The Heterogeneity of the
Value of Statistical Life
W. Kip Viscusi
University Distinguished Professor
Vanderbilt University
kip.viscusi@vanderbilt.edu
American Society of Health Economists
June 20, 2010
Value of Statistical Life (VSL)

Academic Literature
 Definition
 Labor market studies
 Variation with risk levels
 Segmented labor markets
 Age
 Income
.
VSL Outline Cont’d
Policy Arena
 Adoption of the VSL methodology
 Age controversy
 Income controversies
 The Future of VSL

.
Calculating the Value
of Statistical Life
Suppose 1/10,000 risk to 10,000 people so
1 expected death
 Assume each would pay $800 to eliminate
the risk
 VSL =
10,000 people × $800/person = $8,000,000

.
Dominant Approach:
Wage-Risk Tradeoffs

Adam Smith’s theory of compensating
wage differentials
Controlling for other aspects of the job, how
much pay for extra risk?
 Hedonic wage model as workers pick
optimal (risk, wage) combination from
market offer curve.
.

The Average Value of Statistical Life
Median U.S. value is $7 million ($2000) or
$8.7 million ($2009) based on meta analysis
in Viscusi and Aldy (2003)
 Require $870 to face risk of 1/10,000
 Foreign countries have VSL estimates in
expected range, e.g., India is lower
.

Heterogeneity Based on Risk Level

Workers who choose higher risk levels are
on flatter part of market offer curve.
Heterogeneity Based on
Risk Level, cont’d
Early studies found workers with fatality
risk of 1/10,000 (Viscusi 1978, 1979) had
VSL 5 times greater than study of workers
facing risk of 1/1,000
(Thaler and Rosen 1975).
 Differences arise from legitimate
heterogeneity in VSL tradeoffs not failure
of economists to find “the value of life
number.”
.

Segmented Labor Markets
Workers may face different labor market
offer curves
 Settle into separate labor market equilibria
(Viscusi and Hersch 2001)
 Test: If workers face greater risk levels but
receive less total wage compensation for
risk, then cannot be on same market offer
curve.
.

Workers facing different offer curves settle into separate equilibria.
Examples of Separate Labor Market
Offer Curves
Smokers and Nonsmokers
(Viscusi and Hersch 2001)
 Black-white VSL differences
(Viscusi 2003)
 Mexican immigrants versus other
immigrants or native Americans
(Hersch and Viscusi 2010)

.
VSL and Immigrant Status
Fatality Risk*
VSL
Native U.S.
4.35
7.95
Mexican immigrants
5.97
Not significant
All immigrants
4.50
9.35
Mexican immigrants
5.70
Not significant
Mexican immigrants who
speak English
5.70
3.44
Estimates Bases on the CPS
Estimates Based on the NIS
*Fatality rate by industry-immigrant status-age. Risk is annual fatality
rate per 100,000 workers.
Heterogeneity Based on Age
VSL will vary with age because length of
remaining life varies
 Imperfect capital markets
 Life-cycle effects
.

Age and the Labor Market
Series of studies over two decades
 Most recent use age-specific risk data
 Result is inverted-U shape pattern
 Flatter if control for consumption over the
life cycle or cohort effects
 VSL tracks lifetime income and consumption
(Kniesner, Viscusi, and Ziliak 2006)
.

Cohort-Adjusted and Cross-Section
Value of Statistical Life, 1993-2000
VSL (millions 2000$)
10
8
6
Cohort-Adjusted VSL
Cross-Section VSL
4
2
0
18
22
26
30
34
38
42
46
50
54
58
62
What Do We Know About Age-VSL?
VSL does not peak at birth
 VSL does not plummet as we age
 VSL for workers around age 60 is higher
than for workers age 20
.

Value per Year of Life (VSLY)
Not a constant, as assumed and estimated in
Moore and Viscusi (1988), which
developed and estimated VSLY formula
and rate of discount
 Advent of better data makes possible more
refined risk measures. Viscusi-Aldy (2007)
and Aldy-Viscusi (2008) use industry by
age fatality rate.
 VSLY not constant and not steadily
declining with age even though health may
decline
 VSLY rises fairly steadily
.

Value of a Statistical Life-Year
Based on Cohort-Adjusted and Cross-Section
Value of Statistical Life, 1993-2000
VSLY (2000$)
$450,000
$400,000
$350,000
$300,000
$250,000
Cohort-Adjusted VSLY
Cross-Section VSLY
$200,000
$150,000
$100,000
$50,000
$0
18
22
26
30
34
38
42
46
50
54
58
62
Applications of VSL and VSLY to
Private Costs of Cigarettes
Viscusi and Hersch (2008) estimate VSL and
VSLY specific to smoking status
 Calculate the private mortality costs per pack
of cigarettes
 At 3% interest rate, cost per pack is on order
of $200 for men and $100 for women
 At smokers’ estimated labor market discount
for years of life of 14% (Scharff and Viscusi,
2010), cost per pack drops to $24 for men
and $6 for women
.

Income Effects
Proportional for present value of lost
earnings
 Willingness to pay increases with income
 Estimation strategies: meta analyses across
studies and quantile regression estimates
within sample
.

Income Elasticity Estimates
Meta analysis by Viscusi and Aldy (2003) –
elasticity in 0.51 to 0.61 range for
10 different specifications.
 Within sample quantile estimates by
Kniesner, Viscusi, and Ziliak (2010) imply
mean elasticity across quantiles of 1.44.
 Meta analyses may suppress some income
elasticity, but clearly elasticity is positive. .

VSL in the Policy Arena
Adoption of the VSL approach
 Age variations
 Income variations
 Other controversies

.
Valuing Lives for Policy
1982 hazard communication debate
 Life is too sacred to value so OSHA
calculated “cost of death” as present value
of lost earnings
 OMB: Benefits did not exceed costs so
rejected regulatory proposal
 OSHA appealed to V-P Bush
 I analyzed merits of proposal using proper
value of statistical life (VSL) estimates –
10 times the present value of lost earnings .

Using VSL Saves Lives
My 1982 estimates were just over
$3 million
 Benefits now exceeded costs, and regulation
was issued
 Historical context is that VSL was more
supportive of risk regulation than making
lives “priceless”
 VSL now under attack for pricing lives
.

The “Senior Discount” Controversy
EPA used a senior discount of 37% in
analysis of Clear Skies initiative in 2002.
 Political firestorm

Seniors on sale
37% off

EPA backed off approach. Proposed Senate
legislation banning all demographic
adjustments.
.
International “Senior Discounts”
Canada used a VSL 25% lower for those
over 65 compared to those under 65.
 In 2001, European Commission
recommended VSL that declines with age.

.
Does Fairness Provide Any Insight?
Is same value per statistical life equitable?
versus
 Is same value per statistical life year
equitable?
 Return to first principles—willingness to
pay
.

Should Income Levels Matter?
VSL increases with income
 Provide policies poor don’t value?
 Airline safety – should we regulate it more
stringently than highway safety?
 Planes versus guardrails
 DOT adopted Viscusi-Aldy (2003)
elasticity estimate of 0.55.
 Rationale is stronger if beneficiaries of
safety regulation pay for higher costs of
safety.
.

Income at Point of Time or Over Time
DOT’s proposed adjustment is very bold
policy initiative to account for within
population differences.
 Income changes over time for future
generations receive greater support.
 Efficient, but redistributes income from
poorer current generation to richer future
generation.
.

Income at Point of Time or
Over Time, cont’d

Reference dependence effect. Proposed
Senate legislation in 2008 to require income
adjustment for VSL and require that only
increases in VSL be permitted.
.
The 2008 Devaluation of Life
Controversy
Based on conflicting results of 2 meta
analyses (Viscusi and Aldy vs.
Mrozek and Taylor), in 2008.
EPA Air Office lowered the VSL from
$8 million to $7 million
 Economic puzzle since income levels have
risen. Why did studies differ?
 Political firestorm – Bush conspiracy?
.

The 2008 Devaluation of Life
Controversy, cont’d
Proposed Senate legislation in Fall 2008
requiring that agencies must only raise VSL
over time.
 But EPA Air Office number still relatively
high.
.

Other Sources of Variation in
Valuing Life
How people die matters
 Victims of terrorism versus natural disasters
differ by factor of 2 in society’s valuation of
reducing their risks (Viscusi 2009)
 Irresponsible behavior by people who put
themselves at risk reduces their societal
values, e.g., railway trespassers and suicides
(Covey, Robinson, Jones-Lee, and Loomes
2010).
.

Conclusion
VSL has been an integral part of benefits
assessment for a quarter century
 Misunderstanding of the “economic” value
of life may stimulate much of the continued
controversy
 Opposition to VSL is often misguided
 Improved fatality rate data and survey data
have greatly expanded questions that
researchers can address
.

Conclusion, cont’d
Estimates of heterogeneity and sources of
heterogeneity are becoming more refined
 More refined VSL estimates present new
policy challenges
 Treating some risk reductions as “priceless”
may make them “worthless”
.

Selected References






Aldy, Joseph E., and W. Kip Viscusi. 2007. “Age Differences in the
Value of Statistical Life: Revealed Preference Evidence.” Review of
Environmental Economics and Policy, 1(2): 241-260.
Aldy, Joseph E., and W. Kip Viscusi. 2008. “Adjusting the Value of a
Statistical Life for Age and Cohort Effects.” Review of Economics and
Statistics, 90(3): 573-581.
Hersch, Joni, and W. Kip Viscusi. 2010. “Immigrant Status and the
Value of Statistical Life.” Journal of Human Resources.
Kniesner, Thomas J., W. Kip Viscusi, and James P. Ziliak. 2010. “Policy
Relevant Heterogeneity in the Value of Statistical Life: New Evidence
from Panel Data Quantile Regressions.”Journal of Risk and Uncertainty,
40(1): 15-31.
Scharff, Robert L., and W. Kip Viscusi. 2010. “Heterogeneous Rates of
Time Preference and the Decision to Smoke.” Economic Inquiry.
Viscusi, W. Kip. 1979. Employment Hazards: An Investigation of Market
Performance, Harvard Economic Studies No. 148. Cambridge: Harvard
University Press.
Selected References, cont’d







Viscusi, W. Kip. 2003. “Racial Differences in Labor Market Values of
a Statistical Life.” Journal of Risk and Uncertainty, 27(3): 239-256.
Viscusi, W. Kip. 2009. “The Devaluation of Life.” Regulation
and Governance, 3(2): 103-127.
Viscusi, W. Kip. 2009. “Valuing Risks of Death from Terrorism and
Natural Disasters.” Journal of Risk and Uncertainty, 38(3): 191-213.
Viscusi, W. Kip, and Joseph E. Aldy. 2003. “The Value of a Statistical
Life: A Critical Review of Market Estimates throughout the World.”
Journal of Risk and Uncertainty, 27(1): 5-76.
Viscusi, W. Kip, and Joseph E. Aldy. 2007. “Labor Market Estimates
of the Senior Discount for the Value of Statistical Life.” Journal of
Environmental Economics and Management, 53(3): 377-392.
Viscusi, W. Kip, and Joni Hersch. 2001. “Cigarette Smokers as Job
Risk Takers.” Review of Economics and Statistics, 83(2): 269-280.
Viscusi, W. Kip, and Joni Hersch. 2008. “The Mortality Cost to
Smokers.” Journal of Health Economics, 27(4): 943-958.