues for
the industry dummy
variables indicated that
there are important
factors which influence
wages and vary across
industries, but were
omitted from the equa-
tion.
o The mixed findings for
the significance of non-
fatal risks indicates
that wage-risk models
may not be useful for
estimating the willing-
ness to accept compen-
sation for risks that
jre, at least, partially
compensated ex post
through insurance and
workman's compensa-
tion.
o The assumed wage-risk
functional form was
constrained to be
convex.
The risk data used are not
true occupational risks.
The risk they examined is
the extra risk to the in-
surance company of in-
suring individuals who are
in a particular occupa-
tion. This risk will in-
clude both occupational
risks and risks associated
with personal characteris-
tics. This could explain
some surprises in their
risk data. For example,
the risks of death associ-
ated with being a waiter
were twice that of a po-
liceman and three times
that of a fireman. The
potential inappropriate-
ness of the risk data
raises, some concern re-
garding the soundness of
-------
ladle 7-1
Heclonic Wctga-Risk Studies Summary Table
(conl lnue«l)
Sfmly
Variables A
Data Sources
Unique Aspects
Estimation Approach
Results
1982 Dollars
Comments
R. Smith (1976)
ViscusKI978b)
Dilllngham(l979)
o The risk data were ob-
tained from the 1970
Bureau of Labor Statis-
tics Injury rates.
o The risk data were
matched with wage
data and characteris-
tics for individuals
from the 1973 Survey
of Economic Opportu-
nity, U.S. Census.
o Like R. Smith (1974)
Viscusi used risk data
by industry from the
Bureau of Labor Statis-
tics.
o A different source of
wage and socioecon-
omic data was used —
the 1969-70 Survey of
Working Conditions
compiled by the Uni-
versity of Michigan.
o Risk data were com-
piled from the New
York State Workman's
Compensation Board.
o Wage, employment and
socloeconomlc data
came from the 1970
Census.
The large difference be-
tween the Smith (1974)
and the Thaler and Rosen
(1975) results motivated
this study. Smith only
looked at workers In man-
ufacturing industries -to
reduce potential biases in
the measured risks and
from omitted variables.
Viscusi used a set of oc-
cupation and socloecon-
omlc data that contains
variables Indicating whe-
ther the individuals as-
sessed their Job as dan-
gerous as well as a num-
ber of descriptive job
characteristics that could
Influence wages.
This Is the only study to
use actual occupational
risk data, rather than the
BLS industry-wide aver-
ages or the actuarial in-
surance data used by
Thaler and Rosen.
A semilog linear specifi-
cation was used. Two
samples were used — all
workers in manufacturing
and workers on an hourly
wage.
Used linear and semilog
linear specifications. Al-
so ran regressions on all
workers and on a sample
limited to workers who
perceived their job as
dangerous.
All equations were semi-
log specifications. A
number of specifications
were used. Regressions
were run on a sample
comprised of all male
workers and a sample lim-
ited to male blue-collar
workers.
The value-of-life esti-
mates were consistent
across the two samples:
$3.2 million for the all
manufacturing workers
sample and $3.4 million
for the sample consisting
of only hourly workers.
The fatal risk variable
was consistently signifi-
cant. Segmenting the
sample Into only workers
who perceived their jobs
as dangerous had only a
small Influence on the es-
timates. Value-of-life es-
timates were similar to
R. Smith (1976), I.e., ap-
proximately $3 to $4 mil-
lion.
No significant relation-
ship was found between
job risks and wages for
the sample comprised of
all workers. The sample
of blue-collar workers
showed a consistently sig-
nificant relationship be-
tween risks and wages.
The estimated value-of-
life for the sample of
blue-collar workers was
approximately $400,000.
Using data from different
years and a more re-
stricted sample of work-
ers, R. Smith again found
value-of-life estimates
well in excess of the
Thaler and Rosen esti-
mates, although they
were lower than his 1974
study results.
This study addressed one
of the criticisms of
R. Smith's use of the BLS
data. Namely, that the
use of industry average
data introduces measure-
ment errors since the job
risks will vary substan-
tially across occupations.
The self-assessed job dan-
ger variable allowed
Viscusi to incorporate
more Information and
look only at occupations
perceived as risky.
o The Dillingham results
are similar to Thaler
and Rosen's estimates,
and were an order of
magnitude smaller than
R. Smith's or Viscusi's
estimates.
o The lack of a signifi-
cant relationship be-
tween wages and risks
for the all-worker sam-
ple is not surprising due
to the low average risk
level for that sample.
-------
IciMe 2-1
I Icdoiilc Wage-Risk Studies Summary TuMe
(concluded)
Study
Variables &
Data Sources
Unique Aspects
Estimation Approach
Results
1982 Dollars
Comments
Olson (1981)
V.K. Smith (1982)
K)
I
Arnould and Nichols
(1983)
o Used essentially the
same data set as R.
Smith (1976).
o Risk data by Industry
for l973fromDLS
o Wage and socioeconom-
ic data came from the
1973 Survey of
Economic Opportunity,
US. C*BUS.
o Risk data were 1975 in-
dustry injury rales from
the BLS.
o Wage and socioeconom-
ic data were obtained
from the 1978 Current
Population Survey, U.S.
Census.
o The socioeconomic data
were augmented by lo-
cation attributes such
as cost of living and
other factors that could
Influence welfare and
induce workers to ac-
cept different wages.
o The authors use the
same data as Thaler
and Rosen (I97S) aug-
mented by data on
workman's compensa-
tion by occupation.
This study relaxed the re-
strictions placed on the
functional form of the
wage-risk equation to al-
low for concave, as well
as linear and convex
(semilog), functions.
This study made two Im-
portant contributions —
wages were adjusted for
cost of living at different
locations and amenities
available at the location
were considered. Loca-
tional amenities such as
climate, pollution, activi-
ties, etc. have been found
to influence wages.
Attempts to incorporate
the influence of work-
men's compensation on
wage-risk premiums. The
hypothesis is that the
failure to account for
employer paid insurance
biases the wage-risk
premium downwards.
The estimated equations
had the risk variable en-
tered linearly and as a
squared term to allow for
the wage-risk tradeoff
function to be either con-
cave or convex.
V.K. Smith only consi-
dered semilog specifica-
tions. Equations for
males and females, males
only and females only,
were estimated.
Linear and semilog func-
tional forms were consi-
dered.
Olson found a significant
relationship between risks
and wages. The squared
risk variable was signifi-
cant at the 99% confi-
dence level. The negative
sign on the squared risk
variable Indicated that
the hedonic wage-risk lo-
cus is concave. The val-
ue-of-life estimate was
$7.0 million.
A significant relationship
between risks and wages
was found for all samples.
Since the risk variable
was all injuries rather
than only fatal risks, a
value of life must be in-
ferred indirectly. The es-
timate of a value-of-life
was calculated to be $1.0
million.
The addition of a work-
man's compensation vari-
able to the Thaler and
Rosen model increased
the estimated value-of-
life modestly, i.e., by
12%.
This is the only study that
allowed for a concave he-
donic wage-risk function.
All other studies con-
strained the function to
be linear or convex.
Theory indicates that a
concave function may be
appropriate and this is
supported by Olson's find-
ings.
o The use of wages ad-
justed by cost of living
was a significant im-
provement.
o The use of a semilog
specification which
constrained the wage-
risk function to be con-
vex could bias the es-
timate in light of
Olson's results.
o The implied value-of-
life estimate is uncer-
tain because fatal and
nonfatal risks were not
separated.
The use of risk data com-
piled by the Society of
Actuaries is subject to
the same problems as dis-
cussed in the comments
on Thaler and Rosen.
-------
of their occupation. On the other hand,
people who work as policemen or firemen
may be in better physical condition there-
by reducing the incidence of illnesses or
accidents. These personal characteristics
could cause some of the occupations to
have unexpectedly high fatality rates. For
example, elevator operators, bartenders,
and waiters were found to have higher
death rates than policemen or firemen. If
these higher rates are caused by personal
characteristics that are attached to the
individual rather than associated with the
job, there will be no positive compensat-
ing wage differential. In fact, these
characteristics 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 increases the cost of doing busi-
ness. This would result in lower producti-
vity and, therefore, lower wages being
offered to these individuals. The Society
of Actuaries data used by Thaler and
Rosen may have reduced one source of
measurement error only to add another
source of measurement error of an un-
known magnitude.
Even if the Actuaries' occupational risk
data were entirely accurate, it is ques-
tionable that it would match the percep-
tions of individuals in the labor market
who are negotiating their wage-risk pre-
miums. The ranking of occupations by risk
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 conclusion, both data sets suffer from
certain problems. As long as these meas-
urement errors vary randomly across
industries and occupations, the estimated
wage-risk premiums will be unbiased. The
only effect will be to increase the esti-
mated standard errors which makes it
more difficult to obtain statistically signi-
ficant results. If one had to select one
data set as better, the BLS data seems
preferable since it measures only job
related injuries.
2.3 Summary of Estimates from the
Hedonic Wage Studies
These studies often conclude that there is
substantial support for the hypothesis that
wage differentials for job hazards do
exist. The stated reason is that virtually
all of the studies have found job risks to
be significant and positively related to
wages. Still, it is important to consider
how confident a policymaker can be in us-
ing the numerical results from these
studies. The establishment of causality is
always difficult in econometric, studies
and there exist several potential
confounding influences in these wage
studies. This section will summarize the
empirical estimates and, in the context of
these estimates, some of the controversial
issues will be discussed.
It is important to understand that a per-
fect empirical study can never be con-
ducted and that even with weaknesses in
the data or techniques, important insights
may be generated. On the other hand, it
would be a mistake not to recognize these
shortcomings since they are important in
the proper interpretation and application
of the results.
A summary of the empirical estimates is
presented in Table 2-2. Where studies
considered more than one model specifi-
cation or segmented the sample, multiple
estimates are reported. A judgemental
"best" estimate is also presented that
represents either the author's recommen-
dation or a guess by these reviewers based
on judgement and information presented in
the study.
The value-of-life estimates tend to cluster
into two ranges—a $400,000 to $650,000
and a $4,000,000 to $7,500,000. These
estimates differ by roughly an order of
magnitude. The studies that use risk data
for occupations compiled by the Society of
Actuaries (Thaler and Rosen, 1975; and
Arnould and Nichols, 1983) found esti-
mates of the value for reductions in risk in
the low range, while studies using BLS
data on risks by industries tended to
2-7
-------
Table 2-2
Estimates of the Marginal Willingness to Pay for Reductions in Risks
(expressed in May 1982 dollars)0
Value Per
Statistical Life
1.
2.
2.
3.
4.
5.
6.
7.
8.
Mean Risk Level
Study for the Sampleb
R. Smith 1.0 to 1.5
(1974)
Thaler and 11.0
Rosen (1975)
a. Without risk
interaction terms6
Thaler and 11.0
Rosen (1975)
b. With risk
interaction terms f
R. Smith 1.0 to 1.5
(1976)
S. K. Viscusi 1 .2
(I978b)
A. Dillingham 1.7
(1979)
C.Olson 1.0
(1981)
V. K. Smith 3.09 *
(1982)
A mould and 1 1.0
All
Estimates c
$ 7.5 x 106
I3.2x I06
3.90 x I0|
5.05 x I03
5.42 x 105
7.46 x 105
.I4x 105
1.99 x I03
2.75 x I0|
3.36 x I05
3.22 x lOf
3.44 x I06
l.46x (Of
2.23 x I06
2.66 x 10*
3.44 x lOf
3.95 x 10°
4.21 x 10°
4.38 x I06
3.4 x I05
4.0 x 105
4.1 x lOf
4.3 x I03
ll.0x 10^
7.1 x I06
7.3 x I05h
to
20.7 x 105
6.40 x 105
Judgemental
Best Estimates0"
5 7.5 x 106
5.7 x 105
3.3 x I06
3.9 x \06
4.0 x I05
7.1 x I06
I.Ox 10^
6.40 x I05
Nichols (1983)
2-8
-------
Notes to Table 2-2
Adjustments to 1982 dollars were
made by using the consumer price in-
dices for all items published by
Council on Economic Advisors, Eco-
nomic Indicators, December 1982.
The risk level is expressed in annual
deaths per 10,000 workers. The value
should be viewed as an approximate
figure since many of the studies
reported risks in different units re-
quiring transformation to common
units.
The multiple estimates are derived
from the different model specifica-
tions examined. It was felt that
presenting estimates from all the
specifications is better than simply
showing the range of estimates since
one outlier can distort the range.
The judgemental "best" estimate
represents either the author's reco-
mmendation or a guess by these re-
viewers based on judgement and the
information provided by the authors
of each study.
e These estimates are from Thaler and
Rosen (1975) equations that did not
include interaction terms between
risk and other variables.
' From specifications including inter-
actions variables between risk and
nonrisk variables.
9 Calculated by assuming that .4 per-
cent of all injuries are fatal. This is
ratio for the BLS injury statistics is
reported by Viscusi (1978b, p. 365).
h Calculated assuming the risk premium
for risks of fatal injuries ranged from
33 percent to 100 percent of the pre-
mium associated with all risks.
estimate considerably higher values. One
explanation commonly advanced to explain
the differences in these estimates is that
the fatality rates contained in the Society
of Actuaries data are for high risk occupa-
tions. The mean annual risk of death in
the occupations examined by Thaler and
Rosen (1975) is approximately 11.0 x IDA
where the mean annual probability of a
fatal accident in data obtained from BLS
statistics is close to an order of magnitude
lower (I x IO-4 to 1.5 x IO"4). Olson
(1981), R. Smith (1979), Viscusi, (I978b)
and Blomquist (1981) argue that workers
who place a lower value on safety are
likely to be attracted to jobs with higher
risks. In other words, workers who are
least risk averse will be employed by these
high risk jobs and estimates of the
willingness to pay for marginal reductions
in risk will be lower for these workers
than for the average worker.
The implication of this hypothesis is that
the hedonic wage-risk locus is concave.
This implies that wage premiums increase,
but at a decreasing rate, as job risks in-
crease. One inconsistency in the hedonic
wage-risk studies is that while most
authors appeal to the hypothesis of a con-
cave wage-risk locus as one explanation of
the differences between the estimates, in
the empirical work all the studies (with
the exception of Olson, 1981) constrained
the wage-risk locus to be either convex,
through the use of a semi-log specifica-
tion, or linear. Only Olson (1981) allowed
for the existence of a concave wage-risk
locus. He incorporated a squared risk
term in the wage equation and found the
coefficient on the squared term to be
negative and highly significant indicating
that the .function may, indeed, be con-
cave. Constraining the hedonic wage-risk
locus to be convex when it may actually
be concave introduces the possibility of
unknown biases in the estimated coeffi-
cient on the risk variable. Using
essentially the same data as R. Smith
(1976), Olson (1981) found the inclusion of
the squared risk variable resulted in
substantially different estimates of the
value of life. The Olson (1981) results
indicate that the linear or semilog model
used by the other studies will bias the
value of life estimates either upward or
2-9
-------
downward depending on the risk level at
which the value of life is estimated.
The estimates from Dillingham (1979) and
V. K. Smith (1982) further confound the
issue. The Dillingham study used a differ-
ent occupational risk data set and the V.
K. Smith study utilized a more detailed
model specification. The mean job risk
levels for the workers in their samples are
considerably lower than in the Thaler and
Rosen sample, but the estimated values of
life are closer to the Thaler and Rosen
estimates.
2.4 Methodological Issues in the Wage-
Risk Approach: What Confidence Can
Policy Makers have 01 the Estimated
Wage-Risk Relationship?
One of the most often cited factors sup-
porting the existence of wage-risk differ-
entials is the consistent finding of risk as
a positive and significant explanatory
variable in wage models. Although persu-
asive evidence, this fact must be
tempered by the realization that many of
these studies used the same or very simi-
lar data sets and therefore cannot be
viewed as independent verification of the
existence of a risk related wage differen-
tial.
Summary of the Issues Raised by the
Hedontc Studies
A number of theoretic and statistical
issues are raised by the hedonic wage^risk
studies that have been performed. Seven
issues are identified below:
I. The potential for omitted variable
bias: Are additional job characteristic
variables and location specific variables
necessary to control for other factors that
influence wage differentials?
2. The potential biases in the job risk
data sets.
3. Specification of the correct function-
al form (i.eM linear, semi log (convex),
risk-nonrisk interaction variables, or
squared risk variables (which allows the
wage-risk locus to be convex or concave).
4. The paucity of appropriate risk data
sets (i.e., most studies have used one of
two available data sets).
5. The functioning of the labor market
with respect to safety.
6. The separation of the estimated wage
premiums into compensation for risks of
fatal accidents and compensation for risks
of non fata I injuries.
7. Are wage rates adequate for the
estimation of risk related differentials in
total worker compensation which may in-
clude wage and nonwage components as
well as worker compensation and life
insurance?
The first issue—omitted variable bias-
concerns whether the positive relationship
between risks and wages found in these
models might actually be due to a causal
variable omitted from the model that is
also strongly correlated with the measured
job risk variable. If this were the case,
then the job risk variable might not be a
true causal variable but, instead, might be
serving as a proxy for some variable omit-
ted from the model. Even if there is a
causal relationship between risks and the
wage rate, omitting an important explana-
tory variable that is correlated with the
risk variable will lead to a bias in the co-
efficient estimated for job risk.
The reason for being concerned about
potential omitted variable bias is the
limited inclusion of job characteristic
variables other than job risks. The major-
ity of the studies include risk as the prin-
cipal variable distinguishing different
jobs. A number of job characteristics
other than risks could be hypothesized to
affect wage differentials. These charac-
teristics could include such things as
repetitive work, physically tiring work,
unpleasant working conditions (e.g., dirty,
noisy, varying temperature and odors), and
stressful conditions. If job risks are
always associated with poor working
amenities, it may not be possible to dis-
entangle factors associated with daily
working conditions and pure .safety
hazards. This is particularly relevant
when considering the potential transfer-
ability of these willingness-to-pay esti-
2-LO
-------
mates to nonwork related risks that may
not be associated as closely with these
disamenities. In sum, given the circum-
stances and job characteristics of the
risky jobs that have -been considered in
these studies, it is not clear that these
wage differential estimates reflect only
the effects of risks. One could easily see
that working in a pleasant environment at
a job with a I in 10,000 chance of a. work
related fatality could require a very dif-
ferent wage premium than working in a
noisy, dirtfi environment with varying
temperatures at a.job also associated with
the same I in 10,000 risk of death.
The second issue concerns the potential
biases in the job risk data sets. One of
two data sets have been used in all but one
of the studies. Each data source has
potential problems. The BLS data supply
only average injury rates by industry,
ignoring the substantial variation in acci-
dent rates for different occupations within
an industry. The 1967 study by the
Society of Actuaries of differential mor-
tality rates across occupations does not
distinguish between job related and nonjob
related accidents. To the extent that the
risk data from these two sources are
biased or are correlated with important,
but omitted, explanatory variables, the re-
sults of all of the studies will likely suffer
from similar biases.
The third issue concerns the a priori speci-
fication of the wage function to be esti-
mated. In spite of theoretic and empirical
evidence that the hedonic wage-risk locus
may be concave, all but one of the studies
have constrained the function to be either
linear or convex. If the correct function
is concave over the relevant range of
risks, then the estimated coefficients will
be biased in an unknown direction.
A fourth issue is the paucity of data sets
containing information on the risks of
injury for different jobs. Ideally, the wage
or earnings equation should be estimated
with data on individual workers. Such
data are available for income, occupation,
age, education, and other characteristics
of the individual worker (many studies
have used U.S. Census or Current Popula-
tion Surveys), but data for on-the-job risks
are more difficult to obtain. In general,
these have been taken from other sources
and matched to the individual data. One
would like to look at the significant co-
efficients obtained by each of the eight or
nine studies as strong evidence for the
existence of risk related wage differen-
tials. Although persuasive, this evidence
must be tempered with the understanding
that the data sets used in these studies are
not independent. Further, similar tech-
niques using the different data sets tend
to give divergent estimates.
A fifth consideration concerns whether
the labor market operates efficiently with
respect to wage rates and safety. The
underlying assumptions are that workers
act as if they accurately perceive the
risks associated with different jobs and
appropriately account for these risk dif-
ferentials in their choice of job. An addi-
tional assumption is that the labor market
is free of structural constraints that might
prevent workers from changing jobs.
Tests of these underlying model assump-
tions have been limited* This is particu-
larly true for the assumption that all
workers accurately perceive the risks
associated with different jobs. Viscusi
(I978a and I978b) presented information
on whether the workers in his sample con-
sidered their jobs dangerous. This dummy
variable was positively correlated with the
BLS data on industry injury rates, but cer-
tain anomalies were present. In particu-
lar, the fraction of workers in the most
dangerous industries that rated their jobs
as dangerous was less than the fraction of
workers in lower risk jobs who considered
their jobs dangerous.
An interesting potential violation of the
assumptions of an efficiently operating
labor market with respect to safety would
involve the unequal distribution of infor-
mation on job risks across workers. This
could result in some workers overestimat-
ing the risks associated with specific jobs,
some workers underestimating the risks of
This might result from workers in riskier jobs being less risk averse and, therefore,
judging their jobs as not dangerous.
2-11
-------
specific jobs, and some workers with accu-
rate perceptions of job risks. Even if this
job risk information is randomly distri-
buted across workers, a bias in the esti-
mated risk coefficient can result. In a
process somewhat similar to the market
for lemons (see Varian, 1978, p. 232),
workers who underestimate job risks will
gravitate to the riskier jobs, while workers
who overestimate job risks will tend to
accept lower risk jobs. If this is true, the
use of actual risk data in hedonic wage-
risk models rather than the employed wor-
kers' perceived job risks will bias the
estimated wage premium downward. This
results from the firm having only to offer
the wage premium necessary to attract
the marginal worker.
The sixth issue concerns whether the wage
premium can be separated into a premium
associated with fatal risks and a premium
for nonfatal risks. An ability to distin-
guish between these two willingness-to-
pay values would improve the policy
relevance of the estimates and the trans-
ferability of the estimates to nonwork
related safety improvements. Some
empirical data exist but the multicolline-
arity between the fatal and nonfatal acci-
dents tends to confound the results. Many
studies have used only fatal injuries with
the explicit (or implicit) assumption that
these are correlated with nonfatal injuries
and can therefore represent both. Other
studies have used as risk variables the fre-
quency of nonfatal accidents, distinguish-
ing in some cases between temporary and
permanent disabilities, or the number of
workdays lost. None of these measures is
an exact measure of the risks of pain,
inconvenience and decreased freedom of
activity that would represent the loss of
utility to the injured individual. Also, it is
likely that worker's compensation will at
least partially compensate workers for
nonfatal accidents, thereby reducing the
wage premium necessary to attract
workers to industries with high risks of
nonfatal injuries. Since most hedonic
studies have neglected the role of worker's
compensation, using wage differentials to
estimate the willingness to pay to avoid
nonfatal accidents will be biased down-
wards.
The seventh and final issue concerns
whether the use of wage rates rather than
total compensation (wage and nonwage) is
adequate for the estimation of risk related
wage differentials. The most obvious
problem is that worker's compensation and
other insurance benefits may compensate
the worker for incurring risks, a compen-
sation that will not show up in wages.
Ignoring other nonwage benefits may dis-
tort the estimation of wage-risk premiums
if such benefits have any tendency to vary
with the level of risk to which the worker
is exposed. Ideally, a measure of the total
value of a worker's wage and nonwage
compensation should be used in these
estimations. The importance of this
measurement error is not apparent from
the studies completed to date.
Applicability of Wage-Risk Results for
Environmental Policy Decisions
Even if the wage-risk tradeoff is an accu-
rate description of behavior in the labor
market it may or may not provide useful
information for environmental policy deci-
sions. EPA must make decisions concern-
ing the expenditure of resources to
improve or protect public health and safe-
ty. A useful input for these decisions
would be how much such protection is
valued by the public. Wage-risk studies
may be able to provide such input in some
circumstances, but several issues must
first be addressed.
One concern is whether the nature of the
risks involved on the job are comparable
to those associated with a specific policy
question. Individuals may not be con-
cerned only with the probability of death,
but the way which that deathjis likely to
occur. The risk of falling twenty stories
while cleaning windows may not be con-
sidered equivalent to the risk of a slow,
painful death from cancer, even if the
probabilities of each of these occurrences
are equal. Since EPA is often concerned
with nonfatal and fatal effects of pollu-
tants that may be of a very different
nature than on-the-job accidents, esti-
mates of the value of life and safety from
2-12
-------
wage-risk studies may not be transfer-
able.*
Wage-risk studies examine the tradeoffs
made between risks and income for a cer-
tain segment of the population. At best,
this segment includes only members of the
employed labor force, thus under-
representing children, elderly, women and
others. In practice, the studies often look
at an even smaller segment of the popula-
tion by sampling only male workers, full-
time workers, or blue collar workers. If
we expect significantly different valua-
tions on life and safety across different
population groups, the valuations esti-
mated for one group cannot be extended
for the general public or for other specific
groups expected to be affected by a pollu-
tion control decision.
Again, empirical analysis is needed to
determine the nature and extent of dif-
ferences in valuations of life and safety
across the population.
If more information were available concerning the differences in the way people value
different risks, it would be possible to say that premiums for on-the-job risks represent
an upper or lower bound. There is some evidence, for example, the involuntary risks are
considered less tolerable than voluntary risks, but the evidence is as yet inconclusive. It
would also be necessary to know how workers differ from nonworkers in the way they
value risks.
2-13
-------
CHAPTER 3.0
CONSUMER MARKET STUDIES
Individuals make tradeoffs in their lives
between risks and benefits in the con-
sumption of many goods and services.
Studies of these choices may be able to
reveal the implicit valuation that people
are placing on these risks. This approach
is based on the presumption that individu-
als will maximize utility by choosing to
accept risks up to the point where the ex-
pected benefits of accepting these risks
just equal the expected costs of the risk.
If the benefits can be quantified, then the
implicit valuation on the risk is revealed.
Just as with the wage-risk studies, the va-
lidity of these kinds of estimates depends
on people having accurate perceptions of
the risks that alternative activities en-
tail. Two types of risks have been exam-
ined in the three studies that were re-
viewed—risks of automobile accident
fatalities and risks of residential fire in-
juries.* A summary of the three studies is
presented in Table 3-1.
Dardis (1980) used information about how
much people pay for smoke detectors to
infer how much they are willing to pay to
reduce the risk of fatal and nonfatal injur-
ies due to residential fires. The price of
the smoke detectors was used as a meas-
ure of willingness to pay for the increased
safety they provide. This is accurate only
for the marginal consumer. Other pur-
chasers may have substantially higher
willingness to pay than the market price,
reflecting their consumer surplus.
Blomquist (1979) looked at the decrease in
risk of fatal injury when a driver buckles
his seat belt. The only cost of seat belt
use he was able to quantify was the value
of the time it takes. By ignoring the in-
convenience and possible discomfort of
wearing them he underestimated the wil-
lingness to pay for the increased safety
that seat belt use provides. It is also
questionable whether the time it takes to
buckle and unbuckle seat belts is an im-
portant factor in whether or not they will
be used.
Ghosh, Lees and Seal (1975) examined the
trade off that people make in terms of
time saved and increased risk in choosing
a driving speed on the highway. Their cal-
culations assumed that the only benefit of
driving faster is the time it saves. To the
extent that there are additional benefits
of driving faster, their estimate of the
benefit required for people to increase
their risk of death is a lower bound.
Table 3-2 summarizes the value of life
estimates that have resulted from these
three consumer market studies. In each
case, the estimate is based on assumptions
that were made in the analysis and that
may not be valid. In most cases the major
assumptions tend toward an underestimate
of the value of life. It is not surprising
that the estimates are on the low side
compared to many of the wage-risk study
results.
* A third type of risk is examined in Portney (1981). He suggests a methodology for es-
timating the value of reduced risks of mortality by examining premiums paid for homes
in neighborhoods with lower air pollution and the resulting expected reduction in risk of
death associated with the lower pollution level. This is an interesting approach but would
be more complicated to apply than his illustration suggests. An observed air quality
premium can only be interpreted as the willingness to pay of the household that has
chosen to pay that premium. It would therefore be necessary to use the actual housing
premium and air pollution level at which the household is observed in order to calculate
the implied value of life. Portney points out the additional problems of separating aes-
thetic, morbidity and mortality components of the air quality premium.
3-1
-------
Table 3-1
Consumer Market Studies Summary Table
Siinly
Dardis
(1900)
Blomqulsl
(1979)
U)
I
Ghosh, Lees
and Seal
(1975)
Risk
Unique Aspects
Data Sources
Fslimotion Approach/
Major Assumptions
Results
1982 Dollars
Comments
Risks of fatal and
nonfatal hospital-
ized injuries due to
residential fires;
changes in annual
risks of /team of
3.l6x 10-^ and an-
nual risks of injury
of 2.26 x lO"5 asso-
ciated with use of
smoke detectors.
Risks of fatalities in
automobile acci-
dents; changes In
annual risks of death
of 1.514 x IQ-4 as-
sociated with seat
belt use; average
annual risks of death
in automobile acci-
dents are 3.027 x
III •
Use of a market
good which has the
primary purpose of
reducing risk of in-
juries and fatalities
provided a good set-
ting for observing
actual behavior with
respect to risks.
Creative theoretical
and statistical anal-
ysis was used to es-
timate an implied
value of reducing
risks from the ob-
served decision of
whether or not to
use seat belts. Pro-
bit analysis was used
to examine the seat
belt use decision
with income as one
of the explanatory
variables.
Risk data from Nation-
al Fire Protection As-
sociation, National
Fire Prevention Con-
trol Administration and
U.S. Consumer Product
Safety Commission.
Risk data from Third
International Congress
on Auto Safety, High-
way Safety Research
Center, National Safe-
ty Council, Federal
Highway Administra-
tion, Illinois Depart-
ment of Transporta-
tion) seat belt use and
Individual data from
Panel Study of Income
Dynamics, 1972, Uni-
versity of Michigan.
Risks of fatalities in Made use of a be- Automobile accident
automobile acci-
dents on British mo-
torways; risk Iqvels
were not reported.
lievable tradeoff be-
tween time spent
traveling and risks
of fatalities.
and other motorway
data from the Trans-
port and Road Re-
search Laboratory and
Journals Including Traf-
fic Engineering and
Control and Accident
Analysis and Preven-
tion.
Annual!zed price of smoke de-
tectors was taken as a measure
of willingness to pay for the
reduction in risk of death and
Injury that they provide.
Major Assumptions; Price re-
f lee Is willingness to pay.
Concern for property protec-
tion and transaction and Instal-
lation costs are trivial with re-
spect to smoke detector pur-
chases.
Value of time spent buckling
and unbuckling seat belts and
an estimate of what benefits
would have to be to Induce all
drivers to use seat belts were
used to obtain an estimate of
willingness to pay to reduce the
risk of automobile accident fa-
talities.
Major Assumptions; Value of
time is an important considera-
tion in the decision whether to
use seat belts.
Value of time Is a fraction of
the wage rate.
Tradeoff between travel speed
and risk of accident was used
to estimate the value of reduc-
ing risks of accidents using an
estimate of the value of time.
Major Assumptions; Value of
time is equal to the wage rate.
Saving time is the only signifi-
cant benefit of driving faster.
Average value per
life saved was
S318,334 to
$496,688 depending
on the importance
of fatal relative to
nonfatal injuries.
Average value per
life saved was
$540,747.
Average value per
life saved of
$496,966.
Price will understate
willingness to |>uy for
some who Itave already
purchased smoke de-
tectors and will over-
slate it for those who
have not.
Even if the assump-
tions in the model are
correct the estimation
procedure provides on-
ly a lower bound esti-
mate because the dis-
comfort and incon-
venience (other than
time) costs of seat belt
use were ignored and
because the estimate is
applicable only to
those who do not cur-
rently use seat belts.
The assumption that
saving time is the only
benefit of driving fast-
er makes this estimate
likely to be a lower
bound.
-------
TABLE 3-2
Summary of Value of Life Estimates from Consumer Behavior Studies
Study
Dardis
(1976$)
Blomquist
(1972$)
Ghosh, Lees
and Seal
(1973$)
Initial
Risk
Level
8.77 x I0~5
3.027 x IO-4
Not reported
Increment
of Risk
Valued
3.l6x ID'5
1.514 x ID"4
Not reported
Value Per
Life 1982
Dollars
$3 18,334 to
$496,688
$540,747
$496,966
Nature of
Risk
Examined
Residential
fire fatalities
Automobile
accident fatalities*
Automobile accident
fatalities on
British motorways
The consumer market studies require
several of the same assumptions and face
several of the same problems as the wage-
risk studies. They are based on the pre-
sumption that individuals make rational,
well informed, utility maximizing choices
with respect to risks. An important dif-
ference with consumer market studies is
that we are looking at how much consum-
ers will pay (or give up in terms of time
and inconvenience) in order to reduce a
particular risk. Wage-risk studies look at
how much workers must be compensated
in order to accept particular risks. Indivi-
duals' attitudes may be quite different in
these two situations. Workers know that
they are facing risks on the Job that are
earning profits for someone else. Since
the benefits of accepting these risks
accrue to someone else, the worker is
likely to be unwilling to accept these risks
without adequate compensation, and is
likely to err on the side of cautiousness in
his judgement about the magnitude of the
risks he faces. With risks such as traffic
accidents and residential fires, there may
be more of a tendency for the individual
to underestimate the risks with thoughts
like it can't happen to me, or I'm a careful
driver. In these cases the individual must
take the trouble to buy a smoke detector,
or fasten his seat belt, in order to reduce
the risk. He must be convinced that the
risk is troublesome enough for this to
seem worthwhile.
As with wage-risk studies, consumer mar-
ket studies face considerable data source
limitations. Measures of risks that are
available tend to be averages for large
segments of the population. People will
make choices based on the risks they per-
ceive themselves to face, which may ac-
tually be quite different from the average
risks. Risks of traffic accidents are not
the same for all drivers in all parts of the
country and neither are risks of fires the
same for all residences. The benefits of
accepting risks may be even more difficult
to measure, as the studies by Blomquist
(1979) and by Ghosh, Lees and Seal (1975)
demonstrated.
These studies have done a reasonable job
of developing credible-models for the data
with which they had to work, but data
limitations and the uncertainty about the
consistency of people's choices with res-
pect to small changes in risks limit the
general usefulness of this approach for
environmental policy decisions, at least as
far as these examples are concerned. The
results of these studies do, however, con-
firm that people make tradeoffs between
safety and other resources. They do not
do everything they can in order to reduce
a risk; the amount of resources that they
expend in order to reduce risks is limit-
ed. Useful estimates for environmental
policy purposes might be obtained through
this approach if observable tradeoffs are
being made for the kind of risks being con-
sidered, if the data are available and if
behavior consistency can be confirmed.
3-3
-------
CHAPTER 4.0
CONTINGENT MARKET APPROACHES
Contingent market approaches for valuing
life and safety entail the use of surveys in
which respondents are asked to directly or
indirectly place dollar values on changes
in risks of death or injury. They are called
contingent market approaches- because,
for a good that is not normally traded on
markets, a hypothetical market is posed to
the respondent and he is asked what he
would pay for the good, contingent upon
the existence of such a market. This ap-
proach has received considerable attention
recently for its potential in providing es-
timates of willingness to pay for environ-
mental quality and other nonmarket
goods. (See Brookshire et a I., 1982, for an
example of such an application and Rowe
and Chestnut, 1982, for a detailed review
of this technique as applied to the visibili-
ty impacts of air pollution.)
4.1 Background an Contingent Market
Approaches
Contingent market approaches try to eli-
cit, through the use of surveys, what
tradeoffs people are willing to make be-
tween safety and income. Everyone wants
better health and more safety, but the
reality is that the amounts of time and
money that people will expend in order to
obtain better health and more safety are
limited. In fact, people make tradeoffs all
the time between increased risks on the
one hand and monetary or other benefits
on the other. The challenge of the survey
approaches is to elicit accurately the val-
uations on safety that are behind these
kinds of choices.
The most widely applied contingent mar-
ket approach is the contingent bidding
method. In this approach, as applied to
the valuation of risks, respondents are
given information on current and potential
alternative levels of risks in a particular
activity. They are also given hypothetical
markets that describe how payments are
to be made or received by the respondents
for changes in this risk. Next, they are
asked to bid their maximum willingness to
pay (WTP) or minimum willingness to
accept compensation (WTA) to prevent or
incur the change in risk. Respondents may
be asked to pay for reduced risk through
increased taxes, increased product costs
for safety, and increased time spent in
travel and the like. The bids are usually
obtained through one of three approaches-
-posing an open ended WTP or WTA ques-
tion, asking the respondent to choose a
value from a payment card with numerous
alternative payment amounts listed, or
using an iterative bidding procedure where
the interviewer asks if the respondent is
willing to pay (or accept) a specific
amount and then continues to change the
amount until a maximum WTP (or mini-
mum WTA) is determined. These surveys
usually also ask related questions on per-
ceptions and attitudes as well as socio-
economic characteristics of the respon-
dent in order to identify the underlying
determinants of the bias and to check
their reasonableness.
Another contingent market approach is
the contingent ranking technique. With
this procedure, respondents are asked to
rank various sets of alternatives in order
of preference. Each alternative would
include a level of risk and a payment of
some sort so that the rankings would
reveal a valuation without the respondent
having to give dollar estimates directly.
4.2 Summary of Contingent Market
Studies
Five contingent market studies that have
addressed questions of dollar valuations
for changes in risks were reviewed. A
summary description of these studies is
presented in Table 4-1. For the most part,
these studies are best interpreted as tests
of the survey instruments and procedures
because the samples are often nonrandom
or too narrow to provide estimates applic-
4-1
-------
Tolile 'i-l
Contingent Market Studies Summary Table
Study
Risk
Unique Aspects
Hypothetical
Scenario
Survey Procedures
Results
1982 Dollars
Comments
Acton
(1973)
Jones-Lee
(1976)
Murphy
(1979)
Risk of fatalities
from heart attacks;
U.S. overage annual
risk of heart attacks
is one out of 100 and
risk of fatality is two
out of five — total
annual risk of death
of 4 x IO-3.
Airline accident fa-
talities.
Estimates were not
defined for any spe-
cific risk. Focus of
the study was on the
risks of immediate
treatment for illness
versus waiting until
diagnostic test results
are available.
o Well defined scen-
ario and bellevea-
ble levels of risk.
o Presentation of risk
levels was complex
but fairly clear.
Intended as an illus-
tration of a possible
survey procedure for
obtaining estimates
of values of reducing
risks.
Used an indirect val-
uation approach de-
fining a value of life
in terms of the pleas-
ure derived from
life's activities.
Willingness to pay
for emergency
service that would
reduce the risks of
death once a heart
attack occurred in
the form of higher
taxes.
Hypothetical
tradeoffs between
airline prices and
safety records.
Respondents were
asked to rate the
relative pleasure
of life activities
such as sleeping,
eating, working
and leisure, and to
estimate the com-
pensation neces-
sary to induce
them to give up a
few hours leisure
by working over-
time.
o Random household sam-
ple of 32 individuals in
the Boston area and two
additional non-random
samples of 14 each.
o WTP questions concerned
reductions in risks of
death from current U.S.
average and from hypo-
thetically higher levels
with total Initial risk of
death of 2 x IO'2.
o Non random sample of 31
academic and research
workers.
o Respondents were asked
at what fare they would
be indifferent between
one airline with a given
price and safety record
and another airline with
a different safety level.
o A non random sample of
40 patients and staff at a
hospital in Lansing,
Michigan was asked to
estimate time spent at
and relative pleasure of
various activities.
o For those who were em-
ployed, willingness to
accept compensation to
give up some leisure was
used to obtain an implied
estimate of the value of
the net loss in pleasure
from working overtime.
Implied value of $17,000
to $98,000 per life
saved) the lower results
from the elevated risk
questions — WTP did not
increase in proportion to
the increase in risk in-
crement.
Average implied value
of $5,343,000 per life
saved with a range of
$317,000 to $49,423,000
across all respondents.
Implied value per life
was an average of
$2,937,000. The author
extrapolated this esti-
mate from the value of
pleasure from life's var-
ious activities that was
estimated from the sur-
vey results.
o Nonlinear it ies in re-
sults could be a func-
tion of question order
and hypothetical
scenar io.
o Two stage risk — first
of attack, then of
deatli — mode the
questions complex and
may have affected the
bids.
o The scenarios were
reasonably plausible
and well defined, but
presentation was too
terse and probably
confusing.
o Should be interpreted
as a pretest only.
Tradeoff used to obtain
an implied value of life
was based on the value
of a marginal change in
activities. Applying this
value to all pleasure is
probably not a valid ex-
trapolation.
-------
Table 4-1
Contingent Market Studies Summary Table
(continued)
Study
Risk
Unique Aspects
Hypothetical
Scenario
Survey Procedures
Results
1982 Dollars
Comments
Frnnkel
(1979)
Risks of airline acci-
dent fatalities and
changes in life expec-
tancies from unspeci-
fied cause.
Mulligan
(1977)
Risks of fatal and
nonfatal Injury from
nuclear power plant
accidents.
o Hypothetical
changes in risks of
longevity were
carefully communi-
cated.
o Some interesting
comparisons were
made between
changes in life ex-
pectancy and guar-
anteed changes In
life span.
Examined both wlll-
. ingness to pay to ob-
tain reduced risks and
willingness to accept
compensation In ex-
change for higher
risks.
Realistic markets
were not formulat-
ed for most ques-
tions. Respondents
were, for example,
asked their will-
ingness to pay for
a magic amulet
that would ensure
uninjured survival
of on airline flight.
Hypothetical In-
crease In monthly
utility bills In .or-
der to fund in-
creased safety
measures or de-
creases In bills In
exchange for In-
creased risks.
o A non random sample of
169 faculty members and
a few executives at the
University of Illinois re-
sponded to the question-
naire.
o Two levels of risk reduc-
tion were presented for
airline fatalities — a re-
duction of current risks
to zero and a reduction
of a hypothetlcally much
higher risk to zero.
o A random sample of
households In Lew Is ton,
Pennsylvania, provided
82 responses.
o Several different risk In-
crements were presented
numerically with an in-
troduction describing the
kinds of injuries that can
result from a nuclear
plant accident.
o Implied value per life
was an average of
$3,922,000 for the re-
duction in risk from
current levels and was
$60,000 for the much
larger reduction in
risk.
o Life expectancy ques-
tions revealed signifi-
cant risk aversion and
on one case a life val-
ue of $1.78 million.
Average value per life
saved implied by the
WTP responses ranged
from $71,000 to
$322,320,000 assuming
the questions referred to
annual risks.
o The lower value per
life was based on an
unrealislically high
risk of airline acci-
dent fatalities.
o Unrealistic and vague
hypothetical markets
weakened the ques-
tionnaire.
o Questions were poorly
designed in that the
time period was not
defined making the
risk level ambiguous.
o Some risk levels con-
sidered were unrealls-
tically high compared
to estimates of actual
risks of nuclear plant
accidents.
-------
able for public policy analysis. They have
not paid much attention to the emerging
literature on contingent market approach-
es for obtaining estimates of values for
nonmarket goods. Two of the studies con-
ducted some pretests of their survey in-
strument, but all of them could have bene-
fited from the refinements in survey
design that have been evolving in other
areas of environmental quality valuations.
The value of life estimates implied by the
responses to these surveys vary widely
both within studies and across different
studies. These results are summarized in
Table 4-2. The studies do indicate that
most respondents were willing to put posi-
tive dollar valuations on decreases in risks
and that they were willing to make the
effort to answer these questions seriously
and reasonably.
All of these studies had some problems in
the presentation of the scenarios, the
hypothetical market and the change in risk
being valued. Acton's questionnaire was
probably the best such presentation. The
suggested actions for reducing risks of
heart attack fatalities were well defined
and realistic; however r the payment vehi-
cle by which these programs would be sup-
ported was left rather vague and although
all the necessary information about the
change in risk to be valued was given, it
was rather confusing. The Jones-Lee
questions were fairly well presented in
terms of the levels of risk to be evaluated
and the market mechanism, but the sce-
narios in which these choices might have
to be made were not well developed and
the presentation presumed a well educated
audience. The Frankel and Mulligan sur-
veys were both rather weak in the realism
and detail of the scenarios. The Mulligan
survey was especially flawed in terms of
the description of the risks to be valued.
Future survey efforts need to take pains
to develop realistic and detailed scenarios
and to present the tradeoff the individual
is being asked to consider in a straight-
forward and simple manner. A realistic
context in which the individual might have
to make such a tradeoff should be careful-
ly described.
Only in the Mulligan study were respon-
dents questioned about their unwillingness
to answer valuation questions. Mulligan
found that over 80 percent of the respon-
dents said they were unwilling to accept
any compensation to allow risks of nuclear
plant accident injuries to rise. Many of
the explanations offered for this refusal
reflected an aversion to the idea of being
compensated for allowing increased risks
that would also affect other people. This
difficulty suggests that questions about
tradeoffs concerning risks to the public
should be phrased in terms of willingness
to pay for reductions in risks as this is
likely to be a more acceptable concept.
This also indicates that respondents were
having trouble thinking about the risks to
themselves alone as they were directed to
do by the introduction to the question-
naire. If respondents are not distinguish-
ing how much they themselves are
affected by the risks from how much
friends, family and fellow human beings
are also affected, this could be influencing
willingness-to-pay estimates as well. This
might be mitigated by careful presenta-
tion of the question, and by describing a
payment mechanism whereby everyone
pays equally.
Other kinds of problem bids also need to
be explored. Frankel found a rather high
percentage of zero bids and very high bids
relative to the means. These could be
true valuations indicating a great deal of
variation across people's preferences or
they may indicate some difficulty with the
question. Probing people's reasons for
such bids would be helpful in deciding how
to handle them in the analysis. Zero bids
that were given because the respondent
felt he should not have to pay for safety,
for example, should probably not be used
in the calculation of the sample means.
Acton and Jones-Lee also found some in-
consistent or illogical bids over different
increments of risk. These might indicate
confusion about the questions that could
be cleared up during the interview proc-
ess.
It is not expected that willingness to pay
per life saved will be constant across
people or across differences in the level
and type of risk. The results of these
studies provide some indication of the
nature of these nonlinear it ies, but several
questions remain. The Mulligan study
found that higher incomes were associated
with higher willingness to pay for reduced^
4-4
-------
TABLE 4.2
Summary of Value of Life Estimates from Contingent Market Studies
Study
(Year Dollars)
Acton
(1972)
Jones-Lee
(1975)
o
Murphy
(1978)
Frankel
(1979)
Mulligan3
(1977)
Initial
Level
of Risk
4x10-3
4x1 0"3
2x10-2
2xlO-2
0 to 4x1 0-5
_•
I.SxIO-6
lo-4
,0-4
10-5
io-°
lO-J
lO'8
Increment
of Risk
2x10-3
I0"3
IO-23
2xlO-6to2xlO-5
^-r.
I.SxIO-6
lo-4
9xlO~J
9x10-5
9xlO-°
9x10"'
9x1 0~8
Average Value
Per Life
(Thousands/ 1982$)
$64
$98
$17
$27
$3 17 to $49,423
(mean = $5,343)
$2,937
$3,922
$60
$71
$498
$4,151
$34,760
$322,320
Nature of
Risk Examined
heart attack fatalities
airline accident
fatalities
mr^
airline accident
fatalities
nuclear plant
accident injuries
' This table is for summary and comparison purposes. Before using the estimates, the reader should understand the
assumptions and procedures by which they were obtained.
This estimate was not linked to a specific risk or risk increment although the author states that it is relevant only for
small changes in risks.
These are based on the assumption that the survey question referred to annual risks and that all injuries are fatal.
-------
risks. The Acton study, however, found
that income and wealth were not signifi-
cant influences on the bids offered.
If safety is similar to a typical market
good, then additional units will provide
smaller and smaller increases in utility.
This means that for a given starting point,
it can be expected that value per life
saved will fall as the number of lives
saved increases. This was confirmed in
the Acton study where respondents were
asked their willingness to pay for a reduc-
tion from .004 to .002 and then from .004
to .003. The second mean bid was more
than half of the first indicating that the
first .001 reduction was valued more than
the second .001 reduction.
Another expectation regarding nonlineari-
ties in risk valuations is that at higher risk
levels, people will be willing to pay more
for an incremental risk reduction than
they would be willing to pay if they were
at a lower level of risk. People at higher
risk levels have less probability of being
able to enjoy future income and wealth
and are therefore expected to be willing
to part with more money for the decrease
in risk than would a person at a lower risk
level, even though the change in risk is the
same for both individuals. The contingent
market studies have not provided any use-
ful evidence on this question because in
each case where higher risk levels were
hypothesized, the increment of risk being
evaluated was also changed. Problems
may have also resulted because the higher
initial risk levels suggested in these sur-
veys were often outside the range that
most of the respondents would consider
realistic for the topic being discussed.
This question could be more carefully con-
sidered in future survey efforts by keeping
increments constant and changing the ini-
tial risk levels, and by using realistic
ranges of risks.
The work of Tversky and Kahneman (1981)
may shed some light on some of the ap-
parent inconsistencies observed in the sur-
vey responses and on the importance of
how the questions are phrased. They have
developed the proposition that expected
utility theory (individuals make choices
that maximize expected utility) does not
adequately predict peoples' preferences
with respect to risk taking and that their
alternative "prospect theory" is a better
predictor of peoples' choices in the face of
risks. They have found several systematic
patterns: (I) people value risk taking dif-
ferently if it is presented as a potential
loss or a potential gain, (2) breaking down
the probabilities into steps can result in
different valuations even though the net
result is the same, and (3) marginal losses
or gains are less important as they become
a smaller fraction of the total loss or gain
being considered.
The first point is consistent with the
Jones-Lee results that compensation re-
quired to accept a higher risk was more
than the willingness to pay to obtain a
comparable decrease in risk. The third
point is consistent with the Acton results
showing a decreasing marginal value of
additional lives saved when starting from
the same initial risk level. There is no
such clear illustration of the second point,
but it should be noted that Acton's results,
which imply low values per life compared
to most of the other results, are based on
questions that present the risks of heart
attack deaths as a two step probability. It
is not clear whether Tversky and Kahne-
man's results refute the validity of ex-
pected utility theory or simply demons-
trate systematic difficulties people have
in interpreting probabilities, but they
clearly demonstrate that how the question
is phrased and presented can have a signi-
ficant influence on the responses obtained.
The Murphy study was included because it
is an example of an indirect valuation
approach using a survey effort. Respon-
dents were asked to make judgements
about the value of how they spend their
time during a typical week in pleasure, not
dollar terms. The tradeoff between pleas-
ure and income was derived from a second
question so that an implied value of life
could be estimated. Although there were
problems with several assumptions made
along the way in this study, the idea of
indirect valuations is appealing when
things are being considered that people do
not usually think of as being purchased or
traded. It may be easier for people to
think in terms of, for example, time they
are willing to spend to save lives than
money. The problem with any approach of
this nature is that the eventual conversion
4-6
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to dollars that must be made for benefit-
cost analysis is seldom straightforward.
4.3 Applications Issues in the Contingent
Market Approaches
Economists have long been skeptical of
survey approaches because they are sus-
picious that what people say they want or
are willing to pay for, and what they will
actually part with money in order to ob-
tain, are two different things. The chal-
lenge of contingent market approaches is
to design a survey instrument that will
effectively elicit the desired informa-
tion. Valuations received with contingent
market approaches have often varied sub-
stantially with small changes in the appli-
cation of the technique and must, there-
fore be carefully designed and moni-
tored. One of the most important prob-
lems encountered in these approaches is
the design of questions so as to minimize
perception errors and biased responses.
Survey research has found that responses
are most accurate when the questions are
about topics or decisions that are familiar
to the respondent, when the questions are
realistic and credible, and when the time
and inconvenience of answering the ques-
tionnaire is low. (See Crespi 1971, Erskin
1972, and Ajzen and Fishbein 1977.) This
means that a question about willingness to
pay for safety needs to be presented in a
context in which the respondent can imag-
ine having to make such a choice. For
example, a question about how much the
respondent would be willing to pay in
higher automobile prices for improved or
increased safety equipment in an automo-
bile is probably much more effective than
a question that simply asks how much the
respondent would pay to increase his life
expectancy by a specific number of
years. In the first case, the payment
mechanism is concrete and realistic and
the choice is one that the respondent
could imagine having to make, whereas
the second one is vague and difficult to
identify with.
The applicability of the contingent market
approach to the valuation of risk depends
on the ability of respondents to weigh the
importance of small changes in risks. In
most ordinary circumstances, the risks
faced by individuals in any particular ac-
tivity are very small. The average annual
risk of fatality in an automobile accident
is, for example, about .0003 (3 in 10,000),
while for fatal accidents on the job for
blue collar workers, it is about .0002 (2 in
10,000). People do make decisions in their
lives that involve risks of these magni-
tudes and will expend time and money to
reduce such risks by a small amount, but
the survey questions must adequately
communicate the nature and size of the
change in risk being considered in terms of
familar experience. Contingent market
approaches, as well as the market ap-
proaches, could profit from a better
understanding of people's attitudes and
judgement processes about what risks are
acceptable for what benefits. Although
contingent market studies do not rely on
interpreting observed behavior, under-
standing typical behavior and judgement
processes with respect to risk would help
the researcher pose more meaningful
questions.
Usefulness for Policy Analysis
Careful application of these approaches
can provide useful input for environmental
policy decisions. The studies performed to
date have not used state-of-the-art
techniques as found in the current
contingent valuation literature and many
improvements are possible.
Contingent market approaches have the
advantage of a great deal of flexibility.
Constrained only by the necessary realism
of the hypothetical scenarios, the
approach can be structured to address the
specific question at hand. It can therefore
be used in circumstances when no
appropriate market information is
available. The approach is also easily and
quickly implemented, but a careful survey
effort can be expensive, especially if per-
sonal interviews are conducted.
Contingent market approaches can also be
used in conjunction with questions about
attitudes and opinions on environmental
policy. Such information could help to
verify the interpretation of contingent
market responses and the results of actual
market approaches. It may be that mar-
ket distortions and lack of information
prevent observed behavior from reflecting
4-7
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true preferences. Surveys might therefore
provide better willingness-to-pay esti-
mates. It may also be possible to have
respondents describe tradeoffs they would
be willing to make in other than dollar
terms. They could, for example, be asked
how much time they would spend to re-
duce the risk of a certain kind of acci-
dent. Although this approach would avoid
the problem of requiring respondents to
put dollar values on something they do not
typically think of as a marketable item,
the problem still remains of having to put
dollar values on time or whatever measure
is used if the results are to be used in
benefit-cost analysis.
4-8
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CHAPTER 5.0
OTHER VALUE OF LIFE AMD SAFETY ESTIMATION ISSUES
Chapters 2 through 4 have summarized the
available empirical estimates of the will-
ingness to pay for changes in risk levels.
This section will summarize some con-
siderations that are relevant to estimating
the willingness to pay for changes in risks,
but that have remained largely outside the
scope of the currently available empirical
studies.*
5.1 Properties of an Individual's Willing-
ness to Pay for Changes in Mortality
Risks
The hedonic wage-risk studies reviewed in
Chapter 2 do not provide information on
the properties of an individual's willing-
ness to pay function for .changes in risk.
Instead, they map out a set of market
clearing wage-risk combinations. Contin-
gent valuation studies can be used to der-
ive estimates of an individual's demand
curve for safety, but the poor quality of
existing studies linrn'ts their usefulness. A
number of researchers (Weinstein, et a I.,
1980; and Thaler and Gould, 1982) have
used decision theoretic approaches to ex-
plore the likely properties of individual
willingness to pay curves. The principal
conclusion to be drawn from these studies
is that there is no unique value per life
saved. This conclusion rests on two
findings:
I. The willingness to pay for a reduc-
tion in the risk of mortality depends on
the amount of the reduction and the initial
probability of death.
2. The willingness to pay also depends
on whether the decision is ex ante (e.g.,
medical insurance or preventive medicine)
or ex post (e.g., after-the-fact intensive
medical care).
The implication of this first finding is that
the cost effectiveness of programs to re-
duce mortality risks cannot be evaluated
solely by dividing the cost of the program
by the number of lives saved. Instead, the
value of the reductions in risks will depend
upon the specific individuals whose risks
have been reduced and their base risk
level. This implies that it may be desir-
able to devote more effort to reducing
risks for those with high base risk levels.
The second finding states that the value of
a reduction in risk depends upon whether
the reduction is evaluated ex ante-to a
particular health event that increases an
individual's risk or ex post to the event.
As a result, the appropriateness of ex ante
versus ex post valuations is important in
the design of empirical studies. An
example can be given in the context of
kidney dialysis. Each year approximately
one out of 30,000 people suffers kidney
failure and becomes a candidate for dialy-
sis. Without dialysis, the individual will
certainly die, with dialysis the individual
•is likely to live. The theorem states that
if each one of these 30,000 individuals
were asked what compensation he or she
would be willing to accept ex ante to hav-
ing kidney failure to forego the availabili-
ty of a dialysis machine, the sum of these
estimates over the 30,000 people, would
be less than the compensation required by
the one individual to forego having access
to the dialysis machine after having had
kidney failure. This difference in the sell-
ing price per expected life saved between
ex ante and ex post evaluations holds
whenever the individual is risk averse or
risk neutral with respect to assets.
The fact that ex post willingness to pay
tends to exceed the ex ante willingness to
pay seems to support our societal
tendency to invest much more heavily in
A more detailed treatment of each of these topics can be found in the main report.
5-1
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health care for the sick patient than in
preventive health measures. As the
collective public pays a greater share of
health costs, it becomes more compelling
to view the appropriateness of these
.expenditures from an ex ante perspective.
5.2 The Choice Between Ex Ante or Ex
Past Risk Valuations in Policy
Assessment
Since ex ante and ex post willingness to
pay estimates will often differ, there is a
question as to which value is the most ap-
propriate for policy assessment. Broome
(1978) argues that, of these two, the ex
post valuation is the correct one. An ex
post valuation is made at the time the
project is implemented and when all the
details of its effects are known, including
who will be hurt. Since ex post decisions
are based on more information, Broome
contends that they should be preferred.
Most researchers, however, have argued in
favor of using ex ante valuations (see
Thaler, 1982; Thaler and Gould, 1982; and
Mishan, 1982). Thaler (1982) makes the
following arguments in favor of ex ante
valuations:
I. Few projects are instantaneous.
Decisions on whether to implement a risk
reducing project may have to be made
before the affected individuals are
identified.
2. The choices made in ex ante valuat-
ion studies are egalitarian. All individuals
know the forthcoming outcomes and
probabilities.
3. The ex ante "willingness to pay of
individuals with low survival probabilities
should be discounted, because their 'will-
ingness to pay is based in part on their low
survival opportunities. Since they are
likely to die, the dollars they are offering
are in some sense worth less to them." It
is only their inability to trade risks with
individuals in the low risk groups that
allow them to outbid those groups.
4. In the final state, ex ante choices
will save more lives and conserve more
wealth. To the extent that these are the
variables in the decision models, it is hard
to fault ex ante choices.
Although there is not a clear consensus in
the literature, the arguments for the use
of ex ante, unidentified risk valuations in
policy evaluation are persuasive. This has
particularly important implications for
any future contingent valuation studies
since the hypothetical markets can be de-
signed to value either ex ante or ex post
risks. Given the arguments, the ex ante
valuation seems superior for policy
assessment.
5.3 The Valuation of Different Risk
Types
Policy scientists have observed that indiv-
iduals appear to place different values on
different types of risk. For example,
individuals seem to be- more averse to
accepting risks that are felt to be involun-
tary, i.e., risks imposed on individuals by
society. . The classification of risks as
voluntary or involuntary is only one factor
that has been used to characterize differ-
ent types of risk. For example, Litai
(1980) presents twenty-six different risk
characteristics that have been used to
classify risk types.* The basic policy issue
raised by this literature is whether
people's willingness to pay for reductions
in risk varies across risk types. A related
question is whether societal decisions
should reflect these different valuations,
if individuals do appear to value different
risk types differently.
Much of the recent literature has been
concerned with risk conversion factors
(RCF's). The basic premise of the ap-
proach is that actual behavior is useful for
revealing existing social preferences and
values for different risk types. The under-
lying assumption is that, over time and
through a trial and error process, a rough
equilibrium state between risks and com-
mensurate benefits has been arrived at by
The literature addressing risk characteristics includes C. Starr (1969); W. D. Rowe
(1977); H. J. Otway (1977); and Fischhoff et al. (1978).
5-2
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society. By observing society's behavior
towards risk, a quantitative relationship
(i.e., risk conversion factors) can be estab-
lished between different types of risks,
and between risks and benefits.
5.3.1 Risk-Benefit Ratios as Conversion
Foe tors
One of the clearest examples of this soci-
etal revealed preference approach is
C. Starr (1969). Starr concluded that the
public is w.illing to accept voluntary risks
that are roughly 1000 times greater than
involuntary risks, holding benefits from
the two risk taking activities constant.
The Starr analysis admittedly used crude
data and the results should be viewed as
suggestive rather than an attempt to pro-
vide actual numbers for policy purposes.
The method used by Starr was to develop
quantitative correlations between the
risk-benefit ratios associated with differ-
ent activities. The risk measure used was
the statistical probability of fatalities per
hour exposure to the activity. The esti-
mates of social benefits for the different
activities were expressed in terms of an-
nual dollars. In the case of 'Voluntary"
activities, the amount of money spent on
the activity was used as an estimate of
the benefits (e.g., hunting and smoking).
For transportation benefits, the monetary
cost and time saved by the particular
mode relative to a slower competitive
mode (e.g., airplanes compared to auto-
mobiles) was taken as a measure of the
benefits. In the case of involuntary ac-
tivities (e.g., electric power), an estimate
of the contribution of the activity to the
individual's annual income was used. The
final piece of data used in Starr's analysis
was a correlation between mining acci-
dents and injuries. The severity rate of
injuries was found to be roughly approxi-
mated by a third power function of wages
(i.e., the miners risk level was proportion-
al to waaes raised to the third power: risk
~ wages-*). With these data, Starr com-
piled the risk comparison relationship
shown in Figure 5.1.
Choosing a risk level of I x 10 , Figure
5.1 shows that the annual benefits must be
approximately $100 per year before an
individual is willing to accept that level of
voluntary risks. If the 10"' risks are
viewed as involuntary, then the individual
requires compensation on the order of
$2000 per year. This comparison indicates
that society is far more willing to accept
voluntary risks than involuntary risks.
The proper interpretation of Starr's risk-
benefit comparisons is problematic. The
data used in the comparison are extremely
rough and in some cases questionable. For
example, using both the money spent on
air travel as well as the value of time
saved over automobiles may be double
counting the benefits. The willingness of
individuals to pay the higher costs of air-
plane travel is at least partially due to the
value of the time they save. Also, the use
of expenditures for measuring the benefits
of hunting and smoking is at best only the
lower bound since it ignores any consumer
surplus. For example, individuals may be
willing to pay costs in excess of their cur-
rent levels to engage in hunting and smok-
ing. Taking this into account could great-
ly increase the benefit-risk ratio of these
activities. This would tend to reduce the
apparent disparity between benefits re-
quired to undertake voluntary risks and
benefits required to undertake involuntary
risks observed by Starr.
The Starr comparison is based on only
eight data points: four voluntary ac-
tivities (general aviation, railroad travel,
skiing, and hunting), and four involuntary
activities (natural hazards, electric power,
commercial aviation, and motor vehi-
cles). Two additional risks were included
as benchmarks. The risks associated with
the Vietnam war (which were classified as
voluntary risks with benefits of $30 x
10° based on the annual expenditure) and
the risks from all disease were used as
reference points. Starr's comparison has
been criticized by several researchers
(Otway and Cohen, 1975; and Fischhoff et
a I., 1979). These studies showed that re-
gression lines could be fit to the Starr
data in several different ways yielding di-
verse results. Otway and Cohen (1975) fit
regression lines for the data and found
that there does appear to be a greater
tendency to accept voluntary risks as op-
posed to involuntary risks; however, the
difference between acceptance of these
two kinds of risks was considerably
5-3
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FIGURE 5.1
Risk (R) Plotted Relative to Benefit (B) for Various Kinds of
Voluntary and Involuntary Exposure
10-9
2 10 ••
Ł
210-10
f»f oue TO
DISEASE
U.S. POPUUkTION
, MILITMTY MC OW5U*
400 800 1200 1600 2000 2400
AVERAGE ANNUAL BENEFIT/PERSON INVOLVED (COLLARS)
Source: Starr (1969)
smaller than found by Starr and diminished
to zero as benefits increased.
Extensive analysis of the few data points
compiled by Starr is probably not warrant-
ed. They should be viewed as generating
plausible hypotheses that deserve testing
in a more detailed study. Fischhoff et al.
(1979) extend Starr's conceptual approach
to the comparison of the risks and benefits
of 25 activities and technologies. Their
results also show individuals appear to be
more willing to accept voluntary risks;
however, the data points are quite dis-
persed so that the relationship is not very
strong.
5.3.2 Risk Conversion Factors
Rowe (1977) and Litai (1980) develop risk
conversion factors to compare different
types of risks. Their approaches must be
carefully distinguished from those used by
Starr (1969), Otway and Cohen (1975), and
Fischhoff et a I. (1979) since the benefits
of incurring the risks play no part in the
analysis. The focus is only on comparisons
across the different levels of risk indivi-
duals are willing to accept, without regard
to benefits. The Litai study will be the
focus of this discussion. The differences
between the Litai and Rowe approaches is
that Litai works with actual distributions
of risks while Rowe uses only average risk
levels. Otherwise, the two approaches are
essentially identical.
The premise of the Litai study is similar
to Starr's revealed social preference ap-
proach. They both assume that society
has arrived at a rough balancing of various
risks by trial and error. Litai also ob-
serves that for each risk type, the actual
risk level for separate individuals is spread
over a wide range, often extending over
several orders of magnitude. In addition,
the process by which society and indivi-
duals determine the level of acceptable
risk involves a number of human factors
encompassing philosophical and psycholog-
ical factors, as well as potential damage
to property and materials. The risks
classified by Litai were those where fatal-
ities were considered to be the predomi-
nant concern.
5-4
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The method used by Litai is based on ac-
tuarial risk data and therefore the data
are derived from the actual behavior of
people. Litai felt that differing types of
risk could be summarized by the nine
characteristics presented in Table 5-1. A
dichotomous scale was used in assigning
the risk characteristics. For example,
with respect to the characteristic volition,
the risk is classified as either voluntary or
involuntary. Litai argued that this dicho-
tomous classification is an underestimate
of human sensitivity, but is a valid approx-
imation with abundant examples of its use
in the literature. The assumption is that
individuals do not perceive small changes
in the parameters and, therefore, a dicho-
tomous representation is a satisfactory
approximation.
The first step in Litai's analysis was to
classify all the risks by the nine charac-
teristics. In most cases he felt there was
a clear choice regarding the characteris-
tics the majority of individuals would
assign to each risk. For example, automo-
bile travel was assigned the following nine
characteristics: voluntary, ordinary, man-
made, immediate, continuous, control-
lable, old, clear, and necessary. While it
is not clear that every person would pick
these exact characteristics, it was felt
that they represent the opinions of the
vast majority. In cases where the assign-
ment of characteristics were not clear
(e.g., homicides), the risks were not used.
Some risks could be classified in both
categories. For example, nuclear energy
could have both immediate and delayed
fatalities. Both classifications were then
assigned to that risk.
The next step was to search for risks that
only differed with respect to one charac-
teristic. The risk conversion factors were
estimated by dividing one risk distribution
by another risk distribution that varied in
only one of the characteristics. Table 5-2
shows fFe risk conversion factors that
were calculated for each characteristic.
These risk conversion factors can be used
to calculate mean values of each risk type
accepted by U.S. society. These are
shown in Table 5-3. Litai points out that
these values cannot be viewed as currently
acceptable risks when subgroups in. the
populations are affected differently.
These risk levels are average values of a
distribution and many groups may
accept substantially lower or higher risk
levels. Another use of these risk conver-
sion factors is to make different types of
risk comparable. According to Litai, the
risk conversion factors can be used to
show why society spends "unreasonable"
sums to avert selected deaths and refuses
to spend less money in other
circumstances.
The usefulness of these risk conversion
factors in policy analysis is questionable.
As calculated by Rowe (1977) and Litai
(I960), they do not consider the benefits
of incurring the risks. If the benefits of
one of the risks (say, Risk I) are 100 times
higher than the benefits of a second risk
category (Risk 2) used to construct the
ratio, then it would not be surprising that
individuals would be more willing to ac-
cept higher levels of Risk I. The implicit
assumption incorporated in the use of
these risk conversion factors is that the
marginal benefits associated with an addi-
tional increment of each risk type are
equal across all risks. This is not likely to
be the case since risk is only one attribute
of a product or activity comprised of a
number of attributes of varying levels.
Marginal utility may be equated across all
products or activities purchased by an in-
dividual., but, since risk will tend to be
fixed or at least not infinitely variable
within activities, there is no reason to
assume that marginal benefits of incre-
mental risks will be equated across activi-
ties. Thus, the different magnitudes of
benefits associated with different types of
risks could well account for substantial
portions of the risk conversion factors
found by Litai. This is particularly true
since many of these risk conversion fac-
tors are based on the quotient of only two
risk types. Still, if it were possible to
gather data on benefits associated with
the different risk types, better estimates
of^-isk conversion factors could possibly
be obtained.
5.3.3 Conclusions Regard ii
the
Valuation of Different Risk Types
The evidence accumulated by the studies
that have researched this topic indicates
that society may place different values on
• different types of risks. The available
5-5
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TABLE 5-1
Risk Characteristics Used by Litai (I960)
Characteristic
Volition
Severity
Origin
Effect manifestation
Exposure Pattern
Controllability
Familiarity
Benefit
Necessity
Classification
Voluntary
Ordinary
Natural
••"Immediate
Continuous
:" Controllable
Old
Clear
Necessary
Involuntary
Catastrophic
Man-made
Delayed
Occasional
Uncontrollable
New
Unclear
Luxury
empirical data are suggestive of these dif-
ferential valuations and possibly indicate
the likely sign of risk conversion factors,
but the usefulness of these estimates in
policy analysis is questionable. -n.
The risk conversion factors and compara-
tive risk-benefit ratios indicate that soci-
ety does appear to act as if different risks
have different values. However, why
these risks are valued differently is still
an interesting question. One possible
reason could be the existence of certain
psychic costs with different types of risks
and differences in how the risks are per-
ceived. Another reason could be that
benefits have been poorly measured in
these comparisons. Going back to Starr's-""
and Fischhoffs analysis, the use of gross *s,
expenditures on cigarettes and motor-'"
cycles may dramatically underestimate2!
the benefits associated with these "volun-
tary" activities. If properly accounted
for, these risk-benefit ratios might be
considfcrably lower and, therefore, closer
to the risk-benefit ratios of activities or
products associated with "involuntary"
risks. Related to the proper accounting of
benefits in these studies, it may be the
case that individuals value the flexibility
associated with the acceptance of volun-
tary risks. Voluntary risks are usually
associated with activities that could be
discontinued in the future if the indivi- '
dual's risk preference structure were to
chamge. This is not the case with many
involuntary risks (e.g., the widespread use
of nocfear power). The flexibility associ-
ated: with voluntary activities allows
.individuals to appropriately balance their
risk portfolios under a wide range of
future circumstances. This implies that
there-may be some form of option value
associated with voluntary risks that is not
present with involuntary risks. All of
thesei factors could contribute in varying
proportions to the observed risk taking
behavior examined in these studies.
A final- point to be made is that all of
these studies assume that society, through
a trial and error process, has arrived at
some-sort'of satisfactory equilibrium with
respdct" to* balancing different types of
risks; and benefits. If the individuals who
collectively, decide on society's risk taking
base- these, dec is ions on biased information
regarding.the risks associated with differ-
ent activities (e.g., from the news media),
an undesirable equilibrium may result.
Further," 1f individuals are poor probability
processors*, this situation could be aggra-
vated.r Thater (1982) points out that "most
individuate are rather poor at budgeting
their 'Vtwsney but would not want the
government to emulate their ineptness.
"They rtSCff prefer having an expert make
their Hfe-SaVing decisions for them just as
they \ŁoOtd hire an accountant to do their
budgeting rf they could do so cheaply.
5-6
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TABLE 5-2
Risk Conversion Factors (Litai, I960)
Risk Characteristics
Delayed/Immediate
Necessary/Luxury
Ord inary/Catastroph ic
Nature I /Man-made
Voluntary/Involuntary
Controllable/Uncontrollable
Occasional/Continuous
Old/New
RCF Estimated
30
I
30
20
100
5
I
10
Probable Error Factor
10
10
10
10
10
10
10
10
* These mean, for example, that immediate risks require 30 times more compensation
than delayed risks.
5.4 Measuring and Defining Risks to Life
and Safety
This section discusses several dimensions
of risks to life and safety that are impor-
tant for policy assessment but have been
only minimally addressed in empirical
studies. Three issues are examined in this
section. The first is whether expected
years of additional life should be adjusted
for the expected quality of life. The
second issue concerns a suggested proce-
dure for incorporating externalities asso-
ciated with risks (i.e., indirect effects on
others of society) and collective risk aver-
sion with respect to catastrophic acci-
dents. The third issue is the consideration
of risks of nonfatal injuries and/or health
problems.
5.4.1 Quality of Life Adjustments
Several articles have discussed the appro-
priate measures for the analysis of poli-
cies designed to reduce mortality risks.
The two most often used measures are
number of lives saved and years of life
preserved. The selection of the measure
of mortality benefits can affect the policy
decision where one policy is preferred if
the benefit unit is total lives saved while
another policy is preferred if the unit is
total additional years of life. In most ac-
tual policy assessment applications, the
unit used has been the number of statisti-
cal lives lost or saved. The use of total
lives saved is due primarily to the exist-
ence of empirical estimates for the value
of a statistical life from the wage-risk and
consumer behavior studies discussed in
Chapters 2-4. Zeckhauser and Shepard
(1976) have suggested another approach
which uses years of additional life ad-
justed for the quality of life during those
years. This quality of life adjustment
could be particularly important for com-
paring risks of fatalities that are preceded
by a lengthly illness with the risk of
instant death.
The unit of measure in the Zeckhauser and
Shepard work is the quality-adjusted life
year (referred to as a QALY). QALYs are
tallied on a year by year basis and cali-
brated so that year with full function (i.e.
no health impairments) would be assigned
a QALY with the value of I, and a year
without life a QALY with the value of 0.
Calibration of QALY values for years with
partial impairment requires more informa-
tion, but can be performed with proce-
dures that have been used to calibrate
multi-attribute utility functions. These
5-7
-------
TABLE 5-3
Mean Values for Risk Types Accepted by U.S. Society (Litai, 1980)
•o
cd
N
jd
5*
Oi
•a
a
2
i
c
rt
2
Natural
Hazard
Involuntary
Voluntary
j
1 Ł
I— < Ki
O ri
*§
H-t 3
.*
•o «
.-« .^
Otf
S«
rtl
? m
C .rt
2d
^
•o m
>rt ^4
Occ
Controllable Risk
Ordinary
Immediate
Risk
1.3xlO"6
1.3xlO~7
1.3xlO~4
1.3xlO"5
3xlO"5(?)
Delayed
Risk
4xlO"5
4xlO'6
4xlO~3
4xlO"4
10"3(?)
Catastrophic
Immediate
Risk
5xlO"8
5xlO"9
5x!0"6
5xlO"7
lO'6
Delayed
Risk
l.SxlO"6
lj.5xlO"7
l.Sxlfl"4
l.SxlO"5
-
Uncontrollable Risk
Ordinary
Immediate
Risk
3xlO~7
3xlO"8
3x!0"5
3xlO'6
6xlO~6
-------
scaling procedures are similar to the con-
tingent market survey techniques dis-
cussed in Chapter 4.0. As an example of
how these QALY values could be scaled,
consider an individual who has a choice
between living the rest of his life with a
specific impairment or having an opera-
tion that could return full function, while
leaving his expected life span unchanged.
The operation has a probability X of being
successful and a probability I-X of being
immediately fatal. The value of X that
would leave the patient indifferent be-
tween having or not having the operation
is the appropriate value for the QALY
adjusted for that specific level of impair-
ment.
The Zeckhauser and Shepard approach out-
lined above measures benefits of policies
to reduce health hazards in terms of
quantity and quality. Few applications of
this technique have been attempted. In
one application, Weinstein and Stason
(1976) estimated the expenditures per
QALY obtained from treatment for hyper-
tension to be in the range of $3,000 to
$20,000.*
5.4.2 Externalities and The Potential
Usefulness of Decision Analytic
Approaches.
Many of the empirical approaches have,
most often due to limited data, been able
to address only one dimension of the
multi-dimensional risk valuation prob-
lem. That one dimension is the indivi-
dual's willingness to pay for a reduction in
the risk of death. However, there are ex-
ternalities that could be important to the
benefits calculation. These would include
the value family members and others put
on an individual's life and the indirect
economic impacts that can affect society
due to a large catastrophy with many
fatalities, such as a dam break or airplane
accident. Bodily (1980) and Keeney (1980)
argue that risks which may result in a
large number of fatalities cause greater
political, economic and social turmoil.
For benefit-cost approaches to be more
useful to policy makers, it is important
that some of these additional levels of
complexity be included in the analysis.
Several recent contributions to the litera-
ture that have their roots in the fields of
operations research and decision analysis
offer some organizing principles that may
be helpful in addressing some of these
complexities (Bodily, 1980 and Keeney,
1980). The basic approach is similar to
the QALY adjustment just discussed. The
first step is to develop a utility function
that contains the different dimensions of
risk that need to be valued, such as the
potential number of lives lost in a single
incident (a catastrophy dimension),
whether the risks are voluntary or involun-
tary, and externalities such as the effect
on others. Once these dimensions are
specified in a utility function with the
standard properties, then the variables in
the function are scaled and the constants
specified in a manner similar to that used
to scale QALYs. All of these approaches
require subjective scaling of variables and
valuation of the constants through an
elicitation process where either decision
makers or individuals are asked to judge-
mentally estimate these parameters.
Bodily (1980) develops an approach to deal
with several characteristics of risks and
public attitudes that influence the value
of safety programs. The characteristics
included by Bodily are:
I. Individual risk preferences
2. Nonstandard background risks
3. The need to compare the value of
life saving with that of injury
prevention
4. Distinction between voluntary and
involuntary risks
5. Possible psychological effects of
risks
6. Bunching effects, where one incident
involving n-individuals may be
perceived as more serious than n
incidents each involving one
individual
Other related studies that use different measures of health that could be useful in
inferring a quality of life index are Franshel and Bush (1970) and Torrance (.1976).
5-9
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With respect to this lost characteristic,
Bodily observes that the social reaction to
fatalities or injuries seems to be greater
when a large number of people are
affected in a single accident than when
the same number of people are injured in
several smaller incidents. Labeling this
rollective risk aversion, Bodily uses this to
explain why safety standards in jumbo jets
tend to be stricter than for smaller air
craft.
The premise of decision analysis is that
the explicit consideration of these trade-
offs will allow better, more consistent
decisions to be made. An interesting area
of investigation might be an evaluation of
combined economic/decision analytic
approaches (i.e., utility functions scaled in
dollars) in analyzing EPA programs affect-
ing risks. This evaluation could be done in
terms of the acceptability of the decision
analytic process to policy makers and
affected parties as well as whether better
decisions will indeed be made.
5.4J Valuing Nonfatal Risks
This review has emphasized empirical
estimates of the value of preventing fatal-
ities, but many environmental issues con-
cern the prevention of illnesses and dis-
comforts that are not fatal. As a result,
an important consideration will be the
value of preventing or reducing risks of
morbidity.
The bulk of the research that has been
done concerning the value of preventing
nonfatal health effects of manmade pollu-
tion has attempted to estimate the days
lost from work, or otherwise restricted,
attributable to effects of pollution. These
lost or restricted days have then been
valued according to the lost productive
activity (typically measured as the indivi-
dual's daily income) and in some cases the
medical costs of the illness have been
added as well.* Most applications have
made extensive use of the work by Cooper
and Rice (1976) which provides estimates
of income lost and medical expenditures
incurred due to a .variety of illnesses. A
basic problem with this approach is that it
does not measure willingness to pay to
prevent morbidity. It is not even clear
that income and medical expenditure
would be a lower bound on the individual's
willingness to pay because in many cases
the individual may receive sick pay and
insurance payments to cover these
losses. The individual's willingness to pay
to prevent time spent sick is more likely
to be a function of the pain and discom-
fort that accompanies the illness than of
his wage, and there is little empirical evi-
dence available on these valuations.
Cropper (1981) develops an innovative ap-
proach to the estimation of the benefits of
reduced morbidity that goes a few steps
beyond the previously used approaches.
She develops a model of investment in
health that incorporates the possibility
that the individual can influence his health
with a variety of preventive health care
activities. The benefits of reduced pollu-
tion will therefore be the value of the re-
duction in time spent ill plus the value of
the reduction in preventive health care
activities that were being undertaken to
offset the harmful effects of exposure to
pollution. Cropper's estimates are double
the estimates that would be derived from
looking at only the time spent sick. This
approach does not solve the problem of
how to appropriately value the time spent
sick (Cropper still uses the wage for this),
but it provides a more realistic treatment
of the individual's behavior with respect to
the state of his health.
An important question for future efforts
to obtain an estimate of the value of re-
duced morbidity is what constitutes an
appropriate measure of morbidity. The
most common measure has been work days
lost due to illness, but this makes no dis-
tinction between a day spent in mild dis-
comfort and a day spent in extreme dis-
comfort. It also does not capture days
spent sick but at work. A measure that
has been used for nonworkers is "restrict-
ed activity days". These are the measures
that have been used in some of the surveys
Examples using these approaches are Liu and Yu (1976) and Crocker et a I. (1979).
These and similar studies are briefly reviewed by Freeman (I979a).
5-10
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that have provided data for estimation
efforts. These surveys include the annual
Health Interview Survey by the National
Center for Health Statistics (used by
Ostro, forthcoming) and the Michigan
Panel Study of Income Dynamics (used by
Cropper, 1981).
A whole range of possible approaches to
estimation of willingness to pay to prevent
morbidity needs to be explored. The
Cropper study provides evidence that
people make observable expenditures*bf
money and time to prevent illness. These
are the kinds of tradeoffs that need to be
observed in a market approach to estimate
the value of reducing morbidity, such as
those reviewed in Chapter 3 concerning
the value of reducing mortality. Those
studies may in fact provide a starting
point since the activities considered en-
compass both fatal and nonfatal risks. A
few of the wage-risk studies also used
measures of nonfatal injuries but the prob-
lems of overlooking worker's compensation
make most of the resultant estimates
questionable. Contingent market ap-
proaches might also be a fruitful avenue
for obtaining estimates of willingness to
pay to reduce morbidity. Questions about
risks of morbidity might be less emotion-
laden and easier -for respondents to con-
sider than questions about risks of death.
5.5 Perceptions of Risks
All of the willingness-to-pay approaches
assume that people are able to judge for
themselves what the benefits of various
risks are. Several avenues of psychology
research suggest, however, that indivi-
duals may have trouble making consistent
rational choices with respect to risks.
This may be the result of poor information
or differences in the alternatives that the
researcher may have overlooked. What-
ever the cause, these problems raise the
question of whether public policy should
be based on preferences revealed by indiv-
iduals' behavior. The studies discussed in
this section do not provide conclusive evi-
dence one way or the other, but they raise
important questions that need to be
addressed in future research.
.1 Biased Perceptions of Risks
There is some evidence that individuals'
perceptions of risks associated with vari-
ous ' activities may be systematically
biased. If errors in individuals' percep-
tions of risks are random, then the explan-
atory power of the statistical valuations
reviewed in Chapters 2 and 3 would be re-
duced (i.e. the standard errors of the
estimates would be increased), but the
estimates would still be unbiased. How-
ever, if the errors vary in a systematic
manner, then the estimates from these
statistical studies will be biased. The con-
tingent market approaches also rely on a
consistent response by individuals to dif-
ferent levels and kinds of risks, although
they could allow for some inconsistencies
more easily than the actual market
approaches.
Lichtenstein et al. (1978) conducted five
experiments where individuals were asked
to judge the frequency of lethal events.
They found individuals' judgements of risk
were consistent but systematically
biased. Two kinds of bias were identif ied-
-one, there was a tendency to overesti-
mate risks of relatively infrequent events
(e.g., death from botulism) and to underes-
timate the probability of more frequent
events (e.g., death from heart disease);
and two, a tendency to overestimate cer-
tain risks characterized by wide media
exposure, memorability or the imag inabili-
ty of various events. To the extent that
these systematic biases are present in in-
dividuals' perceptions of risk, the results
of the studies reviewed in Chapters 2
through 4 may be biased.
Even though some of the possible causes
of biases in individuals' risk perceptions
were identified by Lichtenstein et al., the
direction of the bias this may cause in the
empirical estimates still is not clear. For
example, a common view is that workers
in risky occupations may underestimate
the probabilty of lethal accidents due to
being uninformed of the risks. In contrast
to this, the Lichtenstein findings indicate
that the likely bias in individuals' percep-
tion of the frequency of these low fre-
quency occurrences would be to overesti-
mate the risks. Bailey (1979) points out
that in dangerous occupations, such as
logging, accidental deaths and injuries are
5-11
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everyday topics of conversation and for
every severe or fatal accident, there are
many near misses. Again following Lich-
tenstein et al., the effect of daily conver-
sations concerning job risks and the in-
creased vividness and imaginability of
accidents from the many near misses
would tend to result '•" workers' overesti-
mating job risks. As a result, additional
research on how individuals perceive the
specific risks that are used in these empir-
ical valuation studies is needed before the
direction of potential risk perception
biases can be identified.
5.5.2 Preference Reversal
The basic issue is whether there is a con-
sistent theory of individual preferences
that can be used to explain an individual's
choices among uncertain or risky out-
comes. The preference reversal phenome-
non suggests, according to Grether and
Plott (1979), that no optimization princi-
ples of any sort underly even simple
choices.
The basic example used to .illustrate
preference reversal is an experiment
where subjects are asked to pick one lot-
tery from among two choices as the
gamble they would prefer to take. After
indicating a preference for which one of
the lotteries in the pair they would rather
play, the subjects are then asked to assign
monetary equivalents to the two lotter-
ies. This is done by putting the subject in
the position of playing each lottery and
asking them the amount of money they
would take with certainty rather than play
the lottery. For example, an individual
facing a lottery with a fifty percent
chance of losing $2.00 and a fifty percent
chance of winning $20.00 might say that
he would take a sure five dollars rather
than undertake the uncertain lottery. The
preference reversal occurs when the lot-
tery that is preferred by the subject when
selecting between the two lotteries is
given a lower monetary value. It is easily
shown that this is inconsistent with tradi-
tional forms of preference theory.
Whether or not this is an important issue
for empirical studies placing a value on
risks to life depends upon the pervasive-
ness of the preference reversal phenome-
non. The studies examining the prefer-
ence reversal phenomenon have used pairs
of lotteries with essentially the same ex-
pected payoff. As a result, these experi-
ments show whether individuals are cap-
able of fine tuning their risk-reward port-
folios. Since there is only a small differ-
ence in the payoffs for the two lotteries,
the penalties associated with an incorrect
decision are very small. If preference
reversal were found for a pair of lotteries
with larger differences in payoffs, then
this would be of greater concern. When
Pommerehne et a I. (1982) increased the
difference in the payoffs by up to 30 per-
cent, the incidence of preference reversal
declined.
In conclusion, the research on preference
reversal has been quite limited and is de-
serving of more study. The evidence to
date does not seem to contradict conven-
tional preference theory. The only con-
clusion that seems warranted is that
individuals may not be able to
appropriately distinguish between risk-
reward choices that have nearly the same
expected payoff. If traditional preference
theory is adequate for predicting choices
among options that' really matter, i..e.,
choices between options with distinctly
different payoffs, then it is probably an
adequate assumption in empirical risk
valuation studies. Whether or not indivi-
duals can accurately select among nearly
equivalent options at the margin is of far
less importance.
5.5.3 Cognitive Dissonance
The theory of cognitive dissonance as ad-
vanced by Akerlof and Dickens (1982) is
based on the concept that individuals not
only have preferences with respect to
states of the world, but also have prefer-
ences regarding the specific beliefs they
hold, even if these beliefs contradict
available information. In other words,
individuals have flexibility in the beliefs
they hold and can use this flexibility to
choose beliefs that maximize utility.
Akerlof and Dickens refer to a great deal
of anecdotal information that suggests
that workers in dangerous jobs are often
quite oblivious to the dangers involved.
They go on to construct a theoretic model
5-12
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of the labor market where people prefer
to believe their work is safe. The worker
chooses his beliefs according to whether
the benefits exceed the costs. If the
psychological benefits in terms of reduced
worry and tension of believing one's job is
safe exceeds the costs due to an increased
chance of accident, the worker will
believe the job to be safe.
Akerlof and Dickens cite the psychological
evidence supporting cognitive disso-
nance. The strength of the evidence is in
the great number of experimental results
easily explained by the theory. Psycholo-
gy experiments show that individuals with
the same information will adopt beliefs
that are in accord with their natural
preferences. For example, people like to
view themselves as having made good
decisions. Investigations have found that
individuals, after having made a decision
(e.g. placed a bet on a horse or selected a
home appliance), systematically hold
stronger beliefs regarding the appropriate
choice than individuals who are just about
to make the choice, even when there has
been no new information.
Akerlof and Dickens conclude that with
additional research cognitive dissonance
can be incorporated into economic models
in a predictive manner. The importance
of cognitive dissonance for estimating the
willingness to pay for reductions in risk is
clear. The tendency for workers or con-
sumers to ignore risks because they are
better off believing the risks are lower
than actual levels will distort the risk
valuations that are based on individuals'
revealed preferences from market behavi-
or. For example, Dardis (1980) used the
purchase of smoke detectors as a measure
of the willingness to pay for increased
safety. The theory of cognitive disso-
nance would allow individuals to obtain
utility from the belief that they were per-
fectly safe when in their home. If this
belief were adopted, then purchases of
smoke detectors would be lower than what
would otherwise be the case and the
observed value associated with the reduc-
tion in risk underestimated. Cognitive
dissonance could potentially have impor-
tant ramifications for risk assessment and
could well explain some of the observed
differences in the valuation of different
risk types addressed in Section 5.3.
5-13
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CHAPTER 6.0
CONCLUSIONS
In spite of the seemingly large amount of
attention this topic has drawn, there has
been no ambitious and consistent research
program to quantify the willingness to pay
for reductions in health risks. The empiri-
cal estimates that do exist should best be
viewed as preliminary, that is, as pointing
out additional hypotheses for analysis.
The purpose of much of the research was
not to provide empirical estimates for use
in policy analysis but to test hypotheses
regarding the workings of markets, parti-
cularly the labor market. This more
limited goal made it less necessary to con-
trol for biases that would change the ac-
tual value of the estimated risk premium,
but not change the direction of the ef-
fect. The most significant contributions
to valuing reductions in risk have been
made by studies focusing on the Depart-
ment of Labor's occupational health and
safety programs. Except for this area, the
research has been scattered with work be-
ing done on different types of risks in dif-
ferent situations, and with little follow-up
to test hypotheses identified in earlier
studies. As a result, many of the impor-
tant questions for environmental policy
assessments have not been addressed in
the empirical work.
This conclusion should not be viewed as
reducing the importance of the contribu-
tions that have been made in this research
area to date. Identifying hypotheses for
research, defining problems that need to
be addressed, and pointing out potential
biases that can be controlled in future
work are important and necessary -steps in
a developing area of research. However,
this conclusion is not encouraging for poli-
cy makers who would like to use these es-
timates now. Still, careful analysis of the
results may provide benchmark numbers
for policy assessment. Since policy deci-
sions are presently being made that trade
off expenditures for reduced risks, it is
important to make the best use possible of
the currently available information.
The balance of this chapter will address
the identification of reasonable ranges for
values of a statistical life, the general
conclusions from the wage-risk studies,
the consumer market studies and the con-
tingent market studies reviewed, and sug-
gestions for research.
6.1 The Value of Life Estimates—Is
There a Reasonable Range?
One of the goals of this review is to sum-
marize the available empirical informa-
tion on the value of life and safety which
is applicable to environmental policy ques-
tions. The results of the wage-risk studies
fall into two groups: those finding
$400,000 to $600,000 (1982 dollars) per
statistical life and those finding
$1,000,000 to $7,000,000 per statistical
life saved. All three of the consumer
market studies found values per statistical
life saved of about $300,000 to $500,000;
these fall close to the lower range of the
wage-risk studies. Two of the contingent
market studies that considered risks of
airline travel found values of $4,000,000
to $5,000,000 per life for changes in risks
at levels close to the actual risk of airline
travel. A few outlying results were found
by contingent market studies—Acton
found $20,000 to $100,000 per life and
Mulligan found $70,000 to $300,000,000
per life. The outlying Acton results can
possibly be explained by the type of risk
analyzed. The risk being valued was a re-
duction in the risk of death after having
had a heart attack by improving emergen-
cy services. Since the occurrence of a
heart attack is a future event, possibly
many years away, and even then not cer-
tain to occur, it is not surprising his esti-
mates of willingness to pay for a reduction
in these risks are lower than other studies
where immediate death from accidents or
fire were considered. The very low and
very high results found by Mulligan are
harder to explain, but problems with the
design of the survey may be the cause.
6-1
-------
Excluding these two studies results in two
ranges of estimates—$300,000 to $600,000
and $1,000,000 to $7,000,000.
Given the wide variation in results and the
variety of techniques used in risk valua-
tion studies, it is difficult to select an
appropriate value-of-life range for policy
evaluation. One attempt to roughly define
this range with respect to public health
and safety policy was made by Bailey
(1979). In a widely read and generally ex-
cellent review, Bailey (1979) tried to ob-
tain an intuitive feel for where within, or
between, these essentially two groups of
value of life estimates a reasonable esti-
mate might fall. He performed some cal-
culations to develop benchmark for the
value of life that might be reasonable,
then applied this test of reasonableness to
the estimates. Bailey concluded that the
lower range of value of life estimates, as
typified by the Thaler and Rosen (1975)
estimates, was reasonable while the higher
estimates found by, for example, R. Smith
(1974, 1976) and Viscusi (1978) were out-
side the range of reasonableness. Unfor-
tunately, Bailey's test of reasonableness
may not be entirely reasonable.
Bailey calculated a family's willingness to
pay for a given reduction in the risk of
death implied by the estimated values for
a statistical life from the different
studies. This willingness to pay was then
compared to the average income for a
family, of four to see if it represented a
"reasonable" fraction of their income, i.e.,
an expenditure that they could reasonably
afford. Bailey used a reduction in risk
from 6 deaths per thousand to 5.5 per
thousand for his calculations. Using the
lower range of estimates, Bailey esti-
mated that a representative family of four
with an income in 1978 of $18,500 would
then pay approximately 3.8 percent of
family income for this reduction in risk.
Bailey concluded that this appears to be a
reasonable expenditure.
Bailey then considered some of the higher
estimates that came from the R. Smith
(1974) and Viscusi (1978) studies. Taking
the highest value from R. Smith (1974) as
an upper bound and performing the same
calculations gave an estimate of a
willingness to pay of $10,000 for this
reduction in risk for the family. This is
about 55 percent of family income. Using
this number, Bailey concluded that these
higher value-of-life estimates are
unquestionably too high.
There are several problems with Bailey's
test of reasonableness. First and most
important, the risk reduction being con-
sidered was far beyond the range of risks
considered in the empirical studies.
Second, the multiplication of the willing-
ness to pay by the number of family mem-
bers was inappropriate. The estimates
from the wage-risk studies are for a wage
earner in the family and the willingness to
pay for a reduction in risks to a wage
earner may be higher than an equivalent
reduction for all family members due to
the more severe impacts on the family
from the loss of a wage earner.
The inapproprlateness of the risk change
used by Bailey deserves more discussion.
He used a reduction in the annual risk of
death for each household member of 5 per
10,000 (5 x IO-4). The risk levels used by
R. Smith (1974, 1976), Viscusi (I978a,
I978b) and Olson (I98J) ranged from
approximately .15 x IO"4 to 3.0 x IO"4.
Thus, the change in risk used by Bailey
exceeded the entire 'risk to individuals
working in the riskiest manufacturing in-
dustry used in their data sets. The mean
risk level in these studies ranged from 1.0
x IO-4 to 1.5 x IO-4. Reducing these risks
by 50 percent, would be a change of be-
tween .5 x IO"4 and .75 x IO"4, a reduction
that is an order of magnitude lower than
the change considered by Bailey. To pror
vide an example of how large a 5 x 10
change in an individual's annual risk of
death is,pne need only compare it to the
2.7 x IO"4 average annual risk of death in
a motor vehicle accident (car, truck or
bus). Bailey used a change in risk that is
close to twice as large as what would be
needed to entirely eliminate the risk of
death in a motor vehicle accident for all
family members. This is far from the
marginal changes in risk to which the re-
sults of the empirical studies are applic-
able.
A better test of reasonableness might con-
sider what a family would be willing -to
pay to reduce by 50 percent the annual
probability of the principal family wage
earner being killed in a job-related acci-
6-2
-------
dent. This would be approximately a
change of between .5 x 10"* and .75 x IO"4
in the risk of death. Using Bailey's adjust-
ed values for Thaler and Rosen gives an
average willingness-to-pay value of about
$22.50 in 1978 dollars. Using the high
value of life estimates from R. Smith
(1976), we find this family would be will-
ing to pay approximately $188.00 per
year. Presented in this manner, both the
lower group of value of life estimates and
the higher group of estimates seem to fall
in reasonable range.
Both economic theory and empirical evi-
dence indicate that there is no reason to
expect the value for a statistical life to be
the same in all circumstances. It may
vary depending upon the size of the
change in risk being considered as well as
with the initial risk level of the population
being affected. Given this expectation,
we will not try to say that the appropriate
value for a statistical life for environ-
mental policy purposes is a certain
amount. Rather, the focus of this discus-
sion will be whether such a value is likely
to be greater than or less than the esti-
mated values for a statistical life avail-
able to date.
In this effort, the wage-risk studies will be
emphasized since as a group they are the
most credible studies. These studies have
consistently found a significant relation-
ship between on-the-job risks and wages.
This is a relationship that makes sense
theoretically and is easy to believe
exists. The consumer market studies have
examined risk choices that are credible,
but none of the results have been vali-
dated by repeated estimation in the same
market. They are all subject to potential
errors in the assumptions that were used
to quantify the benefits of incurring the
risks, or from reductions in risk. Also,
these studies were unable to separate
willingness to pay for reductions in the
risks of death from risks of injury and
property damage. For example, the Blom-
quist (1979) study is based on the assump-
tion that the time it takes to buckle and
unbuckle a seat belt is one basis for the
individual's decision to use or not to use
seat belts. The contingent market studies
performed to date have not used state-of-
the-art techniques and the results are
potentially subject to a great deal of
error. The most carefully performed con-
tingent valuation study was Acton (1973),
but he investigated the willingness to pay
for post heart attack emergency ser-
vices. This risk, conditional on having a
heart attack, is difficult to relate to risk
levels and health outcomes of other
studies.
The wage-risk studies alone still give a
range of $400,000 to $7,000,000 in 1982
dollars per statistical life. However,
these estimates can be used to establish
bounds on the value appropriate for
environmental risks if the direction of the
expected biases can be
uncovered and are uniform in the same
direction. If, for example, a lower bound
can be established, then if the lower bound
benefits of a program exceed the esti-
mated costs, one would be reasonably con-
fident that the program was in fact
worthwh ile.
The lower range of estimates from the
wage-risk studies is from $400,000 to
$600,000. This could be considered to be a
lower bound to the value of a life for use
in policy assessment if the directions of
identified biases in the estimates are all
.downward. Unfortunately, the potential
biases that have been identified are in
both directions and may be large. Still,
we are willing to argue that, subject to
one critical uncertainty, these lower
wage-risk estimates (i.e., $400,000 to
$600,000) for the value of a life are likely
to provide a lower bound to the value of
preventing the life threatening risks that
need to be considered in environmental
policy assessment.
The key potential sources of biases that
have been identified in these wage-risk
studies are:
I. Whether the workers accurately
perceive the risks of different
occupations.
2. Whether the workers in the
occupations examined are more or less
risk averse than the general public.
3. Whether characteristics of
occupational risks, such as voluntary
versus involuntary or delayed versus
immediate as discussed in Litai (1980) and
6-3
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Starr (1969), make the wage-risk
estimates different from what the
estimates for environmental risks would
be.
4. Whether the wage-risk premium
captures only the risk of mortality rather
than risks of both nonfatal and fatal inju-
ries.
5. Whether potentially important
explanatory variables have been omitted
from the estimated equation and,
therefore, bias the results significantly.
Of these five potential sources of biases,
the first three are more likely, in our
opinion, to result in a downward bias on
the value of life estimates. The first
source, workers' perceptions of risk, can in
theory bias the estimated risk valuations
up or down if worker perceptions show a
systematic bias. There is, however, some
evidence that workers are at least able to
roughly rank jobs by their riskiness.* Still,
there is likely to be considerable error in
individuals' judgements of the actual
amount of risk associated with different
industries and occupations. This will have
two effects on the results of wage-risk
studies: one, the error-in-variables prob-
lem will reduce the significance of the
coefficients on the risk variable; and two,
the workers who tend to underestimate
the risks of a particular occupation will
gravitate to that job because they will be
willing to accept a lower wage-risk premi-
um.** This second effect will tend to
produce a downward bias in the estimated
value for a statistical life.
The second identified source of bias should
clearly have a downward effect on the
wage-risk premium. Most of the hedonic
wage-risk studies that produced estimates
in this low range used a data set com-
prised of the higher-risk occupations. It is
generally hypothesized that less risk
averse individuals will tend to take these
jobs. This has been offered as one expla-
nation for the different estimates of
wage-risk premiums that have come from
different data sets. If there is a bias, it
would seem to be downward.
The third source of bias concerns different
risk characteristics. Many environmental
risks have different characteristics than
those related to accidents on the job. In
particular, there is some speculative evi-
dence that the willingness to pay to avoid
involuntary risks, i.e., risks over which the
individual has little control, are greater
than for voluntary risks. Although the
characterization of risks as voluntary or
involuntary is often not clear, it would
seem that the decision to take a job would
be more voluntary than most environ-
mental risks.
The fourth and fifth identified sources of
biases pose a problem because they will
tend to. result in an upward bias in the
estimated value of a life. The fact that
the risk premium may be capturing the
compensation for risks of nonfatal as well
as fatal accidents has a clear upward bias
on the estimate; however, the extent of
this bias is not clear. R. Smith (1974,
1976) was unable to find a statistically
significant risk premium associated with
nonfatal injuries indicating that workers'
compensation may be adequate to com-
pensate for the potential loss and no wage
premium is required. Olson (1981), and
Viscusi (I978b) were able to isolate the
effects of nonfatal risks on the wage pre-
mium. In these cases, the estimated risk
premium for fatal injuries was still in ex-
cess of $600,000. These results indicate
that this potential upward bias, if it does
exist, will probably not be large.
The fifth potential source of bias is the
most significant problem. The willing-
ness-to-pay estimates for changes in the
risk of fatal accidents obtained from the
hedonic wage-risk studies probably cap-
ture more than just the pure valuation of
risk. High levels of risk are closely asso-
ciated with a number of unpleasant work-
ing conditions, but in most cases the only
measure of job unpleasantness used in the
study was the risk of accident. Therefore,
the hedonic wage-risk estimates probably
reflect the wage premium required by that
closely related package of unpleasant job
characteristics, not just risk. This would
produce an upward bias in the estimates.
* Viscusi (1978a) presented data on whether the worker considered his job dangerous.
** This was discussed in Chapter 2.0.
6-4
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bur conclusion is that, depending upon
how one views the potential severity of
the omitted variable problem in the hedo-
nic wage-risk studies, the lower range of
the value-of-life estimates from these
studies probably reflects a lower bound to
the value of fatal risks associated with
environmental problems. Further analysis
of the data sets and techniques used in
these studies performed to date might
yield further refinements to this estimate.
6.2 Suggestions for Future Research
This review has indicated that there has
been no ambitious research program to
quantify the willingness to pay for the re-
duction or prevention of environmental
risks. Many important questions remain.
One overriding issue is whether willingness
to pay based on the revealed preferences
of consumers or workers is an appropriate
basis for valuing risks for use in policy
assessment. Willingness to pay is the
appropriate measure if it is based on accu-
rate perceptions of risks by individuals and
revealed by consistent behavior in actual
markets or in response to hypothetical
markets. However, the observations on
human'behavior that are used to generate
willingness-to-pay estimates for reducing
risks are subject to many, potential emo-
tional and informational biases. If indivi-
duals act irrationally with respect to cer-
tain risks, then should environmental
policy follow the same irrational prin-
ciples?
The discrepancy between the avoidance of
voluntary and involuntary risks found by
Starr (1969) and Litai (1980) is an example
of where it may not be desirable to hove
policy follow revealed preferences. Al-
though both studies suffer from severe
data limitations and theoretic shortcom-
ings, they have offered evidence that in-
dividuals value voluntary and involuntary
risks differently. If a policy is adopted by
the government that allocates more
money for reducing "involuntary" risks
than "voluntary" risks,* then more fatal-
ities will occur than if this characteristic
did not influence the allocation of rev-
enues. Before such a policy would be
adopted, it would be important to deter-
mine whether the government is simply
adopting the irrational behavior of indivi-
duals or if there really are counter-veiling
benefits such as reduced psychological
stress that make involuntary risks a bigger
burden to society.
The conclusion that results from the above
argument is that future research should
try to better incorporate psychological
findings within willingness-to-pay
studies. Before willingness-to-pay esti-
mates based on revealed preference are
used in policy studies, a better
understanding of the reasons for choices
made by individuals to reduce or incur
risks is needed. The work on probability
judgements by Lichtenstein et al. (1978)
and the work on cognitive dissonance by
Akerlof and Dickens (1982) would be use-
ful starting points for this type of analy-
sis. A topic related to this is whether or
not people value risks with different
characteristics differently and, if they do,
why? The most promising approach for
obtaining some of this information seems
to be a melding of the contingent valua-
tion methods used by economists with the
surveys used by psychologists in their re-
search on risk perception and decision
making. The contingent valuation studies
performed to date have not, on the whole,
been well implemented. Contingent mar-
ket approaches provide a great deal of
flexibility to pursue valuation questions
specific to environmental policy decisions
and to probe people's attitudes and pref-
erences regarding the acceptability of
certain risks.
Another area of research that could be
fruitful is the use of utility functions as a
means of organizing the valuation problem
for a specific environmental risk. The
basic approach is illustrated by Keeney
(1980) and Bodily (1980). First a function
is devised that incorporates all of the fac-
tors that are felt to influence the valua-
tion of the risk. The function contains
risk related variables that can be esti-
mated such as the number of fatalities,
* Again, recognize that it is hard to clearly differentiate between voluntary and
involuntary risks.
6-5
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the number of fatalities that occur at one
event (to account for disasters, see Sec-
tion 5.4.2), and the number and types of
nonfatal effects. These variables are
incorporated in a function where the con-
stants (i.e., coefficients and exponents)
are unspecified. The second step is to es-
timate values for these constants through
a scaling process. These estimates could
be obtained through use of surveys similar
to those used in contingent market
studies. As a result, decision theory ap-
proaches are actually very similar to the
contingent market surveys used by econo-
mists. There is no reason why the con-
stant terms in a decision theory frame-
work could not be scaled in terms of dol-
lars and incorporated in a conventional
economic benefit-cost framework. A trial
application of this technique could prove
useful.
To summarize the other research recom-
mendations, they will be presented by ap-
proach, i.e., hedonic wage-risk, consumer
market and contingent market.
Wage-Risk Studies
The goal of many of the wage-risk studies
was not to provide value of life estimates
usable in environmental policy decisions,
but was instead to test hypotheses regard-
ing the operation of the labor market.
Even though these studies are probably the
most credible studies that have been done
for valuing risks, it is not clear how useful
these estimates are to the EPA. The
types of risks that have been considered,
namely accidents on the job, are not for
the most part the kinds of risks that are of
interest to the EPA. Transferability is
difficult because we know so little about
how differences in risks influence the
valuation. Another problem with transfer-
ring results from wage-risk studies is that
they consider only one population group.
Some of the studies have considered a
wide range of occupations and both men
and women, but most considered only male
blue-collar workers- In either case, those
who are not in the labor force are not
represented and how risk valuations may
vary between labor force members and
those who are not in the labor force, or
those who are sensitive to specific en-
vironmental risks, is unknown.
Still, wage-risk studies may provide useful
information. As was argued earlier, they
might be useful in estimating a lower
bound for many environmental risks. The
principal problem with using the current
wage-risk studies as a lower bound bench-
mark is the potential omitted variable bias
resulting from the exclusion of job charac-
teristics other than risk. Other unpleasant
job characteristics, such as noise, dirt and
uncomfortable temperatures, may be high-
ly correlated with job risks.* A hedonic
wage-risk study incorporating these addi-
tional variables could be useful in helping
EPA determine a lower bound for the
value of reducing or preventing environ-
mental risks. Also, if risk conversion fac-
tors that could account for different risk
characteristics and different populations
could be determined from other studies,
the results of the hedonic wage-risk stud-
ies could be transferred and used to value
other risks.
Another problem area in wage-risk studies
that could be corrected is that in most
cases a functional form has been used that
constrains the market equilibrium hedonic
wage-risk function to be linear or con-
vex. The theory indicates that a concave
function is entirely possible and could be
expected to occur if less risk averse work-
ers are found in the riskier jobs. A more
flexible functional form should be used in
future wage-risk studies to allow the func-
tion to be either concave or convex.
Consumer Market Studies
The consumer market studies have a sound
conceptual basis in that they have
examined actual choices that people make
with respect to risks. Data limitations
have resulted in simplifying assumptions in
the studies that examined risks of auto-
mobile accidents, which open the results
* Since the jobs with the highest risks are those associated with moving materials (i.e.,
assembly, loading and machining), it is likely that other unpleasant job conditions are
correlated with job risks.
6-6
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to a great deal of question. Also, the
study that examined risks of residential
fires was not able to use correct consumer
surplus measures. The primary difficulty
in consumer market approaches is that in
cases where a risk is incurred in order to
obtain a benefit (as in the case of automo-
bile transportation) the benefit needs to
be quantified to determine how much the
consumer is having to be compensated in
order to tolerate that risk. Questions also
remain as to whether observed choices are
based on adequate consumer information
and on reasonably accurate perceptions of
risks.
The usefulness of future consumer market
studies for addressing EPA policy
questions depends on whether relevant
consumer choices can be identified and
whether data are available to adequately
analyze these choices. A point that should
be emphasized is that consumer market
studies should not stand on their own.
They should be augmented with surveys to
validate their assumptions. For example,
there are several key assumptions used by
Blomquist (1979) including the assumption
that the disutility of wearing a seat belt is
represented in part by the time cost of
fastening it. Also, in the case of Ghosh et
a I. (1975), the key assumption is that the
benefits of driving faster can be measured
by the savings in driving time. These
assumptions can be validated outside the
models by using surveys similar to those
discussed in Slavic et al. (1977). Too often
these critical underlying assumptions re-
main untested and the policy relevance of
the results unknown.
Contingent Market Studies
The contingent market studies performed
to date have not used state-of-the-art
techniques and the results are subject to a
great deal of error. These studies do not
demonstrate or adequately test the full
potential of this approach for estimating
the value of reducing or preventing risks.
The most important challenge facing con-
tingent market studies is presentation of
the risk choices to survey respondents.
More needs to be learned about people's
attitudes and behaviors with respect to
personal and social risks in order to design
survey instruments that communicate the
risks meaningfully and adequately elicit
the desired information. Due to the pauc-
ity of market data concerning risk
choices, contingent market techniques
may be the more promising, and in some
cases, the only available approach for ad-
dressing a wide range of issues.
Three general areas of improvement and
development need to be pursued in future
contingent market studies. These are
attention to underlying economic theory,
selection of types of risks to be examined,
and development of implementation
methodology.
Contingent market approaches are based
on the economic theory of consumer be-
havior from which is derived certain ex-
pectations about the behavior of rational,
utility maximizing individuals. Future
studies need to pay attention to the
expectations that theory provides about
preferences toward safety in order to pro-
vide evidence concerning the validity of
these expectations. The work of Tversky
and Kahneman (1981) provides some alter-
native predictions of preferences with
respect to risk taking that could be con-
sidered. Two specific areas that need at-
tention are differences in marginal WTP
for safety across individuals and the
underlying causes of zero bids and refusals
to respond to WTP or WTA survey ques-
tions. It could be expected that people
who are at higher risk levels would be
willing to pay more for a given reduction
in risk than people at lower risk levels.
This needs to be carefully tested. It is
also expected that differences in income
and other socioeconomic characteristics
will influence WTP for safety. This needs
to be routinely examined in any contingent
market application. Changes in marginal
WTP for safety as safety increases or de-
creases also need to be examined in order
to determine if the demand for safety be-
haves like more ordinary market goods.
Refusal to respond to the questions or
zero or very large bids may signal a rejec-
tion of the premises of the questions
themselves. These kinds of responses need
to be probed.
The best contingent market results, in
terms of consistency between actual be-
havior and what an individual predicts his
behavior would be, have been obtained
when the hypothetical quest ions relate to
6-7
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behavior that is familiar and frequently
experienced by the individuals. Risks con-
cerning transportation, water quality,
sewage treatment, hazardous wastes and
availability of emergency services are
examples of risks that might be effective-
ly examined. What is most important is
that the topic be connected to decisions
that people can imagine making.
Two areas that may be fruitful for future
contingent market approaches are long
latency risks of death, such as cancer, and
risks of morbidity. . The data constraints
that make examination of long-term
health effects so difficult in market
studies do not constrain contingent market
approaches. The link between an exposure
and a risk could be hypothesized without
having to be proved. Morbidity might be a
very good topic for future contingent
market studies because it may not face
the emotional barriers that the idea of
trading money for lives provokes when
respondents are asked to consider risks of
fatalities.
Many implementation issues need to be
addressed in order to develop credible
contingent market applications for valuing
changes in risks. One of the most impor-
tant of these is the presentation of the
change in risks to be values. Numerical
descriptions are probably not good
enough. How many people actually know
what the numerical risks are for the activ-
ities in which they engage? Other kinds of
presentations need to be developed that
link the risk levels to activities with which
the respondent is familiar. All of the bias
problems that have been found in previous
contingent market applications need to be
considered. Differences in the presenta-
tion of risk in the bidding or valuation
procedure, in the hypothetical payment
mechanism, in the order of the questions,
and in other information provided to the
respondent need to be systematically
examined to see if responses are being
biased by the survey instrument itself.
Another possibility for contingent market
approaches would be to explore indirect
valuation procedures such as contingent
ranked attributes. In these procedures
respondents are asked to rank alternatives
without having to put a dollar value
directly on risks. Their rankings reveal
implicit valuations. Other possibilities
would be to ask about willingness to spend
time, rather than money, in order to de-
crease risks.
Other Research Topics
Some evidence has been provided by Litai
(1980) and Starr (1969) that different risk
types are valued differently. If the ef-
fects of .these differences in risk types on
willingness to pay were known, then the
results from a study valuing one type of
risk could be used to value other types of
risks in environmental benefit studies.
For example, at present it is not clear
whether wage-risk studies, which reflect
the most extensive work done to date on
risk-dollar tradeoffs, provide any useful
information for environmental policy
questions due to the type of risks that
were evaluated. Determining the trans-
ferability of risk valuation estimates could
greatly improve the usefulness of past es-
timates in policy studies.
The work by Starr (1969) and Litai (1980)
provides some initial ideas about how the
nature and circumstances of the risk may
affect willingness to pay. The Litai (I960)
and Starr (1969) studies did not, however,
adequately consider the benefits associ-
ated with the risks examined. As dis-
cussed in Section 5.3, it may be possible to
use their data sets, or other similar data,
along with better estimates of the bene-
fits of. incurring the different risks to ob-
tain risk converse ion factors based on
benefit-cost ratios for risks with different
characteristics. These could then be used
to calculate meaningful risk conversion
factors based on the Litai (1980) ap-
proach. For example, Starr's use of ex-
penditures on cigarette smoking as the
measure of the benefits of cigarette
smoking greatly understate actual benefits
as measured by consumer surplus. The
result is that the benefit-cost ratios he
uses to compare voluntary and involuntary
risks may be badly biased. In most cases
the biases in the benefits estimates seem
to create an artificially large difference
between voluntary and involuntary risks.
The results of an approach that properly
account for the benefits would be very
informative. Whether the data are avail-
able to estimate the benefits of these ac-
tivities with any accuracy is, however,
somewhat uncertain.
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