Syracus e Universit y [615623]

Syracus e Universit y
SUR FACE
Center for P olicy Research Maxwell Schoo l of C itizenship a nd P ublic A ffair s
2011
The V alue of a S tatistical Li fe: E vidence f rom P anel
Data
Thom as J. Knies ner
Syracuse U niversity, TKnie sne@M axwell.Syr.Edu
W. Kip Viscusi
Vanderbilt University
Christophe r W oock
The Co nference Bo ard
Follow thi s and a dditional w orks at:http://s urface.syr.edu/c pr
Part of the Public Policy Common s
This Working Paper is brought to you for f ree and ope n access by the M axwell Schoo l of C itizenship a nd P ublic A ffair s at SURFACE. It has be en
accepted for inclusion in C enter for P olicy Research b y an author ized admini strator of S URFACE. For mor e infor mation, p lease contact
surface@s yr.edu.Recomme nded Citation
Knie sner, Thom as J.; Viscusi, W. Kip; a nd W oock , Christopher, "The V alue of a S tatistical L ife: E vidence from P anel Data" (2011).
Center for Policy Research.Paper 44.
http://s urface.syr.edu/c pr/44

ISSN: 1525 -3066

Center for Policy Research
Working Paper No. 122

THE VALUE OF A STATISTICAL LIFE:
EVIDENCE FROM PANEL DATA

Thomas J. Kniesner, W. Kip Viscusi,
Christopher Woock and James P. Ziliak

Center for Policy Research
Maxwell School of Ci tizenship and Public Affairs
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March 2010

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CENTER FOR POLICY RESEARCH – Spring 2010

Christine L. Himes, Director
Maxwell Professor of Sociology
__________

Associate Directors

Margaret Austin
Associate Director
Budget and Administration

Douglas Wolf John Yinger
Gerald B. Cramer Professor o f Aging Studies Professor of Economics and Public Administration
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SENIOR RESEARCH ASSOCIATES

Badi Baltagi ……………………………………… Economics
Robert Bifulco …………………….. Public Administration
Leonar d Burman .. Public Administration /Economics
Kalena Cortes………………………………Education
Thomas Dennison ……………… Public Administration
William Duncombe ……………… Public Administration
Gary Engelhardt ……………………………….Economics
Deborah Freund .. Public Administration /Economics
Madonna Harrington Meyer …………………. Sociology
William C. Horrace …………………………….Economics
Duke Kao………………………………………… Economics
Eric Kingson ………………………………….. Social Work
Sharon Kioko…………………..Public Administration
Thomas Kniesner ……………………………. Economics
Jeffrey Kubik …………………………………… Economics
Andrew London …………………………………. Sociology
Len Lopoo …………………………. Public Administration
Amy Lutz …………………………………………… Sociology
Jerry Miner ………………………………………. Economics
Jan Ondrich …………………………………….. Economics
John Palmer ……………………… Public Administration
David Popp ……………………….. Public Administration
Christopher Rohlfs ……………………………. Economics
Stuart Rosenthal ………………………………. Economics
Ross Rubenstein ……………….. Public Administration
Perry Singleton……………………………Economics
Margaret Usdansky ……………………………. Sociology
Michael Wasylenko ………………………….. Economics
Jeffrey Weinstein…………………………Economics
Janet Wilmoth ……………………………………. Sociology

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Charles Alamo …………………….. Public Administration
Matthew Baer ……………………… Public Administration
Maria Brown ………………………………… Social Science
Christian Buerger ………………… Public Administ ration
Qianqian Cao ……………………………………. Economics
Il Hwan Chung …………………….. Public Administration
Kevin Cook …………………………. Public Administration
Alissa Dubnicki ………………………………….. Economics
Katie Francis ………………………. Public Administration
Andrew Friedson ……………………………….. Economics
Virgilio Galdo …………………………………….. Economics
Pallab Ghosh …………………………………….. Economics
Clorise Harvey …………………….. Publi c Administration
Douglas Honma ………………….. Public Administration
Becky Lafrancois ……………………………….. Economics
Hee Seung Lee …………………… Public Administration
Jing Li ………………………………………………. Economics
Wael Moussa …………………………………….. Economics
Phuong Nguyen …………………… Public Administration
Wendy Parker ……………………………………… Sociology
Leslie Powell ………………………. Public Administration
Kerri Raissian ……………………… Public Administration
Amanda Ross ……………………………………. Economics
Ryan Sullivan ……………………………………. Economics
Tre Wentling ……………………………………….. Sociology
Coady Wing ………………………… Public Administration
Ryan Yeung ………………………… Public Administration
Can Zhao …………………………. ……….. Social Science
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Abstract
Our research addresses fundamental long -standing concerns in the compensating
wage differentials literature and its public policy implications: the econometric properties
of estimates of the value of statistical life ( VSL) and the wide range of su ch estimates
from about $0 to almost $30 million. Here we address most of the prominent econometric issues by applying panel data, a new and more accurate fatality risk measure, and systematic application of panel data estimators. Controlling for measureme nt error,
endogeneity, latent individual heterogeneity that may be correlated with the regressors, state dependence, and sample composition yields an estimated value of a statistical life of about $7 million–$12 million, which we show can clarify greatly t he cost -effectiveness of
regulatory decisions. We show that probably the most important econometric issue is controlling for latent heterogeneity; less important is how one does it.

JEL No. C23, I10, J17, J28, K00
Key Words: VSL, panel data, fixed effects, random effects, long -differences, PSID

Thomas J. Kniesner, Krisher Professor of Economics, Senior Research Associate, Center for Policy Research, Syracuse University, Syracuse, NY & Research Fellow, IZA
W. Kip Viscusi, University Distinguished Profess or of Law, Economics, and
Management, Vanderbilt University, Nashville, TN
Christopher Woock, Research Associate, The Conference Board, New York, NY
James P. Ziliak, Carol Martin Gatton Chair in Microeconomics, Director, Center for Poverty Research , Univer sity of Kentucky, Lexington, KY
Address correspondence to
tkniesne@maxwell.syr.edu .
We are grateful for the helpful comments of Badi Baltagi and to the U.S. Bureau of Labor Statistics for providing proprietary data on workplace fatalities, which we used to
construct fatality rates. The findings herein do not reflect the opinion of the BLS or any other federal agency.

1. Introduction
The value of statistical life ( VSL) concept based on econometric estimates of
wage -fatality risk tradeoffs in the labor market is well established in the economics
literature. The method provides the yardstick that the U.S. Office of Management and
Budget (OMB) requires agencies to use in valuing fatality risks reduced by regulatory
programs.1
We begin with an econometric framework that is a slight extension of the usual
hedonic wage equation used in the value of statistical life literature. For worker i (i =
1,…,N ) in industry j (j = 1,…,J ) and occupation k (k = 1,…,K ) at time t ( t = 1,…,T ) the
hedonic tradeoff between the wage and risk of fatality is described by
More recently, VSL estimates have also provided the basis for assessing a
broad range of issues from the mortality costs of the Iraq war (Wallsten and Kosec 2005, Bilmes and Stiglitz 2006) to a refined measurement of economic growth (Jena, Mull igan,
Philipson, and Sun 2008) . Notwithstanding the wide use of the VSL approach , there is
still concern over excessively large/small estimates and the wide range of VSL estimates .
One approach to dealing with the dispersion of VSL estimates , which has been used by
the U.S. Environmental Protection Agency , has been to rely on meta analyses of the labor
market VSL literature . Our research demonstrates how using the best available data and
econometric practices affects the estimated VSL so as to narrow the range of estimates .
001 lnijkt i i jkt ijkt ijktw Xu ααα π β+−=++ + + , (1)
where ln w ijkt is the natural log of the hourly wage rate ; πjkt is the industry and occupation
specific fatality rate; X ijkt is a vector containing dummy variables for the worker’s one –
digit occupation (and industry in some specifications), state and region of residence, plus

1 See U.S. Office of Management and Budget Circular A -4, Regulatory Analysis (Se pt. 17, 2003) which is
available at http://www.whitehouse.gov/omb/circulars/a004/a -4.pdf.

the usual demographic variables: worker education, age and age squared, race, marital
status, and union status ; uijkt is an error term allowing conditional heteroskedasticity and
within industry by occupation autocorrelation.2
0()iα+ Equation (1) is slightly unfamiliar as it
contains two latent individual effects: one that is positively correlated with wages and the
fatality rate and one that is positively correlated with wages and negatively
correlated with the fatality rate0()iα−. The first individual effect reflects unmeasured job
productivity that leads more productive/hi gher wage workers to take safer jobs and the
second individual effect reflects unmeasured individual differences in personal safety
productivity that leads higher wage workers to take what appears to be more dangerous jobs because the true danger level for such a worker is lower than the measured fatality
rate. Our research uses equation (1) in conjunction with a variety of econometric
techniques , which demonstrate s the capabilities of individual panel data that incorporate
fatality risk measures that vary by year.
To set the stage, an extremely wide range of labor market VSL estimates from
micro cross -section data has generated a series of prominent econometric controversies
reviewed by Viscusi and Aldy ( 2003 ). Hedonic equilibrium in the labor market means
that equation ( 1) traces out the locus of labor market equilibria involving the offer curves
of firms and the supply curves of workers . A salient concern in estimating and
interpreting equation (1) involve s the fatality risk variable, which ideally should serve as
a measure of the risk beliefs of workers and firms for the particular job. Broadly defined risk measures, such as those pertinent to one’s industry or general occupation, may

2 We adopt a parametric specification of the regression model representing hedonic equilibrium in (1) for
comparison purposes with the existing literature. An importa nt emerging line of research is how more
econometrically free -form representations of hedonic labor markets facilitates identification of underlying
fundamentals, which would further generalize estimates of VSL (Ekeland, Heckman, and Nesheim 2004).

involve substantial measurement error . Other concerns are over the potential endogeneity
of the job risk measure (Ashenfelter and Greenstone 2004a) and possible state
dependence in wages (MaCurdy 2007) . Here we will exploit the capabilities of a very
refined risk measure defined over time and by occupation and industry, couple d with
panel data on workers’ labor market decisions, to resolve many prominent issues in the
hedonic labor market literature . Because o ur focus is on the average VSL across a broad
sample of workers , we will consequently not explore emerging interest in the
heterogeneity of VSL by age and other personal characteristics (Kniesner, Viscusi, and
Ziliak 2006; Aldy and Viscusi 2008) .
We dev ote particular attention to measurement errors, which have been noted in
Black and Kniesner (2003) , Ashenfelter and Greens tone (2004b), and Ashenfelter (2006) .
Although we do not have information on subjective risk beliefs, we use very detailed data on objective risk measures and consider the possibility that workers are driven by risk
expectations . Published industry risk be liefs are strongly correlated with subjective risk
values ,
3
We address the pivotal issue of measurement error in several ways. The fatality
risk variable is not by indust ry or occupation alone, as is the norm in almost all previous
studies, but is a refined measure based on 720 industry -occupation cells. We use not only
one-year but also three -year averages to reduce the influence of random year -to-year and we follow the standard practice of matching to workers in the sample an
objective risk measure. Where we differ from most previous studies is the pertinence of
the risk data to the worker’s pa rticular job, and ours is the first study to account for the
variation of the more pertinent risk level within the context of a panel data study.

3 See Viscusi and Aldy (2003) for a review.

fluctuations.4
As mentioned earlier , potential biases in VSL estimates can arise from unmodeled
worker productivity and safety -related productivity as reflected in Because the fatality rate data are available by year, workers in our panel
who do not change jobs can also have a different fatality risk in different years. In
contrast, the only previous panel -based labor market VSL study used the same
occupational risk meas ure based on the 1967 Society of Actuaries data for 37 narrowly
defined high risk occupations for all years, so that all possible variation in risk was
restricted to workers who changed occupations (Brown 1980). Our research also explores
using adjacent observation differences as well as long er differences, for which the
influence of measurement error should be less pronounced (Griliches and Hausman
1986) . In addition, we examine how instrumental variable estimates for each approach
attenuates measurement error and endogeneity bias. Finally, our rational expectations and
dynamic first- difference models’ estimates make it possible to include longer -run worker
adaptations to changes in their job risk level that may occur if they are not perfectly informed about the risk initially.
0()iα+ and 0()iα−
in
equation (1) (Hwang, Ree d, and Hubbard 1992; Viscus i and Hersch 2001; Shogren and
Stamland 2002) . Panel data allow the researcher to sweep out all such time invariant
individual effects and to infer their relative importance in terms of biasing VSL if ignored
econometrically . In each instance, we use the pertinent instrumental variables estimator.
Our work also distinguishes job movers from job stayers . We find that m ost of the
variation in risk and most of the evidence of positive VSL s stems from people changing

4 The only previous use of the fatality rate data at our level of disaggregation and for different perio ds of
time is in Viscusi (2004). Kniesner, Viscusi, and Ziliak (2006) also used the 720 cell measure but not the
multi -year averages. Neither study employed panel -data econometric techniques.

jobs across occup ations or industries possibly endogenously rather than from variation in
risk levels over time in a given job setting .
Our econometric refinements using panel data have a substantial effect on the
estimated VSL levels. They reduce the estimated VSL by more than 50 percent from the
implausibly large cross -section PSID -based VSL s of $20–30 million . We demonstrate
how systematic econometric modeling narrows t he estimated value of a statistical life
from about $0–$30 million to about $7 million –$12 million, which we then show clarifies
the choice of the proper labor market based VSL for policy evaluations .
2. Panel Data Econometric Framework
Standard panel -data estimators permitting latent worker -specific heterogeneity
through person- specific intercepts in equation (1) are the deviation from time -mean
(within) estimator and the time -difference (first – and long -differences) estimator s. The
fixed effects include all person -specific time -invariant differences in tastes and all aspects
of productivity , which may be correlated with the regressors in X . The two estimators
yield identi cal results when there are two time periods and when the number of periods
converges towards infinity. With a finite number of periods ( T > 2) , estimates from the
two different fixed -effec ts estimators can diverge due to possible non- stationarity in
wages, measurement error, or model misspecification (Wooldridge 2002). Because wages
from longitudinal data on individuals have been shown to be non- stationary in other
contexts (Abowd and Card 1989; MaCurdy 2007 ), we adopt the first -difference model as
a baseline.
The first -difference model eliminates time -invariant effect s by estimating the
changes over time in hedonic equilibrium

1 lnijkt jkt ijkt ijkt w Xuαπ β ∆ = ∆ +∆ +∆ , (2)
where ∆ refers to the first -difference operator (Weiss and Lillard 1978) .
The first -difference model could exacerbate errors -in-variables problems relative
to the within model (Griliches and Hausman 1986). If the fatality rate is measured with a
classical error , then the first -difference estimate of 1ˆα may be attenuated relative to the
within estimate. An advantage of the regression specification in equation (2), which
considers intertemporal changes in hedonic equilibrium outcomes, arises because we can
use so -called wider (2+ year) differences. If ∆ ≥ 2 then measurement error effects are
mitigated in equation (2) relative to within -differences regression (Griliches and
Hausman 1986; Hahn, Hausman, and Kuersteiner 2007). As discusse d in the data section
below , we additionally address the measurement error issue in the fatality rate by
employing multi- year averages of fatalities. For completeness we also note how the first –
difference and longer -differences estimates compare to the within estimates.
Lillard and Weiss (1979) demonstrated that earnings functions may not only have
idiosyncratic differences in levels but also have idiosyncratic differences in growth. To
correct for wages that may not be difference stationary as implied by equation (2) we
estimate a double differenced version of equation (2) that is
2 22 2
1 lnijkt jkt ijkt ijkt w Xuαπ β ∆ = ∆ +∆ +∆ , (3)
where 2
1 tt− ∆ =∆ −∆ , commonly known as the difference -in-difference operator .
Finally, w e also estimate a dynamic version of equation (2) by adding γ∆ ln wijkt−1
to the right -hand side and using two first-difference instrumental variables estimator s: (i)
using the two -period lagged level of the dependent variable as an identifying instrument
for the one -period lagged difference in the dependent variable (Greene 2008, Chapter 15)

and ( ii) using an instrument set that grow s as the time -series dimension of the panel
evolves (Arellano and Bond 1991) . The lagged dependent variable controls for additional
heterogeneity and serial correlation plus sluggish adjustment to equilibrium (state
dependence). We therefore compare the estimated short -run effect, 1ˆα, to the estimated
long-run effect, 1ˆˆ/(1 )αγ−, and their associated VSL s.
2.1 Comparison Estimators
If [ | , ]0ijk jk ijkEu Xπ= and ,
0[ | , ]0i jk ijk EXαπ+−=, which are the zero conditional
mean assumptions of least squares regression, then OLS estimation of the hedonic
equilibrium in equation (1) using pooled cross -section time -series data is consistent. If
the zero conditiona l mean assumption holds, which is unlikely to be the case, then the
two basic estimators frequently employed with panel data, the between -groups estimator
and the random -effects estimator, will yield consistent coefficient estimates.
The between -groups est imator is a cross -sectional estimator using individuals’
time-means of the variables
1 lnijk jk ijk ijk w Xuαπ β δ= + ++ , (4)
with
11ln lnT
ijk ijkt
twwT==∑ and other variables similarly defined. A potential advantage of
the between -groups estimator is that me asurement -error induced attenuation bias in
estimated coefficients may be reduced because averaging smoothes the data generating
process. Because measurement error affects estimates of the VSL (Black and Kniesner
2003; Ashenfelter 2006 ), the between -groups estimator should provide improved
estimates of the wage -fatal risk tradeoff over pooled time -series cross -section OLS
estimates of equation (1).

The random -effects model differs from the OLS model in equation (1) by explicit
inclusion of the latent heter ogeneity terms, 00,iiαα+−, in the model’s error structure, but is
similar to OLS in that this additional source of error is also treated as exogenous to the
fatality risk and other demographic variables. The implication is that selection into possibly risky occupations and industries on the basis of unobserved productivity and tastes is purely random across the population of workers. Although both the pooled least squares and between -groups estimators remain consistent in the presence of random
heterogeneity, the random -effects estimator will be more efficient because it accounts for
person- specific autocorrelation in the wage process. The random -effects estimator is thus
a weighted average of the between -groups variation and the within- groups variation.
Finally, suppose that selection into a particular industry and occupation is not
random with respect to time -invariant unobserved productivity and risk preferences . In
the non- random selection case, estimates of VSL based on the pooled cross -section,
between -groups, or random -effects estimators will be biased and inconsistent; the first –
differences and double -differences estimators in equations (2) and (3) , as well as the
dynamic first-difference estimator , can be consistent despite non- random job switching .
2.2 Research Objective
The focal parameter of interest in each of the regression models we estimate is
1ˆ,α which is used in constructing estimates of the value of a statistical life. Accounting
for the fact that fat ality risk is per 100,000 workers and that the typical work- year is
about 2000 hours, the estimated value of a statistical life at the mean level of wages is
1ˆˆ ( ) 2000 100,000wVSL wαπ∂= =×× ×∂. (5)

Although the VSL function in equation ( 5) can be evaluated at various points in the wage
distribution, most studies report only the mean effect. To highlight the differences in
estimates of the VSL with and without controls for unobserved individual differences, we
follow the standard convention of focusing on VSL in our estimates presented below.
Our primary objective is to examine how following systematic econometric practices for panel data models reduces the estimated range of VSL. However, we also present
estimates of the mean VSL using t he sample average of hours worked,
, in lieu of 2,000
hours . In addition, we provide 95 percent confidence intervals around the mean VSL .
3. Data and Sample Descriptions
The main body of our data come from the 1993–2001 waves of the Panel Study of
Income Dynamics (PSID), which provides individual -level data on wages, industry and
occupation, and demographics. The PSID survey has followed a core set of households since 1968 plus newly formed households as members of the original core have split off
into new families.
3.1 PSID Sample
The sample we use consists of male heads of household ages 18–65 who are in
the random Survey Research Center (SRC) portion of the PSID, and thus excludes the
oversample of the poor in the Survey of Economic Opportunity (SEO) and the Latino sub-sample . The male heads in our regressions (i) worked for hourly or salary pay at
some point in the previous calendar year, (ii) are not permanently disabled or institutionalized, ( iii) are not in agriculture or the armed force s, (iv) have a real hourly

wage greater than $2 per hour and less than $100 per hour, and (v) have no missing data
on wages, education, region, industry, and occupation.
Beginning in 1997 the PSID moved to every other year interviewing. For
consistent spac ing of survey response we use data from the 1993, 1995, 1997, 1999, and
2001 waves . The use of every other year responses will be one of many mechanisms to
reduce the influence of measurement error in our estimated VSL . We do not require
individuals to be present for the entire sample period; we have an unbalanced panel where we take missing values as random events.
5
The focal variable from the PSID in our models of hedonic labor market
equilibrium is the hourly wage rate. For workers paid by the hour the survey records the gross hourly wage rate. The interviewer asks sala ried workers how frequently they are
paid, such as weekly, bi -weekly, or monthly. The interviewer then norms a salaried
worker's pay by a fixed number of hours worked depending on the pay period. For example, salary divided by 40 is the hourly wage rate constructed for a salaried worker paid weekly. We deflate the nominal wage by the personal consumption expenditure deflator for 2001 base year. We then take the natural log of the real wage rate to minimize the influence of outliers and for ease of compariso n with others’ estimates. Our sample f ilters yield 2,036 men and
6,625 person- years. About 40 percent of the men are present for all five waves (nine
years); another 25 percent are present for at least four waves.
The demographic controls in the model include years of formal education, a
quadratic in age, dummy variables for state of residence, dummy indicators for region of country (northeast, north central, and west with south the omitte d region), race (white =

5 Ziliak and Kniesner (1998) show that when there is nonrandom a ttrition our differenced data models
should remove it along with the other time -invariant factors.

1), union status (coverage = 1), marital status (married = 1), and one -digit occupation.
Table 1 presents summary statistics.
3.2 Fatality Risk Measures
We use the fatality rate for the worker’s two -digit industry by one -digit
occupation group. We distinguished 720 industry -occupation groups using a breakdown
of 72 two- digit SIC code industries and the 10 one -digit occupational groups. After
constructing codes for two- digit industry by one -digit occupation in the PSID we then
match ed each worker to the relevant industry -occupation fatality risk. We constructed a
worker fatality risk variable using proprietary U.S. Bureau of Labor Statistics data from
the Census of Fatal Occupational Injuries (CFOI) for 1992–2002.6
The CFOI provides the most comprehensive inventory to date of all work -related
fatalities in a given year . The CFOI data come from reports by the Occupational Safety
and Health Administration, workers’ compensation reports, death certificates, and medical examiner reports. To be classified as a work -related injury the decedent must
have been employed at the time of the fatal event and engaged in legal work activity that required the worker be present at the site of the fatal incident. In each case the BLS
verifies the work status of the decedent with two or more of the above source documents or with a follow -up questionnaire in conjunction with a source document .
The underlying assumption in our research and almost the entire hedonic
literature more generally is that the s ubjective risk assessments by workers and firms can

6 The fatality data can be obtained on CD -ROM via a confidential agreement with the U.S. Bureau of Labor
Statistics. Our variable construction procedure follows that in Viscusi (2004), which describes the
properties of the 720 industry -occupation breakdown in greater detail. In our basic estimation sample we
limit observations to those where the annual change in fatality risk is no less than − 75 percent and no more
than +300 per cent. In our subsequent robustness checks in Table 8 we examine what happens to VSL if we
apply the same screen to the three- year change or eliminate the screen completely.

be captured by objective measures of the risk. Workers and firms use available
information about the nature of the job and possibly the accident record itself in forming
risk beliefs . The models do not as sume that workers and firms are aware of the published
risk measures at any point in time . Rather, the objective measures serve as a proxy for the
subjective beliefs . Previous research reviewed in Viscusi and Aldy (2003) has indicated a
strong correlation between workers’ subjective risk beliefs and published injury rates .
Because our fatality risk variable is by industry and by occupation, it will provide a much more pertinent measure of the risk associated with a particular job than a more broadly
based i ndex, such as the industry risk alone, which is the most widely used job risk
variable. For example, miners and secretaries in the coal mining industry face quite
different risks , so that taking into account the occupation as well as the industry as we do
here substantially reduces the measurement error in the fatality risk variable. The importance of the industry -occupation structure of our risk variable is
especially great within the context of a panel data analysis . The previous panel study by
Brown (1980) used a time -invariant fatality risk measure for 37 relatively high risk
occupations . By using a fatality risk variable that varies over time and is defined for 720
industry -occupation groups, we greatly expand the observed variance in workers’ job
risks across different periods .
We construct two measures of fatal risk, which differ according to the numerator.
The first measure simply uses the number of fatalities in each industry -occupation cell.
The second measure uses a three -year average of fataliti es surrounding each PSID survey
year (1992–1994 for the 1993 wave, 1994–1996 for the 1995 wave, and so on). The denominator for each measure used to construct the fatality risk is the number of

employees for that industry -occupation group in survey year t . Both of our two measures
of the fatality risk are time -varying because of changes in both the numerator and the
denominator.7
We expect there to be less measurement error in the 3 -year average fatality rates
relative to the annual rate because the averagi ng process will reduce the influence of
random fluctuations in fatalities as well as mitigate the small sample problems that arise
from many narrowly defined job categories. We also expect less reporting error in the industry information than in the occupa tion information, so even our annual measure
should have less measurement error than if the worker’s occupation were the basis for matching (Mellow and Sider 1983, Black and Kniesner 2003). But to further reduce the
influence of large swings in fatality ri sk, we drop person- years where the percentage
change in fatality risk exceeds a positive 300 percent or negative 75 percent . Table 1 lists
the means and standard deviations for both fatality risk measures. The sample mean fatality risk for the annual measu re is 6.4/100,000. As expected, the variation in the
annual measure exceeds that of the 3 -year average.
Our research also avoids a problem plaguing past attempts to estimate the wage –
fatal risk tradeoff with panel data. If the fatality rate is an aggregat e by industry or
occupation the within or first -difference transformation leaves little variation in the
fatality risk measure to identify credibly the fatality parameter. Most of the variation in aggregate fatal ity risk is of the so- called between -groups variety (across occupations or
industries at a point in time) and not of the within -groups variety (within either
occupations or industries over time). Although between -group variation exceeds within-

7 We used the bi -annual employment averages from the U.S. Burea u of Labor Statistics, Current Population
Survey, unpublished table, Table 6, Employed Persons by Detailed Industry and Occupation for 1993–
2001.

group variation (Table 2) , the within variation in our m ore disaggregate measures is
sufficiently large ( about 33–40 percent of the between variation) so that it may be
feasible to identify the fatal risk parameter and VSL in our panel data models. Finally, we
also address the issue that between -group variation in fatality risk may be generated by
endogenous job switching.
4. Wage Equation Estimates
Although we suppress the coefficients for ease of presentation, each regression
model we use controls for a quadratic in age, years of schooling, indicators for reg ion,
marital status, union status, race, and one -digit occupation. Because of the substantial
heterogeneity of jobs in different occupations , the regressions include a set of one -digit
occupation dummies. In addition, because there might be unmeasured diff erences in labor
markets across states that do not vary with time, we include a full set of state fixed
effects . Likewise, workers in a given year may face common macroeconomic shocks to
wages, and so we include a vector of year dummies in all models . Howe ver, o ur baseline
estimating equations do not include industry dummy variables as well because doing so could introduce substantial multicollinearity with respect to the fatality risk variable,
which involves matching workers to fatality risk based on thei r industry and occupation.
(In our subsequent robustness checks we add industry dummies.) Reported standard errors are clustered by industry and occupation and are also robust to the relevant heteroskedasticity and serial correlation. N ote that our first -difference regressions
automatically net out the influence of industry and other job characteristics that do not change over time, and the double -difference regressions net out additional trending
factors .

Because our primary focus is on the panel estimat es, we do not include regressor s
that exhibit little variation across the time periods . Within the panel data context workers’
compensation benefit levels are fixed in real terms for most workers. The main benefit
measures that have been used in the hedoni c literature pertain to the weekly benefit level
for temporary partial disability. The associated wage re placement rate changed for only
five states during the nine years of our data, and the changes were minor. There is also
not much variation across stat es in replacement rates. For half the states the rep lacement
rate is at two -thirds of the worker’s wage , and many other states have similar time –
invariant replacement rates such as 70 percent. States exhibit greater variation with respect to the maximum we ekly benefits that will be paid for temporary partial disability.
However, the benefit maximums tend to increase steadily over time, reflecting adjustments for price inflation. Indeed, during 1992–2001, 34 states had benefit growth
rates that were confined to a 1.7 percent growth rate band surrounding the rate of price
inflation. Thus, with the panel data context workers’ compensation benefit lev els will
tend to be fixed for most workers in the sample, and we do not include a workers’ compensation variable . However, to the extent that there is cross -state variation in benefit
levels these differences will be absorbed in our controls for state fixed effects.
4.1 Focal Estimates from Panel Data
The baseline first -difference estimates from equation (2) appear in Table 3. The
results begin our attempt to address systematically not only latent heterogeneity and
possibly trended regressors, but also measurement error. Comparing estimates both down
a column and across a row reveals the effect of measurement error. The results are
reasonable from both an econometric and economic perspective and provide the

comparison point for our core research issue, which is how badly VSL can be mis –
represented if certain basic econometric issues are mis -handled.
The VSL implied by the baseline model’s coefficient for the annual fatality rate in
Table 3 using the sample mean wage of $21 in (5) is $6.9 million , with a confidence
interval of $6.8 million –$7.1 million.8
2001 1993ln lnww− We emphasize that a novel aspect of our research
is that it help s clari fy the size of possible measurement error effects. If measurement error
in fatality risk is random it will attenuate coefficient estimates and should be reduced by
letting the fatality rate encompass a wider time interval. Compared to VSL from the m ore
typical annual risk measure, the estimated VSL in Table 3 is about 13 percent larger when
fatality risk is a three -year average. The last two columns of Table 3 report the results for
widest possible differences ( ) as well as difference -in-differences from
equation (3) , which should remove possible spurious est imated effects from variables that
are not difference stationary. The main message from Table 3 is that correcting for measurement error in most cases enlarge s estimated VSL , and that even for the relatively
basic panel models using differencing , the range for VSL is not uncomfortably large:
about $7 million –$9 million when using a 2000 hour work year (CI = $6.8 million –$9.7
million) and about $8 million –$10 million when u sing sample average hours to compute
VSL (CI = $7.5 million –$10.9 million) .
An issue seldom addressed in panel wage equations producing VSL is endogeneity
of the fatality change regressor, which may result from dynamic decisions workers make to change job s (Solon 1986, 1989; Spengler and Schaffner 2006). S ome changes in
fatality risk will occur because of within industry -occupation cell changes and others will

8 The confidence interval uses a first -order Taylor series expansion to estimate the variance of the mean
VSL, which from equation (5) is ( )22
122
1ˆˆ ( ) 2000 *100, 000 * * ( ) ( )Var VSL w Var Var wαα = + .

occur because workers switch industry -occupation cells. Within the context of potentially
hazardo us employment, much of the mobility stems from workers learning about the
risks on the job and then quitting if the compensating differential is insufficient given that
information (Viscusi 1979). Within the context of multi- period Bayesian decisions, a
desire to switch does not require that workers initially underestimated the risk, as
imprecise risk beliefs can also generate a greater willingness to incur job risks than is warranted by the mean risk level. Interestingly, for th e job changers in our sample , 51
percent switch to lower fatality risk jobs and 46 percent switch to higher fatality risk jobs
so that on balance there is some effort to sort into safer employment.
We examine the practical importance of job changing status for panel -based
estimation in Table 4, where we stratify the data by whether ∆
πt is due to within or
between cell changes, including immediately before and after a worker changes cell s. The
main econometric contribution to compensating differentials for fatality risk comes from work ers who generate differences in risk over time by switching industry -occupation
cells. The difference in estimated VSL in Table 4 comes from the fact that
2
tπσis at least 8
times larger for switchers (see Table 2). There is too little within -cells variation to reveal
much of a compensating differential for job stayers . More important, because so much of
the variation producing the wage differential in Table 3 comes from job changers , and the
variation for switchers may be related to wa ges, it is imperative to treat ∆ π as
endogenous.
The estimated range for VSL narrow s even further when we allow for endogeneity
and instrument the change in fatality risk. The instrumental variables regressions in Table
5 control for both classical measurement errors and endogeneity. Specifically, based on

the results of Griliches and Hausman (1986) we interchangeably use the (t −1) and (t−3)
levels of the fatality risk, or the (t −1) less (t−3) difference . We limit the focus to the
annual fatality rate so as to have enough lagged fatality and fatality differences as
instruments.9
Table 6 presents our final focal panel results from dynamic first- difference
regressions. The short -run effects from the dynamic model appear in column 1 and the
long-run (steady state) estimates appear in column 2. Note that our first -differences
estimator focuses on changes in wages in response to changes in risk. The mechanism by which the changes will become reflected in the labor market hinges on how shifts in the risk level will affect the tangencies of the constant expected utility loci with the market offer curve. To the extent that the updating of risk beliefs occurs gradually over time, which is not unreasonable because even release of the government risk data is not contemporaneous, one would expect the long -run effects on wages of changes in job ri sk
to exceed the short -run effects. Limitations on mobility will reinforce a lagged influence
(state dependence) . The main result is a fairly narrow range for the estimated VSL ,
approximately $7 million –$8 million when we instrument the annual change in fatality
risk (CI = $6.6–$8 million) .
As one would then expect , the steady state estimates of VSL after the estimated
three- year adjustment period in the results in Table 6 are lar ger than the short -run
estimates. T he difference between the short -run and long -run VSL is about $2 million,
ranging from $7 million –$8 million versus $ 9 million –$10 million using a standard work

9 Greene (2008, Chapter 15) notes that the large sample variance of the dynamic difference estimator is
smaller when lagged levels rather than lagged differences are part of the instruments, which h ere include all
exogenous explanatory variables. The first -stage results here and in subsequent tables pass the standard
weak instruments check based on a partial R2 of at least 0.10 .

year and about $8 million –$9 million versus about $10 millio n–$11 million using sample
average annual hours worked. Again , the range of VSL estimates is not great whe n panel
data are used with estimators that accommodate endogeneity, weak instruments,
measurement error, latent heterogeneity and possible state depen dence.
4.2 Comparison Results From Cross -Section Estimators
Table 7 presents the comparison models that flesh out the most salient
econometric issues when compared to the focal panel results from Tables 3 –6 just
presented .
One problematic result in the literature is the regularly occurring large value for
VSL when the PSID is used as a c ross-section ( Viscusi and Aldy 2003). Notice that the
cross -section estimators in columns 1 and 2 of Table 7 produce large implied VSL s, about
$16 million –$28 million.
In contrast, column 3 of Table 7 reports estimates from the panel random -effects
estimator , where a Breusch -Pagan test supports heterogeneous intercepts . Recall that the
random -effects estimator accounts for unobserved heterogeneity, which is assumed to be
uncorrelated with observed covariates. It is fairly common in labor -market research to
reject the assumption of no correlation between unobserved heterogeneity and observed
covariates ; and Hausman test results indicate a similar rejection here. T he simple f ixed
effects within estimator in the last column is preferred over the simple random effects estimator , with an estimated VSL of about $6–$8 million. Allowing for the possibility of
unobserved productivity and preferences for risk, even if it is improperly assumed to be
randomly distributed in the population, reduces the estimated VSL by up to 60 percent
relative to a model that ignores latent heterogeneity.

The difference in estimated VSL with versus without latent individual
heterogeneity in the model is consistent with the theoretical emphasis in Shogren and
Stamland (2002) that failure to control for unobserved skill results in a potentially
substantial upward bias in the estimated VSL . Taking into account the influence of
individual heterogeneity implie s that, on balance, unobservable person- specific
differences in safety -related productivity and risk preferences are a more powerful
influence than unobservable productivity generally, which Hwang, Reed, and Hubbard (1992) hypothesize to have the opposite effect.
4.3 Panel Data Estimator Specification Checks
As a final dimension of our research we present Tables 8 –10, which contain
results from an extensive set of specification checks designed to examine whether the level and range of VSL from panel data d iscussed thus far are sensitive to the many
options the research er has in estimating a linear pa nel model . In particular, we further
explore the importance of econometric modeling choices for covariates, endogeneity,
dynamics , expectations, and sample composition in panel data based estimates of VSL .
The results of Table 8 show little effect on VSL from whether or not one trims the
set of observations by the size of change in fatality rates between observation years o r
adds an additional control for indust ry. What matter s more to the size of VSL is how the
researcher addresses injury risk expectations and w age dynamics, which we now discuss.
It is possible that workers base their willingness to work in a given setting on an
expected rather than actual observed fatality risk. A simple econometric implementation of the expectations possibility would be to use the lagged fatality measure rather than a concurrent fatality measure as the focal regressor , which is the set of results in the first

column of Table 8. Direct substitution of a lagged regressor is also a simple IV estimator
for an endogenous fatality regressor. The simple substitution of lagged fatality lowers the
estimated VSL to $4 million –$6 million (CI = $3.4 million –$5.9 million) . To be fair, one
should also check more sophisticated representations of expectations such as rational
expectations , that are IV estimates using multiple fatality lags, which are the
specifications in Table s 5 and 9. When we estimate more sophisticated rational
expectations type models with multiple lagged values as instruments, as in Table 9, the
comparison results are similar to our earlier findings: the model passes the standard weak instrument check and VSL is about $7 million –$9 million using a standard (2000 hour)
work year and about $8 million –$10 million using the higher sample average work year .
Our final comparison model is the most complex econometric approach, which is
the Arellano -Bond dynamic first differences model. In the previously discussed IV
models that include dynamics presented in Table 6 the instrument set for the lagged wage regressor always contains two (further) lagged values. In the Arellano- Bond model
lagged values of wages are instruments but the instrument set grows as the sample
evolves temporal ly so that the last time period observation has the most instruments and
the earliest time perio d observat ion has the fewest instruments.
10
5. Implications for Regulatory Cost -Effectiveness The Arellano -Bond
results in Table 10 produce VSL s that are about the same or a little higher than the
dynamic models that use much smaller temporally fixed instrument sets, as in Table 6.
Obtaining reliable estimates of compensating differential equations has long been
challenging because of the central roles of individ ual heterogeneity and state dependence

10 The Arellano -Bond model has also proved useful in studying job injur y risk is the outcome of interest.
See Kniesner and Leeth (2004).

in affecting both the market offer curve and individual preferences. The often conflicting
influence of different unobservable factors has led to competing theories with predictions of different direction .
The wide va riation of VSL estimates in the literature also has generated concern
that underlying econometric problems may jeopardize the validity of those estimates. The range for VSL in the existing literature is extremely wide, from about $0 million to $20
million. Previous studies using the Panel Study of Income Dynamics have often yielded
extremely high VSL estimates of $20+ million, which is also the case in our own cross –
section based estimates with the PSID. Earlier research did not control for the host of
econ ometric problems we address here. A most important finding here is that controlling
for latent time -invariant heterogeneity is crucial – much more so than how one does it
econometrically.
Our first-difference estimati on results use more refined fatality ri sk measures than
employed in earlier studies control for measurement errors and workplace safety
endogeneity in econometric specifications considering state dependence, expectations
and heterogeneity when examining the wage -fatality risk tradeoff. Comparis on of the
various fi rst-difference results with various cross -section estimates implies that
controlling for latent worker -specific heterogeneity reduces the estimated VSL by as
much as two -thirds and narrows greatly the VSL range to about $7 million –$12 m illion
dependin g on the time -frame (short -run versus long -run) and work year (standard or
sample average) in the calculation.
Narrowing VSL as we do here has substantial benefits for policy evaluation. In its
Budget Circular A4 (Sept. 17, 2003), the U.S. O ffice of Management and Budget requires

that agencies indicate the range of uncertainty around key parameter values used in
benefit -cost assessments . Attempting to bound the VSL based on a meta analysis
produces a wide range of estimates from nearly $0 to $20+ million . In addition to the
issue of what studies should be included in the meta analysis given the differences in data sets, specifications, and study quality, we can also produce VSL s that mimic the literature
with ones as low as $0 if we limit the sample to workers who never change jobs and ones as high as $28 million if we use the between estimator with the PSID as a cross -section
(CI = −$5.4 million –$28.1 million) . As a consequence of the perceived indeterminacies
in VSL , agencies often have failed to provide any boundaries at all to the key VSL
parameter in their benefit assessments.
The advantage of using our VSL range in policy assessments can be illustrated b y
an example of the cost -effectiveness of U.S. health and safety regulations . Using the
widely cited cost estimates from the U.S. Office of Management and Budget cited by
Breyer (1993), among others, and updating the values to $2001 to be consistent with our VSL estimates , we illustrate the reduction of policy uncertainty achievable by appli cation
of our estimates . Applying the meta analysis VSL range, 10 policies pass a benefit -cost
test, 20 fail a benefit -cost test, and 23 are in the indeterminate zone . Using our estimated
VSL range, the distributions becomes 27 policies that clearly pass a benefit -cost test, 2 3
that fail a benefit -cost test, with only 3 polic ies in the indeterminate range . Our narrowing
of the acceptable cost-per-life-saved range greatly reduces the range of indeterminacy
and is of substantial practical consequence g iven the actual distribution of regulatory
policy performance.

From a more conceptual standpoint, our research has resolved the econometric
issues giving rise to the very high /low levels and wide ranges of published VSL estimates .
The disparate results in previous studies may reflect the influence of omitted
unobservable effects, among other repairable econometric specification errors . Failure to
address the underlying econometric issues may have produced continuing controversy in the economics literature over the hedonic method and unduly muddled the policy debate over the use of VSL estimates in benefit calculations for government policies .

Table 1: Selected Summary Statistics
Mean Standard
Deviation
Real Hourly Wage 20.610 13.041
Log Real Hourly Wage 2.862 0.566
Age 40.832 8.452
Marital Status (1=Married) 0.817 0.386
Race (1=White) 0.758 0.428
Union (1=member) 0.230 0.421
Years of Schooling 13.506 2.221
Live in Northeast 0.172 0.378
Live in Northcentral 0.283 0.451
Live in South 0.376 0.484
Live in West 0.168 0.374

One-Digit Industry Groups:
Mining 0.008 0.089
Construction 0.127 0.333
Manufacturing 0.231 0.421
Transportation and Public Utilities 0.115 0.319
Wholesale and Retail Trade 0.139 0.346
Fire, Insurance, and Real Estate 0.045 0.206
Business and Repair Services 0.070 0.256
Personal Services 0.010 0.098
Entertainment and Professional Services 0.188 0.391
Public Administration 0.067 0.250

One-Digit Occupation Groups:
Executive and Managerial 0.191 0.393
Professional 0.158 0.365
Technicians 0.042 0.202
Sales 0.031 0.174
Administrative Support 0.050 0.219
Services 0.082 0.274
Precision Production Crafts 0.231 0.421
Machine Operators 0.079 0.270
Transportation 0.090 0.286
Handlers and Labors 0.046 0.209

Annual Fatality Rate (per 100,000) 6.415 9.144
3-Year Fatality Rate (per 100,000) 5.716 8.390

Number of Men = 2,036
Number of Person Years = 6,625

Table 2: Between and Within Group Variation for Industry by
Occupation Fatality Rates

Overall
Variance Between
Group
Variance Within
Group
Variance
Annual Fatality Rate
(per 100,000) 69.866 50.447 19.419
3-Year Fatality Rate
(per 100,000) 52.077 39.401 12.676

Never Change Industry -Occupation
Annual Fatality Rate
(per 100,000 ) 71.646 68.356 3.290
3-Year Fatality Rate
(per 100,000) 52.458 51.629 0.828

Ever Change Industry -Occupation
Annual Fatality Rate
(per 100,000) 69.094 42.799 26.295
3-Year Fatality Rate
(per 100,000) 51.914 34.189 17.726

Only When Change Industry -Occupation
Annual Fatality Rate
(per 100,000) 70.591 46.240 24.351
3-Year Fatality Rate
(per 100,000) 64.927 43.908 21.019

Table 3: First -Difference Estimates of Wage -Fatal Risk Tradeoff
Static First
Difference
Estimates First-Difference
Estimator for
2001minus1993 Difference in
Differences
Estimator

Annual Fatality Rate x 1,000 1.6007 1.9438 1.4851
(0.4793) (1.7223) (0.5196)

Implied VSL ($Millions) 6.9 9.1 6.7
95% CI [6.8, 7.1] [8.5, 9.7] [6.5, 6.9]
VSL – using average hours 7.9 10.2 7.7
95% CI [7.7, 8.1] [9.5, 10.9] [7.5, 7.9]

Number of Person -Years 4338 1017 2788

3-Year Fatality Rate x 1,000 1.7785 1.8627 1.8567
(0.5435) (1.5412) (0.6339)

Implied VSL ($Millions) 7.8 8.8 8.5
95% CI [7.7, 8.0] [8.3, 9.3] [8.3, 8.7]
VSL – using average hours 9.0 9.9 9.8
95% CI [8.8, 9.1] [9.3, 10.5] [9.5, 10.0]

Number of Person- Years 4916 1171 2992
Notes: Standard errors are recorded in parentheses. Standard errors are robust to
heteroskedasticity and within industry -by-occupation autocorrelation. Each model controls for a
quadratic in age, years of schooling, indicators for region, marital status, union status, race, one-
digit occupation, state, and year effects. To construct the VSL using equation (5) the coefficients in
the table are divided by 1,000. 95% Confidence Intervals are constructed based on a 1st order
Taylor series expansion.

Table 4: Estimates of Wage -Fatal Risk Tradeoff by Job Change Status
Static First –
Difference First-Difference
Estimator for 2001
minus 1993
Never Change Industry -Occupation
Annual Fatality Rate x 1,000 0.1234 0.3097
(1.4164) (3.0008)

Implied VSL ($Millions) 0.6 1.6
[0.2, 0.9] [-0.2, 3.4]
VSL – using average hours 0.7 1.8
[0.2, 1.1] [-0.3, 3.9]

3-Year Fatality Rate x 1,000 -0.8074 0.5758
(3.4029) (5.0319)

Implied VSL ($Millions) -3.8 3.0
[-4.7, -3.0] [0.0, 6.0]
VSL – using average hours -4.4 3.4
[-5.4, -3.4] [0.0, 6.9]

Number of Per son-Years 1303 / 1390 282 / 296
Ever Change Industry -Occupation
Annual Fatality Rate x 1,000 1.6405 1.9125
(0.5088) (1.7859)

Implied VSL ($Millions) 6.8 8.6
[6.7, 7.0] [7.9, 9.3]
VSL – using average hours 7.8 9.6
[7.6, 8.0] [8.8, 10.4]

3-Year Fatality Rate x 1,000 1.9845 1.8399
(0.5776) (1.5713)

Implied VSL ($Millions) 8.3 8.4
[8.1, 8.5] [7.8, 9.0]
VSL – using average hours 9.4 9.4
[9.2, 9.7] [8.7, 10.1]

Number of Person -Years 3035 735 / 868
Notes: Standard errors are recorded in parentheses. Standard errors are robust to
heteroskedasticity and within industry -by-occupation autocorrelation. Each model controls for
a quadratic in age, years of schooling, indicators for region, marital status, unio n status, race,
one-digit occupation, state, and year effects. To construct the VSL using equation (5) the
coefficients in the table are divided by 1,000. 95% Confidence Intervals are constructed based
on a 1st order Taylor series expansion.

Table 4 cont: Estimates of Wage -Fatal Risk Tradeoff by Job Change Status
Static First –
Difference First-Difference Estimator for
2001 minus 1993
Only When Change Industry -Occupation
Annual Fatality Rate x 1,000 1.6607 1.7111
(0.5471) (1.8036)

Implied VSL ($Millions) 6.9 7.4
[6.7, 7.1] [6.7, 8.1]
VSL – using average hours 7.8 8.2
[7.6, 8.1] [7.4, 9.0]

3-Year Fatality Rate x 1,000 1.9156 1.6764
(0.5660) (1.5877)

Implied VSL ($Millions) 8.2 7.4
[7.9, 8.4] [6.7, 8.0 ]
VSL – using average hours 9.3 8.2
[9.0, 9.5] [7.5, 8.9]

Number of Person -Years 1920 / 2261 597 / 699
Notes: Standard errors are recorded in parentheses. Standard errors are robust to
heteroskedasticity and within industry -by-occupation autocorrelation. Each model controls for a
quadratic in age, years of schooling, indicators for region, marital status, union status, race, one-
digit occupation, state, and year effects. To construct the VSL using equation (5) the coefficients
in the table are divided by 1,000. 95% Confidence Intervals are constructed based on a 1st order
Taylor series expansion.

Table 5: Instrumental Variables Estimates of Wage -Fatal Risk Tradeoff
First-Difference IV
Estimator, t− 1 and t−3
Fatality as Instruments First-Difference IV
Estimator, Lag Differenced
Fatality as Instrument

Annual Fatality Rate x 1,000 1.5574 1.5926
(0.6412) (0.6429)

Implied VSL ($Millions) 6.7 6.9
95% CI [6.6, 6.9] [6.7, 7.0]
VSL – using a verage hours 7.7 7.9
95% CI [7.5, 7.9] [7.7, 8.0]

First Stage Results

t−1 fatality rate 0.7752
(0.0118)

t−3 fatality rate -0.7553
(0.0118)

(t−1 rate) − (t−3 rate) 0.7653
(0.0108)

R2 0.63 0.63
Partial R2 0.54 0.54
Robust Wald {p -value} 106 {0.00} 163 {0.00}
Number of Person -Years 4338 4338
Notes: Standard errors are recorded in parentheses. Standard errors are robust to
heteroskedasticity and within industry -by-occupation autocorrelation. Each model controls
for a quadratic in age, years of schooling, indicators for region, marital status, union status,
race, one- digit occupation, state, and year effects. First stage regressions include all
exogenous explanatory variables in addition to the noted instruments. To construct the VSL
using equation (5) the coefficients in the table are divided by 1,000. 95% Confidence
Intervals are constructed based on a 1st order Taylor series expansion.

Table 6: Dynamic First Difference Estimates of Wage -Fatal Risk Tradeoff
Dynamic First -Difference Estimates
with lag differenced wage instrumented

Short -Run Effect Long -Run Effect

Annual Fatality Rate x 1,000 1.6023 1.9546
(0.5346) [0.039]

Implied VSL ($Millions) 7.2 8.8
95% CI [7.1, 7.4] [8.6, 9.1]
VSL – using average hours 8.3 10.2
95% CI [8.1, 8.6] [9.9, 10.4]

First Stage Partial R2 0.15
Robust Wald {p -value} 230,100 {0.00}
Number of Person -Years 2788

3-Year Fatality Rate x 1,000 1.7427 2.2164
(0.6175) [0.062]

Implied VSL ($Millions) 8.0 10.2
95% CI [7.8, 8.2] [10.0, 10.5]
VSL – using average hours 9.2 11.7
95% CI [9.0, 9.5] [11.4, 12.0]

First Stage Partial R2 0.15
Robust Wald {p- value} 75,527 {0.00}
Number of Person -Years 3162
Notes: S tandard errors are recorded in parentheses and p-values of the null hypothesis that
the long- run effect is zero are recorded in square brackets. Standard errors are robust to
heteroskedasticity and within industry -by-occupation autocorrelation. Each model controls for
a quadratic in age, years of schooling, indicators for region, marital status, union status, race,
one-digit occupation, state, and year effects. One and two period lags of the independent
variables, except for the fatality rates, are included as instruments for the lag wage. To
construct the VSL using equation (5) the coefficients in the table are divided by 1,000. 95%
Confidence Intervals are constructed based on a 1st order Taylor series expansion.

Table 7: Cross Section and Panel D ata Estimates of Wage -Fatal Risk Tradeoff
Pooled Cross
Section Time
Series
Estimator Between-
Group
Estimator Random –
Effects
Estimator Fixed -Effects
Estimator

Annual Fatality Rate x 1,000 4.625 5.9552 2.6043 1.7979
(1.2082) (1.5108) (0.5950) (0.6339)

Implied VSL ($Millions) 19.1 24.5 10.7 7.4
95% CI [18.8, 19.4] [24.1, 25.0] [10.6, 10.9] [7.3, 7.5]
VSL – using average hours 21.5 27.6 12.1 8.4
95% CI [21.1, 21.8] [27.2, 28.1] [11.9, 12.3] [8.2, 8.5]

Number of Person -Years 6625 2036 6625 6468

3-Year Fatality Rate x 1,000 3.7666 4.4039 2.087 1.4516
(1.2696) (1.6207) (0.7003) (0.7566)

Implied VSL ($Millions) 16.2 18.9 9.0 6.2
95% CI [15.9, 16.5] [18.6, 19.3] [8.8, 9.1] [6.1, 6.4]
VSL – using average hours 18.4 21.5 10.2 7.1
95% CI [18.0, 18.8] [21.1, 21.9] [10.0, 10.4] [6.9, 7.3]

Breusch -Pagan Test for
Random Effects {p -value} 2807
{0.00}

Hausman Test for Fixed – vs.-
Random Effects {p -value} 454
{0.00}

Number of Person -Years 5866 2012 5866 5728
Notes: Standard errors are recorded in parentheses. Standard errors for the pooled times series
cross- section estimator and the first difference estimator are robust to heteroskedasticity and within
industry -by-occupation autocorrelation. Each model controls for a quadratic in age, years of
schooling, indicators for region, marital status, union status, race, one- digit occupation, state, and
year effects . To construct the VSL using equation (5) the coefficients in the table are divided by
1,000. 95% Confidence Intervals are constructed based on a 1st order Taylor series expansion.

Table 8: Specification Checks for First -Difference Estimates of Wage- Fatal Risk
Tradeoff
First Difference
Estimates using
Lagged Fatality
Rates First-Difference
Estimates with
Industry
Dummies First-Difference
Estimates with
Untrimmed
Fatality Rates First-Difference
Estimates Using
Alternative Trim
Horizon

Annual Fatality Rate x 1,000 1.1611 1.3455 1.4281 1.4988
(0.5356) (0.5136) (0.4253) (0.4332)

Implied VSL ($Millions) 5.1 5.8 6.3 6.6
95% CI [4.9, 5.2] [5.7, 5.9] [6.2, 6.4] [6.5, 6.7]
VSL – using average hours 5.8 6.6 7.2 7.5
95% CI [5.7, 5.9] [6.5, 6.8] [7.1, 7.4] [7.4, 7.7]

Number of Person -Years 4406 4338 5242 4916

3-Year Fatali ty Rate x 1,000 0.7777 1.4107 1.7186 1.9304
(0.5553) (0.6050) (0.5366) (0.5729)

Implied VSL ($Millions) 3.5 6.2 7.6 8.3
95% CI [3.4, 3.6] [6.1, 6.3] [7.5, 7.7] [8.2, 8.5]
VSL – using average hours 4.0 7.1 8.7 9.5
95% CI [3.9, 4.2] [6.9, 7.3] [8.5, 8.9] [9.3, 9.7]
Number of Person -Years
3695 4916 5242 4338
Notes: Standard errors are recorded in parentheses. Standard errors are robust to heteroskedasticity
and within industry -by-occupation autocorrelation Each model controls for a quadratic in age, years of
schooling, indicators for region, marital status, union status, race, one- digit occupation, state, and year
effects. To construct the VSL using equation (5) the coefficients in the table are divided by 1,000. 95%
Confidence Intervals are constructed based on a 1st order Taylor series expansion. For the alternative
trim horizon person- years are dropped from the annual fatality rate equation if the three- year average
fatality rate exceeds positive 300 percent or negative 75 percent; likew ise person- years are dropped
from the three- year average fatality rate equation if the annual fatality rate exceeds positive 300 percent
or negative 75 percent.

Table 9: Specification Checks for Instrumental Variables Estimates of Wage- Fatal
Risk Tradeoff
First-Difference
IV Estimator, t− 2
and t−3 Fatality
as Instruments First-Difference
IV Estimator,
Lag Differenced
Fatality as
Instrument First-Difference
IV Estimator,
t−2 and t−4
Fatality as
Instruments First-Difference IV
Estimator, Lag
Differenced
Fatality as
Instrument

Annua l Fatality Rate x 1,000 2.0237 2.019 1.6134 1.589
(0.7849) (0.7845) (0.7498) (0.7496)

Implied VSL ($Millions) 8.7 8.7 7.1 7.0
95% CI [8.6, 8.9] [8.5, 8.9] [6.9, 7.3] [6.8, 7.2]
VSL – using average hours 10.0 10.0 8.2 8.1
95% CI [9.8, 10.2] [9.7, 10.2] [8.0, 8.4] [7.8, 8.3]

First Stage Results

t−2 fatality rate 0.6994
(0.0134)

t−3 fatality rate -0.7019
(0.0132)

(t−2 rate) − (t−3 rate) 0.7008
(0.0122)

t−2 fatality rate 0.6476
(0.0155)

t−4 fatality rate -0.6570
(0.0141)

(t−2 rate) − (t−4 rate) 0.6537
(0.0135)

R2 0.54 0.54 0.55 0.55

Number of Person -Years 4338 4338 3235 3235
Notes: Standard errors are recorded in parentheses. Standard errors are robust to heteroskedasticity and
within industry -by-occupation autocorrelation. Each model controls for a quadratic in age, years of
schooling, indicators for region, marital status, union status, race, one- digit occupation, state, and year
effects. First stage regressions include all exogenous explanatory variab les in addition to the noted
instruments. To construct the VSL using equation (5) the coefficients in the table are divided by 1,000. 95%
Confidence Intervals are constructed based on a 1st order Taylor series expansion.

Table 10: Arellano -Bond Dynam ic First Difference Estimates of Wage –
Fatal Risk Tradeoff
Dynamic First -Difference Estimates
with lag differenced wage instrumented

Short -Run Effect Long -Run Effect

Annual Fatality Rate x 1,000 1.9094 2.2893
(0.9150) [0.039]

Implied VSL ($Millions) 8.6 10.4
95% CI [8.4, 8.9] [10.1, 10.7]
VSL – using average hours 9.9 11.9
95% CI [9.7, 10.3] [11.5, 12.3]

Number of Person -Years 2788

3-Year Fatality Rate x 1,000 1.7056 2.1563
(0.9050) [0.062]

Impli ed VSL ($Millions) 7.9 9.9
95% CI [7.6, 8.1] [9.7, 10.2]
VSL – using average hours 9 11.4
95% CI [8.8, 9.3] [11.1, 11.7]

Sargan Overidentifying Restrictions
Test-Annual Fatality {p -value} 79.78
{0.16}

Sargan Overidentifying Restrictio ns
Test-3-Year Fatality {p -value} 88.96
{0.05}

Number of Observations 3162
Notes: Standard errors are recorded in parentheses and p-values of the null hypothesis that
the long- run effect is zero are recorded in square brackets. Standard errors are robust to
heteroskedasticity and within industry -by-occupation autocorrelation. Each model controls
for a quadratic in age, years of schooling, indicators for region, marital status, union status,
race, one- digit occupation, state, and year effects. On e and two year lags of the independent
variables, except for the fatality rates, are included as instruments for the lag wage. To
construct the VSL using equation (5) the coefficients in the table are divided by 1,000. 95%
Confidence Intervals are construc ted based on a 1st order Taylor series expansion.

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