Table 2 continued
Men Women
Comparison Injured
Comparison Injured
Group Group
Group Group
Part of body injured Head neck, or back
0.39 0.31
0.39 0.31
0.49 0.46
0.49 0.46
Back only 0.35
0.27 0.34
0.28 0.48
0.45 0.48
0.45 Upper extremities
0.23 0.26
0.23 0.34
Carpal tunnel syndrome 0.42
0.44 0.42
0.47 0.00
0.03 0.01
0.09 0.05
0.16 0.10
0.28 Trunk, multiple, or different injuries
0.18 0.23
0.23 0.23
0.39 0.42
0.42 0.42
Lower extremities 0.20
0.21 0.15
0.12 0.40
0.40 0.36
0.33 Earnings and employment
Pretax earnings one quarter before 5,746
6,263 3,756
4,198 injury
3,572 3,625
2,709 2,737
Median 5,489
6,098 3,324
3,787 Frequency of pre-injury employer
0.09 0.09
0.09 0.08
change 0.29
0.28 0.16
0.15 Total number of observations
4,413 31,870
2,004 16,022
Difference between comparison and injured groups significant, p ⬍ .05 Note: Standard deviations are in parentheses. Statistical analysis is based on these data.
injured workers. Immediately post-injury, the wages of the injured workers fall below those of the comparison group. Injured workers’ earnings then rise, but re-
main below the level of the comparison group. Note that the trend in earnings in both the pre-injury period and in the period beginning two to three quarters after
injury is similar for both groups. However, the pre-injury difference in earnings implies that it would be inappropriate to use means unadjusted for covariates to
estimate losses.
D. The Final Specification
Equation 1b would capture an injury-related change in earnings that occurred in the post-injury period, but it does not fully capture the time-profile of workers’ earnings
as shown in Figure 2. Figure 2, shows a time trend in pre-injury earnings, a drop in earnings in the injury period, a further drop in the next periods, and an eventual
long-term trend. We build these into the model of earnings that we estimate, which is an extension of Equation 1b that allows for pre-injury trends and post-injury effects
that vary over time:
Figure 2 Average Earnings, Control and Injured Group, Wisconsin Injuries, 1989–1990
3 y
i
⫽ α
1i
⫹ γ
t
⫹ α
2
X
i
⫹ α
3
I
i
⫹ α
4
I
i
∗ t ⫹
冱
k⫽ 0,5
δ
k
∗ F
k
⫹
冱
k⫽ 1,5
δ
kI
F
k
∗ I
i
∗ X
i
⫹
冱
k⫽ 0,5
η
k
H
k
∗ J
i
⫹ ε
i
In Equation 3, the independent variable is earnings, not log earnings because the substantial number of periods with zero earnings would make estimation of a log
earnings panel model problematic. The subscript i refers to the individual worker and t represents the calendar quarter for example, the first quarter of 1992. Quar-
terly time dummies,
γ
t
, capture economic conditions affecting all workers in a given period. F
k
k ⫽ 1,4 are dummy variables for the injury quarter and the three follow- ing quarters, each equal to zero before the quarter of interest and one during and
after; and F
5
is the trend in earnings following this period.
7
F
k
is the marginal impact of the injury in each quarter, so the impact of injury on wages in a given quarter is the
sum of the F
k
for that quarter and the preceding ones. The first line of the Equation 3 captures impacts of noninjury factors on earnings, and the second line captures the
impacts of injuries. The terms α
3
I
i
and α
4
I
i
∗ t where t is a time trend capture respectively any difference in the mean and trend of pre-injury earnings between
7. Where q is the quarter relative to injury q ⫽ 0 in the quarter of injury, these variables are defined as:
F ⫽
q if q ⬍ 0, ⫽ 0 otherwise
F
k
⫽ 1 if q ⬎ ⫽ k ⫺ 1, ⫽ 0 otherwise
F
5
⫽ q ⫺
3 if q ⬎ ⫽ 4, ⫽ 0 otherwise
the comparison group and the injured group. In addition, the terms ∑
k⫽ 0,5
δ
k
∗ F
k
are included to estimate common time-from-injury effects for all individuals. We need
to estimate the coefficients of these terms to take into account an artifact of our data, which we collected for people with a workplace injury in a given quarter. As dis-
cussed above, because 100 percent of this group must have been employed in the quarter of injury, employment rates will be lower in quarters before and after the
injury, even if people lost no time from work because of their injuries. This data- collection artifact makes the use of a comparison group essential.
In the first line of Equation 3, X
i
is a vector of observed fixed and time-varying individual characteristics that we would expect to affect earnings. This vector is
composed of age, age
2
, age
3
, age
4
; job tenure at the time of the injury ⬉6 months, 6.1 months to 1 year, 1.1 to 5 years, 5.1 to 10 years, greater than ten years; two-
digit SIC dummies; one-digit Census occupational categories; log number of the employees of the firm at the time of the injury; stability of pre-injury earnings
coefficient of variation of quarterly earnings; and frequency of pre-injury change of employer number of changes divided by total changes possible for the observed
pre-injury period. Except for age and employer size, all variables in X
i
are inter- acted with a pre-injury trend and a post-injury trend.
The second line of Equation 3 captures the injury-related drop, recovery, and long- term trend in earnings. It includes an interaction of injury status with the five post-
injury time-dummy or trend variables F
k
. We allow this interaction to vary with X
i
, a vector of worker, employer, job, and injury characteristics which may not be the
same as X
i
. X
i
includes: age at injury category less than 25, 25–54, at least 55, employment size category 1–50, 51–250, 251–1,000, and more than 1,000 employ-
ees, tenure category, two-digit industry, two-digit Census occupation, stability of pre-injury earnings, frequency of pre-injury employer change, and back and carpal
tunnel injuries. It differs from X
i
essentially by including variables measured only
at the time of injury. For example, X
i
includes age in the current quarter and time
trends for earnings by occupation, industry, and tenure, while X
i
includes age in the quarter of injury and no time trends.
Finally, about 30 percent of workers in our sample had more than one injury during the study period that is, by the end of 1993. The model we use also accounts
for the effects of injuries subsequent to the initial one with the term ∑
k⫽ 0,5
H
k
∗ J
i
, where J indicates a second injury. The H
k
are parallel to the F
k
, but refer to periods relative to the second injury.
E. Estimates of Losses
