Compensating Differentials and Income Taxes: Are the Wages of Dangerous Jobs More
Responsive to Tax Changes than the Wages of Safe Jobs?
Author(s): David Powell
Source: The Journal of Human Resources, Vol. 47, No. 4 (Fall 2012), pp. 1023-1054
Published by: University of Wisconsin Press
Stable URL: http://www.jstor.org/stable/23798525
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Compensating Differentials and
Income Taxes
Are the Wages of Dangerous Jobs More
Responsive to Tax Changes than the Wages
of Safe Jobs?
David Powell
ABSTRACT
Income taxes distort the relationship between wa
ities. When the marginal tax rate increases, amen
able as the compensating differential for low-amen
While there is evidence that the provision of amen
the literature has ignored the consequences for jo
cannot fully adjust. This paper compares the wag
jobs to the wage response of safe jobs. When tax
see the pretax compensating differential for on-th
pirically, I find large differences in the wage res
their riskiness.
I. Introduction
The theory of compensating differentials has been well-established
since the writings of Adam Smith in 1776. Nonwage amenities should impact work
ers' wages, and much empirical research has been dedicated to studying the rela
tionship between wages and amenities. There is little research studying how these
compensating differentials interact with income and wage taxes. While nonwage
David Powell is an economist at RAND. He is grateful to David Autor, Arthur Campbell, Tom Chang,
Jesse Edgerton, Michael Greenstone, Tal Gross, Jon Gruber, Jerry Hausman, Helen Hsi, Konrad Menzel,
Whitney Newey, Amanda Pallais, Jim Poterba, Nirupama Rao, Hui Shan, and Carmen Taveras for their
comments. He thanks Dan Feenberg and Inna Shapiro for their help with NBER's Taxsim program.
Katharine Earle of the U.S. Census Bureau provided invaluable industry crosswalks. Special thanks to
Suzanne Marsh of the National Institute for Occupational Health and Safety for providing detailed occu
pational fatality data. With the exception of restricted fatality numbers, the data used in this article can
be obtained beginning May 2013 through April 2016 from David Powell; 1776 Main St., Santa Monica,
CA 90407, dpowell@rand.org. This research was supported by the National Institute on Aging, Grant
Number P01-AG05842.
[Submitted June 2011; accepted January 2012]
ISSN 022-166X E-ISSN 1548-8004 © 2012 by the Board of Regents of the University of Wisconsin System
THE JOURNAL OF HUMAN RESOURCES •47*4
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] 024 The Journal of Human Resources
amenities are untaxed, the compensating differential is subject to taxation. Wh
rates change, the pretax wages of jobs with different nonwage amenities must
differentially. Consequently, observed compensating differentials are a funct
tax rates. We should observe heterogeneity in the incidence of income taxes
on the amenity level of the job. This paper provides theoretical and empiric
dence for the relationship between compensating differentials and marginal tax
This paper compares the wage response of jobs with different levels of ameni
to legislative tax changes. I focus on industries with varying on-the-job hazard
for three reasons. First, occupational safety is easy to measure. Second, a va
erature has studied the existence and magnitude of compensating differentials
respect to occupational hazards. Individuals working in risky jobs should be
pensated for the additional risk with higher wages. Third, while many ame
likely respond to tax changes, some amenities cannot fully adjust and are si
fixed characteristics of a job. Occupational safety is an example where the m
dangerous jobs never become as safe as the safest jobs, regardless of the tax
ronment. Risk rates may adjust to some extent, but it is still possible to mea
compensating differential under different tax regimes.
This paper looks at how the pretax wages of dangerous jobs respond to t
changes relative to the pretax wages of safe jobs. When marginal tax rates
increase, the compensating differential associated with dangerous jobs is taxed a
The key parameter is the marginal net-of-tax rate, the fraction of an additional
of earnings that a worker keeps. If a high risk job pays an extra $1 as a compens
differential, the worker keeps $( 1 —c). Workers are paid in taxable earning
nontaxable amenities, such as safety. When tax rates increase, all workers a
pacted, but workers paid disproportionately in monetary wages are affected
In response, the pretax compensating differential must increase, implying that
wages of the dangerous jobs must increase more than the wages of the safe jobs
a given difference in risk.
It is well-known that individuals and firms respond to tax changes. Taxes dist
individual labor supply decisions and occupational choices. Similarly, firms may
the generosity of their nontaxable amenities in response to taxes. Both of t
phenomenon have been studied in the tax literature. However, these effects d
fully encapsulate the magnitude of the distortion resulting from taxes. Nont
amenities cannot completely adjust in response. Jobs have some fixed character
which are incapable of responding to tax changes. Instead, wages must adjust
sequently, taxes may distort the cross-industry relationship between pretax wa
Although this effect has been essentially ignored in the literature, the magn
of the results of this paper suggests that this is an important consideration
evaluating income tax policy. The substantial heterogeneity found in this pap
lustrates that the mean tax incidence is not a relevant measure for many indus
High tax rates disproportionately harm industries that primarily pay their work
taxable earnings and are inherently low-amenity jobs. Tax rates distort the rela
ship between taxable earnings and nontaxable amenities, but this distortion i
limited to individual occupational changes and firm-level changes in amenit
vision. Instead, the tax system favors high-amenity industries. The results o
paper provide important evidence that the inability to tax amenities is a signifi
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Powell 1025
source of distortion. To my knowledge, this is the first paper to estimate t
ential incidence of income tax rates based on variation in an amenity.
I use the 1983-2002 March Current Population Survey (CPS) with Bure
Labor Statistics (BLS) injury data and National Institute for Occupation
and Health (NIOSH) fatality data to estimate the relationship between wage
and fatality rates, and marginal net-of-tax rates ( 1 —c). Because tax rates a
tion of wages, I use an IV strategy similar in spirit to Currie and Gruber
where identification originates solely from legislative federal tax changes an
sectional differences in risk. This strategy allows me to control separately
tax rate and the risk rates and look at the impact of the interaction. Similar
able to control for fixed wage differences through the inclusion of indus
fixed effects.
I find large differences in the wage response of industries to tax chang
on the riskiness of those industries. When tax rates increase, the wages of d
industries increase relative to the wages of safe industries. These relat
changes are large and economically meaningful. The preferred estimates of t
imply that a 10 percent increase in the marginal net-of-tax rate decreases t
wages of dangerous industries by 1-3 percent more than the pretax wage
industries, when defining dangerous industries as the 75th percentile of risk
safe industries as the 25th percentile. When the 90th percentile is compar
10th percentile, the dangerous jobs experience a 5-7 percent wage decreas
to safe jobs. I provide evidence that these estimates are not driven by secu
trends during this time period. Furthermore, the results are robust to the
of individual fixed effects using the Panel Study of Income Dynamics (PS
paper makes a key contribution to the tax literature by illustrating that inco
have effects beyond individual-level behaviors and the average firm-level re
Instead, amenities and tax rates interact such that some industries are dispr
ately harmed by higher tax income tax rates. Income taxes levied on individ
as taxes on low-amenity industries.
Furthermore, the results illustrate the importance of amenities and comp
differentials in the labor market. Estimating cross-sectional compensating d
tials is problematic for reasons discussed thoroughly in the literature, bu
mates in this paper provide evidence that these differentials are econom
portant. The results of this paper suggest that research on the relationship
amenities and wages must explicitly account for income taxes.
II. Literature Review
A. Compensating Differentials
A vast literature has studied and estimated compensating differentials associated with
various job characteristics in the labor market. Typically, research in this area com
pares the wages of jobs based on the provision of specific amenities at those jobs.
Kniesner and Leeth (2010) provide an overview on compensating wage differentials.
Most relevant to this paper is the literature studying the empirical relationship be
tween occupational risk and wages. Viscusi and Aldy (2003) provide a thorough
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1026 The Journal of Human Resources
review of this literature. Adopting similar notation as Viscusi and Aldy (200
typical hedonic wage specification is as follows:
( 1 ) w,j= a + X'ijj + fi]pJ + $2qj + P tfjWCi + e¡j
where w¡j is the wage of worker i in industry j. XtJ is a set of control variab
is the fatality rate, q¡ is the injury rate, and WCj is the workers' compen
replacement rate. Most of this literature estimates the cross-sectional relati
between risk and wages, expecting positive coefficients on the injury and f
rate variables.
This specification accounts explicitly for workers' compensation, and the empir
ical work of this paper also requires identifying and estimating the differential impact
of workers' compensation on wages. Workers' compensation in the United States is
a public insurance program that pays workers and their families a benefit upon injury
or death incurred on-the-job. The benefit is a function of earnings, subject to a
minimum or maximum determined by the state. The replacement rate is a variable
which may differentially affect the wages based on occupational risk. Workers in
dangerous industries are more likely to benefit from high replacement rates. If work
ers value this insurance, then wages may adjust accordingly.
B. Income Taxes and Amenities
It is well known that wage taxes distort the demand for nonwage amenities. Pap
such as Gruber and Lettau (2004) study the provision of these amenities as a
sponse to this tax subsidy. When tax rates change, the relative price between taxa
income and nontaxable amenities shifts. Firms respond to workers' demands
providing more or less generous amenities.
Powell and Shan (2012) study individual-level occupational responses to tax
changes, another possible margin of distortion. When tax rates increase, the retur
to a high wage (low amenity) job decreases. Powell and Shan (2012) find that,
expected, individuals move to higher wage occupations when tax rates decrea
This paper is complementary to Powell and Shan (2012) as both papers look at
interplay between taxes, amenities, and wages. The Powell and Shan (2012) met
odology explicitly accounts for occupation wage changes and looks at worker m
ment to occupations with different compensating differentials when tax rates chan
This paper looks at the actual differential wage movements resulting from tax sch
ule changes.
Amenity provision also shifts over time as I will show with my injury and fatality
rate data. Hamermesh (1999) discusses the growing inequality of amenities. Shifts
in on-the-job risk are important in my context and my empirical strategy accounts
for these without any assumptions on the exogeneity or endogeneity of such shifts
to legislative tax changes. By focusing on the compensating differential (which uses
cross-sectional variation in risk), the empirical strategy accounts for changes in the
levels of the risk rates over time.
A separate literature studies the incidence of income taxes. Leigh (2010) uses
state-level changes in Earned Income Tax Credit (EITC) generosity to identify the
impact of taxes on wages and finds an economically meaningful effect. Kubik (2004)
uses the Tax Reform Act of 1986 to study whether occupations that were dispro
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Powell 1027
portionately affected experienced larger pretax wage changes. The paper
dence that occupations with the largest tax decreases incurred the larges
creases. These results are dependent on the inclusion of occupation-speci
trends, suggesting that the change in the tax rate is not exogenous. While I
estimating the same parameters as Kubik (2004), an advantage of my app
that I am separately controlling for the change in the tax rate and looking
"within-tax rate." In other words, I add another "difference," reducing conc
trends are biasing the results.
Albouy (2009) examines how a nonlinear tax schedule differentially affe
with higher wages. These higher wages can be thought as a compensating dif
for working and living in a city with a low quality of life. Taxes disproport
burden high-compensating differential geographic areas in the same wa
impact high-compensating differential industries.
In my context, is is plausible that firms respond to higher taxes by in
safety standards to reduce fatality and injury risks, and I will discuss ho
pirical strategy is robust to this possibility. However, on a basic level, some
simply riskier than others by their inherent nature. Thus, firms must resp
different margin than the provision of the nonwage amenity. This paper
how pretax wages respond when a nonwage amenity is prohibitively cost
vide.
III. Theory
A. Model
I include a very simple model to illustrate the relationships between wages, taxes,
and amenities. The model is similar in spirit to the one found in Powell and Shan
(2012), which also studies the relationship between tax rates and amenities. It is
certainly possible that risk levels are themselves responsive to taxes, implying that
risk is an endogenous variable. A more complicated model could factor in the cost
to the firm of improving occupational safety and weigh these costs against the higher
wages. In my context, this is unnecessary. This paper does not study how taxes
affect risk or wages. Instead, this paper examines how changes in the marginal tax
rate impact the compensating differential, the wage-risk relationship. I will not be
using changes—endogenous or exogenous—in risk for identification. Consequently,
the model illustrates the relationship between the compensating differential and the
marginal tax rate without imposing assumptions on firm-level behavior.
In this model, workers maximize utility which is a function of consumption (c)
dw(R) r .
and on-the-job risk (/?). w(R) is the market wage function wdR
represents the tax burden given total income z where z will simply be the sum of
the wage and nonlabor income (y).
The marginal worker faces the following maximization problem:
maxU(c,R) s.t. c = w(i?) + y— rfwf/îj + y]
c,R
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1028 The Journal of Human Resources
This reduces to
max t/ {w(R) + y—7"[ w(/?) + y ],/?}
c.R
The first-order condition defines the compensating differential, the wage function
that keeps the marginal worker indifferent between jobs with different risk levels:
(2) dw= \_]¿R
dR 1 -T' Uc
This paper is interested in how changes in the marginal tax rate impact the com
pensating differential. Taking the derivative of Equation 2 with respect to -——r, we
arrive at a testable result:
d2w U R
(3) TTT=~tf>0dRd
1 -T
dw
The inequality follows assuming UR<0,Uc>0. This result states that — increases
dR
when -——7 increases (when T increases). Stated differently, this equation shows
dw
that ——j—- is larger for high risk jobs. Thus, the response of wages to taxes is
\1 -T,
higher for jobs with higher risk (fewer nonwage amenities). The model also illus
trates that the marginal net-of-tax rate (1 — T ) is the relevant tax parameter since
the additional earnings received due to risk are taxed at the marginal rate.
tí. Identification Implied by Model
The model implies the following underlying experiment. Assume an economy with
a flat tax and two occupations—one dangerous (d) and one safe (s). In Period 1, we
observe compensating differential
Rdl~Rsl
In Period 2, tax rates increase. Risk rates also change though the model imposes no
assumptions on the behavior of risk. Risk levels may converge (though it is necessary
that Rd2 ¥= Rs2). The Period 2 compensating differential is
wd2-ws2
Rd2~Rs2
The model states that the pretax compensating differential should increase since
workers receive less of this hazard pay after taxes. The underlying experiment is to
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Powell 1029
compare the compensating differential in a low tax environment to the com
differential in a high tax environment. Thus, identification only requires
tional variation in risk and time series variation in taxes. These are the sources of
variation that I use.
IV. Data
Several data sets are used in my analysis. More detailed explanations
of the data and variables are provided in the Appendix. I use the 1983-2002 March
CPS, which provides individual-level data on income, hours worked, industry, and
other characteristics. These years were chosen because the Census industrial coding
system used by the CPS stays relatively stable over the time period. I calculate tax
rates by using the National Bureau of Economic Research's Taxsim program (Feen
berg and Coutts 1993). This program takes information on different forms of income,
number of dependents, and filing status. It provides state and federal marginal taxes
and the marginal Federal Insurance Contributions Act (FICA) tax rates for each
household. The wage income variable in the CPS is pretax wage income for the
previous year. I divide this quantity by the hours worked in the previous year to get
my wage variable. The resulting sample covers 1982-2001. My final sample includes
workers in the private, nonagricultural labor force ages 25-55 that are not self
employed.
The U.S. Chamber of Commerce publishes a series, Workers' Compensation Laws,
which provides detailed parameters regarding each state's workers' compensation
coverage. Using CPS wage data, I calculate each observation's after-tax replacement
rate for injuries with the temporary total disability parameters. I also calculate each
observation's replacement rate in cases of fatal injury. Both of these rates are
important since I look at both injury and fatality rates in this paper. The "death
benefit" replacement rate, however, must be treated differently because it is not
relevant for workers that are single with no children. In these cases, I simply force
the effect of this replacement rate to be zero. The replacement rate formula used is
potential weekly benefit
(weekly earnings)(l-x)
The National Institute for Occupational Safety and Health collected fatality data
between 1980 and 2001 through the National Traumatic Occupational Fatality Sur
veillance System (NTOF) (Marsh and Lay ne 2001). The NTOF records fatalities
listed as work-related on death certificates which are coded as externally caused for
those that were 16 or older. These fatalities are then categorized by industry. By
request, I received detailed fatality data from the NTOF system. It was provided for
49 separate industry categories. Figure 1 shows the trend in fatality rates over the
time period studied in this paper. There is a noticeable downward trend throughout
my sample. More details about the fatality rates are provided in the Appendix,
including a discussion of the NTOF undercount relative to the Census of Fatal
Occupational Injuries (CFOI). To illustrate the magnitudes and variation in these
data, I list the fatality rates for the top ten and bottom ten industries during 1982
2001 in Appendix Table Al.
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1030 The Journal of Human Resources
o
o
i/i
— ^
a
o ^
o ^
o
o
o3 ^
D
CA
<U
•lO
~s ^CO
Ph
cn -
1982 1984 1986 1988 1990 1992 1994 ¡996
Year
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Year
Figure 1
Fatality Rates, 1982-2001
The Bureau of Labor Statistics has recorded injury rates by detailed industry since
1976 as part of their series Occupational Injuries and Illnesses in the United States
by Industry. They survey about 250,000 firms every year. Over 1982-2001, two
variables are consistently recorded—the total injury (and illness) rate and the rate
of injuries (and illnesses) resulting in 1 + days away from work. I focus on this
latter variable because it is more commonly used in the literature. After merging
these data into CPS industries, there are about 180 separate industries. The aggregate
injury rate is charted by year in Figure 2. Table A2 shows the ten most dangerous
industries and the ten least dangerous industries ranked by the overall injury rate.
The correlation between the injury and fatality rates in my data is 0.39.
I report full-sample estimates, but I also split the sample into two smaller time
periods. The Census industrial coding system changes in 1992, corresponding to
1991 wages. The classification changes were minor, but "crossing" this 1991 thresh
old requires aggregating a few industries together (Tristao 2006). Consequently, I
concentrate on the time periods 1982-90 and 1991-2001.
V. Empirical Strategy
A. Specification
The model shows that the tax rate should have a differential effect on wages based
on the risk level. Therefore, the variables of interest for this paper are R xln(l —x).
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Powell 1031
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Year
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Year
Figure 2
Injury Rates, 1982-2001
The ln( 1 — x) variable is used throughout the tax literature (see Gruber and Saez (2002)
for one example). The workers' compensation replacement rate also should impact
the relationship between wages and risk since workers in high risk jobs benefit more
from a high replacement rate. Because the tax rate directly affects the replacement
rate, these variables are not orthogonal and it is important to separately account for
the replacement rate. I nonparametrically account for differences between industries
through the inclusion of industry-state fixed effects.
Because of nonlinearities in the tax schedule, different industries experience dif
ferent tax changes. Consequently, I must separately account for ln(l —x) to ensure
that all comparisons of industries with different risk levels occur for a given tax
change. I treat the coefficient on ln(l —x) as a nuisance parameter and do not inter
pret it as the incidence of the income tax. Similarly, I include ln(WC) independently.
This strategy can be interpreted as a differences-in-differences framework. I control
for ln(l—x) and R and then look at the interaction of the two variables.
The final specification is
(4) In wijks, = y,+ asj + X,8, + Rk,p + [i0 In ( 1 —xijkst) + In (WCijkst) ' p,
+ [Rk,ln(l—Xyfc,,)] P2+ [^*iln(WC,y*j<)] P3 + Eijkst
where i indexes individual, j industry, k industry aggregate, s state, t year. wijkst
represents the wage, xijkst is the marginal tax rate (0.5 * FICA + federal + state),
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1032 The Journal of Human Resources
WC¡jkst refers to the workers' compensation after-tax replacement rate (for injur
deaths, or both), and X, is a vector of individual-level covariates. Rkt refers to
injury rate, the fatality rate, or both for industry aggregate k at year t. Since t
are no national-level workers' compensation changes and identification of p, re
on state-level changes over time, I include state-industry interactions. More de
about this specification are included in the Appendix.
pi is the coefficient of interest and we expect it to be negative. An increase
the marginal net-of-tax rate should cause the pretax wages of dangerous indust
to decrease relative to those of safe industries. We should expect P3 to be nega
as well. A high replacement rate benefits workers in dangerous industries dis
portionately. In response, pretax wages should decrease relative to the wages
workers in safe industries.
In my instruments, only cross-sectional risk variation is used. Consequently, each
industry-state fixed effect is associated with only one risk level in the instrument.
These fixed effects account for the cross-sectional correlation between risk and un
observed factors in a completely flexible manner. All standard errors are adjusted
for clustering at the industry aggregate level.
B. Heterogeneity in Tax Incidence
din w
The incidence of the tax rate is —, -, holding all other variables constant. While
3
\1-T/
changes in the tax rate also directly affect the workers' compensation replacement
rate, the incidence of the tax rate holds this constant (this is suppressed in the
notation). This paper focuses on how income taxes distort the relative value of wages
and amenities. Tax changes also affect the expected value of wage replacement from
the workers' compensation system. While it is important to explicitly account for
the effect of this change in the after-tax replacement rate, the estimate of interest
should exclude this channel. Consequently, I hold the after-tax replacement rate
constant in the following calculations. In practice, this choice has little effect on the
results. I will discuss this issue again briefly when presenting the results.
Evaluating Equation 4, we get
(5) iln"
V,
= -(Po + tf'P2)
Tax incidence focuses on the wage response to tax changes. Identification of P0
is unclear and I have cautioned against interpreting this coefficient as the mean
incidence of income taxes. Since this paper looks at heterogeneity in the tax inci
dence, it should not be surprising that this term is differenced out below.
To parameterize heterogeneity in the incidence of the tax rate, I compare a risky
industry (defined as the 75th percentile most dangerous industry) to a safe industry
(defined as the 25th percentile). For example, when I use injuries only, I can calculate
P(Injury < Injury,) = 0.25,P(Injury < Injuryh) = 0.75
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Powell 1033
The tax incidence heterogeneity metric is
= - [3o + ^(Injury h)] + [P0 + ^(Injury ,)\(6)
= fi2( Injury,-Injury h)
As expected, the (30 term drops out. I've treated this term as a nuisance parameter
because I am not convinced that it can be interpreted solely as the incidence of the
marginal tax rate. P2 is the only relevant estimate to derive the heterogeneity mea
sure. The calculation using only fatality rates is similar. When both risk rates are
included, the following equations are used
P(P0 + R p2 < ¥,) = 0.25, P(p0 + R'P2 < %,) = 0.75
The resulting tax incidence heterogeneity metric is
(7) Tax Incidence Heterogeneity = lPA—SP,
When both risk rates are used, the percentiles of "riskiness" are implicitly a
weighted average of the injury and fatality rates using the regression coefficients as
weights. I also present tax heterogeneity metrics which compare the 90th percentile
to the 10th percentile. The percentiles defining the dangerous and safe jobs will use
the last year of the sample that is used to estimate the coefficients. Because the
variation in occupational riskiness is decreasing over time, the early sample coeffi
cients are multiplied by a larger number. It is important to note that there is little
reason to think that the tax heterogeneity metric magnitudes will be similar when
injury rates or fatality rates are used. These rates may signal certain types of jobs
and correlate with different amenities.
C. Description of Instruments
OLS estimation of Specification 4 is problematic since tax rates and replacement
rates are functions of the pretax wage. Instead, I employ an instrumental variables
(IV) strategy that relies on federal legislative tax changes, state level workers' com
pensation policy changes, and cross-sectional variation in risk.
A central point of this paper is to understand the consequences of tax changes
when amenities do not fully adjust. For this reason, I control separately for the risk
level. I also hold risk constant in the instrument when interacting with the tax rate.
Holding risk constant has several benefits. First, it ensures that identification only
originates from tax schedule changes and not shifts in risk over time. Each risk level
in the instruments has a fixed effect associated with it, nonparametrically accounting
for omitted variables correlating with risk.
Second, it eliminates biases due to year-to-year measurement error in the risk
variables. While risk levels may change exogenously and endogenously to taxes,
these changes only impact the strength of the first stage and do not affect the validity
of the final results.
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1034 The Journal of Human Resources
Since the marginal tax rate is a function of an individual's wage, I must instr
the tax variables. In the spirit of Currie and Gruber (1996a,b), I use a "sim
instrument" by holding a baseline sample constant and allowing the instrum
vary due to federal tax schedule changes only.1
To implement this strategy, I create a baseline sample for each industry and
let tax rates change based on tax schedule changes only. To illustrate this ap
I will detail how I calculate predicted tax rates for each industry in 1985
federal tax variation only.
1. Create baseline sample (1982 CPS).
2. Inflate incomes to 1985 values.
3. Find tax rate for each person using 1985's federal tax schedule (and FICA).
4. Average marginal tax rates by industry to get predicted tax rate (t,*,)
When I focus on my later (1991-2001) sample, my baseline sample is the 1991
CPS. The resulting instrument is ln(l-xjkl). The variation comes solely from feder
tax schedule changes. Industry-state interactions account for fixed wage level di
ferences.
The workers' compensation replacement rate also must be instrumented since the
replacement rate is a function of the wage. The predicted replacement rate is forme
in the exact same way that the predicted tax rates are created, except that the baselin
sample also depends on state. The baseline sample is adjusted for inflation for eac
year and that state-year's workers' compensation parameters are applied to each
observation. The replacement rates are calculated and averaged by industry and state
to get In(WCJkst). Variation within a state-industry originates solely from state-leve
policy changes.
While risk rates change differentially across industries over time in equation (4),
I have outlined why it is desirable for exogenous variation in /?¡,ln(l — Tytj() to
originate only from changes in the tax schedule. The corresponding instrument i
teracts the log of the predicted net-of-tax rate (as described above) with a risk proxy
that does not allow for industry-specific changes over time. An obvious candidat
for this risk proxy is the average risk for an industry over the sample period.
The final instruments are:
1. ln(l-x#()
2. In(WCJksl)
3. R¡xln(l-x^,)
4. Rkx\n(WCjkJ
1. The results are not meaningfully changed if state-level tax changes are also used.
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Powell 1035
PCr-1 i
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Year
P4, i
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Year
Figure 3
Average Marginal Tax Rate, 1982-2001
D. Sources of Variation
This paper relies on legislative federal tax changes for identification. The Economic
Recovery Tax Act of 1981 (ERTA1981) changed marginal tax rates from 1982 to
1984. The Tax Reform Act of 1986 (TRA1986) is the major tax change during the
sample period. TRA1986 drastically reduced the number of income tax brackets and
the top federal income tax rate was cut to 28 percent. The Omnibus Budget Rec
onciliation Act of 1990 and 1993 subsequently increased the number of income tax
brackets and the top federal income tax rate. In addition, the EITC was significantly
expanded during my sample. Figure 3 shows the progression of the average marginal
tax rate during the time period 1982-2001.
The paper also uses state-level changes in the workers' compensation temporary
total disability benefits for identification. These changes may occur because of state
changes in compensation rates, minimum benefit levels, and maximum benefit levels.
Cross-sectional risk variation is also necessary and was discussed in the Data
section. I argued that there are several advantages to fixing the risk rate in the
instrument. Thus, my instruments assume that there is some correlation in risk across
year within an industry. If risk rates were randomly assigned each year, then this
would not be true and there would not be a first stage. My first stage tests this
assumption implicitly.
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1036 The Journal of Human Resources
VI . Results
A. Main Results
OLS results are difficult to interpret and are included in the Appendix (Table A4
for reference. The Appendix also includes the first stage results. Table A5 present
the first stage for the entire sample when both risk rates are included. I report partia
/■"-statistics, which measures the explanatory power of the instruments for each en
dogenous variable independent of the other variables. The first stage is relatively
strong for all the variables.
Since most of the tax changes occur in the early part of the sample, the first stage
should be much stronger for the 1982-90 sample than the 1991-2001 one. Table
A6 shows that this is the case. The partial /-"-statistics decrease substantially for the
later sample. Consequently, we should expect the estimates from the early sample
to be much more precise than those from the later one.
The tax incidence heterogeneity numbers compare the elasticity of the wage with
respect to the marginal net-of-tax-rate for the 75th (90th) percentile most dangerous
industry to the 25th (10th) percentile for the last year of the relevant sample (1990
or 2001) using Equation 7. For reference, Table A7 lists the industries and their risk
rates, which are used in these calculations. For example, the full sample uses the
2001 risk distribution. The 25th percentile of the injury rate variable is the Scientific
and Controlling Instrument Industry with an injury rate of 0.9 injuries per 100 em
ployees. The 75th percentile is the Engine and Turbines Industry with an injury rate
of 2.3. The fatality rates are also included. Table A8 presents the same information
for the 90th and 10th percentile.
The main results of this paper are shown in Tables 1-3. The reader is encouraged
to focus on the tax heterogeneity estimates at the bottom, but the coefficients ar
also presented. Each table has three columns where each column represents a sepa
rate regression based on which risk rate is included—injury (Column 1), fatality
(Column 2), and both (Column 3). The IV results imply tax incidence heterogeneity
of 0.1 to 0.3. This suggests that when the marginal net-of-tax rate decreases 10
percent that the 75th percentile most dangerous job experiences a pretax wage in
crease 1-3 percent larger than the 25th percentile most dangerous job. Comparing
the 90th to 10th percentile, the implied heterogeneity is 0.5-0.7. Thus, a 10 percent
decrease in the marginal net-of-tax rate causes the wages of the most dangerous jobs
to increase by 5-7 percent more than the wages of the safest jobs. Using the mean
summary statistics (ignoring variation in initial wages and tax rates between indus
tries), these estimates imply that each percentage point increase in the marginal tax
rate increases the pretax wage differential (75th vs. 25th) by $0.07. The 90th vs.10th
differential increases by $0.18.
As expected, the estimates for P3 are also negative. These results suggest that
wages differentially respond to changes in the workers' compensation replacement
rate. When replacement rates increase, the pretax wages of dangerous jobs decreas
relative to those of safe jobs. Changes in the tax rate also affect the after-tax workers
compensation replacement rate. Instead of holding the replacement rate constant,
can look at how the wage differential changes due to the change in the tax rate,
including its indirect effect operating through the replacement rate. The implied
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Powell 1037
Table 1
IV Results, 1982-2001
Dependent Variable: log(wage)
(1) (2) (3)
Injury rate 0.008*** 0.008***
(0.003) (0.003)
Fatality rate 0.660 -0.460
(0.869) (0.880)
ln(l-x) -1.093*** -0.658*** -1.060***
(0.237) (0.236) (0.258)
Injury ratexln(l— t) -0.219*** —0.194***
(0.034) (0.045)
Fatality rate x ln( 1 — t) -48.015*** -15.099
(8.331) (10.285)
ln( WC') -0.034 0.003
(0.022) (0.041)
ln(WCF) -0.049** -0.048
(0.024) (0.038)
Injury ratexln(WC') -0.033*** -0.029**
(0.010) (0.012)
Fatality ratexln(WCF) -5.523** -1.201
(2.798) (3.095)
N 594,119 598,438 591,920
Fixed effects Industry*state Industry*state Industry*State
Implied Fleterogeneity:
75th-25th 0.307*** 0.090*** 0.274***
(0.048) (0.016) (0.066)
90th-10th 0.577*** 0.526*** 0.674***
(0.091) (0.091) (0.103)
Dependent Variable: log(wage)
(1) (2) (3)
Injury rate 0.008*** 0.008***
(0.003) (0.003)
Fatality rate 0.660 -0.460
(0.869) (0.880)
ln(l-T) -1.093*** -0.658*** -1.060***
(0.237) (0.236) (0.258)
Injury ratexln(l—t) -0.219*** —0.194***
(0.034) (0.045)
Fatality rate x ln( 1 — t) -48.015*** -15.099
(8.331) (10.285)
ln(WC') -0.034 0.003
(0.022) (0.041)
ln(WCF) -0.049** -0.048
(0.024) (0.038)
Injury ratexln(WC') -0.033*** -0.029**
(0.010) (0.012)
Fatality ratexlnf WCF) -5.523** -1.201
(2.798) (3.095)
N 594,119 598,438 591,920
Fixed effects Industry*state Industry*state Industry*State
Implied Heterogeneity:
75th-25th 0.307*** 0.090*** 0.274***
(0.048) (0.016) (0.066)
90th-10th 0.577*** 0.526*** 0.674***
(0.091) (0.091) (0.103)
Significance levels: * 10 percent, **5 percent, ***1 percent. Standard errors in parentheses are clustered
by industry aggregate. The "Implied Heterogeneity" results use Equation 7. Covariates include the follow
ing individual characteristics interacted with year dummies: age dummies, gender dummy, race dummies,
education dummies.
incidence heterogeneity is now 0.10 to 0.35 using the 75th and 25th percentiles.
Using the 90th and 10th, I find incidence heterogeneity of 0.60 to 0.66. While I
believe that it is important to directly account for and separately identify the after
tax replacement rate, the final calculations are not meaningfully impacted when they
are included.
The coefficients of interest are very similar when I focus on the 1982-90 time
period as shown in Table 2. These results suggest that a marginal net-of-tax rate
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1038 The Journal of Human Resources
Table 2
IV Results, 1982-90
Dependent Variable: log(wage)
(1) (2) (3)
Injury rate -0.002 -0.004
(0.003) (0.003)
Fatality rate -1.463* 1.242*
(0.809) (0.743)
ln(l— t) -0.824*** -0.345 -0.725***
(0.224) (0.242) (0.243)
Injury ratexln(l — t) -0.158*** -0.115***
(0.026) (0.036)
Fatality rate xln(1 — x) -47.006*** -25.423***
(7.642) (8.264)
ln(WC7) 0.014 -0.025
(0.035) (0.046)
ln(WCF) 0.066** 0.071**
(0.032) (0.036)
Injury ratex ln(WC7) -0.014 -0.006
(0.012) (0.014)
Fatality rate x ln( VVC7) -4.455 -3.779
(3.543) (3.758)
N 249,806 254,371 249,242
Fixed effects Industry*State Industry*State Industry*State
Implied heterogeneity:
75th-25th 0.520*** 0.126*** 0.427***
(0.084) (0.020) (0.120)
90th-10th 0.857*** 0.648*** 0.962***
(0.139) (0.105) (0.171)
Dependent Variable: log(wage)
(1) (2) (3)
Injury rate -0.002 -0.004
(0.003) (0.003)
Fatality rate -1.463* 1.242*
(0.809) (0.743)
ln(l-x) -0.824*** -0.345 -0.725***
(0.224) (0.242) (0.243)
Injury ratexln(l —t) -0.158*** -0.115***
(0.026) (0.036)
Fatality ratexln(l—x) -47.006*** -25.423***
(7.642) (8.264)
ln(WC7) 0.014 -0.025
(0.035) (0.046)
ln(WCF) 0.066** 0.071**
(0.032) (0.036)
Injury ratexln(WC7) -0.014 -0.006
(0.012) (0.014)
Fatality ratexln(WCF) -4.455 -3.779
(3.543) (3.758)
N 249,806 254,371 249,242
Fixed effects Industry*State Industry*State Industry*State
Implied heterogeneity:
75th-25th 0.520*** 0.126*** 0.427***
(0.084) (0.020) (0.120)
90th-10th 0.857*** 0.648*** 0.962***
(0.139) (0.105) (0.171)
Significance levels: * 10 percent, ** 5 percent, *** 1 percent. Standard errors in parentheses are clustered
by industry aggregate. The "Implied Heterogeneity" results use Equation 7. Covariates include the follow
ing individual characteristics interacted with year dummies: age dummies, gender dummy, race dummies,
education dummies.
decrease of 10 percent increases the wages of dangerous jobs by 1-5 percent more
than the wages of safe jobs. When comparing the 90th to the 10th percentile jobs,
the implied heterogeneity is 0.6 to 1.0.
There are large tax schedule changes during the 1982-90 time period. The first
stage strength is much weaker after 1990. Table 3 reports results from 1991-2001.
Despite the weaker first stages, the tax incidence heterogeneity estimates are con
sistent with those of the earlier time period.
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Powell 1039
Table 3
IV Results, 1991-2001
Dependent Variable: log(wage)
(1) (2) (3)
0.017** 0.016**
(0.007) (0.007)
1.579 0.773
(2.764) (2.612)
-0.094 0.201 -0.099
(1.740) (1.946) (1.804)
-0.343* -0.228
(0.178) (0.210)
-96.650 -84.672
(69.870) (85.497)
-0.046 -0.070
(0.060) (0.068)
0.011 0.029
(0.060) (0.066)
-0.140*** -0.142**
(0.050) (0.061)
-16.095* -9.451
(8.245) (9.028)
311,502 311,634 310,579
Industry*State Industry*State Industry*State
0.479* 0.182 0.461**
(0.249) (0.132) (0.216)
0.902* 1.058 1.482*
Injury rate
Fatality rate
In(l-t)
Injury ratexlnO— t)
Fatality ratexln(l—t)
In(WC')
ln(WCF)
Injury ratexln(WC')
Fatality ratexln(WCF)
V
Fixed Effects
Implied heterogeneity:
75th-25th
90th-10th
(0.468) (0.765) (0.784)
Dependent Variable: log(wa
(1) (2) (3)
Injury rate 0.017** 0.016**
(0.007) (0.007)
Fatality rate 1.579 0.773
(2.764) (2.612)
ln(l-t) -0.094 0.201 -0.099
(1.740) (1.946) (1.804)
Injury ratexln(l— t) -0.343* -0.228
(0.178) (0.210)
Fatality rate x ln( 1 — t) -96.650 -84.672
(69.870) (85.497)
ln(WC') -0.046 -0.070
(0.060) (0.068)
ln(WCF) 0.011 0.029
(0.060) (0.066)
Injury ratexln(WC') -0.140*** -0.142**
(0.050) (0.061)
Fatality ratexln( WCF) -16.095* -9.451
(8.245) (9.028)
N 311,502 311,634 310,579
Fixed Effects Industry*State Industry*State Industry*Stat<
Implied heterogeneity:
75th-25th 0.479* 0.182 0.461**
(0.249) (0.132) (0.216)
90th-10th 0.902* 1.058 1.482*
(0.468) (0.765) (0.784)
Significance levels: * 10 percent, **5 percent, ***1 percent. Standard errors in parentheses are clustered
by industry aggregate. The "Implied Heterogeneity" results use Equation 7. Covariates include the follow
ing individual characteristics interacted with year dummies: age dummies, gender dummy, race dummies,
education dummies.
These results illustrate that income taxes impact compensating differentials. The
incidence of taxes is economically important because the entity that actually pays a
tax is not always the one that bears the burden of that tax. A tax levied on workers
may actually be paid by firms. Income taxes distort the relationship between wages
and amenities, but this distortion may occur at the firm level. The results suggest
that income taxes act as taxes on firms with low levels of amenities. When tax rates
are high, industries that must pay large compensating differentials because of the
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1040 The Journal of Human Resources
dangerous nature inherent in their jobs are disproportionately harmed. Thus, diffe
ential changes in pretax wages imply that income taxes act as taxes on occupation
risk at the industry level. The economic implications are potentially profound.
wages are affected, it is likely that other industry-level factors are affected as wel
If income taxes act as industry-level taxes on occupational risk, then marginal tax
rate increases should shift the marginal cost curve of dangerous industries furth
than those for safe industries. While beyond the scope of this paper, we should
expect to see income taxes differentially affecting the price and output of industri
based on their risk level. Such a result implies that the relative production in th
economy is not optimal, distorted by income taxation. The tax literature has no
studied this possible source of distortion, though the results of this paper sugge
that it is a critical consideration for tax policy.
B. Robustness Checks
1. Wage Trends
A large literature details the growth of wage inequality during the time period
my sample. A major concern of the analysis in this paper is that wage trends a
driving the results. The main results have already provided some evidence that wag
trends are not problematic since I use all tax changes as sources of exogenous
variation. While TRA1986 did decrease taxes, there are also periods where taxe
increased during my sample. The 1991-2001 estimates are more imprecisely m
sured than the earlier period estimates, but they still suggest very large effects during
a period where tax rates increased on average. Thus, legislative tax increases and
tax decreases seem to generate similar results, suggesting that secular trends are no
driving the results. However, it is useful to account for wage trends more explicitl
In Table 4, I summarize a series of regressions that controls explicitly for initi
wages. Each block represents the same regressions seen in the previous tables, bu
I only report the resulting tax heterogeneity incidence estimates for the sake o
simplicity. I compare industries within wage deciles by interacting the year fixe
effects with fixed effects based on 1982 (or 1991) wage deciles. These interaction
allow low-wage and high-wage industries to experience different year-to-year wa
growth. The estimates are consistent with the earlier findings.
It is useful to discuss why the empirical strategy of this paper is robust to wag
trends. To drive the results of this paper, these wage trends must occur within
given tax rate. My specification separately controls for the after-tax rate and, ther
fore, implicitly compares industries with similar initial wages. Note that the ta
instruments are a function of wage earnings in the first year of the sample. B
controlling for the tax rate, I am implicitly accounting for initial wages. In oth
words, my strategy is similar to a differences-in-differences framework where
control for the tax rate and the risk rate and then look at the interaction of the two.
Wage trends are problematic only if industries with similar initial wages but differe
risk levels follow different trends. I am not suggesting that the after-tax rate is a
adequate proxy for wage trends if one wanted to study wage trends specifically
Instead, because identification originates from tax changes, any spurious correlation
due to wage trends must occur within a given tax change. The fact that I am im
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Powell 1041
Table 4
IV Results Controlling for Wage Decile x Year Interactions
Implied Heterogeneity
Injury Fatality Both
75th-25th
1982-2001
1982-1990
1991-2001
0.319***
(0.052)
0.538***
(0.085)
0.479*
(0.249)
0.092***
(0.016)
0.121***
(0.023)
0.182
(0.132)
0.304***
(0.074)
0.478***
(0.125)
0.462**
(0.216)
90th-10th
1982-2001
1982-1990
1991-2001
0.601***
(0.097)
0.887***
(0.140)
0.902*
(0.468)
0.536***
(0.093)
0.624***
(0.118)
1.058
(0.765)
0.673***
(0.133)
1.005***
(0.200)
1.482*
(0.784)
Implied Heterogeneity
Injury Fatality Both
75th-25th
1982-2001
1982-1990
1991-2001
0.319***
(0.052)
0.538***
(0.085)
0.479*
(0.249)
0.092***
(0.016)
0.121***
(0.023)
0.182
(0.132)
0.304***
(0.074)
0.478***
(0.125)
0.462**
(0.216)
90th-10th
1982-2001
1982-1990
1991-2001
0.601***
(0.097)
0.887***
(0.140)
0.902*
(0.468)
0.536***
(0.093)
0.624***
(0.118)
1.058
(0.765)
0.673***
(0.133)
1.005***
(0.200)
1.482*
(0.784)
Significance levels: * 10 percent, ** 5 percent, *** 1 percent. Standard errors in parentheses are clustered
by industry aggregate. The "Implied Heterogeneity" results use Equation 7. Regressions control for wage
deciles (based on 1982 or 1991 wage levels) interacted with year fixed effects. Covariates include the
following individual characteristics interacted with year dummies: age dummies, gender dummy, race
dummies, education dummies.
plicitly comparing industries with similar initial wages is consistent with the ro
bustness of my estimates when initial wages are more explicitly accounted for.
2. Individual level Heterogeneity
Finally, it could be argued that simply accounting for industry-state heterogeneity is
inadequate. Instead, we might be concerned that when taxes change, the skill com
position of industries change based on risk. This story suggests that when tax rates
change, workers resort themselves across industries. To consider this possibility, I
use individual-level panel data to account for individual heterogeneity.
The Panel Survey of Income Dynamics (PSID) records wage and income infor
mation for families for multiple years. I estimate the following specification for the
years 1981-96:2
2. The PSID becomes a biennial survey after 1997. Wages, tax rates, and industry are needed in each year
to estimate the specification. Tax rates can only be derived for the previous year, but the industry of the
worker is unknown in that year.
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1042 The Journal of Human Resources
Table 5
Individual-Level Data, 1981-96
Implied Heterogeneity
Injury Fatality Both
75 th—25 th 0.409*** 0.070 0.358**
(0.153) (0.047) (0.160)
90th-10 th 0.721*** 0.328 0.672**
(0.270) (0.220) (0.329)
N 40,556 43,194 40,556
Fixed effects Individual Individual Individual
Implied Heterogeneity
Injury Fatality Both
75th-25th 0.409*** 0.070 0.358**
(0.153) (0.047) (0.160)
90th-10 th 0.721*** 0.328 0.672**
(0.270) (0.220) (0.329)
N 40,556 43,194 40,556
Fixed effects Individual Individual Individual
Significance levels: * 10 percent, **5 percent, ***1 percent. Standard errors in parentheses are clustered
by industry aggregate and individual. The "Implied Heterogeneity" results use Equation 7. Covariates
include the following individual characteristics interacted with year dummies: age dummies, gender dummy,
race dummies, education dummies, tenure at current job, tenure squared.
(8) 'n wijkst - Yt + + + Rk,p + P0ln(l—Ty,.,,,) + In(WCijks¡) (3,
+ [#¡,ln(l—c,7te)]'p2+ [RkM(WCijks,j]'$3 ^ijkst
The strategy is similar. I use tax rates predicted at the industry level in the in
struments. Risk rates are held constant in the instrument and assume that the indi
vidual does not change industries. Similarly, predicted tax rates are assigned assum
ing that the individual does not change industries. Thus, as before, all variation
originates from tax schedule changes.
Most people are included in the sample for a significant length of time. It could
be argued that an individual fixed effect spanning 16 years is inadequate. Instead, I
treat each five-year span for an individual as a separate "person'Vfixed effect. In
other words, a person in my sample for 1981-90 is treated as two separate people—
one for 1981-85 and one for 1986-90.3 The standard errors must be appropriately
adjusted and I use the multi-dimensional clustering algorithm suggested by Cameron,
Gelbach, and Miller (2011) to account for clustering at the individual level and the
levels of the risk measures. Because the injury and fatality rates are provided at
different levels, this method implies that I adjust for two-way clustering when one
risk rate is included and three-way clustering when both are included.
The PSID sample is much smaller than the CPS so we would expect the estimates
to be less precise. There is some evidence of this, but the results in Table 5 are
consistent with the CPS results, suggesting that skill and taste heterogeneity are not
driving the results presented in this paper. These findings confirm the main results
of this paper but are also independently interesting. Hwang, Reed, and Hubbard
(1992) presents a model illustrating how skill heterogeneity can bias cross-sectional
compensating differential estimates. The results of this paper are likely robust to this
3. The results are robust to other permutations of this breakdown.
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Powell 1043
type of critique since identification originates from tax changes, which work
as given. It is reassuring that including individual fixed effects does not
change the estimates.
By controlling for individual heterogeneity, the results in the section sugg
the pretax compensating differential fully adjusts to tax changes. Rosen (19
ents a model that shows that estimation of compensating differentials by lo
the relationship between an amenity and wages provides the valuation of
ginal worker. This point is relevant to my strategy as well. When tax rates
the marginal worker might change and pretax wages may not fully adju
re-sorting. In terms of interpreting my parameter of interest, this re-sortin
of the effect of interest since it impacts the observed compensating differe
workers re-sort to such an extent that pretax compensating differentials ad
then this will manifest itself in my result and I will find less heterogeneity
tax incidence metrics. However, the robustness of the result to individual
fects suggests that re-sorting is not impacting the final estimates. Instea
appear to fully adjust, keeping the marginal worker relatively constant.
C. Implications for Estimating Compensating Differentials
The results of this paper illustrate that pretax compensating differentials sh
marginal net-of-tax rates. A vast literature studies the relationship between
job risk and wages for the purposes of estimating the value of a statistical li
The VSL parameter is the implicit tradeoff that individuals make between
and their own probability of dying. This parameter is important for pr
benefit analysis of policies which save lives. If a policy costs $3 million
saved, it is necessary to understand the amount that individuals value th
saved (or, equivalently, the reduction in their own probability of dying). Eq
is the hedonic wage regression typically used in the literature to derive th
I can calculate how the "observed VSL" (the VSL if pretax wages are used
with taxes. I differentiate Equation 4 with respect to the fatality rate (super
all coefficients on fatality variables with F), holding the workers' compe
variables constant. I evaluate at the mean wage since the specification use
of the wage and multiply by 200,000 since the fatality rate variable is exp
fatalities per 200,000 hours. The equation of interest is
Observed VSL= pF + |3Fln(l-T)xvvx200,000
I calculate how the VSL estimate changes for a one percentage point increa
marginal tax rate. I perform this calculation at the sample mean margina
(t = 0.34):
(9) Observed VSL|t = 035-Observed VSL|t = 034
= (if [ln( 1 -0.35)-ln(l -0.34)] x w x 200,000
Much of the VSL literature does not account for injury rates. Thus, I first plug in
the estimated coefficient from Column 2 of Table 1. Equation 9 suggests that a one
percentage point increase in the marginal tax rate increases the observed VSL by
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1044 The Journal of Human Resources
over $2.6 million. When the Column 3 coefficient estimate is used, the impl
increase is about $820,000, though this is insignificant.
These changes in the VSL are relatively large when compared to VSL estimat
found in the literature (see Viscusi and Aldy 2003). One concern with VSL estim
generated from studying the cross-sectional relationship between wages and ris
that skill heterogeneity biases the coefficient on risk downward. The Hwang, Ree
and Hubbard (1992) model focuses on skill heterogeneity where high-skilled worke
want to be compensated for their skill with a combination of additional safety
wages relative to low-skilled workers. In other words, high-skilled workers sort i
safer jobs. The empirical strategy of this paper, however, is likely unaffected by s
heterogeneity. Identification originates from tax changes, which workers tak
given and are likely orthogonal to skill level. Consequently, the change in the
(estimated above) is unaffected by this critique, while the VSL estimates in
literature are potentially impacted.
The results of this paper produce some meaningful evidence for the VSL a
compensating differential literatures. First, cross-sectional wages are a functio
risk and other amenities. If workers were not compensated for risk, then taxes wo
have no effect on the compensating differential. Second, pretax compensating
ferentials respond to marginal tax rates and tax rates should be explicitly conside
when estimating compensating differentials.
VII. Conclusion
The income tax literature has provided evidence that income taxe
distort individuals' decisions concerning the optimal combination of wages a
amenities. Individuals may change occupations to consume different levels of am
ities or firms may respond in the provision of their amenities. However, the litera
has generally ignored the possibility that some amenities may be, to some exte
defining features of a job and prohibitively costly to change. In these cases, pr
wages must adjust. Thus, tax increases should increase the size of compensat
differentials.
I look at the interaction of tax rates and on-the-job safety, finding significantly
different wage responses between safe and dangerous jobs. When the marginal net
of-tax rate decreases by 10 percent, the pretax wages of the 75th percentile most
dangerous job increase by 1-5 percent more than the pretax wages of the 25th
percentile. When comparing the 90th to the 10th percentile, the wages of the dan
gerous job increase by 6-10 percent more. These results suggest that tax increases
disproportionately hurt low amenity, high-compensating differential industries and
that income taxes act as taxes on low levels of amenities at the industry level.
Heterogeneity in the wage response to taxes is economically meaningful and an
important component of the total distortion of income taxation.
This research illustrates that income taxes can have profound effects on the wage
amenity distortion at the industry level, increasing costs for dangerous industries
relative to safe industries. These increases in costs could potentially distort the rela
tive output of those industries. Legislative tax rate increases cause compensating
differentials to grow, implicitly taxing dangerous industries.
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Powell 1045
Data Appendix
A. Fatality Rates
The National Institute for Occupational Safety and Health collected fatal
between 1980 and 20014 through the National Traumatic Occupational Fat
veillance System (NTOF). The NTOF records fatalities listed as work-rel
death certificates, which are coded as externally caused for those that we
older. These fatalities are then categorized by industry. The NTOF typically
these data at the one-digit SIC level. There are only ten such divisions (in
agriculture/forestry/fishing and public administration, both of which are ra
in this type of analysis), severely limiting the amount of useful variation a
ing any confidence that such a fatality rate accurately describes the true
rienced by the workers.
By request, I received more detailed fatality data for 49 separate indus
gories. To give an example of the importance of this breakdown, the aggreg
set reports one fatality rate for manufacturing. The more detailed data lists
rates for 16 different categories within the manufacturing industry. I divid
tality numbers by the total number of hours worked in that industry-year a
to the March CPS to arrive at my fatality rate variable.
In the NTOF data, 5.7 percent of fatalities are listed as "Not Classified." I c
the percentage of classified fatalities that occur in each industry and mak
sumption that the unclassified fatalities occurred randomly. Thus, an indust
2 percent of all classified fatalities in 1985 will be assigned 2 percent o
classified fatalities in that year as well. Fatality rates were merged to CI
system using the crosswalk provided in Appendix II of Fatal Injuries to
Workers in the United States, 1980-95.
Using death certificates as the only raw data source leads to an undercount
number of fatalities. This undercount can be estimated by comparisons to th
of Fatal Occupational Injuries (CFOI). The Bureau of Labor Statistics cur
maintains the CFOI which is a highly regarded source for the number of
by industry. However, the CFOI did not begin until 1992. Due to the relative
federal tax schedule changes between 1992 and 2001, this paper requires
data for the pre1992 period.
I compared the CFOI and NTOF rates for 1992-2001. The NTOF record
percent as many fatalities as the CFOI. This number was extremely consis
time. The annual values ranged from 78.5 percent to 83.3 percent, sugges
the overall average can be assumed for the pre-1992 period. It is also wort
that the correlation by NTOF industry-year between NTOF and CFOI fatal
over this time period is 0.95. This correlation suggests that there is no sy
bias by industry.
B. Injury Rates
Injury data were found in the Survey of Occupational Injuries and Illness
and online at the Bureau of Labor Statistics website (www.bls.gov). I used
4. The 2001 data exclude fatalities resulting from the September 11 terrorist attacks.
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1046 The Journal of Human Resources
able titled "Cases involving days away from work." The 1982-88 data are categ
rized by the 1977 Standard Industrial Classification system while the 1989-200
data use the 1987 Standard Industrial Classification system. The data are publishe
at the two-, three-, or four-digit level based on industry. The Census Industrial Cla
sification system used by the CPS, however, is most related to the three-digit S
level. The four-digit level (reported for manufacturing industries) is too detailed an
never used while a few two-digit industries correspond directly to the CIC system
If no injury rate is reported for a given three-digit industry,5 I impute the valu
using the injury rate given for its two-digit industry and the other three-digit ind
tries in that two-digit category. The SOU also reports employment data, so I ca
calculate the injury rate of the "missing industries" within a two-digit category
use a crosswalk to assign each industry to a CIC category. When one CIC indust
corresponds to multiple SIC industries, I average the injury rates, weighted by e
ployment, to the CIC level.
Before 1992, these numbers included fatalities. Since fatalities make up an e
tremely small percentage of all injuries, it should be acceptable to merge the pr
1992 and 1992-2001 data together. Injury rates are reported to one decimal poin
Even the injury rates of the highest fatality rate industries would be unaffected b
excluding fatality rates at this level. I also show results for an early sub-sample
which does not cross this 1992 data change and the estimates appear to be una
fected. The BLS simultaneously collects hours data from the surveyed firms an
constructs injuries per 200,000 hours (or 100 full-time equivalent workers).
C. Sample
My sample includes all workers in the private labor force ages 25-55 that are not
self-employed. I exclude all agricultural industries. This leaves me with 757,647 ob
servations. I drop 45,365 observations with allocated wage income, hours worked, or
weeks worked. I drop 6,622 observations because they have wages below $2 or above
$200 in 2001 dollars. I exclude 19,813 observations because I attribute a workers'
compensation replacement rate (injury or fatality) over 200 percent6 to them. Finally,
I only use workers who are listed as the head of the household or the spouse of the
head of the household, which excludes 81,490 observations. I am more confident
about the tax rates of household heads and their spouses because it is otherwise
difficult to determine the tax filing situation. I am left with 604,352 observations.
Table A3 presents summary statistics for the entire sample and subsamples based
on overall risk for the entire 1982-2001 period. Wages are listed in 2001 dollars.
D. Estimation Details
"Industry aggregate" refers to the level of variation of the risk variable. Each "in
dustry aggregate" includes one or more industries. This is different depending on
whether the injury rate is included or the fatality rate is included. The "industry
category refers to the level that the industry fixed effects control for and the leve
5. There are several reasons that an injury rate might be missing but, in general, these tend to be ver
small industries.
6. These workers tend to report very low hours worked per week.
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Powell 1047
of variation for the tax instrument. There are 204 of these industries. To
value of the risk variables can be the same for several of these industries within a
year. The exogenous tax variation, however, will vary for each industry.
I "attach" the injury rate to the temporary total disability replacement rate and the
fatality rate to the death benefit replacement rate. I control for the replacement rate(s)
related to the risk measures included. I force the coefficient on the death benefit
replacement rate to be equal to 0 for single workers with no children. I accomplish
this by setting ln(WCfjto)=0.
The covariates are allowed to have different coefficients for each year. The returns
to individual characteristics, especially education, are changing over this time period
and it is important to account for these changes. I include the following covariates: five
year age group dummies, gender dummies, education dummies, and race dummies.
In practice, I de-mean the risk variables within each year because identification
originates from cross-sectional variation in risk. I de-mean the tax and replacement
rates by industry because identification originates from industry-specific changes in
taxes and replacement rates. De-meaning the input variables is customary with in
teraction terms and does not meaningfully impact the final results here.
Table Al
Top and Bottom Ten Fatality Rates by Industry, 1982-2001 NTOF Data
Fatalities per 100,000 Injuries per 100
Industry FTE Workers FTE Workers
Forestry & fisheries 44.15 3.59
Metal/coal/nonmetal mining 28.14 4.54
Lumber & wood 26.54 6.32
Oil & gas extraction 21.98 3.33
Trucking/warehousing/storage 20.55 6.13
Agricultural production 18.88 3.54
Construction 14.08 4.87
Agricultural services 11.56 3.72
Other transportation 9.81 4.97
Electric light & power 9.57 1.38
Mean 4.43 2.73
Printing/publishing/allied 1.41 2.27
Insurance & real estate 1.27 1.08
Apparel & accessory stores 1.24 1.16
Electrical machinery 1.20 2.08
Other professional services 1.10 1.03
Educational services 0.76 1.22
Health services, except hospitals 0.74 2.69
Hospitals 0.69 3.29
Apparel & other textile 0.65 2.35
Banking and Other Finance 0.64 0.48
Fatalities per 100,000 Injuries per 100
Industry FTE Workers FTE Workers
Forestry & fisheries 44.15 3.59
Metal/coal/nonmetal mining 28.14 4.54
Lumber & wood 26.54 6.32
Oil & gas extraction 21.98 3.33
Trucking/warehousing/storage 20.55 6.13
Agricultural production 18.88 3.54
Construction 14.08 4.87
Agricultural services 11.56 3.72
Other transportation 9.81 4.97
Electric light & power 9.57 1.38
Mean 4.43 2.73
Printing/publishing/allied 1.41 2.27
Insurance & real estate 1.27 1.08
Apparel & accessory stores 1.24 1.16
Electrical machinery 1.20 2.08
Other professional services 1.10 1.03
Educational services 0.76 1.22
Health services, except hospitals 0.74 2.69
Hospitals 0.69 3.29
Apparel & other textile 0.65 2.35
Banking and Other Finance 0.64 0.48
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1048 The Journal of Human Resources
Table A2
Top and Bottom Ten Injury Rates by Industry, 1982-2001 BLS
Fatalities
Injuries per 100 per 100,000
Industry FTE Workers FTE Workers
Logging 8.66 27.03
Ship and boat building and repairing 8.02 2.99
Leather: tanned, curried, and finished 7.27 5.87
Wood building and mobile homes 7.27 25.07
Air transportation 7.15 9.69
Coal mining 6.58 28.20
Beverage industries 6.44 4.13
Other primary iron and steel industries 6.32 8.97
Trucking service 6.22 20.38
Nursing and personal care facilities 6.18 0.74
Mean 2.73 4.52
Beauty shops 0.62 2.27
Offices and clinics of dentists 0.57 0.74
Insurance 0.55 1.26
Banking 0.54 0.64
Offices and clinics of physicians 0.52 0.74
Credit agencies 0.34 0.62
Brokerage and investments 0.34 0.63
Computer and data programming service 0.34 2.33
Legal services 0.31 1.10
Accounting, auditing, bookkeeping services 0.29 1.11
Fatalities
Injuries per 100 per 100,000
Industry FTE Workers FTE Workers
Logging 8.66 27.03
Ship and boat building and repairing 8.02 2.99
Leather: tanned, curried, and finished 7.27 5.87
Wood building and mobile homes 7.27 25.07
Air transportation 7.15 9.69
Coal mining 6.58 28.20
Beverage industries 6.44 4.13
Other primary iron and steel industries 6.32 8.97
Trucking service 6.22 20.38
Nursing and personal care facilities 6.18 0.74
Mean 2.73 4.52
Beauty shops 0.62 2.27
Offices and clinics of dentists 0.57 0.74
Insurance 0.55 1.26
Banking 0.54 0.64
Offices and clinics of physicians 0.52 0.74
Credit agencies 0.34 0.62
Brokerage and investments 0.34 0.63
Computer and data programming service 0.34 2.33
Legal services 0.31 1.10
Accounting, auditing, bookkeeping services 0.29 1.11
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Powell 1049
Table A3
Summary Statistics
Entire Sample Lowest Fatality Rate Industries
Standard Standard
Mean Deviation Mean Deviation
Wage 17.76 13.24 Wage 18.73 14.54
T 0.33 0.11 X 0.34 0.10
Injury rate 2.81 1.96 Injury rate 1.93 1.55
Fatality rate 4.36 5.77 Fatality rate 1.05 0.48
Age 39.23 8.34 Age 39.43 8.31
Percent college 50.02 50.00 Percent college 62.18 48.50
Percent female 45.65 49.81 Percent female 61.57 48.64
Percent white 87.70 32.90 Percent white 87.20 33.41
WC1 0.91 0.23 WC1 0.92 0.24
WCF 0.92 0.26 WCF 0.94 0.26
Middle Fatality Rate Industries Highest Fatality Rate Industries
Standard Standard
Mean Deviation Mean Deviation
Wage 16.59 12.54 Wage 17.92 11.83
T 0.32 0.12 X 0.32 0.11
Injury rate 2.62 1.53 Injury rate 4.45 2.07
Fatality rate 2.85 0.87 Fatality rate 11.80 7.51
Age 39.03 8.40 Age 39.21 8.30
Percent college 45.87 49.83 Percent college 36.58 48.17
Percent female 43.13 49.53 Percent female 23.83 42.61
Percent white 87.00 33.63 Percent white 89.32 30.89
WC1 0.91 0.23 WC1 0.88 0.22
WCF 0.93 0.26 WC1 0.89 0.25
Entire Sample Lowest Fatality Rate Industries
Standard Standard
Mean Deviation Mean Deviation
Wage 17.76 13.24 Wage 18.73 14.54
T 0.33 0.11 X 0.34 0.10
Injury rate 2.81 1.96 Injury rate 1.93 1.55
Fatality rate 4.36 5.77 Fatality rate 1.05 0.48
Age 39.23 8.34 Age 39.43 8.31
Percent college 50.02 50.00 Percent college 62.18 48.50
Percent female 45.65 49.81 Percent female 61.57 48.64
Percent white 87.70 32.90 Percent white 87.20 33.41
WC1 0.91 0.23 WC1 0.92 0.24
WCF 0.92 0.26 WCF 0.94 0.26
Middle Fatality Rate Industries Highest Fatality Rate Industries
Standard Standard
Mean Deviation Mean Deviation
Wage 16.59 12.54 Wage 17.92 11.83
T 0.32 0.12 X 0.32 0.11
Injury rate 2.62 1.53 Injury rate 4.45 2.07
Fatality rate 2.85 0.87 Fatality rate 11.80 7.51
Age 39.03 8.40 Age 39.21 8.30
Percent college 45.87 49.83 Percent college 36.58 48.17
Percent female 43.13 49.53 Percent female 23.83 42.61
Percent white 87.00 33.63 Percent white 89.32 30.89
WC1 0.91 0.23 WC1 0.88 0.22
WCF 0.93 0.26 WC1 0.89 0.25
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1050 The Journal of Human Resources
Table A4
OLS Results, 1982-2001
Dependent Variable: log(wage)
(1) (2) (3)
Injury rate 0.003 0.003
(0.002) (0.002)
Fatality rate 1.686 0.507
(0.690) (0.987)
ln( 1 —x) — 1 791*** —1.697*** -1.780***
(0.015) (0.021) (0.017)
Injury rate x ln( 1 — x) -0.018** -0.031***
(0.007) (0.008)
Fatality rate x ln( 1 — x) 1.085 8.195***
(2.286) (2.468)
\n(WC') -0.953*** -0.753***
(0.012) (0.013)
In (WCF) —0.779*** -0.239***
(0.011) (0.011)
Injury ratexln(VFC') -0.016*** -0.016**
(0.006) (0.006)
Fatality ratexln(WCF) -1.222 0.479
(2.464) (2.438)
N 594,119 598,438 591,920
Fixed Effects Industry*State Industry*State Industry*State
Implied heterogeneity:
75th-25th 0.025** -0.002 0.039***
(0.010) (0.004) (0.011)
90 th-10 th 0.047** -0.012 0.066***
(0.019) (0.025) (0.022)
Significance levels: * 10 percent, ** 5 percent, *** 1 percent. Standard errors in parentheses are clustered
by industry aggregate. The "Implied Heterogeneity" results use Equation 7. Covariates include the follow
ing individual characteristics interacted with year dummies: age dummies, gender dummy, race dummies,
education dummies.
Dependent Variable: log(wage)
(1) (2) (3)
Injury rate 0.003 0.003
(0.002) (0.002)
Fatality rate 1.686 0.507
(0.690) (0.987)
ln(l— t) — 1 791*** —1.697*** -1.780***
(0.015) (0.021) (0.017)
Injury rate x ln( 1 — x) -0.018** -0.031***
(0.007) (0.008)
Fatality rate x ln( 1 — x) 1.085 8.195***
(2.286) (2.468)
\n(WC') -0.953*** -0.753***
(0.012) (0.013)
In (WCF) —0.779*** -0.239***
(0.011) (0.011)
Injury ratexln(WC') -0.016*** -0.016**
(0.006) (0.006)
Fatality ratexIndVC^j -1.222 0.479
(2.464) (2.438)
N 594,119 598,438 591,920
Fixed Effects Industry*State Industry*State Industry*State
Implied heterogeneity:
75th-25th 0.025** -0.002 0.039***
(0.010) (0.004) (0.011)
90 th-10 th 0.047** -0.012 0.066***
(0.019) (0.025) (0.022)
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Powell 1051
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1052 The Journal of Human Resources
Table A6
Partial F-Statistics by Sample
1982-2001 1982-90 1991-2001
ln( 1 —t) 101.49 117.98 5.98
Injury xln(l-T) 285.50 517.33 62.68
Fatal xln(l-x) 100.21 165.57 4.48
ln(WC') 568.63 583.51 347.42
ln(WCF) 61.44 93.60 115.89
Injury xln(WC') 246.24 286.66 114.96
Fatal xln(WCF) 164.46 236.72 41.45
N 591,920 249,242 310,579
1982-2001 1982-90 1991-2001
ln( 1 — t) 101.49 117.98 5.98
Injury xln(l—x) 285.50 517.33 62.68
Fatal xln(l-x) 100.21 165.57 4.48
ln(WC') 568.63 583.51 347.42
ln(WCF) 61.44 93.60 115.89
Injury xln(WC') 246.24 286.66 114.96
Fatal xln(WCF) 164.46 236.72 41.45
N 591,920 249,242 310,579
Each column reports the partial F-statistics for each variable for that sample. Covariates include Indus
try*State dummy variables and the following individual characteristics interacted with year dummies: age
dummies, gender dummy, race dummies, education dummies.
Table A7
Injury and Fatality Rates for Tax Incidence Heterogeneity Calculation (75th-25th
Injury Rates
75th Percentile 25th Percentile
Engines and Turbines Scientific and Controlling
2.3 per 100 Instrument
0.9 per 100
Crude petroleum & natural gas Colleges and universities
extraction 1.7 per 100
5.0 per 100
Fatality Rates
75th Percentile 25th Percentile
1001 Motor Vehicles/Auto Supply Dealer Other Professional
2.7 per 100,000 0.8 per 100,000
1990 Motor vehicles/auto supply dealer Insurance and real estate
3.9 per 100,000 1.2 per 100,000
Injury Rates
75th Percentile 25th Percentile
2001 Engines and Turbines Scientific and Controlling
2.3 per 100 Instrument
0.9 per 100
1990 Crude petroleum & natural gas Colleges and universities
extraction 1.7 per 100
5.0 per 100
Fatality Rates
75th Percentile 25th Percentile
2001 Motor Vehicles/Auto Supply Dealer Other Professional
2.7 per 100,000 0.8 per 100,000
1990 Motor vehicles/auto supply dealer Insurance and real estate
3.9 per 100,000 1.2 per 100,000
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Powell 1053
Table A8
Injury and Fatality Rates for Tax Incidence Heterogeneity Calculation (90th-1Oth)
Injury Rates
90th Percentile 10th Percentile
2001 Construction Banking
3.0 per 100 0.4 per 100
1990 Construction Other health services
6.2 per 100 0.8 per 100
Fatality Rates
90th Percentile 10th Percentile
2001 Construction Apparel & accessory store
11.5 per 100,000 0.5 per 100,000
1990 Construction Banking
14.5 per 100,000 0.7 per 100,000
Injury Rates
90th Percentile 10th Percentile
Construction Banking
3.0 per 100 0.4 per 100
Construction Other health services
6.2 per 100 0.8 per 100
Fatality Rates
90th Percentile 10th Percentile
Construction Apparel & accessory store
11.5 per 100,000 0.5 per 100,000
Construction Banking
14.5 per 100,000 0.7 per 100,000
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