Post-injury work outcomes revisited.
Baldwin, Marjorie L. ; Conway, Karen Smith ; Huang, Ju-Chin 等
1. Introduction
Workers' compensation claims data have provided a rich
resource for studies of post-injury returns to work and durations of
work absence. Most existing studies use information current to the time
of injury to construct explanatory variables for the models. One would
like to include information from the post-injury job as well, but data
on the nature of post-injury employment, including wages, employers, and
job accommodations, are not typically available. Even when the data are
available, taking advantage of the data in empirical analyses is less
than straightforward because of the natural data truncation, such that
post-injury job information is observable only for those who return to
work. More generally, a worker's post-injury work experience is
probably best viewed as a bundle of attributes, including wages, job
accommodations, and durations of work absence, theoretically determined
through a search process that incorporates incentives and preferences of
both the injured worker and potential employers.
In this study we use a unique data set for injured workers from
Ontario to provide more comprehensive evidence regarding the
relationships among key post-injury work outcomes, including durations
of work absence, job accommodations, post-injury wages, and whether or
not the worker is able to return to the pre-injury employer. We view
these post-injury job characteristics as jointly determined, and our
models explore the extent of empirical difficulties this presents,
beginning with descriptive analyses to explore associations among the
post-injury work outcomes and moving to a more structural duration model
with controls for endogeneity. In so doing, we show robust patterns of
the post-injury work outcomes, yet uncover some of the pitfalls
associated with estimating the relationships separately.
One key finding is the significant difference in post-injury work
experiences of workers who return to the same or different employers.
Others have noted an advantage for workers who return to their
pre-injury employers (Galizzi and Boden 2003), but the extent of
differences between "stayers" and "changers" has not
been explored before. Workers who return to the same employer are not
only more likely to receive accommodations, but those accommodations
have different effects on post-injury wages and durations of work
absence for stayers and changers. Workers who return to the pre-injury
employer earn higher post-injury wages, all else equal, as others have
shown, but we also find that associations between pre- and post-injury
wages and between disability benefits and durations of work absence are
significantly different for stayers and changers.
Our results demonstrate the importance of controlling for
endogenous job accommodations in duration models. Treating
accommodations as exogenous often yields the counterintuitive result
that accommodations lengthen spells of work absence. In models that
control for endogeneity, the variables are more likely to have a
negative effect, as expected if job accommodations mitigate the effects
of functional impairments resulting from work-related injuries. While we
do not claim to have solved definitively the econometric problem of
endogeneity in a work absence duration model, the results reveal
important relationships that are obscured in more naive models.
2. Background
According to standard search theory, durations of work absence are
determined by an injured worker's reservation wage and the
distribution of wage offers she receives. The typical empirical approach
is to use the pre-injury wage as a proxy for the post-injury wage offer,
and workers' compensation temporary disability benefits as a proxy
for the reservation wage (e.g., Butler and Worrall 1985; Johnson and
Ondrich 1990). This practice has the advantage of using predetermined
variables defined for all injured workers, whether or not they have
returned to work, but it also has several shortcomings. First,
pre-injury wages do not reflect the impact of the injury on worker
productivity and, therefore, are likely to be a poor proxy of
post-injury wage offers for workers with more severe injuries. Second,
the strong correlation between workers' compensation temporary
disability benefits and pre-injury wages makes it difficult to separate
the effects of the two (Meyer, Viscusi, and Durbin 1995). Perhaps more
significantly, the practice of estimating duration models with data from
the time of injury ignores other key factors that may influence both the
reservation wage and the distribution of post-injury wage offers, such
as whether an injured worker is offered job accommodations or whether he
is able to return to his time-of-injury employer.
Three recent studies incorporate post-injury job information into a
model of work absence and in so doing demonstrate some of the empirical
difficulties of using these data to estimate causal relationships. Hyatt
(1996) uses data from the Ontario Survey of Workers with Permanent
Impairments to estimate the effects of permanent partial disability
benefits on probabilities of return to work, incorporating information
on post-injury wages in the model. He imputes post-injury wages for
workers who have not returned to work from a selection-corrected wage
equation. Results indicate the generosity of permanent partial
disability benefits is negatively associated with the probability of
return to work, while higher post-injury wages increase the likelihood
of a return.
Galizzi and Boden (2003) examine how returning to the
time-of-injury employer affects post-injury work experiences. They
construct a database that includes post-injury job information by
merging Wisconsin workers' compensation claims files with earnings
histories from the state unemployment compensation system. The authors
treat post-injury wages and returns to the time-of-injury employer as
endogenous, computing predicted values of the post-injury wage and
probability of changing employers that are then incorporated in the
duration models. The main finding is that durations of work absence are
significantly shorter for injured workers who return to the same
employer. Without controls for endogeneity, however, returning to the
time-of-injury employer is associated with longer spells of work
absence.
Most recently Campolieti (2005) uses the Ontario data to examine
the effects of job accommodations on durations of post-injury
employment. He estimates hazard models that control for worker
characteristics, expected permanent disability benefits, and job
accommodations on the first post-injury job, restricting the sample to
injured workers who have returned to work. The results suggest that
accommodations have a smaller effect on post-injury work outcomes than
previous studies would suggest, and that type of accommodation matters
(flexible schedules and modified equipment are the only types of
accommodation associated with significantly longer durations of
post-injury employment).
Previous studies demonstrate the challenging data and modeling
issues involved in incorporating post-injury job information into a
duration model and strongly suggest that the different post-injury
employment outcomes are interrelated. Other studies, although not
focused specifically on durations of work absence, also hint at the
complex relationships between job accommodations, post-injury wages, and
whether the worker returns to his time-of-injury employer (Gunderson and
Hyatt 1996; Campolieti 2004). To date, however, no study has
investigated the post-injury work experience collectively, including
durations of work absence, job accommodations, post-injury wages, and
returning to the same or different employers, in models that begin to
address the difficult econometric issues this presents. In this article
we report a number of key findings from a more comprehensive model of
post-injury work experience than has been estimated before. In so doing,
we hope to encourage others to refine the duration model further,
looking at the entire bundle of attributes of post-injury work
experience, rather than studying individual variables in isolation.
3. Data and Descriptive Statistics
Ontario Survey Data
We use data from the Ontario Survey of Workers with Permanent
Impairments, conducted by the Workers' Compensation Board of
Ontario (WCB) in 1989-1990. The survey population includes all workers
who were examined for permanent partial disability assessment by WCB
physicians between June 1989 and June 1990. (1) This data set is used by
four of the five previous studies that examine post-injury job
information (Gunderson and Hyatt 1996; Hyatt 1996; Campolieti 2004,
2005).
The Ontario workers' compensation system, like its
counterparts in the United States, is designed to provide financial
assistance to workers who are injured on the job and are temporarily or
permanently unable to work. Workers' compensation disability
benefits are paid by the WCB (now renamed the Workplace Safety and
Insurance Board) and funded through employer assessments based on total
payrolls and risk experience. (2)
Injured workers who are absent from work longer than four days
receive temporary total disability (TD) benefits while they recover from
their injury. The weekly benefit rate is a fixed percentage of the
worker's average pre-injury wage, subject to statutory minimum and
maximum benefit rates. TD benefits are paid until a worker is reemployed
or until it is determined that the worker has a permanent residual
disability, and he or she receives a permanent partial disability (PPD)
award. (3)
Most studies of post-injury work absence focus on workers who
receive temporary disability benefits only because these represent the
majority of indemnity claims. The larger portion of costs, however, is
incurred from compensation to workers with permanent impairments.
Webster and Snook (1994), for example, analyze costs of cumulative
trauma upper extremity claims filed with a large national workers'
compensation insurer in 1989 and find that the most costly 25% of claims
account for 89% of indemnity costs.
In this study we focus on post-injury job outcomes of the
potentially high-cost claims from workers with permanent impairments
resulting from a workplace injury. Workers with minor work-related
injuries, not resulting in permanent impairments, are not represented in
the data. We exclude workers who have not returned to work by the survey
date because they do not have the critical post-injury job information.
(4) These exclusions leave an analysis sample of 4116 observations.
Descriptive Statistics
Table 1 gives definitions of variables used in our analyses and
reports summary statistics for the samples of workers who returned to
the same (3535 stayers) or different (581 changers) employers. (5)
Post-injury job information includes the post-injury wage, types of job
accommodations received, and whether or not the worker returned to the
pre-injury employer. (6) Demographic and human capital characteristics
include age, education, gender, and marital status. Nature of injury is
a vector of seven injury categories constructed from information on
injury type and part of body injured reported in workers'
compensation claims files. (7) Labor market characteristics include
union membership, size of the time-of-injury firm, year of injury, a
binary variable identifying workers in the high-unemployment northeast
region of Ontario, and controls for six occupation/industry categories.
(8) Expected workers' compensation temporary disability benefits
are calculated using the benefit formulae in effect on the date of
injury, taking account of statutory maximum and minimum benefits.
Although workers with permanent impairments have all received a
permanent disability settlement, we focus on temporary benefits in our
analyses because TD benefits are conditional on work absence, while the
permanent settlement is not.
The vast majority (86%) of workers in our sample return to their
time-of-injury employers and have better post-injury work outcomes, on
average, than workers who change employers. Mean duration of work
absence is 29 weeks (202 days) for stayers, compared to 74 weeks (518
days) for changers. Stayers have a higher pre-injury hourly wage ($14.33
vs. $12.44) and earn 99% of that wage on return to work, compared to 86%
for changers.
Workers who return to the pre-injury employer are more likely to
receive job accommodations (48% vs. 39%) and tend to receive different
types of accommodations than those who change employers. The results
suggest that stayers are more likely to receive accommodations that
enable a return to the same job (38% vs. 21% receive light work
accommodations), while changers are more likely to be accommodated for a
different job (3% vs. 11% receive special training).
We also observe some differences in the demographic and pre-injury
job characteristics of eventual stayers and changers but not in the
distributions of injury types. On average, stayers are older (40 vs.
35), are more likely to belong to a union (67% vs. 33%), are more likely
to have been employed in medium- or large-size firms (45% vs. 15%), and
are less likely to be employed in construction work (11% vs. 20%). The
injury distributions of both groups reflect the importance of repetitive
trauma injuries in workers' compensation: Nearly 60% of workers
have permanent impairments resulting from back or non-back sprains or
strains, or cumulative trauma injuries.
To visualize the complexity of relationships between post-injury
employment outcomes, Figures 1-3 present histograms showing the two-way
associations between post-injury wages, job accommodations, and duration
of work absence, comparing stayers and changers. Workers who stay with
the pre-injury employer consistently have higher wages, both pre- and
post-injury, than those who change employers (Figure 1), with the
exception of the unusual case (n = 27) of workers who return to a
different employer within three months. Among workers who return to the
same employer, post-injury wages are fairly insensitive to duration of
work absence; whereas, wages drift downward as work absences lengthen
for workers who eventually change employers.
[FIGURE 1 OMITTED]
[FIGURE 2a OMITTED]
[FIGURE 2b OMITTED]
Patterns of accommodations over time are depicted in Figures 2a
(stayers) and 2b (changers). Among stayers the likelihood of receiving
most types of accommodations increases over time; although, there is a
decline in the likelihood of the most common accommodation, light work,
after a two-year absence. The upward trend likely reflects, at least in
part, the greater need for accommodations among more severely injured
workers, who take longer to "recover" from their injuries.
Time trends in accommodations are less clear among changers, but two
patterns are notable: Changers are more likely to receive special
training than stayers, and this difference increases with duration, but
changers are also less likely to receive light work accommodations,
regardless of duration. Taken together, the accommodations results are
consistent with the hypothesis that changing employers involves an
intrinsic change in job responsibilities and loss of job-specific human
capital that is less likely to occur among injured workers who return to
the same employer.
Figure 3 charts mean pre- and post-injury wages for stayers and
changers, comparing those who do or do not receive job accommodations.
Workers who receive accommodations "pay for" those
accommodations in terms of lower wages, but the wage penalty is greater
for those who change employers. Among stayers the mean post-injury wage
is 0.2% lower than the mean pre-injury wage when there are no
accommodations but is 1.8% lower if the worker receives accommodations.
Among changers the wage loss is 13% without accommodations but 17% for
those who receive accommodations. In other words, the combination of
moving to a different employer and receiving accommodations is
associated with economic losses of nearly 20% of pre-injury wages.
[FIGURE 3 OMITTED]
4. Models
The descriptive analyses reveal that receiving job accommodations
and returning to one's pre-injury employer are not random events
but are correlated with one another, with the post-injury wage, and with
the decision of when to return to work. The post-injury work outcomes
are also correlated with worker and job characteristics; however, and
this may confound the observed associations. For example, if more
productive (for example, more educated) workers are more likely to earn
high wages (pre- and post-injury), to return to the same employer, and
to receive job accommodations, the descriptive statistics may make these
outcomes appear more strongly related than they truly are. Our first
step, therefore, is to estimate a set of descriptive models in which we
analyze the relationships among post-injury work outcomes controlling
for worker and job characteristics.
Next, we deal with the possible endogeneity of post-injury
variables in a duration model. Ideally, duration would be estimated
jointly with other post-injury work outcomes, but that complex model is
beyond the reach of our data. (9) Instead, we use an instrumental
variables approach to control for endogeneity, where the probability of
receiving accommodations, staying with the pre-injury employer, and the
predicted post-injury wage are instruments estimated in first-stage
models. For comparison, we also estimate a naive duration model in which
all other post-injury work outcomes are assumed exogenous.
We are unable to estimate the duration models stratified by stay
because our sample of changers is so small. (10) Instead, each duration
model includes a set of interaction terms between "stay" and
other post-injury outcomes. In this way we obtain a more complete
picture of the magnitude and significance of differences between the two
groups. This approach is less demanding of the data and makes the
differences between stayers and changers more transparent.
More specifically, the descriptive duration model has the form
lnD = [alpha] + [beta]w + [??]w*stay + [delta]B + [??]B*stay +
[gamma]stay + [phi]A + [??]A*stay + Z[GAMMA],
where lnD is the natural log of work absence duration in days. The
key post-injury outcomes are the wage w, accommodations A, and whether
the worker returns to the pre-injury employer stay. Interaction terms
allow the effects of wages and accommodations to differ between stayers
and changers. Disability benefits B, while determined pre-injury, are a
key policy variable, and so we allow the effects of benefits to vary by
stay as well. The remaining independent variables are worker
demographics, injury type, and characteristics of the pre-injury job,
denoted by the vector Z. We estimate six specifications of the model:
one with a binary variable for any accommodation, the others including
binary variables for each of five types of accommodations, one at a
time.
We next estimate a duration model with the post-injury job
information treated as endogenous using an instrumental variables
approach. In the above equation, this means that all variables except
benefits and the vector Z require instruments. Stay, accommodations, and
their interaction are discrete variables, so we use estimated
probabilities as instruments. Specifically we estimate the marginal
probabilities of staying with the pre-injury employer (Pr(stay = 1)),
receiving an accommodation (Pr(,4 = 1)), and the joint probability
(Pr(stay = 1 and A = 1)) with a bivariate probit. Independent variables
in the model, denoted by the vector X, include all exogenous variables
in the descriptive equation (benefits and the vector Z), plus a set of
identifying variables discussed below.
The post-injury wage is a continuous variable, so its instrument is
the predicted value from a first-stage equation estimated via ordinary
least squares. The remaining endogenous variables, interactions between
benefits and stay (B x stay) and wage and stay (w x stay), are nonlinear
functions of endogenous variables. Following the approach suggested by
Wooldridge (2002, pp. 235-236), we estimate B x stay as a function of X
and B x X, and w x stay as a function of the full set of interactions
and squares among the exogenous variables, X x X. (11)
Identification is always an issue in structural models, and ours is
no exception, especially with the large number of endogenous variables.
Nonetheless, to explore the possible role of endogeneity we must select
identifying variables. We choose the pre-injury wage, the year of
injury, a set of industry/occupation dummies, and a dummy variable
identifying workers from the high-unemployment northeast region of
Ontario. These variables capture labor market conditions and as such
should affect firms' willingness to offer accommodations and wages,
as well as the ability to return to the pre-injury firm. While certainly
not without criticism, we believe these identifying variables are the
best we can do with the data available, and we are reassured by their
ability to easily pass all of the typical tests of instrument validity
(see note 11). We are also reassured by the overall robustness of our
results to differing (smaller) sets of instruments and different model
specifications (for example, only allowing the accommodation
coefficients to vary with stay, or fully stratifying the sample and
correcting for self-selection).
We estimate this multistage duration model for each type of
accommodation separately, and for receiving any type of accommodation.
All models are estimated conditional on the decision to return to work,
excluding workers who have not returned to work by the interview date.
Our results should be interpreted with this restriction, as well as with
any possible shortcomings of our identifiers, in mind.
5. Results
Job Accommodations and Stay
Results of the bivariate probit model for job accommodations and
stay are reported in Table 2 for "any accommodation." Focusing
first on the results for accommodations, workers in the
high-unemployment northeast region are significantly less likely to
receive accommodations than workers in other regions, while workers with
more recent injuries are more likely to receive accommodations than
workers whose injuries occurred further in the past. Noting that the
unemployment rate in Canada declined throughout the 1980s (from an
all-time high of 12.9% in December 1982 to 7.9% in December 1987), the
results strongly suggest that local and regional labor market conditions
are a key factor in determining the probability of accommodations. Men
are less likely to receive any accommodation than are women. Compared to
the omitted injury category (fractures), workers with occupational
illnesses or cumulative trauma injuries are less likely to receive
accommodations. Some industry/ occupation variables are significant as
well. (12)
Turning to the bivariate results for stay, it is a combination of
individual and pre-injury job characteristics that appear most important
in determining outcomes. Married workers, older workers, union members,
and workers from larger firms are more likely to return to their
pre-injury employer, with all the advantages that entails. Compared to
workers whose impairments result from fractures, workers with cumulative
trauma injuries and, to a lesser extent, back injuries or occupational
illnesses, are less likely to return to their pre-injury employer.
Finally, receiving an accommodation and returning to one's
pre-injury employer remain positively associated, even after controlling
for other characteristics, as revealed by the positive and statistically
significant estimate of the correlation coefficient (p).
Post-Injury Wage
Selected results for the post-injury wage equation are reported in
Table 3 for models that control for any accommodation and each
individual type of accommodation. This descriptive wage model is a
structural equation, differing from the first-stage reduced-form wage
equation that will be used later to generate instruments for the
duration model in that it includes other post-injury work outcomes
(accommodations and stay) as independent variables. The estimates of the
structural model test whether associations observed in the descriptive
statistics remain once we control for worker and firm characteristics.
Across all specifications, the pre-injury wage is significantly and
positively associated with post-injury wages, and the relationship is
much stronger for those who return to the pre-injury employer than for
those who change employers. The coefficient estimate for stay is
negative and significant in every model, but this dampens only somewhat
the powerful effect of the correlation between pre- and post-injury
wages for those who return to the same employer. Workers tend to pay for
job accommodations in the form of lower wages, as Gunderson and Hyatt
(1996) report, but here we see the penalty is much greater for those who
change employers. There is also substantial variability in the effects
of different types of accommodations on post-injury wages: Workers who
require special training pay a substantial wage penalty; whereas,
flexible schedules and modified equipment can be accommodated with no
significant effect.
To estimate the magnitude of the effects of returning to one's
employer and receiving accommodations, we employ the estimator proposed
by Kennedy (1981), which describes the estimated impact of a dummy
variable in a log model. (13) The calculations for stay show that
returning to one's pre-injury employer leads to an estimated 25-32%
higher post-injury wage among workers who do not receive accommodations.
Among workers who receive accommodations, the wage effect of returning
to one's pre-injury employer is typically smaller and varies from
around 12-24%, depending on the type of accommodation. Modified
equipment and special training are outliers: Among workers who receive
modified equipment accommodations, returning to one's employer
increases wages by 43%, and among workers who receive special training,
returning decreases wages by about 4%.
The calculations for receiving accommodations show an even stronger
effect of special training. The negative effect of special training on
wages is approximately 6% for stayers and 23% for changers. Other
accommodations are associated with much smaller reductions in wages, but
the finding that changers are penalized more than stayers is robust.
Specifically, changers suffer reductions in their wages of 4-13% if they
receive accommodations, versus 0.82.6% for stayers. Thus, the
relationships between wages, accommodations, and returning to one's
pre-injury employer revealed in our descriptive analyses remain largely
unchanged after controlling for worker and job characteristics.
Naive Duration Model
Empirical results from the naive duration models are summarized in
Table 4 for key variables and interaction terms. (14) Results are
reported for six models, namely, with controls for any accommodation and
for each of five distinct accommodation types. A fairly consistent story
emerges: Workers who return to their pre-injury employers have
significantly shorter durations of work absence than workers who change
employers; although, the effect differs if they also receive
accommodations. Specifically, setting the wage and benefits to the
sample means and assuming no accommodations are received, the Kennedy
estimator yields a predicted reduction in duration of 72-75% if a worker
returns to the pre-injury employer. If accommodations are received, the
effect is smaller, with estimated reductions of 40-48% except for
special training (23%) and reduced hours (26%).
Higher post-injury wages are associated with significantly shorter
durations of work absence for both stayers and changers, with
elasticities (in absolute value) only slightly higher for stayers. In
contrast, temporary disability benefits exhibit distinctly different
associations with duration for stayers and changers. Among workers who
return to the pre-injury employer, higher expected temporary disability
benefits are associated with significantly longer durations of work
absence, as theory predicts. (The associated elasticity is 0.30-0.37;
that is, a 10% increase in benefits lengthens duration by approximately
3-3.7%.) Among workers who change employers, however, the association
between expected benefits and duration has a counterintuitive negative
sign and is only marginally significant at best. The difference in
results may reflect the much longer average durations of work absence in
the group that changes employers. In the Ontario system temporary
disability benefits are paid until a worker returns to work or reaches
"maximum medical improvement" with some residual permanent
disability. At this point the worker typically receives a lump-sum
settlement with no work restrictions. Hence changers, with more lengthy
work absences, are more likely to return to work after temporary
benefits have ceased, so it may not be surprising that their decision to
return to work is insensitive to the benefit amount. Once again we are
struck with the complexity of relationships between durations of work
absence, economic incentives to return to work, and the opportunity to
return to the pre-injury employer.
Results for job accommodations are also distinctly different for
stayers and changers. Among stayers we generally observe the
counterintuitive result that receiving accommodations is associated with
significantly longer durations of work absence. The result is
statistically significant and of a sizable magnitude for all types of
accommodations (receiving an accommodation increases duration by an
estimated 21-79%). Among changers there is no significant association
between accommodations and absence duration.
Duration Model with Controls for Endogeneity
The naive duration model likely confounds the effect of
accommodations in facilitating returns to work with the effect of the
(unobserved) injury severity gradient associated with greater
probabilities of receiving accommodations. That is, workers with more
severe injuries are more likely to need both accommodations and longer
recovery periods before returning to work, so accommodations are
correlated with unobservables in the duration model. To address this and
other sources of endogeneity, we reestimate the duration model using
predicted values of post-injury job characteristics from the first-stage
bivariate probit (accommodations and stay) and post-injury wage models.
(15) Results are reported in Table 5.
Controlling for endogeneity does not alter our general conclusions
regarding the advantage of returning to the pre-injury employer. In all
specifications of the informed model we find the coefficient estimate of
stay has a negative sign, and the effects are statistically significant
in the models for any accommodation, special training, and light work.
For a 10% increase in the probability of stay, the duration of work
absence decreases by an estimated 12-31%. The results are consistent
with those reported by Galizzi and Boden (2003) using Wisconsin data.
Results for post-injury variables other than stay change
dramatically when we control for endogeneity. A surprising result is
that expected temporary disability benefits become insignificant in the
duration model. We may be asking too much of the data with so many
instruments, but the finding is robust across numerous variations of the
model we have estimated.
In the informed duration model the expected post-injury wage has
the significant negative effect predicted by theory only for workers who
return to the pre-injury employer (with estimated elasticities ranging
from -0.13 to -0.21, such that a 10% increase in post-injury wage
reduces duration by approximately 1.3-2.1%). For those who change
employers, the expected wage has a counterintuitive positive effect on
duration that is significant in every model (with estimated elasticities
from 0.29 to 0.38). We might speculate that the expected wage represents
not only an offer wage but also a worker's reservation wage, and
that injured workers with higher reservation wages who cannot return to
the pre-injury employer have greater difficulty securing an acceptable
wage offer than those with lower reservation wages. In the first-stage
wage equation the pre-injury wage is by far the most important
explanatory variable, suggesting that injured workers may use the
pre-injury wage as the reservation wage for their job search. As shown
in Figure 3, there is a much larger gap between pre--and post-injury
wages for workers who change employers, so changers with high wage
expectations may search a while before receiving an acceptable offer or
lowering their reservation wage. On the other hand, the counterintuitive
result could reflect the greater difficulty in forecasting the
post-injury wage for workers who change employers, especially those
workers with higher pre-injury wages. This is confirmed by the much
lower [R.sup.2] for wage equations estimated for changers versus
stayers, and the disproportionately lower [R.sup.2] for changers with
higher pre-injury wages. (16)
The results for accommodations are now much more aligned with
theory. Among changers, receiving accommodations either has a large,
negative, significant effect on duration of work absence (special
training, light work) or no significant effect (reduced hours, flexible
schedule, modified equipment). Thus, for workers who return to different
employers certain types of accommodations appear to compensate, at least
in part, for the work limitations associated with a permanent impairment
so the worker is able to return to work. Whenever the main effect of
accommodations is significant, however, its interaction with stay is
significant, positive, and of sufficient magnitude to eliminate the
effect of accommodations altogether. For example, a 10% increase in the
probability of receiving light work (special training) accommodations
decreases expected duration by 42% (91%) for workers who change
employers, but increases expected duration by 5% (12%) for stayers. In
other words, the significant negative effect of accommodations on
duration is completely eliminated and perhaps even reversed for workers
who return to their pre-injury employer. (Results for "any
accommodation" follow the same pattern, with p-values just above
10% for both main effect and interaction.)
Our results suggest that job accommodations have the intended
effect (facilitating returns to work and reducing spells of work
absence) for workers who cannot return to their pre-injury employer. The
effect can be observed, however, only when the endogeneity of job
accommodations is taken into account. When job accommodations are
treated as exogenous, the correlation with severity of injury (more
severely injured workers have longer durations of work absence and are
more likely to need accommodations) appears to generate spurious
positive effects in the duration model. In both models accommodations
appear far less likely to reduce duration of work absence for workers
who return to their pre-injury employers.
6. Concluding Remarks
Most previous research on post-injury work absence has focused on
the effects of wages and benefits using information from the pre-injury
job. Once information from the post-injury job becomes available, it is
apparent that the post-injury work experience is multifaceted, where the
key variables are the post-injury wage offers, the possibility of
returning to the pre-injury employer, and the likelihood of receiving
job accommodations. Incorporating post-injury job information in a
duration model becomes empirically complicated because of endogeneity
and censoring issues (post-injury job offers are unobserved for workers
who have not yet returned to work). While a few studies consider some
aspect of the post-injury work experience, this article attempts a more
comprehensive analysis of the relationships between all key variables
and how they jointly affect the outcome of greatest interest, namely,
the speed at which injured workers return to work.
All our analyses show the importance to injured workers of
returning to the same employer. Returning to one's pre-injury
employer is consistently associated with more favorable post-injury work
outcomes than changing employers. On average, workers who return to the
pre-injury employer receive higher wages, return to work sooner, and are
more likely to receive job accommodations than changers, even after
controlling for the pre-injury wage and other worker and job
characteristics. Stayers also pay a smaller "wage penalty" for
the accommodations they receive.
Our results also demonstrate the importance of controlling for the
endogeneity of post-injury j ob characteristics in a duration model. The
naive model, without controls for endogeneity, yields the
counterintuitive, positive effects of accommodations on duration that
other researchers have noted. The informed model indicates that several
types of accommodations have the expected negative effect on duration of
absence for workers who change employers, but no significant effect for
those who stay with the same employer. Controlling for endogeneity also
changes the estimated effects of the post-injury wage and expected
benefits in the duration model.
The analyses also uncover several findings that require future
investigation. First, our descriptive analyses suggest that the benefits
of returning to one's pre-injury employer expire after two to three
years. Our data are not rich enough to explore the time effects further
in a multivariate framework, but the result seems plausible in light of
existing insurance policy in Canada during the period of study. During
the time our data were collected, there was no legal requirement that
employers accommodate their injured workers, and the economic incentives
to do so diminish over time.
Second, the estimated effect of receiving job accommodations on
durations of work absence appears more consistent with theory when the
issue of endogeneity is addressed. This result makes sense: One would
expect workers with the most severe injuries (unobservable to the
analyst) to have the greatest need for accommodations and to take longer
to return to work. We leave it to future research to explore different
empirical approaches with possibly richer data to determine if our
findings with respect to job accommodations, duration of work absence,
and the different effects of accommodations for stayers and changers are
robust.
Finally, the overwhelming evidence that workers who return to the
pre-injury employer have distinctly different, and advantageous,
post-injury work experiences relative to those who change employers has
powerful implications for state policy makers. A policy that imposes
legal obligations on time-of-injury employers to rehire injured workers
would have obvious benefits for workers. The policy would be consistent
with the original spirit of workers' compensation laws, which were
established in acknowledgement of the obligations of society, employers
in particular, to mitigate the economic losses of persons injured on the
job.
Received July 2004; accepted August 2008.
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(1) See Butler, Johnson, and Baldwin (1995) for a more detailed
description of the survey.
(2) The extent of experience rating varies among industries and
firms, with the assessments of larger firms more closely tied to
accident experience than the assessments of smaller firms. At the time
our data were collected, firms were under no legal obligation to return
injured workers to their jobs, or provide job accommodations, unless
such provisions were part of a union contract.
(3) In workers' compensation parlance, this is called MMI, the
point of "maximum medical improvement." PPD benefits are
awarded according to a fixed schedule, based on physicians'
assessments of the loss of functional capacity resulting from an injury.
PPD benefits are not conditional on a worker's employment status.
(4) In preliminary analyses we include workers who have not yet
returned to work and attempt to control for self-selection via a
two-stage Heckman approach. The results are similar to those reported
here. Because of the additional identification such an approach
requires, we emphasize models that simply exclude these workers and
caution the reader to view the results as being conditional on the
workers having chosen to return to work.
(5) Seventy-six observations had no information on injury type and
so were omitted from the analysis. Four more observations were omitted
because of extreme values (greater than $100 Canadian) for either the
pre- or post-injury wage.
(6) Typically in the duration model, the pre-injury wage and
replacement rate (expected temporary disability benefits/pre injury
wage) are used as proxies for the unavailable post-injury wage and
reservation wage, respectively. Using post-injury wages directly makes
it less problematic to use the actual level of temporary disability
benefits, rather than the replacement rate in the duration model. We
believe the actual benefit level is a more important determinant of the
post-injury reservation wage than is the replacement rate; although, the
results are similar regardless of which of the measures is used.
(7) The seven categories of work-related injuries are back sprains
and strains, non-back sprains and strains, fractures, inflammations,
lacerations and contusions, occupational illnesses, cumulative injuries
(for example, carpal tunnel syndrome and tendonitis), and other
injuries.
(8) The data do not include information on transfer payments other
than workers' compensation disability payments. Labor market
variables include three occupation dummies (professional/manager,
processing, and construction) and three industry dummies (service,
transportation, and mining). The northeast had the highest unemployment
rate of any region in Ontario throughout the period in which our data
were collected.
(9) The complex model would require simultaneous estimation of four
equations, with a combination of discrete, censored, and continuous
variables.
(10) This limitation becomes especially critical in the more
complicated models that control for endogeneity. As discussed shortly,
the more complicated models require multiple instruments that severely
strain the small sample of changers and lead to volatile results.
However, the salient differences between stayers and changers persist in
such models, and the results for stayers are quite similar to those
reported here. The results from these exercises are available on
request.
(11) Our results are reasonably robust to using smaller subsets of
instruments. Furthermore, we subject all our instrument sets to (i)
tests of joint significance in the first-stage equation and (ii)
overidentification tests in the second stage. Each of the instrument
sets easily pass both tests.
(12) However, in the bivariate probit models for individual types
of accommodations, we find women are significantly more likely to
receive flexible schedules, reduced hours, and modified equipment
accommodations than are men, but men are significantly more likely to
receive light work assignments. As one might expect, the injury
variables also have a different effect depending on the type of
accommodation. Complete results are available from the authors upon
request.
(13) The general form of the Kennedy estimator is exp([??]- 1/2
V[??]r([??])) - 1, where [??] is the estimated coefficient of the dummy
variable. As shown in Derrick (1984), the Kennedy estimator is superior
to the commonly used estimator X exp([??]) - 1; the Kennedy estimator is
a biased estimator, but the alternative unbiased estimator is quite
complicated and yields minimal improvement over the Kennedy estimator.
We therefore follow Derrick's recommendation and use the Kennedy
estimator to compute all the estimated effects of accommodations and
returning to one's employer on post-injury wage and absence
duration. Because of the interactions with stay, the total effect of
stay is a function of other variables, such as the pre-injury wage. In
all calculations we evaluate these variables at the mean for the total
(stayers + changers) sample. The actual estimates are available upon
request.
(14) The full set of results is available upon request.
(15) The reader is reminded that the wage model reported in Table 3
is not the first-stage wage regression. The first-stage model is a
reduced-form equation that includes exogenous variables only. Results
are available from the authors. Note also that the effects of stay and
accommodations are included here as predicted probabilities, such that
the Kennedy estimator is no longer appropriate for calculating the
predicted effects in this context. However, the total effects are still
functions of several estimated coefficients, many of which are not
statistically significant and so should be interpreted with caution.
(16) The results of separate wage equations for stayers and
changers are available upon request.
Marjorie L. Baldwin, Arizona State University, P.O. Box 874506,
Tempe, AZ 85287-4506, USA; E-mail marjorie.baldwin@asu.edu;
corresponding author.
Karen Smith Conway, University of New Hampshire, McConnell Hall,
Durham, NH 03824, USA; E-mail ksconway@cisunix.unh.edu.
Ju-Chin Huang, University of New Hampshire, MeConnell Hall, Durham,
NH 03824, USA; E-mail jchuang@cisunix.unh.edu.
Earlier drafts of this research were presented at the Southern
Economic Association Meetings, the University of New Hampshire Economics
Seminar, the Workers' Compensation Research Group, and the W. E.
Upjohn Institute for Employment Research. Our research has benefited
from these presentations, and we thank the participants for their
insightful comments.
Table 1. Variable Definitions and Summary Statistics for Stayers
and Changers
Returned to Same
Employer (Stayers)
Variable Definition Mean SD
Days absent Duration of first work 201.63 234.76
absence (days)
Pre-wage Pre-injury wage 14.33 5.39
(Canadian $1989)
Post-wage Post-injury wage 14.19 5.26
(Canadian $1989)
Benefits Expected hourly TD 9.40 3.02
benefits
Age Age at time of injury 40.29 11.18
Accommodations =1 if any 48%
accommodations on
first return
Reduced hours =1 if reduced hours on 15%
first return
Special training =1 if special training 3%
on first return
Light work =1 if light work on 38%
first return
Flexible =1 if flexible schedule 15%
schedule on first return
Modified =1 if modified equipment 3%
equipment on first return
Back =1 if back sprain or 39%
strain
Other strain =1 if non-back sprain or 18%
strain
Fracture =1 if fracture 11%
ILC =1 if inflammation, 14%
laceration, or
contusion
Occupational =1 if occupational 2%
illness illness
Cumulative injury =1 if cumulative trauma 3%
disorder
Other injury =1 if other injury 13%
Union =1 if union member 67%
Male =1 if male 74%
Married =1 if married 78%
High school =1 if high school degree 35%
University =1 if university degree 2%
Professional =1 if professional/ 6%
managerial
Processing =1 if processing worker 35%
Construction =1 if construction worker 11%
Mining =1 if mining industry 4%
Transportation =1 if transportation 8%
industry
Service =1 if service industry 11%
Northeast =1 if northeast labor 11%
market region
Medium-size firm =1 if time-of-injury firm 23%
has 200-1000 full-time
workers
Large firm =1 if time-of-injury firm 22%
has > 1000 full-time
workers
Year of injury % injured in 1975-1979 3%
% injured in 1980-1984 10%
% injured in 1985-1989 87%
Returned to Different
Employer (Changers)
Variable Definition Mean SD
Days absent Duration of first work 517.70 419.92
absence (days)
Pre-wage Pre-injury wage 12.44 5.75
(Canadian $1989)
Post-wage Post-injury wage 10.67 6.21
(Canadian $1989)
Benefits Expected hourly TD 8.40 3.30
benefits
Age Age at time of injury 35.85 10.50
Accommodations =1 if any 39%
accommodations on
first return
Reduced hours =1 if reduced hours on 13%
first return
Special training =1 if special training 11%
on first return
Light work =1 if light work on 21%
first return
Flexible =1 if flexible schedule 21%
schedule on first return
Modified =1 if modified equipment 4%
equipment on first return
Back =1 if back sprain or 39%
strain
Other strain =1 if non-back sprain or 15%
strain
Fracture =1 if fracture 12%
ILC =1 if inflammation, 14%
laceration, or
contusion
Occupational =1 if occupational 3%
illness illness
Cumulative injury =1 if cumulative trauma 4%
disorder
Other injury =1 if other injury 13%
Union =1 if union member 33%
Male =1 if male 71
Married =1 if married 68%
High school =1 if high school degree 36%
University =1 if university degree 2%
Professional =1 if professional/ 5%
managerial
Processing =1 if processing worker 38%
Construction =1 if construction worker 20%
Mining =1 if mining industry 2%
Transportation =1 if transportation 6%
industry
Service =1 if service industry 14%
Northeast =1 if northeast labor 11%
market region
Medium-size firm =1 if time-of-injury firm 14%
has 200-1000 full-time
workers
Large firm =1 if time-of-injury firm 1%
has > 1000 full-time
workers
Year of injury % injured in 1975-1979 2%
% injured in 1980-1984 12%
% injured in 1985-1989 86%
N = 3535 slayers, 581 changers. SD = standard deviation.
Source: Survey of Workers with Permanent Impairments (1989-1990).
Table 2. Selected Coefficient Estimates from the Bivariate Probit
Model of Accommodations and Stay
Any Accommodation Stay
Log (pre-wage) -0.141 (0.12) 0.235 (0.16)
Log (benefits) 0.141 (0.13) 0.019 (0.17)
Male -0.096 * (0.05) 0.036 (0.07)
Married 0.012 (0.05) 0.139 ** (0.06)
High school graduate 0.045 (0.04) 0.058 (0.06)
College graduate -0.088 (0.16) 0.122 (0.21)
Union member -0.059 (0.05) 0.532 *** (0.06)
Age at injury -0.001 (0.002) 0.016 *** (0.003)
Year of injury 0.035 *** (0.01) 0.020 (0.01)
Northeast region -0.368 *** (0.07) -0.047 (0.09)
Firm size: medium 0.009 (0.05) 0.230 *** (0.07)
Firm size: large 0.035 (0.06) 0.450 *** (0.09)
Back -0.029 (0.07) -0.153 * (0.09)
Other strain -0.220 *** (0.08) -0.090 (0.10)
Inflammation, laceration, -0.119 (0.08) -0.050 (0.11)
or contusion
Occupational illness -0.291 * (0.15) -0.288 * (0.18)
Cumulative injury -0.310 ** (0.13) -0.470 *** (0.16)
Other injury -0.253 *** (0.08) -0.104 (0.11)
Log likelihood -4252.27
Wald statistic (df) 473.99 (48)
Rho 0.137 ***
N = 4116. The model also includes controls for six industry/occupation
categories (complete results available from the authors). Robust
standard errors are reported in parentheses.
Source: Survey of Workers with Permanent Impairments (1989-1990).
***, **, and * denote statistical significance at the 0.01 level or
better, at the 0.05 level, and at the 0.1 level, respectively.
Table 3. Selected Coefficient Estimates from the Post-Injury Wage
Equations
Accommodation Type
Any Accommodation Reduced Hours
Log(pre-wage) 0.387 ***(0.06) 0.389 *** (0.06)
Log(pre-wage) X stay 0.445 *** (0.06) 0.444 *** (0.06)
Stay -0.909 ***(0.14) -0.893 ** (0.13)
Accommodation -0.086 ** (0.04) -0.138 ** (0.07)
Accommodation x stay 0.071 * (0.04) 0.119 * (0.07)
Accommodation Type
Flexible Schedule Special Training
Log(pre-wage) 0.390 *** (0.06) 0.378 *** (0.06)
Log(pre-wage) X stay 0.443 *** (0.06) 0.455 *** (0.06)
Stay -0.884 ***(0.13) -0.934 *** (0.13)
Accommodation -0.043 (0.05) -0.262 *** (0.07)
Accommodation x stay 0.038 (0.06) 0.197 *** (0.07)
Accommodation Type
Modified Equipment Light Work
Log(pre-wage) 0.392 *** (0.06) 0.392 *** (0.06)
Log(pre-wage) X stay 0.442 *** (0.06) 0.438 *** (0.06)
Stay -0.870 *** (0.13) -0.881 *** (0.13)
Accommodation 0.086 (0.09) -0.127 ** (0.05)
Accommodation x stay -0.071 (0.09) 0.103 * (0.05)
The models also include controls for workers' demographic
characteristics, characteristics of the pre-injury job, and nature and
year of injury (complete results available from the authors). Robust
standard errors are reported in parentheses.
Source: Survey of Workers with Permanent Impairments (1989-1990).
***, **, and * denote statistical significance at the 0.01 level or
better, at the 0.05 level, and at the 0.1 level, respectively.
[R.sup.2] = 0.70 for all models.
Table 4. Coefficient Estimates for Key Variables from the Naive
Duration Model
Accommodation Type
Coefficient Any Accommodation Reduced Hours
Stay -2.227 *** (0.26) -2.229 *** (0.26)
Log(post-injury wage) -0.363 *** (0.08) -0.375 *** (0.08)
Log(post-injury wage) x stay -0.059 (0.10) -0.035 (0.10)
Log(expected benefits) -0.169 * (0.10) -0.183 * (0.10)
Log(expected benefits) x stay 0.489 *** (0.13) 0.487 *** (0.13)
Accommodation 0.029 (0.07) 0.027 (0.12)
Accommodation x stay 0.259 *** (0.08) 0.513 *** (0.13)
Accommodation Type
Flexible Schedule Special Training
Stay -2.070 *** (0.26) -2.026 *** (0.26)
Log(post-injury wage) -0.361 *** (0.08) -0.348 *** (0.08)
Log(post-injury wage) x stay -0.098 (0.10) -0.096 (0.11)
Log(expected benefits) -0.168 * (0.10) -0.160 * (0.10)
Log(expected benefits) x stay 0.515 *** (0.13) 0.498 *** (0.13)
Accommodation 0.092 (0.09) 0.122 (0.10)
Accommodation x stay 0.144 (0.10) 0.474 *** (0.14)
Accommodation Type
Modified Equipment Light Work
Stay -2.068 *** (0.26) -2.182 *** (0.26)
Log(post-injury wage) -0.362 *** (0.08) -0.361 *** (0.08)
Log(post-injury wage) x stay -0.104 (0.11) -0.069 (0.10)
Log(expected benefits) -0.160 (0.10) -0.159 (0.10)
Log(expected benefits) x stay 0.529 *** (0.13) 0.502 *** (0.13)
Accommodation 0.123 (0.16) -0.036 (0.08)
Accommodation x stay 0.109 (0.19) 0.237 ** (0.10)
N from = 4116. The models also include controls for workers'
demographic characteristics, characteristics of the pre-injury job,
and six injury categories (complete results available the authors).
Robust standard errors ace reported in parentheses.
Source: Survey of Workers with Permanent Impairments (1989-1990).
***, **, and * denote statistical significance at the 0.01 level or
better, at the 0.05 level, and at the 0.1 level, respectively.
Table 5. Coefficient Estimates for Key Variables from the Duration
Models with Controls for Endogeneity
Accommodation Type
Coefficient Any Accommodation Reduced Hours
P(stay) -2.251 * (1.19) -0.459 (0.64)
P(log(post-injury wage)) 0.373 *** (0.15) 0.366 *** (0.14)
P(log(post-injury wage) X stay) -0.505 *** (0.09) -0.518 *** (0.09)
Log(Expected benefits) -0.104 (0.24) -0.062 (0.25)
P(log(expected benefits) X 0.196 (0.24) 0.164 (0.24)
stay)
P(accommodation) -2.860 (1.87) 0.702 (2.17)
P(accommodation X stay) 3.404 (2.15) -0.917 (2.41)
Accommodation Type
Coefficient Flexible Schedule Special Training
P(stay) -0.335 (0.86) -1.127 * (0.58)
P(log(post-injury wage)) 0.380 *** (0.14) 0.299 *** (0.14)
P(log(post-injury wage) X stay) -0.526 *** (0.09) -0.512 *** (0.09)
Log(Expected benefits) -0.131 (0.24) 0.027 (0.23)
P(log(expected benefits) X 0.194 (0.24) 0.116 (0.24)
stay)
P(accommodation) 1.148 (2.30) -9.135 ** (3.83)
P(accommodation X stay) -0.805 (2.78) 10.411 ** (4.98)
Accommodation Type
Modified
Coefficient Equipment Light Work
P(stay) -0.685 (0.55) -1.964 ** (1.00)
P(log(post-injury wage)) 0.375 *** (0.36) 0.366 * (0.15)
P(log(post-injury wage) X stay) -0.516 *** (0.09) -0.507 *** (0.09)
Log(Expected benefits) -0.080 (0.22) -0.075 (0.23)
P(log(expected benefits) X 0.172 (0.24) 0.172 (0.24)
stay)
P(accommodation) -1.477 (7.14) -4.237 * (2.56)
P(accommodation X stay) 2.622 (7.97) 4.763 * (2.87)
N = 4116. The regressors reported in the above table are predicted
from a bivariate probit model of stay and each accommodation and a
reduced form post-injury wage equation that includes exogenous
variables only. Results of the first-stage equations are available from
the authors. The duration models also include controls for workers'
demographic characteristics, characteristics of the pre-injury job, and
six injury categories (complete results available). Robust standard
errors are reported in parentheses.
Source: Survey of Workers with Permanent Impairments (1989-1990).
***, **, and * denote statistical significance at the 0.01 level or
better, at the 0.05 level, and at the 0.1 level, respectively.
