J. Benefit Cost Anal. 2017; 8(2):226–250
doi:10.1017/bca.2017.12
c Society for Benefit-Cost Analysis, 2017. This is an Open Access article, distributed under the terms
of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which
permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is
properly cited.
W. Kip Viscusi* and Clayton J. Masterman
Income Elasticities and Global Values of a
Statistical Life
Abstract: Countries throughout the world use estimates of the value of a statisti-
cal life (VSL) to monetize fatality risks in benefit-cost analyses. However, the vast
majority of countries lack reliable revealed preference or stated preference estimates of the VSL. This article proposes that the best way to calculate a populationaverage VSL for countries with insufficient or unreliable data is to transfer a base
VSL from the United States calculated using labor market estimates from Census of Fatal Occupational Injuries data, coupled with adjustments for differences
in income between the United States and the country of interest. This approach
requires estimation of two critical inputs: a base U.S. VSL and the income elasticity of the VSL. Drawing upon previous meta-analyses that include adjustments
for publication selection biases, we adopt a base VSL of $9.6 million. We utilize
a sample of 953 VSL estimates from 68 labor market studies of the VSL covering fourteen lower-middle income to high income nations. We estimate the income
elasticity of the VSL within the United States to be from 0.5 to 0.7 and to be just
above 1.0 for non-U.S. countries. Quantile regression reveals that much of the disparity in income elasticities is attributable to income differences between the United
States and other countries, as the income elasticity increases for lower income populations. Using income classifications from the World Bank, we calculate average VSLs in lower income, lower-middle income, upper-middle income, and upper
income countries to be $107,000, $420,000, $1.2 million, and $6.4 million, respectively. We also present VSL estimates for all 189 countries for which World Bank
income data are available, yielding a VSL range from $45,000 to $18.3 million.
Keywords: value of a statistical life; income elasticity; meta-analysis; publication
selection bias.
JEL classifications: I18; I12; K32; J17; J31.
*Corresponding author: W. Kip Viscusi, University Distinguished Professor of Law,
Economics, and Management, Vanderbilt Law School, 131 21st Ave. South, Nashville, TN
37203, USA, e-mail: kip.viscusi@vanderbilt.edu
Clayton J. Masterman: Vanderbilt Law School, Ph.D. Program in Law and Economics,
USA
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Income Elasticities and Global Values of a Statistical Life
227
1 Introduction
The value of a statistical life (VSL) is often the critical policy parameter in benefitcost analyses of health and safety risk regulations and other policies.1 Despite the
importance of the VSL in identifying efficient regulatory policies, many nations
lack accurate VSL measures. Economists have devoted substantial attention to calculating the VSL in the United States and other developed nations, but there is
a relative paucity of studies measuring the VSL in poorer nations. Labor market
revealed preference studies of the VSL are virtually nonexistent outside of higher
income countries, and reliable stated preference estimates are often unavailable as
well. The countries that lack these VSL estimates cannot simply adopt United States
or other higher income nations’ numbers because there is substantial heterogeneity
among countries across dimensions that likely affects the VSL. Income levels, life
expectancies, and social norms regarding risk and death may influence a particular nation’s VSL and thus make it inappropriate to simply transfer the VSL across
countries (Hammitt, 2017).
Most countries lack either reliable stated preference studies or labor market
studies for setting a population-average VSL. A VSL could be calculated for every
country by fielding stated preference studies that ask citizens for their preferences
concerning money-risk tradeoffs (Hoffmann, Krupnick & Qin, 2017). Stated preference studies estimating the VSL have become increasingly common in recent
years, in part because such studies can estimate a VSL from any form of fatality risk that the researcher wishes to investigate (Cropper, Hammitt & Robinson,
2011). However, policymakers generally prefer revealed preference methods for
monetizing regulatory benefits and costs because they are based on actual rather
than hypothetical transactions.2
Labor market hedonic wage studies that measure the compensating differentials
for workplace fatality risks provide an alternative to stated preference studies, but
most countries lack sufficiently detailed workplace fatality data and employment
datasets. VSL estimates that utilize insufficiently detailed fatality data will exhibit
attenuation bias toward zero from measurement error. Publication selection bias,
which occurs whenever journals and researchers are systematically less willing to
report or publish estimates falling outside of an accepted range, is greater when
available data suffer from significant measurement error. As a result, in the absence
1 The VSL is the monetary value of small changes in mortality risks, scaled up to reflect the value
associated with one expected fatality in a large population.
2 For example, the U.S. Office of Management and Budget (2003) has advised regulatory agencies
to utilize revealed preference data over stated preference data when both are available in a particular
context and of similar quality.
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228
W. Kip Viscusi and Clayton J. Masterman
of detailed and accurate data on workplace fatalities, VSL estimates will suffer from
attenuation and publication selection biases (Viscusi, 2015). These biases are even
more prevalent in non-U.S. labor market studies than U.S. studies (Viscusi & Masterman, 2017). While some of the bias in non-U.S. VSL estimates is attributable
to data deficiencies, much of the rampant publication selection bias in international
estimates exists because non-U.S. researchers anchor on U.S. estimates of the VSL
(Viscusi & Masterman, 2017).3 To the extent that stated preference studies are also
subject to biases from the use of U.S. evidence as an anchor for what values are reasonable and merit publication, these estimates likewise may suffer from publication
selection effects. More research is needed to determine the extent to which stated
preference VSL studies also suffer from publication selection biases. Fortunately,
U.S. VSL estimates that utilize the Census of Fatal Occupational Injuries (CFOI)
data are not subject to many of the biases that plague VSL estimates using other
data, both in the United States and internationally (Viscusi, 2015, 2017; Viscusi &
Masterman, 2017).
This article proposes that countries adopt VSL estimates for public policy by
adjusting a base U.S. VSL using our estimate of the international income elasticity of the VSL and the relative incomes of the United States and the country of
interest. This benefit transfer method of coupling income elasticities with a baseline VSL is used in Viscusi (1993) to derive VSL estimates for airline safety based
on labor market VSL estimates for a population that has lower income than airline passengers. Hammitt and Robinson (2011) expand on this technique, including
its potential applicability in international studies. This approach provides policymakers with a VSL based on the best available empirical evidence while preserving the flexibility to choose their preferred methodology for calculating the critical input parameters: the base VSL, the income elasticity of the VSL, and the
measure of income for the United States and the country of interest. The flexibility to choose among various base U.S. VSLs, measures of income, and income
elasticities may be important; regulators and researchers often fail to agree on the
optimal way to infer the policy-relevant VSL value from the economic literature.4
We use this benefit transfer method to calculate VSL estimates for 189 different
countries.
3 Throughout this article, we use “international” to refer to estimates of the VSL in countries other than
the United States.
4 For example, even within the United States, different agencies differ on the appropriate way to extrapolate a VSL from the literature. The U.S. Department of Transportation (2016) uses an average of the
single best estimate from studies utilizing the CFOI data series. The U.S. Environmental Protection
Agency (2016) uses an average value from both revealed preference and stated preference studies.
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Income Elasticities and Global Values of a Statistical Life
229
Section 2 presents a brief summary of our preferred VSL and existing estimates
of the income elasticity of the VSL in the literature. The preferred base VSL of $9.6
million for our calculations is the estimate from U.S. CFOI studies after controlling
for publication selection bias drawn from Viscusi (2015) and Viscusi and Masterman (2017).5 Given the absence of substantial publication selection biases for VSL
studies using the CFOI data, others may prefer either the mean or median CFOI
estimates without bias adjustments, and we present those as well.
While there have been numerous estimates of the income elasticity of the VSL,
there are no estimates based on labor market data that distinguish the elasticities for
the United States and non-U.S. countries. Section 3 presents our dataset of 953 labor
market VSL estimates from 68 studies to estimate the income elasticity of the VSL
for U.S. and non-U.S. VSLs. Section 4 presents our estimates of the income elasticity. In Section 4.1, we compare the elasticities for U.S. studies and non-U.S. studies, finding substantial evidence that the income elasticity of the VSL for the United
States is smaller than the elasticity in non-U.S. countries. Section 4.2 examines the
income elasticity of the VSL throughout the VSL distribution, demonstrating that
the elasticity is larger for small VSLs and vice versa, thus providing the empirical rationale for why the international income elasticity of the VSL exceeds the
domestic value and suggesting that the income elasticity is larger at lower income
levels.
Section 5 presents VSL estimates for countries throughout the world using our
benefit transfer approach. We present two sets of transferred VSLs. The first set uses
2015 World Bank gross national income (GNI) per capita and income level classifications to demonstrate VSLs for low, lower-middle, upper-middle, and upper
income economies. The World Bank GNI per capita measure of income is convenient because it is the largest collection of national income measures available,
and the World Bank’s income classification levels are widely used as meaningful reference points. Our preferred international income elasticity of 1.0 results in
a transferred VSL of $107,000 for low income economies, $420,000 for lowermiddle income economies, $1.2 million for upper-middle income economies, and
$6.4 million for upper income economies. The second set of estimates applies our
methodology to all 189 countries for which 2015 GNI per capita numbers are available. The transferred VSLs vary greatly across countries, as do the national incomes
they are based upon. The VSLs range from a low of $45,000 for Burundi to a high
value of $18.3 million for Bermuda.
5 Unless otherwise noted, all dollar figures in this article are expressed in 2015 dollars.
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W. Kip Viscusi and Clayton J. Masterman
2 Reviewing base VSLs and the income elasticity
literature
2.1 Choosing a base VSL
Our calculations utilize a base U.S. VSL of $9.6 million. Viscusi (2015) and Viscusi
and Masterman (2017) derived this value from a meta-analysis of VSL estimates
utilizing CFOI estimates that accounted for publication selection bias. This estimate
is similar to the $9.4 million value used by the U.S. Department of Transportation
(2016), the $9.7 million ($2013) value used by the U.S. Environmental Protection
Agency (2016), and the $9.6 million ($2014) value used by the U.S. Department
of Health and Human Services (2016). Our point estimate corrected for estimated
publication selection effects, though the estimated biases were not statistically significant in the 2017 study. Nonetheless, if policymakers prefer other VSLs to our
$9.6 million value, the transfer method accommodates alternative values. If base
income is held constant, different base VSLs result in a proportional change in
the transferred VSL. The unadjusted median and mean VSL estimates based on
the CFOI data are $13.1 million and $11.1 million, while the median and mean
using only the best estimates from these studies using the CFOI data are $10.2 million and $11.8 million.6 Our baseline VSL estimate is slightly below the median
of all labor market VSL estimates in our sample, $9.7 million, and $2.4 million
smaller than the full mean of the sample at $12.0 million.7 Our baseline estimate
is also lower than the full sample best set median and mean of $10.1 million and
$12.2 million. The VSL estimates using fatality rates from the CFOI are superior
to all other U.S. labor market estimates. Because the CFOI is a complete census of
occupational fatalities rather than a survey subject to voluntary responses, the data
are subject to significantly less measurement error than other sources. The resulting
VSL estimates exhibit less attenuation and publication selection biases.
The U.S. CFOI base VSL is larger than base values that others have used to estimate VSLs for non-U.S. countries. For example, the World Bank uses a base VSL
of $3.8 million, calculated using a base GDP per capita of $37,350 as their mea6 An estimate is in the “best estimate” set if it is the author’s preferred specification. Stanley and
Doucouliagos (2012) provide a discussion of the merits of the best estimate versus all set approaches to
VSL meta-analysis. We prefer using the set of all estimates to avoid the biases that preferred estimates
create (Viscusi, 2017).
7 This mean includes all zero and negative VSL estimates as well. All of the estimates we present in this
section do not drop the 72 negative VSL estimates that we do in the analysis throughout the paper for
which the dependent variable is the natural log of the VSL. We discuss the negative observations, which
are inconsistent with basic economic theory, and our method of correcting for the bias we introduce by
dropping them in Section 3.
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Income Elasticities and Global Values of a Statistical Life
231
sure of income (both figures in $2011, calculated using purchasing power parity)
(Narain & Sall, 2016). The Organisation for Economic Co-operation and Development (OECD) uses a base mean of $3.0 million for all OECD countries, using a
base GDP per capita of $34,661, and $3.6 million for the European Union, using a
base GDP per capita of $31,858 (each of these figures in $2005, calculated using
purchasing power parity) (OECD, 2012). Each of the World Bank and OECD values is derived by taking the mean of a set of studies that meet a certain threshold
for reliability. All of the studies in their datasets are based on stated preference
methods. We prefer the U.S. CFOI values to a value derived from stated preference
studies because revealed preference studies avoid hypothetical bias (Murphy et al.,
2005). Moreover, a meta-analytic approach is preferable to constraining the set of
studies and taking a mean of the constrained set, which induces potential biases in
terms of the selection of studies. An alternative to constraining the set of studies
is to control for preferred estimate characteristics in a meta-analytic regression and
calculating a mean fitted value using the preferred attributes.
2.2 Existing estimates of the VSL income elasticity
There have been numerous estimates of the income elasticity of the VSL. The
most common methodology for estimating the income elasticity of the VSL has
been a meta-analysis of existing VSL estimates, which is the approach we adopt
here.8 Most past estimates of the population-average VSL income elasticity for
the United States and other high income countries fall between 0.6 and 1.0, with
numbers closer to 0.6 being more common. Meta-analyses that estimate elasticities
in that range include Viscusi and Aldy (2003) (0.46–0.61) and Bellavance, Dionne
and Lebeau (2009) (0.4–0.75). Doucouliagos, Stanley and Viscusi (2014) estimated
income elasticities of 0.25 to 0.63 in their meta-meta-analysis of income elasticity
estimates, with most of the estimates between 0.5 and 0.63. OECD (2012) estimated income elasticities using stated preference studies from multiple countries;
the estimated elasticities were between 0.7 and 0.9 using their preferred screening criteria for studies included in the analysis, although the elasticities were as
low as 0.3 in some subsets of their data and increased to 1.0 with an unscreened
sample. Hoffmann et al. (2017) estimated income elasticities between 0.2 and 0.6
using stated preference studies covering several countries. Doucouliagos, Stanley
and Giles (2012) demonstrated that controlling for publication selection bias results
8 Two other methodologies exist in the literature: Doucouliagos et al. (2014) performed a meta-metaanalysis of existing elasticity estimates, while Kniesner et al. (2010) utilized quantile regressions on
panel data to estimate an income elasticity across the quantiles of the wage distribution.
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W. Kip Viscusi and Clayton J. Masterman
in a lower estimated VSL income elasticity, finding a range of elasticities between
0.20 and 0.38. A few studies have found elasticities that greatly exceed the 0.6 to 1.0
range – for example, Costa and Kahn (2004) found elasticities of 1.5–1.7 based on
changes in worker income levels over time, and Kniesner, Viscusi and Ziliak (2010)
also estimated income elasticities above 1.0 across the wage distribution. There are
no VSL income elasticity estimates based on labor market data that distinguish the
elasticities for the United States and non-U.S. countries.
3 Sample description for estimation of the
income elasticity of the VSL
Our sample of labor market VSL estimates contains estimates from each study
included in Viscusi and Aldy (2003), Bellavance et al. (2009), Viscusi (2015),
and Viscusi and Masterman (2017). The full list of papers from which we draw
VSL estimates can be found in the Supplementary materials. Our whole sample
includes 953 estimates reported in 68 different studies. Of this group, 763 of the
estimates constituting 43 studies estimate the VSL in the United States. A substantially smaller set of 190 VSL estimates in 25 studies are from non-U.S. countries.
The 13 countries covered in those studies are Australia, Austria, Canada, Chile,
Germany, India, Japan, Pakistan, Poland, South Korea, Switzerland, Taiwan, and
the United Kingdom. As of 2015, the World Bank classifies ten of these countries as high income and two of these countries as lower-middle income. The GNIs
per capita of the high income countries range from $13,400 to $84,630, while the
lower-middle income economies have GNIs per capita of $1440 and $1600.
We use a fixed effects specification to estimate the income elasticity of the
VSL.9 The base regression for the fixed effects model is of the natural log of the
VSL on the natural log of the average income for the sample. The estimating equation is of the form:
Ln(VSL js ) = β0 + β1 × Ln(Income js ) + βs + ε js .
(1)
The coefficient β1 provides the income elasticity of the VSL. The coefficient βs
is the fixed effect for each article s. We exclude 72 negative VSL estimates from
9 We prefer a fixed effect estimator over a weighted least squares or other meta-analysis specification
because previous research demonstrates that fixed effects estimators are preferable for studying the
effects of income on the VSL (Viscusi, 2015).
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Income Elasticities and Global Values of a Statistical Life
233
the sample to utilize this log-log specification.10 We prefer the log-log specification
because it is the most straightforward and conventional method of estimating the
income elasticity of the VSL. However, excluding 72 negative estimates from the
sample may introduce a positive bias into our estimate of the VSL income elasticity.
This bias is akin to publication selection bias, which also causes negative estimates
of the VSL to be removed from the distribution.11 Publication selection bias itself
will positively bias estimates of the income elasticity because negative and low
VSL estimates associated with positive incomes are omitted from the regression.
To address the selection biases, we estimate an additional specification that
includes the standard error for each observation j.12 The estimating equation takes
the form:
Ln(VSL js ) = β0 + β1 × Ln(Income js ) + β2 × Standard Error j + βs + ε js . (2)
Including standard error in the estimating equation corrects for the natural publication selection bias in the VSL sample as well as the selection bias we impose
by restricting the sample to positive values of the VSL. The statistical properties
of this correction for publication selection effects and related biases are documented in Egger et al. (1997), Stanley (2005, 2008), and Stanley and Doucouliagos
(2012). The particular correction is the statistical analog of funnel asymmetry testing. Including the inverse standard error rather than the standard error in equation
(2) is known as the precision effect test. We present the precision effect test as a
robustness check of our estimates of equation (2) below. More precise estimates –
those with lower standard errors – should be closer to the true value of the VSL.
VSL estimates should be normally distributed around the true value of the VSL
– if less precise estimates tend to be disproportionately higher or lower than the
true value, it indicates that the sample is skewed and suffers from some form of
selection bias. Controlling for standard error in the regression equation undoes this
skew by accounting for the portion of high estimates attributable to selection. We
10 Economic theory requires the VSL to be positive. However, random sampling of individuals in labor
markets will occasionally result in a negative observed relationship between wages and fatal workplace
risks. Unbiased VSL estimates should be symmetrically distributed around the sample mean.
11 Publication selection bias manifests whenever researchers are less likely to report (or journals less
likely to publish) estimates that are inconsistent with theory or are outside of a conventional range. Thus,
even though the set of all VSL estimates should have a normal distribution, many lower estimates will
never be reported. The mean of the distribution of published estimates will exhibit a positive bias relative
to the true VSL value.
12 Fourteen percent of our sample did not provide sufficient information to calculate a standard error
of the VSL. To impute a standard error, we estimated a regression of the VSL estimate’s standard error
divided by the VSL on the sample size used in the estimation. We then assigned values for the missing
standard errors using the results of this estimation and the VSL’s level of sample size.
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W. Kip Viscusi and Clayton J. Masterman
Table 1 Summary Statistics.
Whole sample
VSL estimates ($ millions)
Standard error
Income ($ thousands)
Ln income ($ thousands)
Workers’ compensation
Nonfatal injury
Wage specification
Correct standard errors
Observations
U.S. sample
International sample
13.529
13.025
15.551
(14.987)
(10.399)
(26.272)
7.951
5.969
15.909
(19.415)
(7.568)
(39.853)
42.311
45.073
31.221
(13.692)
(12.113)
(14.084)
3.671
3.772
3.265
(0.450)
(0.274)
(0.714)
0.502
0.607
0.079
(0.500)
(0.489)
(0.270)
0.375
0.371
0.389
(0.484)
(0.483)
(0.489)
0.099
0.111
0.047
(0.298)
(0.315)
(0.213)
0.438
0.535
0.047
(0.496)
(0.499)
(0.213)
953
763
190
Note: Sample excludes 72 negative VSL values.
also estimate a version of this equation (2) that includes a vector X i of variables
controlling for the specification of the equation estimating the VSL.
Table 1 provides summary statistics for the studies in our sample. The overall
average VSL is $13.5 million. The U.S. average is slightly smaller at $13.0 million,
while the international average is $15.6 million. The international sample’s larger
average is attributable to greater publication selection bias in the international sample, as these studies often anchor on the U.S. estimates, which should be higher
given international income differences (Viscusi & Masterman, 2017). The international sample’s large average standard error – nearly three times larger than the U.S.
standard error – is illustrative. The average income in the U.S. sample is $45,073,
much larger than the international average of $31,221.
The remaining variables in Table 1 are indicator variables describing the variables and specification used to estimate the VSL and its standard error in the underlying study. The indicator variables for nonfatal injury and workers’ compensation
are equal to one if the estimating equation included controls for nonfatal injury job
risk and the applicable workers’ compensation scheme, and a value of zero otherwise. Omitted variables bias will affect VSL estimates lacking these controls.
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Income Elasticities and Global Values of a Statistical Life
235
Sixty percent of estimates in the U.S. sample control for workers’ compensation.
Only eight percent of international estimates control for workers’ compensation, in
part because some of the countries in our sample lack workers’ compensation programs. Just under 40 percent of estimates in both samples controlled for nonfatal
injury rates.
The wage specification indicator variable is equal to one if the estimating equation used a linear rather than semilogarithmic wage equation to estimate the VSL.
The correct standard errors indicator variable equals one if the VSL estimate’s
standard errors were correctly adjusted to account for the covariation of income
and fatal risk.13 These specification variables are correlated with the passage of
time. Wage specifications were more common in the early literature, while correct
standard errors are more common in more recent papers. The U.S. sample’s estimates are twice as likely to be based on a wage specification, and more than an
order of magnitude more likely to report correct standard errors.
4 Estimating the income elasticity of the VSL
4.1 Fixed effects estimates
Table 2 provides our base fixed effects estimates of the VSL income elasticity. Panel
A presents results from equation (1), while Panel B presents the results based on
equation (2). As a robustness check, Panel C presents the precision effect estimator
as an alternative to the standard error estimator for addressing publication selection bias. Heteroskedasticity-robust standard errors are in parentheses, and standard errors that are robust and clustered on article are in brackets. The first column
corresponds to the elasticity for the whole sample, while the latter two columns
estimate equation (1) separately for the U.S. and international samples. In Panel A,
the income elasticity for the whole sample is 0.826. The elasticity for the U.S. sample is smaller at 0.717, while the international elasticity is higher at 1.083. Our U.S.
and international elasticities are significantly different using robust standard errors
( p = 0.04), but the significance drops below the usual levels when using robust and
clustered errors ( p = 0.18). Likewise, the U.S. elasticity is significantly different
13 When using a semilog equation to estimate the VSL, the VSL is equal to the coefficient on fatal
risk multiplied by the mean sample wage, scaling the units to reflect annual compensation per expected
fatality. Many papers in the VSL literature fail to account for the fact that average wage is a random
variable when constructing standard errors for the estimated VSL.
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W. Kip Viscusi and Clayton J. Masterman
from 1.0 using robust standard errors ( p = 0.02), but not clustered standard errors
( p = 0.32). The international elasticity is never significantly different from 1.0.14
The differences in the elasticity estimates for the U.S. and international samples
are more pronounced in the Panel B estimates, which also control for publication
selection effects. Consistent with Doucouliagos et al. (2014), we find a positive
selection bias affecting the income elasticity of the VSL. Controlling for the standard error to address publication selection biases decreases the estimated elasticity
in the U.S. sample to 0.519. The point estimate for the international sample elasticity increases slightly to 1.103. The two estimates are significantly different using
both robust ( p < 0.01) and clustered ( p = 0.02) standard errors. The international
elasticity is statistically indistinguishable from 1.0,15 but the U.S. elasticity estimate is significantly different from 1.0.16 As expected, the coefficient on the standard error is significant and positive, demonstrating that the sample exhibits positive
sample selection bias, as published VSL estimates overstate the bias-corrected values. Panel C demonstrates that our results are not sensitive to the estimator we use
to address publication selection bias. Using the precision effect estimator results in
a slightly lower estimate of the international VSL income elasticity and a slightly
higher estimate of the U.S. VSL income elasticity, but the results remain consistent
with our conclusion that the international VSL income elasticity exceeds the VSL
income elasticity in the United States.
Table 3 presents the estimates of equation (2) with additional variables controlling for the specification of the VSL estimating equation.17 The results of primary
interest are almost identical to the results from Panel B of Table 2. The income
elasticities for the whole sample, U.S. sample, and international sample are 0.775,
0.511, and 1.102, respectively. As in Table 2, the U.S. and international samples
have significantly different elasticity estimates, and the international estimate is
statistically indistinguishable from 1.0 using either set of standard errors.18 The
U.S. elasticity is significantly different from 1.0.19
The coefficients on the secondary variables are consistent with our expectations
and previous meta-analyses. The workers’ compensation variable varies in significance, but is negative when it is significant. This result is consistent with workers
14 Using robust standard errors, p = 0.53. Using clustered standard errors, p = 0.20.
15 Using robust standard errors, p = 0.49. Using clustered standard errors, p = 0.16.
16 Using robust standard errors, p < 0.01. Using clustered standard errors, p = 0.04.
17 Using the precision effect estimator also yielded consistent results for the Full Model version of
equation (2).
18 For the test of equality of the U.S. and international elasticities, p < 0.01 using robust standard
errors, and p = 0.02 using clustered standard errors. For the test that the international elasticity is equal
to 1, p = 0.49 using robust standard errors, and p = 0.16 using clustered standard errors.
19 Using robust standard errors, p < 0.01. Using clustered standard errors, p = 0.04.
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Income Elasticities and Global Values of a Statistical Life
237
Table 2 Base Regression Estimates of the Log VSL.
Panel A: Regression Estimates with Base Specification
Whole sample
Ln income ($ thousands)
Constant
Observations
R-squared
U.S. sample
International sample
0.826
0.717
1.083
(0.107)***
(0.124)***
(0.133)***
[0.200]***
[0.278]**
[0.063]***
–0.922
–0.492
–1.831
(0.393)**
(0.467)
(0.438)***
[0.733]
[1.050]
[0.207]***
953
763
190
0.550
0.517
0.567
Panel B: Regression Estimates Controlling for Publication Selection Bias
with Standard Error Estimator
Whole sample
Ln income ($ thousands)
Standard error
Constant
Observations
R-squared
U.S. sample
International sample
0.782
0.519
1.103
(0.111)***
(0.118)***
(0.146)***
[0.193]***
[0.225]**
[0.070]***
0.017
0.045
0.014
(0.004)***
(0.008)***
(0.004)***
[0.008]**
[0.012]***
[0.008]*
–0.891
–0.013
–2.120
(0.405)**
(0.433)
(0.482)***
[0.697]
[0.834]
[0.187]***
953
763
190
0.592
0.564
0.635
Panel C: Regression Estimates Controlling for Publication Selection Bias
with Precision Effect Estimator
Whole sample
Ln income ($ thousands)
1/Standard error
U.S. sample
International sample
0.778
0.691
0.991
(0.100)***
(0.123)***
(0.147)***
[0.197]***
[0.275]**
[0.093]***
–0.015
–0.089
–0.009
(0.006)**
(0.017)***
(0.005)*
[0.011]
[0.013]***
[0.006]
Continued on next page.
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238
W. Kip Viscusi and Clayton J. Masterman
Table 2 (Continued).
Constant
Observations
R-squared
–0.702
–0.309
–1.439
(0.372)*
(0.465)
(0.494)***
[0.731]
[1.036]
[0.342]***
953
763
190
0.567
0.593
0.581
Note: Robust standard errors are in parentheses, robust and clustered standard errors are in brackets.
All regressions control for article fixed effects. *** p < 0.01, ** p < 0.05, * p < 0.1.
Table 3 Log VSL Regression Estimates with Full Model.
Whole sample
Ln income ($ thousands)
Standard error
Workers’ compensation
Nonfatal injury
Wage specification
Correct standard errors
Constant
Observations
R-squared
U.S. sample
International sample
0.775
0.511
1.102
(0.112)***
(0.117)***
(0.147)***
[0.197]***
[0.231]**
[0.070]***
0.017
0.045
0.014
(0.004)***
(0.008)***
(0.004)***
[0.008]**
[0.012]***
[0.008]*
–0.352
–0.638
0.029
(0.191)*
(0.258)**
(0.159)
[0.294]
[0.416]
[0.033]
–0.234
–0.222
–0.152
(0.081)***
(0.086)**
(0.218)
[0.079]***
[0.083]**
[0.253]
–0.729
–0.703
0.023
(0.188)***
(0.181)***
(0.204)
[0.340]**
[0.318]**
[0.000]***
0.768
0.735
–
(0.209)***
(0.206)***
[0.355]**
[0.337]**
–0.867
0.171
–2.063
(0.424)**
(0.467)
(0.497)***
[0.748]
[0.915]
[0.204]***
953
763
190
0.599
0.577
0.636
Note: Robust standard errors are in parentheses, robust and clustered standard errors are in brackets.
All regressions control for article fixed effects. *** p < 0.01, ** p < 0.05, * p < 0.1.
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Income Elasticities and Global Values of a Statistical Life
239
who are covered by higher compensation rates requiring lower compensating risk
differentials. The coefficient on nonfatal injury is consistently negative and significant in the whole sample and U.S. sample equations, as expected from the omitted
variables bias that an equation lacking nonfatal injury would exhibit. Estimating
equations utilizing a wage specification find lower VSLs, while equations that calculate correct standard errors receive a premium. The signs of the coefficients are
consistent with researchers using log wage equations and correct standard errors
more as VSL estimates have increased over time.
4.2 Quantile regression estimates
The fixed effects estimates of the VSL demonstrated that the income elasticity of the
VSL is larger in international studies of the VSL than in the United States. However,
the fixed effect estimates cannot demonstrate whether the difference is a function of
different income levels or different preferences over fatal risk and money tradeoffs.
We utilize quantile regression estimates to investigate whether the income elasticity
of the VSL declines over the entire VSL distribution. If so, it indicates that some of
the difference between U.S. and international VSL elasticities is likely attributable
to differences in income levels. Our quantile regression estimator is of the form:
(q)
(q)
(q)
Ln(VSL j )(q) = β0 + β1 × Ln(Income j ) + ε j .
(3)
(q)
Using this equation, β1 is the income elasticity of the VSL at the q quantile of the
distribution. As with equation (1), we also estimate a version of equation (3) that
includes the standard error of the VSL estimate to address publication selection
bias.
Table 4 presents the results of estimating equation (3). For reference, Panel A
presents the distribution of VSL estimates in our sample. The median VSL estimate
is $10.3 million. The right tail of the distribution is about twice as long as the left
tail – the 95th percentile estimate is at $36.5 million, while the 5th percentile is
$0.7 million.
Panel B presents our estimates of the income elasticity throughout the VSL
distribution. The results indicate that the income elasticity of the VSL is largest for
the smallest VSLs, and smallest for the largest estimates. In particular, the elasticity is 2.58 at the 5th percentile, and it falls to 0.35 by the 95th percentile. The
elasticity almost decreases monotonically. The one exception is an increase at the
90th percentile to 0.64 from 0.44 at the 75th percentile. Each elasticity estimate
from the lower half of the distribution is statistically significantly different from the
estimate of the elasticity of the median.20 Conversely, each elasticity estimate from
20 We used bootstrapped standard errors using 500 repetitions to test for significant differences between
the quantiles. The test for the 5th percentile and 25th percentile had p < 0.01, while the test for the 10th
percentile had p = 0.02.
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240
Panel A: Raw Distribution of VSL Estimates
VSL estimate
($ millions)
5%
10%
25%
50%
75%
90%
95%
0.735
1.960
5.805
10.343
16.108
25.927
36.463
Panel B: Base Case Log VSL Quantile Regression
Ln income
($ thousands)
Constant
Pseudo R 2
5%
10%
25%
50%
75%
90%
95%
2.576
(0.502)***
–9.583
(1.886)***
0.101
1.497
(0.448)***
–4.745
(1.755)***
0.082
1.181
(0.139)***
–2.658
(0.526)***
0.056
0.460
(0.093)***
0.625
(0.356)*
0.024
0.438
(0.033)***
1.136
(0.110)***
0.022
0.643
(0.090)***
0.892
(0.337)***
0.050
0.347
(0.165)**
2.230
(0.636)***
0.045
Panel C: Log VSL Quantile Regression Controlling for Standard Error
Ln income
($ thousands)
Standard error
Constant
Pseudo R 2
5%
10%
25%
50%
75%
90%
95%
2.566
(0.369)***
0.014
(0.007)**
–9.576
(1.354)***
0.117
1.476
(0.443)***
0.010
(0.004)**
–4.716
(1.718)***
0.096
1.201
(0.118)***
0.009
(0.003)***
–2.790
(0.444)***
0.073
0.393
(0.095)***
0.033
(0.010)***
0.689
(0.356)*
0.068
0.331
(0.045)***
0.047
(0.003)***
1.214
(0.164)***
0.151
0.337
(0.090)***
0.054
(0.005)***
1.478
(0.339)***
0.240
0.249
(0.172)
0.055
(0.030)*
1.938
(0.514)***
0.298
Note: N = 953. Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.
W. Kip Viscusi and Clayton J. Masterman
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Table 4 Quantile Regression.
Income Elasticities and Global Values of a Statistical Life
241
the upper half of the distribution is statistically indistinguishable from the median
elasticity.21
Panel C extends the results from Panel B by adding standard error to the estimation.22 The coefficient on standard error is positive and significant at each quantile and tends to get larger in the upper half of the distribution. The elasticity estimates in Panel C are similar to those in Panel B. In the lower half of the distribution, the inclusion of the standard error changed each estimated elasticity by less
than 0.02. The changes are larger at the median and above. The 50th percentile,
75th percentile, and 95th percentile estimates decrease by between 0.07 and 0.10,
and the 90th percentile estimate decreases by 0.30. The pattern of elasticity estimates has a more monotonically decreasing pattern in Panel C because of the large
effect of including standard error on the upper half of the distribution. The income
elasticity of the VSL drops sharply from the 5th percentile of the distribution to the
median and then continues to drop at a much slower pace from the median to the
95th percentile.
Table 4 provides indirect support for the proposition that the income elasticity
of the VSL decreases as income increases. Because the income elasticity of the
VSL is positive, incomes increase over the distribution of the VSL. The pattern
in elasticities in Table 4 is thus consistent with elasticities increasing as incomes
decrease. However, Table 4 cannot rule out an elasticity that is constant with respect
to income but varies with factors that may correlate with income. More detailed
effects are difficult to identify with the available set of labor market VSL studies.23
Particularly confounding for present purposes is that out of the thirteen non-U.S.
countries in our data, only India and Pakistan are not upper income economies. As
the VSL literature for lower income countries continues to grow, researchers and
policymakers should refine our understanding of the relationship between the VSL
income elasticity and income levels.
5 International VSL transfer results
Section 3 demonstrated that the average income elasticity of the VSL in non-U.S.
countries is at least as high as 1.0. Table 5 summarizes the findings from Section 3,
presenting the income elasticities (and their corresponding confidence intervals)
21 p = 0.83, 0.19, and 0.48 for the 75th, 90th, and 95th percentile tests, respectively.
22 The test for the 5th percentile and 25th percentile had p < 0.01, while the test for the 10th percentile
had p = 0.02.
23 We attempted to directly identify nonconstant effects by adding (Ln(Income j ))2 to equation (1) or
(2). The coefficient on (Ln(Income j ))2 was highly insignificant ( p > 0.30 in all specifications), but a
test of the joint significance of both income coefficients always had p < 0.001.
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242
W. Kip Viscusi and Clayton J. Masterman
Table 5 Summary of VSL Income Elasticities for Different Samples and Specifications.
Whole sample
U.S. sample
International sample
Base mean estimates
Elasticity point estimate
Confidence intervals
0.781
0.519
1.103
(0.111)***
(0.118)***
(0.146)***
[0.193]***
[0.225]**
[0.070]***
(0.564, 1.000)
(0.287, 0.750)
(0.814, 1.391)
[0.396, 1.167]
[0.064, 0.973]
[0.958, 1.247]
0.775
0.511
1.102
(0.112)***
(0.117)***
(0.147)***
[0.197]***
[0.231]**
[0.070]***
(0.555, 0.995)
(0.281, 0.742)
(0.811, 1.394)
[0.382, 1.168]
[0.045, 0.977]
[0.957, 1.248]
953
763
190
Covariate mean estimates
Elasticity point estimate
Confidence intervals
Observations
Note: Base mean elasticities are from Table 2, Panel B and covariate mean elasticities are from Table 3.
Robust standard errors and corresponding 95% confidence intervals are in parentheses, and robust and
clustered standard errors and corresponding 95% confidence intervals are in brackets. *** p < 0.01,
** p < 0.05, * p < 0.1.
from estimating equation (1) in the specifications from Panel B of both Tables 2
and 3. The 95% confidence intervals for the income elasticity for the international
sample extend from 0.81 to 1.39 using robust standard errors and from 0.96 to
1.25 using standard errors clustered on article. Using these income elasticities, we
can transfer VSLs from the United States to other countries. If we assume that the
income elasticity is constant and equal across the countries of interest, for a country
c, the transferred VSL is given by:
YC η
VSLc = VSLUS ×
.
(4)
YUS
Equation (4) is derived by Hammitt and Robinson (2011). In equation (4), Y
denotes either country c or the United States’ average income, while η denotes
the income elasticity of the VSL. The income measure we use to transfer VSLs is
the GNI per capita from the World Bank.24 In 2015, the U.S. GNI per capita was
24 We use the World Bank’s GNI per capita numbers calculated using the Atlas method which is based
on exchange rates and inflation rates. We prefer the Atlas method over the purchasing power parity GNI
per capita data because the World Bank’s income classification groups are calculated using the Atlas
method. VSLs can be transferred using either method of calculating income.
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Income Elasticities and Global Values of a Statistical Life
243
Table 6 Projected VSL Levels by World Bank Income Group ($ millions).
International
Income level used
Mean low income economy
U.S. elasticity
Unit elasticity
elasticity
Highly elastic
0.519
1.0
1.103
2.0
0.931
0.107
0.067
0.001
1.191
0.171
0.113
0.003
1.895
0.420
0.304
0.018
2.425
0.676
0.514
0.047
3.309
1.229
0.995
0.157
4.356
2.088
1.784
0.453
7.787
6.395
6.131
4.247
$621.07
Low income economy threshold
$1026.00
Mean lower-middle economy
$2440.61
Lower-middle economy threshold
$4036.00
Mean upper-middle economy
$7146.35
Upper-middle economy threshold
$12,476.00
Mean upper income economy
$37,172.50
Note: U.S. and international elasticities are from Table 5. Base U.S. income is $55,980. Base U.S. VSL
of $9.631 million is from Viscusi and Masterman (2017) and Viscusi (2015).
$55,980. As discussed in Section 2, we use the $9.6 million base CFOI estimate as
the base U.S. VSL.
Table 6 presents the results of transferring VSLs for economies at various
income levels. To divide countries into low income, lower-middle income, uppermiddle income, and upper income, we use the World Bank’s income classification
groups. The World Bank classifies an economy as low income if it has a GNI per
capita of $1025 or less, lower-middle income if it has a GNI per capita between
$1026 and $4035, upper-middle income if it has a GNI per capita between $4036
and $12,475, and upper income if it has a GNI per capita of $12,476 or higher.
Table 6 presents our estimate of the VSL both using the mean GNI of countries in
each income group and a country at the income threshold. Out of the 189 countries that the World Bank provides GNI per capita measures for in 2015, 28 are
low income, 49 are lower-middle income, 52 are upper-middle income, and 60 are
upper income.
We utilize four different elasticities: our estimated base U.S. elasticity of 0.52
from Table 5, an elasticity of 1.0, our estimated base international elasticity of 1.10
from Table 5, and an elasticity of 2.0 from our estimates of the income elasticity
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244
W. Kip Viscusi and Clayton J. Masterman
in the lowest parts of the VSL distribution in Table 4. Using an income elasticity
of 1.0, the average VSL in a low income economy is $107,000. An economy at the
lower income threshold has a VSL of $171,000. A lower-middle income economy
has an average VSL of $420,000, while an economy at the lower-middle income
threshold has a VSL of $676,000. The average upper-middle income economy has
an average VSL of $1.23 million. An economy at the upper-middle income threshold has a VSL of $2.09 million. Finally, the average upper income country has a
VSL much higher than the rest at $6.40 million.25
Comparing the unit-elasticity VSLs to the other rows of Table 6 demonstrates
the importance of correctly estimating the income elasticity. If we apply the average base U.S. elasticity from Table 5, our estimate of the VSL for other nations
increases dramatically. The mean low income, lower-middle income, and uppermiddle income VSLs increase to $931,000, $1.90 million, and $3.31 million,
respectively. The upper income average also receives a relatively smaller bump
to $7.79 million. Applying our estimated average base international elasticity from
Table 5 similarly decreases the VSL for each country. The effect is again largest for
the low income economies, which decreases to $67,000, with the others similarly
following suit. Finally, utilizing an elasticity of 2.0 likewise greatly reduces the
VSL for low and middle income countries. The mean low income, lower-middle
income, and upper-middle income VSLs decrease to $1000, $18,000, and $157,000
when an elasticity of 2.0 is used.
In Table 7, we apply equation (4) to all 189 countries for which GNI per capita
numbers are available from the World Bank. We use an elasticity of 1.0 because
it is tractable and because we fail to reject the hypothesis that the international
elasticity is equal to 1.0 in any of our specifications. The large range of GNIs per
capita induce an equally large range of VSL estimates. The country with the largest
VSL is Bermuda at $18.3 million, with a GNI per capita of $106,140. The smallest
VSL is from Burundi equal to $45,000 using its GNI per capita of $260.
On the whole, our transferred VSLs exceed the values that policymakers in
foreign nations have utilized in the past.26 The United Kingdom’s Department of
Transport used a VSL of $2.3 million in 2015, while we find a U.K. VSL of $7.4
million. In 2014, Australia used a baseline VSL of $2.7 million. Transferring a VSL
based on the U.S. numbers demonstrates that Australia’s VSL is $10.3 million.
25 Transferred VSLs using the purchasing power parity GNI per capita data are largely consistent with
these. The transferred VSLs for mean low income, lower-middle income, upper-middle income, and
upper income economies are $127,000, $397,000, $1.3 million, and $5.7 million, respectively.
26 Each of the following example values are drawn from Narain and Sall (2016) and converted to
2015 dollars. We adjust the values for inflation alone, not income growth, as these reflect the VSLs the
countries used in the past.
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Income Elasticities and Global Values of a Statistical Life
245
Table 7 International Income-Adjusted Estimates of the VSL.
GNI per capita
VSL
GNI per capita
($ thousands) ($ millions)
VSL
($ thousands) ($ millions)
Afghanistan
0.610
0.105 Cambodia
1.070
0.184
Albania
4.280
0.736 Cameroon
1.320
0.227
Algeria
4.870
0.838 Canada
47.540
8.179
Andorra
43.270
7.444 Central African Republic
0.330
0.057
Angola
4.180
0.719 Chad
0.880
0.151
Antigua and Barbuda
13.270
2.283 Chile
14.100
2.426
Argentina
12.460
2.144 China
7.930
1.364
Armenia
3.880
0.668 Colombia
7.140
1.228
Australia
60.070
10.335 Comoros
0.780
0.134
Austria
47.410
Azerbaijan
6.560
8.157 Congo, Dem. Rep.
0.410
0.071
1.129 Congo, Rep.
2.540
0.437
10.400
1.789
Bahamas, The
20.740
3.568 Costa Rica
Bahrain
19.840
3.413 Côte d’Ivoire
Bangladesh
Barbados
1.420
0.244
1.190
0.205 Croatia
12.700
2.185
14.510
2.496 Cyprus
25.990
4.471
Belarus
6.460
1.111 Czech Republic
18.140
3.121
Belgium
44.250
7.613 Denmark
58.550
10.073
Belize
4.490
0.772 Dominica
6.800
1.170
Benin
0.840
0.145 Dominican Republic
6.240
1.074
6.030
1.037
Bermuda
106.140
18.261 Ecuador
Bhutan
2.380
0.409 Egypt
3.340
0.575
Bolivia
3.000
0.516 El Salvador
3.940
0.678
Bosnia and Herzegovina
4.670
0.803 Equatorial Guinea
12.820
2.206
Botswana
6.460
1.111 Estonia
18.360
3.159
Brazil
Brunei Darussalam
9.850
38.010
1.695 Ethiopia
0.590
0.102
6.539 Fiji
4.830
0.831
Bulgaria
7.480
1.287 Finland
46.550
8.009
Burkina Faso
0.640
0.110 France
40.540
6.975
Burundi
0.260
0.045 Gabon
9.200
1.583
Cabo Verde
3.280
0.564 Gambia, The
0.460
0.079
Continued on next page.
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W. Kip Viscusi and Clayton J. Masterman
Table 7 (Continued).
Georgia
4.160
0.716
Lebanon
7.710
1.326
Germany
45.940
7.904
Lesotho
1.280
0.220
Ghana
1.480
0.255
Liberia
0.380
0.065
Greece
20.320
3.496
Lithuania
14.940
2.570
Grenada
8.650
1.488
Luxembourg
77.000
13.247
Guatemala
3.590
0.618
Macao
67.180
11.558
Guinea
0.470
0.081
Macedonia, FYR
5.140
0.884
Guinea-Bissau
0.590
0.102
Madagascar
0.420
0.072
Guyana
4.090
0.704
Malawi
0.340
0.058
Haiti
0.810
0.139
Malaysia
10.570
1.819
1.196
Honduras
2.280
0.392
Maldives
6.950
Hong Kong
41.000
7.054
Mali
0.760
0.131
Hungary
12.980
2.233
Malta
23.930
4.117
Iceland
50.140
8.626
Marshall Islands
4.770
0.821
India
1.600
0.275
Mauritania
1.370
0.236
Indonesia
3.440
0.592
Mauritius
9.780
1.683
Iran
6.550
1.127
Mexico
9.710
1.671
Iraq
5.820
1.001
Micronesia, Fed. Sts.
3.560
0.612
Ireland
52.580
9.046
Moldova
2.240
0.385
Isle of Man
85.290
14.674
Mongolia
3.870
0.666
Israel
35.770
6.154
Montenegro
7.220
1.242
Italy
32.810
5.645
Morocco
3.030
0.521
0.102
Jamaica
5.050
0.869
Mozambique
0.590
Japan
38.840
6.682
Myanmar
1.160
0.200
Jordan
4.680
0.805
Namibia
5.190
0.893
Kazakhstan
Kenya
Kiribati
11.390
1.960
Nauru
15.420
2.653
1.340
0.231
Nepal
0.730
0.126
8.406
3.390
0.583
Netherlands
48.860
27.450
4.723
New Zealand
40.020
6.885
Kosovo
3.970
0.683
Nicaragua
1.940
0.334
Kuwait
42.150
7.252
Niger
0.390
0.067
Kyrgyz Republic
1.170
0.201
Nigeria
2.820
0.485
Lao PDR
1.740
0.299
Norway
93.740
16.127
14.980
2.577
Oman
16.910
2.909
Korea, Rep.
Latvia
Continued on next page.
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Income Elasticities and Global Values of a Statistical Life
247
Table 7 (Continued).
Pakistan
1.440
0.248
St. Vincent
6.630
1.141
Palau
12.180
2.095
Sudan
1.920
0.330
Panama
11.880
2.044
Suriname
9.360
1.610
Papua New Guinea
2.240
0.385
Swaziland
3.280
0.564
Paraguay
4.190
0.721
Sweden
57.920
9.965
Peru
6.130
1.055
Switzerland
84.630
14.560
Philippines
3.550
0.611
Tajikistan
1.280
0.220
Poland
13.340
2.295
Tanzania
0.920
0.158
Portugal
20.530
3.532
Thailand
5.720
0.984
Puerto Rico
19.320
3.324
Timor-Leste
2.180
0.375
Qatar
83.990
14.450
Tonga
4.280
0.736
9.500
1.634
Togo
0.540
0.093
11.450
1.970
Trinidad and Tobago
17.640
3.035
0.700
0.120
Tunisia
3.980
0.685
Romania
Russian Federation
Rwanda
Samoa
3.930
0.676
Turkey
9.950
1.712
São Tomé and Principe
1.760
0.303
Turkmenistan
7.380
1.270
23.550
4.052
Tuvalu
6.230
1.072
0.980
0.169
Uganda
0.700
0.120
Saudi Arabia
Senegal
Serbia
Seychelles
Sierra Leone
Singapore
5.540
0.953
Ukraine
14.760
2.539
United Arab Emirates
2.640
0.454
43.090
7.413
0.620
0.107
United Kingdom
43.390
7.465
52.090
8.962
United States
55.980
9.631
15.720
2.705
Slovak Republic
17.570
3.023
Uruguay
Slovenia
22.190
3.818
Uzbekistan
2.160
0.372
Solomon Islands
1.920
0.330
Vanuatu
3.170
0.545
South Africa
6.080
1.046
Vietnam
1.990
0.342
South Sudan
0.790
0.136
West Bank and Gaza
3.090
0.532
0.196
Spain
Sri Lanka
St. Kitts and Nevis
St. Lucia
28.530
4.908
Yemen, Rep.
1.140
3.800
0.654
Zambia
1.490
0.256
15.060
2.591
Zimbabwe
0.860
0.148
7.350
1.265
Note: All VSLs are calculated using an income elasticity of 1.0. Base U.S. VSL of $9.631 is from
Viscusi and Masterman (2017).
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248
W. Kip Viscusi and Clayton J. Masterman
Colombia used a VSL of $1.1 million to evaluate water sanitation in 2008, very
close to our transferred Colombian VSL of $1.2 million.
6 Conclusion
This article has analyzed the full set of labor market VSL studies to measure the
income elasticity of the VSL. Our results demonstrate that the income elasticity
ranges for the United States are not consistent with the income elasticities in nonU.S. countries. While estimates of the income elasticity for the whole sample and
U.S. sample of VSL estimates fall within a range of 0.5–1.0, our point estimate of
the international estimate is above the range at about 1.1. Using the conventional
range of elasticities derived from U.S. studies can dramatically overstate the VSL
once the U.S. VSL is transferred to other countries. Current data support using an
elasticity of at least 1.0 for non-U.S. countries.
That international estimates of the income elasticity may be greater is borne
out in our quantile regression analysis, which demonstrated that the VSL income
elasticity falls as the VSL level increases. This finding echoes the quantile regression results in Kniesner et al. (2010) in which the VSL income elasticity declines
for U.S. workers with higher income levels. Combined with our results showing
that the U.S. income elasticity is significantly smaller than the international VSL
elasticity, the quantile regression results show that the international income elasticity of the VSL likely falls as income rises. Further research on the relationship
between income and the elasticity of income may refine this dependence of the
income elasticity on the VSL, especially as more labor market studies in low and
middle income economies emerge.
Our approach is able to derive a VSL for almost 200 countries using a base U.S.
VSL of $9.6 million, a U.S. income of $55,980, and a VSL elasticity of 1.0 to calculate a VSL for each country. We also estimate that low income, lower-middle
income, upper-middle income, and upper income countries should use average
VSLs of $107,000, $420,000, $1.2 million, and $6.4 million, respectively, based
on the World Bank income group criteria. The international differences in the VSL
will have ramifications for efficient regulatory policies, which will tend to be more
stringent in more affluent countries. Because many countries will continue to lack
detailed data on employment and workplace fatalities, transferring VSLs from the
full sample of VSL estimates remains the most reliable way to generate a revealed
preference VSL estimate for low and middle income countries. This benefit transfer approach will remain desirable until researchers develop more credible countryspecific VSL estimates.
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Income Elasticities and Global Values of a Statistical Life
249
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doi:10.1017/bca.2017.12
c Society for Benefit-Cost Analysis, 2017. This is an Open Access article, distributed under the terms
of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which
permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is
properly cited.
W. Kip Viscusi* and Clayton J. Masterman
Income Elasticities and Global Values of a
Statistical Life
Abstract: Countries throughout the world use estimates of the value of a statisti-
cal life (VSL) to monetize fatality risks in benefit-cost analyses. However, the vast
majority of countries lack reliable revealed preference or stated preference estimates of the VSL. This article proposes that the best way to calculate a populationaverage VSL for countries with insufficient or unreliable data is to transfer a base
VSL from the United States calculated using labor market estimates from Census of Fatal Occupational Injuries data, coupled with adjustments for differences
in income between the United States and the country of interest. This approach
requires estimation of two critical inputs: a base U.S. VSL and the income elasticity of the VSL. Drawing upon previous meta-analyses that include adjustments
for publication selection biases, we adopt a base VSL of $9.6 million. We utilize
a sample of 953 VSL estimates from 68 labor market studies of the VSL covering fourteen lower-middle income to high income nations. We estimate the income
elasticity of the VSL within the United States to be from 0.5 to 0.7 and to be just
above 1.0 for non-U.S. countries. Quantile regression reveals that much of the disparity in income elasticities is attributable to income differences between the United
States and other countries, as the income elasticity increases for lower income populations. Using income classifications from the World Bank, we calculate average VSLs in lower income, lower-middle income, upper-middle income, and upper
income countries to be $107,000, $420,000, $1.2 million, and $6.4 million, respectively. We also present VSL estimates for all 189 countries for which World Bank
income data are available, yielding a VSL range from $45,000 to $18.3 million.
Keywords: value of a statistical life; income elasticity; meta-analysis; publication
selection bias.
JEL classifications: I18; I12; K32; J17; J31.
*Corresponding author: W. Kip Viscusi, University Distinguished Professor of Law,
Economics, and Management, Vanderbilt Law School, 131 21st Ave. South, Nashville, TN
37203, USA, e-mail: kip.viscusi@vanderbilt.edu
Clayton J. Masterman: Vanderbilt Law School, Ph.D. Program in Law and Economics,
USA
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Income Elasticities and Global Values of a Statistical Life
227
1 Introduction
The value of a statistical life (VSL) is often the critical policy parameter in benefitcost analyses of health and safety risk regulations and other policies.1 Despite the
importance of the VSL in identifying efficient regulatory policies, many nations
lack accurate VSL measures. Economists have devoted substantial attention to calculating the VSL in the United States and other developed nations, but there is
a relative paucity of studies measuring the VSL in poorer nations. Labor market
revealed preference studies of the VSL are virtually nonexistent outside of higher
income countries, and reliable stated preference estimates are often unavailable as
well. The countries that lack these VSL estimates cannot simply adopt United States
or other higher income nations’ numbers because there is substantial heterogeneity
among countries across dimensions that likely affects the VSL. Income levels, life
expectancies, and social norms regarding risk and death may influence a particular nation’s VSL and thus make it inappropriate to simply transfer the VSL across
countries (Hammitt, 2017).
Most countries lack either reliable stated preference studies or labor market
studies for setting a population-average VSL. A VSL could be calculated for every
country by fielding stated preference studies that ask citizens for their preferences
concerning money-risk tradeoffs (Hoffmann, Krupnick & Qin, 2017). Stated preference studies estimating the VSL have become increasingly common in recent
years, in part because such studies can estimate a VSL from any form of fatality risk that the researcher wishes to investigate (Cropper, Hammitt & Robinson,
2011). However, policymakers generally prefer revealed preference methods for
monetizing regulatory benefits and costs because they are based on actual rather
than hypothetical transactions.2
Labor market hedonic wage studies that measure the compensating differentials
for workplace fatality risks provide an alternative to stated preference studies, but
most countries lack sufficiently detailed workplace fatality data and employment
datasets. VSL estimates that utilize insufficiently detailed fatality data will exhibit
attenuation bias toward zero from measurement error. Publication selection bias,
which occurs whenever journals and researchers are systematically less willing to
report or publish estimates falling outside of an accepted range, is greater when
available data suffer from significant measurement error. As a result, in the absence
1 The VSL is the monetary value of small changes in mortality risks, scaled up to reflect the value
associated with one expected fatality in a large population.
2 For example, the U.S. Office of Management and Budget (2003) has advised regulatory agencies
to utilize revealed preference data over stated preference data when both are available in a particular
context and of similar quality.
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228
W. Kip Viscusi and Clayton J. Masterman
of detailed and accurate data on workplace fatalities, VSL estimates will suffer from
attenuation and publication selection biases (Viscusi, 2015). These biases are even
more prevalent in non-U.S. labor market studies than U.S. studies (Viscusi & Masterman, 2017). While some of the bias in non-U.S. VSL estimates is attributable
to data deficiencies, much of the rampant publication selection bias in international
estimates exists because non-U.S. researchers anchor on U.S. estimates of the VSL
(Viscusi & Masterman, 2017).3 To the extent that stated preference studies are also
subject to biases from the use of U.S. evidence as an anchor for what values are reasonable and merit publication, these estimates likewise may suffer from publication
selection effects. More research is needed to determine the extent to which stated
preference VSL studies also suffer from publication selection biases. Fortunately,
U.S. VSL estimates that utilize the Census of Fatal Occupational Injuries (CFOI)
data are not subject to many of the biases that plague VSL estimates using other
data, both in the United States and internationally (Viscusi, 2015, 2017; Viscusi &
Masterman, 2017).
This article proposes that countries adopt VSL estimates for public policy by
adjusting a base U.S. VSL using our estimate of the international income elasticity of the VSL and the relative incomes of the United States and the country of
interest. This benefit transfer method of coupling income elasticities with a baseline VSL is used in Viscusi (1993) to derive VSL estimates for airline safety based
on labor market VSL estimates for a population that has lower income than airline passengers. Hammitt and Robinson (2011) expand on this technique, including
its potential applicability in international studies. This approach provides policymakers with a VSL based on the best available empirical evidence while preserving the flexibility to choose their preferred methodology for calculating the critical input parameters: the base VSL, the income elasticity of the VSL, and the
measure of income for the United States and the country of interest. The flexibility to choose among various base U.S. VSLs, measures of income, and income
elasticities may be important; regulators and researchers often fail to agree on the
optimal way to infer the policy-relevant VSL value from the economic literature.4
We use this benefit transfer method to calculate VSL estimates for 189 different
countries.
3 Throughout this article, we use “international” to refer to estimates of the VSL in countries other than
the United States.
4 For example, even within the United States, different agencies differ on the appropriate way to extrapolate a VSL from the literature. The U.S. Department of Transportation (2016) uses an average of the
single best estimate from studies utilizing the CFOI data series. The U.S. Environmental Protection
Agency (2016) uses an average value from both revealed preference and stated preference studies.
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Income Elasticities and Global Values of a Statistical Life
229
Section 2 presents a brief summary of our preferred VSL and existing estimates
of the income elasticity of the VSL in the literature. The preferred base VSL of $9.6
million for our calculations is the estimate from U.S. CFOI studies after controlling
for publication selection bias drawn from Viscusi (2015) and Viscusi and Masterman (2017).5 Given the absence of substantial publication selection biases for VSL
studies using the CFOI data, others may prefer either the mean or median CFOI
estimates without bias adjustments, and we present those as well.
While there have been numerous estimates of the income elasticity of the VSL,
there are no estimates based on labor market data that distinguish the elasticities for
the United States and non-U.S. countries. Section 3 presents our dataset of 953 labor
market VSL estimates from 68 studies to estimate the income elasticity of the VSL
for U.S. and non-U.S. VSLs. Section 4 presents our estimates of the income elasticity. In Section 4.1, we compare the elasticities for U.S. studies and non-U.S. studies, finding substantial evidence that the income elasticity of the VSL for the United
States is smaller than the elasticity in non-U.S. countries. Section 4.2 examines the
income elasticity of the VSL throughout the VSL distribution, demonstrating that
the elasticity is larger for small VSLs and vice versa, thus providing the empirical rationale for why the international income elasticity of the VSL exceeds the
domestic value and suggesting that the income elasticity is larger at lower income
levels.
Section 5 presents VSL estimates for countries throughout the world using our
benefit transfer approach. We present two sets of transferred VSLs. The first set uses
2015 World Bank gross national income (GNI) per capita and income level classifications to demonstrate VSLs for low, lower-middle, upper-middle, and upper
income economies. The World Bank GNI per capita measure of income is convenient because it is the largest collection of national income measures available,
and the World Bank’s income classification levels are widely used as meaningful reference points. Our preferred international income elasticity of 1.0 results in
a transferred VSL of $107,000 for low income economies, $420,000 for lowermiddle income economies, $1.2 million for upper-middle income economies, and
$6.4 million for upper income economies. The second set of estimates applies our
methodology to all 189 countries for which 2015 GNI per capita numbers are available. The transferred VSLs vary greatly across countries, as do the national incomes
they are based upon. The VSLs range from a low of $45,000 for Burundi to a high
value of $18.3 million for Bermuda.
5 Unless otherwise noted, all dollar figures in this article are expressed in 2015 dollars.
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230
W. Kip Viscusi and Clayton J. Masterman
2 Reviewing base VSLs and the income elasticity
literature
2.1 Choosing a base VSL
Our calculations utilize a base U.S. VSL of $9.6 million. Viscusi (2015) and Viscusi
and Masterman (2017) derived this value from a meta-analysis of VSL estimates
utilizing CFOI estimates that accounted for publication selection bias. This estimate
is similar to the $9.4 million value used by the U.S. Department of Transportation
(2016), the $9.7 million ($2013) value used by the U.S. Environmental Protection
Agency (2016), and the $9.6 million ($2014) value used by the U.S. Department
of Health and Human Services (2016). Our point estimate corrected for estimated
publication selection effects, though the estimated biases were not statistically significant in the 2017 study. Nonetheless, if policymakers prefer other VSLs to our
$9.6 million value, the transfer method accommodates alternative values. If base
income is held constant, different base VSLs result in a proportional change in
the transferred VSL. The unadjusted median and mean VSL estimates based on
the CFOI data are $13.1 million and $11.1 million, while the median and mean
using only the best estimates from these studies using the CFOI data are $10.2 million and $11.8 million.6 Our baseline VSL estimate is slightly below the median
of all labor market VSL estimates in our sample, $9.7 million, and $2.4 million
smaller than the full mean of the sample at $12.0 million.7 Our baseline estimate
is also lower than the full sample best set median and mean of $10.1 million and
$12.2 million. The VSL estimates using fatality rates from the CFOI are superior
to all other U.S. labor market estimates. Because the CFOI is a complete census of
occupational fatalities rather than a survey subject to voluntary responses, the data
are subject to significantly less measurement error than other sources. The resulting
VSL estimates exhibit less attenuation and publication selection biases.
The U.S. CFOI base VSL is larger than base values that others have used to estimate VSLs for non-U.S. countries. For example, the World Bank uses a base VSL
of $3.8 million, calculated using a base GDP per capita of $37,350 as their mea6 An estimate is in the “best estimate” set if it is the author’s preferred specification. Stanley and
Doucouliagos (2012) provide a discussion of the merits of the best estimate versus all set approaches to
VSL meta-analysis. We prefer using the set of all estimates to avoid the biases that preferred estimates
create (Viscusi, 2017).
7 This mean includes all zero and negative VSL estimates as well. All of the estimates we present in this
section do not drop the 72 negative VSL estimates that we do in the analysis throughout the paper for
which the dependent variable is the natural log of the VSL. We discuss the negative observations, which
are inconsistent with basic economic theory, and our method of correcting for the bias we introduce by
dropping them in Section 3.
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Income Elasticities and Global Values of a Statistical Life
231
sure of income (both figures in $2011, calculated using purchasing power parity)
(Narain & Sall, 2016). The Organisation for Economic Co-operation and Development (OECD) uses a base mean of $3.0 million for all OECD countries, using a
base GDP per capita of $34,661, and $3.6 million for the European Union, using a
base GDP per capita of $31,858 (each of these figures in $2005, calculated using
purchasing power parity) (OECD, 2012). Each of the World Bank and OECD values is derived by taking the mean of a set of studies that meet a certain threshold
for reliability. All of the studies in their datasets are based on stated preference
methods. We prefer the U.S. CFOI values to a value derived from stated preference
studies because revealed preference studies avoid hypothetical bias (Murphy et al.,
2005). Moreover, a meta-analytic approach is preferable to constraining the set of
studies and taking a mean of the constrained set, which induces potential biases in
terms of the selection of studies. An alternative to constraining the set of studies
is to control for preferred estimate characteristics in a meta-analytic regression and
calculating a mean fitted value using the preferred attributes.
2.2 Existing estimates of the VSL income elasticity
There have been numerous estimates of the income elasticity of the VSL. The
most common methodology for estimating the income elasticity of the VSL has
been a meta-analysis of existing VSL estimates, which is the approach we adopt
here.8 Most past estimates of the population-average VSL income elasticity for
the United States and other high income countries fall between 0.6 and 1.0, with
numbers closer to 0.6 being more common. Meta-analyses that estimate elasticities
in that range include Viscusi and Aldy (2003) (0.46–0.61) and Bellavance, Dionne
and Lebeau (2009) (0.4–0.75). Doucouliagos, Stanley and Viscusi (2014) estimated
income elasticities of 0.25 to 0.63 in their meta-meta-analysis of income elasticity
estimates, with most of the estimates between 0.5 and 0.63. OECD (2012) estimated income elasticities using stated preference studies from multiple countries;
the estimated elasticities were between 0.7 and 0.9 using their preferred screening criteria for studies included in the analysis, although the elasticities were as
low as 0.3 in some subsets of their data and increased to 1.0 with an unscreened
sample. Hoffmann et al. (2017) estimated income elasticities between 0.2 and 0.6
using stated preference studies covering several countries. Doucouliagos, Stanley
and Giles (2012) demonstrated that controlling for publication selection bias results
8 Two other methodologies exist in the literature: Doucouliagos et al. (2014) performed a meta-metaanalysis of existing elasticity estimates, while Kniesner et al. (2010) utilized quantile regressions on
panel data to estimate an income elasticity across the quantiles of the wage distribution.
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W. Kip Viscusi and Clayton J. Masterman
in a lower estimated VSL income elasticity, finding a range of elasticities between
0.20 and 0.38. A few studies have found elasticities that greatly exceed the 0.6 to 1.0
range – for example, Costa and Kahn (2004) found elasticities of 1.5–1.7 based on
changes in worker income levels over time, and Kniesner, Viscusi and Ziliak (2010)
also estimated income elasticities above 1.0 across the wage distribution. There are
no VSL income elasticity estimates based on labor market data that distinguish the
elasticities for the United States and non-U.S. countries.
3 Sample description for estimation of the
income elasticity of the VSL
Our sample of labor market VSL estimates contains estimates from each study
included in Viscusi and Aldy (2003), Bellavance et al. (2009), Viscusi (2015),
and Viscusi and Masterman (2017). The full list of papers from which we draw
VSL estimates can be found in the Supplementary materials. Our whole sample
includes 953 estimates reported in 68 different studies. Of this group, 763 of the
estimates constituting 43 studies estimate the VSL in the United States. A substantially smaller set of 190 VSL estimates in 25 studies are from non-U.S. countries.
The 13 countries covered in those studies are Australia, Austria, Canada, Chile,
Germany, India, Japan, Pakistan, Poland, South Korea, Switzerland, Taiwan, and
the United Kingdom. As of 2015, the World Bank classifies ten of these countries as high income and two of these countries as lower-middle income. The GNIs
per capita of the high income countries range from $13,400 to $84,630, while the
lower-middle income economies have GNIs per capita of $1440 and $1600.
We use a fixed effects specification to estimate the income elasticity of the
VSL.9 The base regression for the fixed effects model is of the natural log of the
VSL on the natural log of the average income for the sample. The estimating equation is of the form:
Ln(VSL js ) = β0 + β1 × Ln(Income js ) + βs + ε js .
(1)
The coefficient β1 provides the income elasticity of the VSL. The coefficient βs
is the fixed effect for each article s. We exclude 72 negative VSL estimates from
9 We prefer a fixed effect estimator over a weighted least squares or other meta-analysis specification
because previous research demonstrates that fixed effects estimators are preferable for studying the
effects of income on the VSL (Viscusi, 2015).
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Income Elasticities and Global Values of a Statistical Life
233
the sample to utilize this log-log specification.10 We prefer the log-log specification
because it is the most straightforward and conventional method of estimating the
income elasticity of the VSL. However, excluding 72 negative estimates from the
sample may introduce a positive bias into our estimate of the VSL income elasticity.
This bias is akin to publication selection bias, which also causes negative estimates
of the VSL to be removed from the distribution.11 Publication selection bias itself
will positively bias estimates of the income elasticity because negative and low
VSL estimates associated with positive incomes are omitted from the regression.
To address the selection biases, we estimate an additional specification that
includes the standard error for each observation j.12 The estimating equation takes
the form:
Ln(VSL js ) = β0 + β1 × Ln(Income js ) + β2 × Standard Error j + βs + ε js . (2)
Including standard error in the estimating equation corrects for the natural publication selection bias in the VSL sample as well as the selection bias we impose
by restricting the sample to positive values of the VSL. The statistical properties
of this correction for publication selection effects and related biases are documented in Egger et al. (1997), Stanley (2005, 2008), and Stanley and Doucouliagos
(2012). The particular correction is the statistical analog of funnel asymmetry testing. Including the inverse standard error rather than the standard error in equation
(2) is known as the precision effect test. We present the precision effect test as a
robustness check of our estimates of equation (2) below. More precise estimates –
those with lower standard errors – should be closer to the true value of the VSL.
VSL estimates should be normally distributed around the true value of the VSL
– if less precise estimates tend to be disproportionately higher or lower than the
true value, it indicates that the sample is skewed and suffers from some form of
selection bias. Controlling for standard error in the regression equation undoes this
skew by accounting for the portion of high estimates attributable to selection. We
10 Economic theory requires the VSL to be positive. However, random sampling of individuals in labor
markets will occasionally result in a negative observed relationship between wages and fatal workplace
risks. Unbiased VSL estimates should be symmetrically distributed around the sample mean.
11 Publication selection bias manifests whenever researchers are less likely to report (or journals less
likely to publish) estimates that are inconsistent with theory or are outside of a conventional range. Thus,
even though the set of all VSL estimates should have a normal distribution, many lower estimates will
never be reported. The mean of the distribution of published estimates will exhibit a positive bias relative
to the true VSL value.
12 Fourteen percent of our sample did not provide sufficient information to calculate a standard error
of the VSL. To impute a standard error, we estimated a regression of the VSL estimate’s standard error
divided by the VSL on the sample size used in the estimation. We then assigned values for the missing
standard errors using the results of this estimation and the VSL’s level of sample size.
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W. Kip Viscusi and Clayton J. Masterman
Table 1 Summary Statistics.
Whole sample
VSL estimates ($ millions)
Standard error
Income ($ thousands)
Ln income ($ thousands)
Workers’ compensation
Nonfatal injury
Wage specification
Correct standard errors
Observations
U.S. sample
International sample
13.529
13.025
15.551
(14.987)
(10.399)
(26.272)
7.951
5.969
15.909
(19.415)
(7.568)
(39.853)
42.311
45.073
31.221
(13.692)
(12.113)
(14.084)
3.671
3.772
3.265
(0.450)
(0.274)
(0.714)
0.502
0.607
0.079
(0.500)
(0.489)
(0.270)
0.375
0.371
0.389
(0.484)
(0.483)
(0.489)
0.099
0.111
0.047
(0.298)
(0.315)
(0.213)
0.438
0.535
0.047
(0.496)
(0.499)
(0.213)
953
763
190
Note: Sample excludes 72 negative VSL values.
also estimate a version of this equation (2) that includes a vector X i of variables
controlling for the specification of the equation estimating the VSL.
Table 1 provides summary statistics for the studies in our sample. The overall
average VSL is $13.5 million. The U.S. average is slightly smaller at $13.0 million,
while the international average is $15.6 million. The international sample’s larger
average is attributable to greater publication selection bias in the international sample, as these studies often anchor on the U.S. estimates, which should be higher
given international income differences (Viscusi & Masterman, 2017). The international sample’s large average standard error – nearly three times larger than the U.S.
standard error – is illustrative. The average income in the U.S. sample is $45,073,
much larger than the international average of $31,221.
The remaining variables in Table 1 are indicator variables describing the variables and specification used to estimate the VSL and its standard error in the underlying study. The indicator variables for nonfatal injury and workers’ compensation
are equal to one if the estimating equation included controls for nonfatal injury job
risk and the applicable workers’ compensation scheme, and a value of zero otherwise. Omitted variables bias will affect VSL estimates lacking these controls.
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Income Elasticities and Global Values of a Statistical Life
235
Sixty percent of estimates in the U.S. sample control for workers’ compensation.
Only eight percent of international estimates control for workers’ compensation, in
part because some of the countries in our sample lack workers’ compensation programs. Just under 40 percent of estimates in both samples controlled for nonfatal
injury rates.
The wage specification indicator variable is equal to one if the estimating equation used a linear rather than semilogarithmic wage equation to estimate the VSL.
The correct standard errors indicator variable equals one if the VSL estimate’s
standard errors were correctly adjusted to account for the covariation of income
and fatal risk.13 These specification variables are correlated with the passage of
time. Wage specifications were more common in the early literature, while correct
standard errors are more common in more recent papers. The U.S. sample’s estimates are twice as likely to be based on a wage specification, and more than an
order of magnitude more likely to report correct standard errors.
4 Estimating the income elasticity of the VSL
4.1 Fixed effects estimates
Table 2 provides our base fixed effects estimates of the VSL income elasticity. Panel
A presents results from equation (1), while Panel B presents the results based on
equation (2). As a robustness check, Panel C presents the precision effect estimator
as an alternative to the standard error estimator for addressing publication selection bias. Heteroskedasticity-robust standard errors are in parentheses, and standard errors that are robust and clustered on article are in brackets. The first column
corresponds to the elasticity for the whole sample, while the latter two columns
estimate equation (1) separately for the U.S. and international samples. In Panel A,
the income elasticity for the whole sample is 0.826. The elasticity for the U.S. sample is smaller at 0.717, while the international elasticity is higher at 1.083. Our U.S.
and international elasticities are significantly different using robust standard errors
( p = 0.04), but the significance drops below the usual levels when using robust and
clustered errors ( p = 0.18). Likewise, the U.S. elasticity is significantly different
13 When using a semilog equation to estimate the VSL, the VSL is equal to the coefficient on fatal
risk multiplied by the mean sample wage, scaling the units to reflect annual compensation per expected
fatality. Many papers in the VSL literature fail to account for the fact that average wage is a random
variable when constructing standard errors for the estimated VSL.
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W. Kip Viscusi and Clayton J. Masterman
from 1.0 using robust standard errors ( p = 0.02), but not clustered standard errors
( p = 0.32). The international elasticity is never significantly different from 1.0.14
The differences in the elasticity estimates for the U.S. and international samples
are more pronounced in the Panel B estimates, which also control for publication
selection effects. Consistent with Doucouliagos et al. (2014), we find a positive
selection bias affecting the income elasticity of the VSL. Controlling for the standard error to address publication selection biases decreases the estimated elasticity
in the U.S. sample to 0.519. The point estimate for the international sample elasticity increases slightly to 1.103. The two estimates are significantly different using
both robust ( p < 0.01) and clustered ( p = 0.02) standard errors. The international
elasticity is statistically indistinguishable from 1.0,15 but the U.S. elasticity estimate is significantly different from 1.0.16 As expected, the coefficient on the standard error is significant and positive, demonstrating that the sample exhibits positive
sample selection bias, as published VSL estimates overstate the bias-corrected values. Panel C demonstrates that our results are not sensitive to the estimator we use
to address publication selection bias. Using the precision effect estimator results in
a slightly lower estimate of the international VSL income elasticity and a slightly
higher estimate of the U.S. VSL income elasticity, but the results remain consistent
with our conclusion that the international VSL income elasticity exceeds the VSL
income elasticity in the United States.
Table 3 presents the estimates of equation (2) with additional variables controlling for the specification of the VSL estimating equation.17 The results of primary
interest are almost identical to the results from Panel B of Table 2. The income
elasticities for the whole sample, U.S. sample, and international sample are 0.775,
0.511, and 1.102, respectively. As in Table 2, the U.S. and international samples
have significantly different elasticity estimates, and the international estimate is
statistically indistinguishable from 1.0 using either set of standard errors.18 The
U.S. elasticity is significantly different from 1.0.19
The coefficients on the secondary variables are consistent with our expectations
and previous meta-analyses. The workers’ compensation variable varies in significance, but is negative when it is significant. This result is consistent with workers
14 Using robust standard errors, p = 0.53. Using clustered standard errors, p = 0.20.
15 Using robust standard errors, p = 0.49. Using clustered standard errors, p = 0.16.
16 Using robust standard errors, p < 0.01. Using clustered standard errors, p = 0.04.
17 Using the precision effect estimator also yielded consistent results for the Full Model version of
equation (2).
18 For the test of equality of the U.S. and international elasticities, p < 0.01 using robust standard
errors, and p = 0.02 using clustered standard errors. For the test that the international elasticity is equal
to 1, p = 0.49 using robust standard errors, and p = 0.16 using clustered standard errors.
19 Using robust standard errors, p < 0.01. Using clustered standard errors, p = 0.04.
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Income Elasticities and Global Values of a Statistical Life
237
Table 2 Base Regression Estimates of the Log VSL.
Panel A: Regression Estimates with Base Specification
Whole sample
Ln income ($ thousands)
Constant
Observations
R-squared
U.S. sample
International sample
0.826
0.717
1.083
(0.107)***
(0.124)***
(0.133)***
[0.200]***
[0.278]**
[0.063]***
–0.922
–0.492
–1.831
(0.393)**
(0.467)
(0.438)***
[0.733]
[1.050]
[0.207]***
953
763
190
0.550
0.517
0.567
Panel B: Regression Estimates Controlling for Publication Selection Bias
with Standard Error Estimator
Whole sample
Ln income ($ thousands)
Standard error
Constant
Observations
R-squared
U.S. sample
International sample
0.782
0.519
1.103
(0.111)***
(0.118)***
(0.146)***
[0.193]***
[0.225]**
[0.070]***
0.017
0.045
0.014
(0.004)***
(0.008)***
(0.004)***
[0.008]**
[0.012]***
[0.008]*
–0.891
–0.013
–2.120
(0.405)**
(0.433)
(0.482)***
[0.697]
[0.834]
[0.187]***
953
763
190
0.592
0.564
0.635
Panel C: Regression Estimates Controlling for Publication Selection Bias
with Precision Effect Estimator
Whole sample
Ln income ($ thousands)
1/Standard error
U.S. sample
International sample
0.778
0.691
0.991
(0.100)***
(0.123)***
(0.147)***
[0.197]***
[0.275]**
[0.093]***
–0.015
–0.089
–0.009
(0.006)**
(0.017)***
(0.005)*
[0.011]
[0.013]***
[0.006]
Continued on next page.
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W. Kip Viscusi and Clayton J. Masterman
Table 2 (Continued).
Constant
Observations
R-squared
–0.702
–0.309
–1.439
(0.372)*
(0.465)
(0.494)***
[0.731]
[1.036]
[0.342]***
953
763
190
0.567
0.593
0.581
Note: Robust standard errors are in parentheses, robust and clustered standard errors are in brackets.
All regressions control for article fixed effects. *** p < 0.01, ** p < 0.05, * p < 0.1.
Table 3 Log VSL Regression Estimates with Full Model.
Whole sample
Ln income ($ thousands)
Standard error
Workers’ compensation
Nonfatal injury
Wage specification
Correct standard errors
Constant
Observations
R-squared
U.S. sample
International sample
0.775
0.511
1.102
(0.112)***
(0.117)***
(0.147)***
[0.197]***
[0.231]**
[0.070]***
0.017
0.045
0.014
(0.004)***
(0.008)***
(0.004)***
[0.008]**
[0.012]***
[0.008]*
–0.352
–0.638
0.029
(0.191)*
(0.258)**
(0.159)
[0.294]
[0.416]
[0.033]
–0.234
–0.222
–0.152
(0.081)***
(0.086)**
(0.218)
[0.079]***
[0.083]**
[0.253]
–0.729
–0.703
0.023
(0.188)***
(0.181)***
(0.204)
[0.340]**
[0.318]**
[0.000]***
0.768
0.735
–
(0.209)***
(0.206)***
[0.355]**
[0.337]**
–0.867
0.171
–2.063
(0.424)**
(0.467)
(0.497)***
[0.748]
[0.915]
[0.204]***
953
763
190
0.599
0.577
0.636
Note: Robust standard errors are in parentheses, robust and clustered standard errors are in brackets.
All regressions control for article fixed effects. *** p < 0.01, ** p < 0.05, * p < 0.1.
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Income Elasticities and Global Values of a Statistical Life
239
who are covered by higher compensation rates requiring lower compensating risk
differentials. The coefficient on nonfatal injury is consistently negative and significant in the whole sample and U.S. sample equations, as expected from the omitted
variables bias that an equation lacking nonfatal injury would exhibit. Estimating
equations utilizing a wage specification find lower VSLs, while equations that calculate correct standard errors receive a premium. The signs of the coefficients are
consistent with researchers using log wage equations and correct standard errors
more as VSL estimates have increased over time.
4.2 Quantile regression estimates
The fixed effects estimates of the VSL demonstrated that the income elasticity of the
VSL is larger in international studies of the VSL than in the United States. However,
the fixed effect estimates cannot demonstrate whether the difference is a function of
different income levels or different preferences over fatal risk and money tradeoffs.
We utilize quantile regression estimates to investigate whether the income elasticity
of the VSL declines over the entire VSL distribution. If so, it indicates that some of
the difference between U.S. and international VSL elasticities is likely attributable
to differences in income levels. Our quantile regression estimator is of the form:
(q)
(q)
(q)
Ln(VSL j )(q) = β0 + β1 × Ln(Income j ) + ε j .
(3)
(q)
Using this equation, β1 is the income elasticity of the VSL at the q quantile of the
distribution. As with equation (1), we also estimate a version of equation (3) that
includes the standard error of the VSL estimate to address publication selection
bias.
Table 4 presents the results of estimating equation (3). For reference, Panel A
presents the distribution of VSL estimates in our sample. The median VSL estimate
is $10.3 million. The right tail of the distribution is about twice as long as the left
tail – the 95th percentile estimate is at $36.5 million, while the 5th percentile is
$0.7 million.
Panel B presents our estimates of the income elasticity throughout the VSL
distribution. The results indicate that the income elasticity of the VSL is largest for
the smallest VSLs, and smallest for the largest estimates. In particular, the elasticity is 2.58 at the 5th percentile, and it falls to 0.35 by the 95th percentile. The
elasticity almost decreases monotonically. The one exception is an increase at the
90th percentile to 0.64 from 0.44 at the 75th percentile. Each elasticity estimate
from the lower half of the distribution is statistically significantly different from the
estimate of the elasticity of the median.20 Conversely, each elasticity estimate from
20 We used bootstrapped standard errors using 500 repetitions to test for significant differences between
the quantiles. The test for the 5th percentile and 25th percentile had p < 0.01, while the test for the 10th
percentile had p = 0.02.
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240
Panel A: Raw Distribution of VSL Estimates
VSL estimate
($ millions)
5%
10%
25%
50%
75%
90%
95%
0.735
1.960
5.805
10.343
16.108
25.927
36.463
Panel B: Base Case Log VSL Quantile Regression
Ln income
($ thousands)
Constant
Pseudo R 2
5%
10%
25%
50%
75%
90%
95%
2.576
(0.502)***
–9.583
(1.886)***
0.101
1.497
(0.448)***
–4.745
(1.755)***
0.082
1.181
(0.139)***
–2.658
(0.526)***
0.056
0.460
(0.093)***
0.625
(0.356)*
0.024
0.438
(0.033)***
1.136
(0.110)***
0.022
0.643
(0.090)***
0.892
(0.337)***
0.050
0.347
(0.165)**
2.230
(0.636)***
0.045
Panel C: Log VSL Quantile Regression Controlling for Standard Error
Ln income
($ thousands)
Standard error
Constant
Pseudo R 2
5%
10%
25%
50%
75%
90%
95%
2.566
(0.369)***
0.014
(0.007)**
–9.576
(1.354)***
0.117
1.476
(0.443)***
0.010
(0.004)**
–4.716
(1.718)***
0.096
1.201
(0.118)***
0.009
(0.003)***
–2.790
(0.444)***
0.073
0.393
(0.095)***
0.033
(0.010)***
0.689
(0.356)*
0.068
0.331
(0.045)***
0.047
(0.003)***
1.214
(0.164)***
0.151
0.337
(0.090)***
0.054
(0.005)***
1.478
(0.339)***
0.240
0.249
(0.172)
0.055
(0.030)*
1.938
(0.514)***
0.298
Note: N = 953. Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.
W. Kip Viscusi and Clayton J. Masterman
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Table 4 Quantile Regression.
Income Elasticities and Global Values of a Statistical Life
241
the upper half of the distribution is statistically indistinguishable from the median
elasticity.21
Panel C extends the results from Panel B by adding standard error to the estimation.22 The coefficient on standard error is positive and significant at each quantile and tends to get larger in the upper half of the distribution. The elasticity estimates in Panel C are similar to those in Panel B. In the lower half of the distribution, the inclusion of the standard error changed each estimated elasticity by less
than 0.02. The changes are larger at the median and above. The 50th percentile,
75th percentile, and 95th percentile estimates decrease by between 0.07 and 0.10,
and the 90th percentile estimate decreases by 0.30. The pattern of elasticity estimates has a more monotonically decreasing pattern in Panel C because of the large
effect of including standard error on the upper half of the distribution. The income
elasticity of the VSL drops sharply from the 5th percentile of the distribution to the
median and then continues to drop at a much slower pace from the median to the
95th percentile.
Table 4 provides indirect support for the proposition that the income elasticity
of the VSL decreases as income increases. Because the income elasticity of the
VSL is positive, incomes increase over the distribution of the VSL. The pattern
in elasticities in Table 4 is thus consistent with elasticities increasing as incomes
decrease. However, Table 4 cannot rule out an elasticity that is constant with respect
to income but varies with factors that may correlate with income. More detailed
effects are difficult to identify with the available set of labor market VSL studies.23
Particularly confounding for present purposes is that out of the thirteen non-U.S.
countries in our data, only India and Pakistan are not upper income economies. As
the VSL literature for lower income countries continues to grow, researchers and
policymakers should refine our understanding of the relationship between the VSL
income elasticity and income levels.
5 International VSL transfer results
Section 3 demonstrated that the average income elasticity of the VSL in non-U.S.
countries is at least as high as 1.0. Table 5 summarizes the findings from Section 3,
presenting the income elasticities (and their corresponding confidence intervals)
21 p = 0.83, 0.19, and 0.48 for the 75th, 90th, and 95th percentile tests, respectively.
22 The test for the 5th percentile and 25th percentile had p < 0.01, while the test for the 10th percentile
had p = 0.02.
23 We attempted to directly identify nonconstant effects by adding (Ln(Income j ))2 to equation (1) or
(2). The coefficient on (Ln(Income j ))2 was highly insignificant ( p > 0.30 in all specifications), but a
test of the joint significance of both income coefficients always had p < 0.001.
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W. Kip Viscusi and Clayton J. Masterman
Table 5 Summary of VSL Income Elasticities for Different Samples and Specifications.
Whole sample
U.S. sample
International sample
Base mean estimates
Elasticity point estimate
Confidence intervals
0.781
0.519
1.103
(0.111)***
(0.118)***
(0.146)***
[0.193]***
[0.225]**
[0.070]***
(0.564, 1.000)
(0.287, 0.750)
(0.814, 1.391)
[0.396, 1.167]
[0.064, 0.973]
[0.958, 1.247]
0.775
0.511
1.102
(0.112)***
(0.117)***
(0.147)***
[0.197]***
[0.231]**
[0.070]***
(0.555, 0.995)
(0.281, 0.742)
(0.811, 1.394)
[0.382, 1.168]
[0.045, 0.977]
[0.957, 1.248]
953
763
190
Covariate mean estimates
Elasticity point estimate
Confidence intervals
Observations
Note: Base mean elasticities are from Table 2, Panel B and covariate mean elasticities are from Table 3.
Robust standard errors and corresponding 95% confidence intervals are in parentheses, and robust and
clustered standard errors and corresponding 95% confidence intervals are in brackets. *** p < 0.01,
** p < 0.05, * p < 0.1.
from estimating equation (1) in the specifications from Panel B of both Tables 2
and 3. The 95% confidence intervals for the income elasticity for the international
sample extend from 0.81 to 1.39 using robust standard errors and from 0.96 to
1.25 using standard errors clustered on article. Using these income elasticities, we
can transfer VSLs from the United States to other countries. If we assume that the
income elasticity is constant and equal across the countries of interest, for a country
c, the transferred VSL is given by:
YC η
VSLc = VSLUS ×
.
(4)
YUS
Equation (4) is derived by Hammitt and Robinson (2011). In equation (4), Y
denotes either country c or the United States’ average income, while η denotes
the income elasticity of the VSL. The income measure we use to transfer VSLs is
the GNI per capita from the World Bank.24 In 2015, the U.S. GNI per capita was
24 We use the World Bank’s GNI per capita numbers calculated using the Atlas method which is based
on exchange rates and inflation rates. We prefer the Atlas method over the purchasing power parity GNI
per capita data because the World Bank’s income classification groups are calculated using the Atlas
method. VSLs can be transferred using either method of calculating income.
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Income Elasticities and Global Values of a Statistical Life
243
Table 6 Projected VSL Levels by World Bank Income Group ($ millions).
International
Income level used
Mean low income economy
U.S. elasticity
Unit elasticity
elasticity
Highly elastic
0.519
1.0
1.103
2.0
0.931
0.107
0.067
0.001
1.191
0.171
0.113
0.003
1.895
0.420
0.304
0.018
2.425
0.676
0.514
0.047
3.309
1.229
0.995
0.157
4.356
2.088
1.784
0.453
7.787
6.395
6.131
4.247
$621.07
Low income economy threshold
$1026.00
Mean lower-middle economy
$2440.61
Lower-middle economy threshold
$4036.00
Mean upper-middle economy
$7146.35
Upper-middle economy threshold
$12,476.00
Mean upper income economy
$37,172.50
Note: U.S. and international elasticities are from Table 5. Base U.S. income is $55,980. Base U.S. VSL
of $9.631 million is from Viscusi and Masterman (2017) and Viscusi (2015).
$55,980. As discussed in Section 2, we use the $9.6 million base CFOI estimate as
the base U.S. VSL.
Table 6 presents the results of transferring VSLs for economies at various
income levels. To divide countries into low income, lower-middle income, uppermiddle income, and upper income, we use the World Bank’s income classification
groups. The World Bank classifies an economy as low income if it has a GNI per
capita of $1025 or less, lower-middle income if it has a GNI per capita between
$1026 and $4035, upper-middle income if it has a GNI per capita between $4036
and $12,475, and upper income if it has a GNI per capita of $12,476 or higher.
Table 6 presents our estimate of the VSL both using the mean GNI of countries in
each income group and a country at the income threshold. Out of the 189 countries that the World Bank provides GNI per capita measures for in 2015, 28 are
low income, 49 are lower-middle income, 52 are upper-middle income, and 60 are
upper income.
We utilize four different elasticities: our estimated base U.S. elasticity of 0.52
from Table 5, an elasticity of 1.0, our estimated base international elasticity of 1.10
from Table 5, and an elasticity of 2.0 from our estimates of the income elasticity
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244
W. Kip Viscusi and Clayton J. Masterman
in the lowest parts of the VSL distribution in Table 4. Using an income elasticity
of 1.0, the average VSL in a low income economy is $107,000. An economy at the
lower income threshold has a VSL of $171,000. A lower-middle income economy
has an average VSL of $420,000, while an economy at the lower-middle income
threshold has a VSL of $676,000. The average upper-middle income economy has
an average VSL of $1.23 million. An economy at the upper-middle income threshold has a VSL of $2.09 million. Finally, the average upper income country has a
VSL much higher than the rest at $6.40 million.25
Comparing the unit-elasticity VSLs to the other rows of Table 6 demonstrates
the importance of correctly estimating the income elasticity. If we apply the average base U.S. elasticity from Table 5, our estimate of the VSL for other nations
increases dramatically. The mean low income, lower-middle income, and uppermiddle income VSLs increase to $931,000, $1.90 million, and $3.31 million,
respectively. The upper income average also receives a relatively smaller bump
to $7.79 million. Applying our estimated average base international elasticity from
Table 5 similarly decreases the VSL for each country. The effect is again largest for
the low income economies, which decreases to $67,000, with the others similarly
following suit. Finally, utilizing an elasticity of 2.0 likewise greatly reduces the
VSL for low and middle income countries. The mean low income, lower-middle
income, and upper-middle income VSLs decrease to $1000, $18,000, and $157,000
when an elasticity of 2.0 is used.
In Table 7, we apply equation (4) to all 189 countries for which GNI per capita
numbers are available from the World Bank. We use an elasticity of 1.0 because
it is tractable and because we fail to reject the hypothesis that the international
elasticity is equal to 1.0 in any of our specifications. The large range of GNIs per
capita induce an equally large range of VSL estimates. The country with the largest
VSL is Bermuda at $18.3 million, with a GNI per capita of $106,140. The smallest
VSL is from Burundi equal to $45,000 using its GNI per capita of $260.
On the whole, our transferred VSLs exceed the values that policymakers in
foreign nations have utilized in the past.26 The United Kingdom’s Department of
Transport used a VSL of $2.3 million in 2015, while we find a U.K. VSL of $7.4
million. In 2014, Australia used a baseline VSL of $2.7 million. Transferring a VSL
based on the U.S. numbers demonstrates that Australia’s VSL is $10.3 million.
25 Transferred VSLs using the purchasing power parity GNI per capita data are largely consistent with
these. The transferred VSLs for mean low income, lower-middle income, upper-middle income, and
upper income economies are $127,000, $397,000, $1.3 million, and $5.7 million, respectively.
26 Each of the following example values are drawn from Narain and Sall (2016) and converted to
2015 dollars. We adjust the values for inflation alone, not income growth, as these reflect the VSLs the
countries used in the past.
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Income Elasticities and Global Values of a Statistical Life
245
Table 7 International Income-Adjusted Estimates of the VSL.
GNI per capita
VSL
GNI per capita
($ thousands) ($ millions)
VSL
($ thousands) ($ millions)
Afghanistan
0.610
0.105 Cambodia
1.070
0.184
Albania
4.280
0.736 Cameroon
1.320
0.227
Algeria
4.870
0.838 Canada
47.540
8.179
Andorra
43.270
7.444 Central African Republic
0.330
0.057
Angola
4.180
0.719 Chad
0.880
0.151
Antigua and Barbuda
13.270
2.283 Chile
14.100
2.426
Argentina
12.460
2.144 China
7.930
1.364
Armenia
3.880
0.668 Colombia
7.140
1.228
Australia
60.070
10.335 Comoros
0.780
0.134
Austria
47.410
Azerbaijan
6.560
8.157 Congo, Dem. Rep.
0.410
0.071
1.129 Congo, Rep.
2.540
0.437
10.400
1.789
Bahamas, The
20.740
3.568 Costa Rica
Bahrain
19.840
3.413 Côte d’Ivoire
Bangladesh
Barbados
1.420
0.244
1.190
0.205 Croatia
12.700
2.185
14.510
2.496 Cyprus
25.990
4.471
Belarus
6.460
1.111 Czech Republic
18.140
3.121
Belgium
44.250
7.613 Denmark
58.550
10.073
Belize
4.490
0.772 Dominica
6.800
1.170
Benin
0.840
0.145 Dominican Republic
6.240
1.074
6.030
1.037
Bermuda
106.140
18.261 Ecuador
Bhutan
2.380
0.409 Egypt
3.340
0.575
Bolivia
3.000
0.516 El Salvador
3.940
0.678
Bosnia and Herzegovina
4.670
0.803 Equatorial Guinea
12.820
2.206
Botswana
6.460
1.111 Estonia
18.360
3.159
Brazil
Brunei Darussalam
9.850
38.010
1.695 Ethiopia
0.590
0.102
6.539 Fiji
4.830
0.831
Bulgaria
7.480
1.287 Finland
46.550
8.009
Burkina Faso
0.640
0.110 France
40.540
6.975
Burundi
0.260
0.045 Gabon
9.200
1.583
Cabo Verde
3.280
0.564 Gambia, The
0.460
0.079
Continued on next page.
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W. Kip Viscusi and Clayton J. Masterman
Table 7 (Continued).
Georgia
4.160
0.716
Lebanon
7.710
1.326
Germany
45.940
7.904
Lesotho
1.280
0.220
Ghana
1.480
0.255
Liberia
0.380
0.065
Greece
20.320
3.496
Lithuania
14.940
2.570
Grenada
8.650
1.488
Luxembourg
77.000
13.247
Guatemala
3.590
0.618
Macao
67.180
11.558
Guinea
0.470
0.081
Macedonia, FYR
5.140
0.884
Guinea-Bissau
0.590
0.102
Madagascar
0.420
0.072
Guyana
4.090
0.704
Malawi
0.340
0.058
Haiti
0.810
0.139
Malaysia
10.570
1.819
1.196
Honduras
2.280
0.392
Maldives
6.950
Hong Kong
41.000
7.054
Mali
0.760
0.131
Hungary
12.980
2.233
Malta
23.930
4.117
Iceland
50.140
8.626
Marshall Islands
4.770
0.821
India
1.600
0.275
Mauritania
1.370
0.236
Indonesia
3.440
0.592
Mauritius
9.780
1.683
Iran
6.550
1.127
Mexico
9.710
1.671
Iraq
5.820
1.001
Micronesia, Fed. Sts.
3.560
0.612
Ireland
52.580
9.046
Moldova
2.240
0.385
Isle of Man
85.290
14.674
Mongolia
3.870
0.666
Israel
35.770
6.154
Montenegro
7.220
1.242
Italy
32.810
5.645
Morocco
3.030
0.521
0.102
Jamaica
5.050
0.869
Mozambique
0.590
Japan
38.840
6.682
Myanmar
1.160
0.200
Jordan
4.680
0.805
Namibia
5.190
0.893
Kazakhstan
Kenya
Kiribati
11.390
1.960
Nauru
15.420
2.653
1.340
0.231
Nepal
0.730
0.126
8.406
3.390
0.583
Netherlands
48.860
27.450
4.723
New Zealand
40.020
6.885
Kosovo
3.970
0.683
Nicaragua
1.940
0.334
Kuwait
42.150
7.252
Niger
0.390
0.067
Kyrgyz Republic
1.170
0.201
Nigeria
2.820
0.485
Lao PDR
1.740
0.299
Norway
93.740
16.127
14.980
2.577
Oman
16.910
2.909
Korea, Rep.
Latvia
Continued on next page.
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Income Elasticities and Global Values of a Statistical Life
247
Table 7 (Continued).
Pakistan
1.440
0.248
St. Vincent
6.630
1.141
Palau
12.180
2.095
Sudan
1.920
0.330
Panama
11.880
2.044
Suriname
9.360
1.610
Papua New Guinea
2.240
0.385
Swaziland
3.280
0.564
Paraguay
4.190
0.721
Sweden
57.920
9.965
Peru
6.130
1.055
Switzerland
84.630
14.560
Philippines
3.550
0.611
Tajikistan
1.280
0.220
Poland
13.340
2.295
Tanzania
0.920
0.158
Portugal
20.530
3.532
Thailand
5.720
0.984
Puerto Rico
19.320
3.324
Timor-Leste
2.180
0.375
Qatar
83.990
14.450
Tonga
4.280
0.736
9.500
1.634
Togo
0.540
0.093
11.450
1.970
Trinidad and Tobago
17.640
3.035
0.700
0.120
Tunisia
3.980
0.685
Romania
Russian Federation
Rwanda
Samoa
3.930
0.676
Turkey
9.950
1.712
São Tomé and Principe
1.760
0.303
Turkmenistan
7.380
1.270
23.550
4.052
Tuvalu
6.230
1.072
0.980
0.169
Uganda
0.700
0.120
Saudi Arabia
Senegal
Serbia
Seychelles
Sierra Leone
Singapore
5.540
0.953
Ukraine
14.760
2.539
United Arab Emirates
2.640
0.454
43.090
7.413
0.620
0.107
United Kingdom
43.390
7.465
52.090
8.962
United States
55.980
9.631
15.720
2.705
Slovak Republic
17.570
3.023
Uruguay
Slovenia
22.190
3.818
Uzbekistan
2.160
0.372
Solomon Islands
1.920
0.330
Vanuatu
3.170
0.545
South Africa
6.080
1.046
Vietnam
1.990
0.342
South Sudan
0.790
0.136
West Bank and Gaza
3.090
0.532
0.196
Spain
Sri Lanka
St. Kitts and Nevis
St. Lucia
28.530
4.908
Yemen, Rep.
1.140
3.800
0.654
Zambia
1.490
0.256
15.060
2.591
Zimbabwe
0.860
0.148
7.350
1.265
Note: All VSLs are calculated using an income elasticity of 1.0. Base U.S. VSL of $9.631 is from
Viscusi and Masterman (2017).
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248
W. Kip Viscusi and Clayton J. Masterman
Colombia used a VSL of $1.1 million to evaluate water sanitation in 2008, very
close to our transferred Colombian VSL of $1.2 million.
6 Conclusion
This article has analyzed the full set of labor market VSL studies to measure the
income elasticity of the VSL. Our results demonstrate that the income elasticity
ranges for the United States are not consistent with the income elasticities in nonU.S. countries. While estimates of the income elasticity for the whole sample and
U.S. sample of VSL estimates fall within a range of 0.5–1.0, our point estimate of
the international estimate is above the range at about 1.1. Using the conventional
range of elasticities derived from U.S. studies can dramatically overstate the VSL
once the U.S. VSL is transferred to other countries. Current data support using an
elasticity of at least 1.0 for non-U.S. countries.
That international estimates of the income elasticity may be greater is borne
out in our quantile regression analysis, which demonstrated that the VSL income
elasticity falls as the VSL level increases. This finding echoes the quantile regression results in Kniesner et al. (2010) in which the VSL income elasticity declines
for U.S. workers with higher income levels. Combined with our results showing
that the U.S. income elasticity is significantly smaller than the international VSL
elasticity, the quantile regression results show that the international income elasticity of the VSL likely falls as income rises. Further research on the relationship
between income and the elasticity of income may refine this dependence of the
income elasticity on the VSL, especially as more labor market studies in low and
middle income economies emerge.
Our approach is able to derive a VSL for almost 200 countries using a base U.S.
VSL of $9.6 million, a U.S. income of $55,980, and a VSL elasticity of 1.0 to calculate a VSL for each country. We also estimate that low income, lower-middle
income, upper-middle income, and upper income countries should use average
VSLs of $107,000, $420,000, $1.2 million, and $6.4 million, respectively, based
on the World Bank income group criteria. The international differences in the VSL
will have ramifications for efficient regulatory policies, which will tend to be more
stringent in more affluent countries. Because many countries will continue to lack
detailed data on employment and workplace fatalities, transferring VSLs from the
full sample of VSL estimates remains the most reliable way to generate a revealed
preference VSL estimate for low and middle income countries. This benefit transfer approach will remain desirable until researchers develop more credible countryspecific VSL estimates.
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Income Elasticities and Global Values of a Statistical Life
249
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