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
We estimate our final earnings model Equation 3 for men and women separately and together, based on our unbalanced panel. We note that if the error term is corre-
lated across individuals, the resulting OLS estimator will be inefficient and the esti- mated variances will be biased. But such bias can be removed by estimating the
difference-in-differences model using GLS. In fact, we find substantial first-order autocorrelation in earnings, so we have estimated the first-differences version of
Equation 3 using GLS and allowing for first-order autocorrelaton.
8
8. The estimates of first order autocorrelation in the first-difference specification are ρ ⫽ ⫺0.33 for men
and ρ ⫽ ⫺0.35 for women, p ⬍ 0.001.
Table 3 presents regression coefficients that measure average post-injury earnings relative to the comparison group for the base case, which is a 25–54 year old un-
skilled blue-collar worker who had been working at least 10 years at a firm in durable manufacturing with more than 1,000 workers, whose earnings were constant during
the observed pre-injury period, and whose injury did not involve low back pain or carpal tunnel syndrome.
Among men, the estimate of pre-injury earnings growth for the comparison group is 21 per quarter less than that for other injured workers p ⫽ 0.07. For women,
Table 3 GLS Estimates of Quarterly Earnings, First Differences, Lost-Time Injuries in
Wisconsin, 1989–1990
Men Women
All n ⫽ 36,283
n ⫽ 18,026 n ⫽ 54,309
Selected Variables Coefficient
Coefficient Coeffcient
Variables-affecting earnings α
1
Constant trend ⫺
5.9 ⫺
108.4 ⫺
26.6 26.1
25.1 19.2
Age
2
0.70 0.59
0.55 0.24
0.22 0.17
Age
3
⫺ 0.105
⫺ 0.068
⫺ 0.083
0.020 0.018
0.015 Female
— —
⫺ 5.2
3.1 Injury impact
δ
kI
Pre-injury trend 21.9
2.3 14.7
12.1 12.4
9.1 Loss in injury Quarter 1
⫺ 1497.1
⫺ 1025.0
⫺ 1372.9
48.9 51.4
36.8 Additional loss in Quarter 2
⫺ 459.8
⫺ 444.8
⫺ 460.5
51.6 54.6
39.0 Recovery in Quarter 3
1153.0 684.5
1012.5 51.6
54.7 39.0
Recovery in Quarter 4 112.6
107.3 107.4
49.3 51.9
37.2 Trend in loss after Quarter 4
34.8 55.5
36.4 15.3
17.0 11.8
Injury impacts of selected charac- teristics
δ
KI
Age 15–24 Change in injury Quarter 1
280.4 164.8
236.0 35.3
35.7 26.4
Additional change in Quarter 2 272.2
44.1 196.2
36.7 37.4
27.5
Table 3 continued
Men Women
All n ⫽ 36,283
n ⫽ 18,026 n ⫽ 54,309
Selected Variables Coefficient
Coefficient Coeffcient
Additional change in Quarter 3 ⫺
147.5 ⫺
53.0 ⫺
112.8 36.8
37.5 27.6
Additional change in Quarter 4 0.6
⫺ 7.5
⫺ 8.1
35.1 35.5
26.2 Trend in loss after Quarter 4
30.7 5.9
21.1 8.5
8.6 6.4
Age 25–54 base case
base case base case
Age 55⫹ Change in injury Quarter 1
162.8 101.1
159.0 44.1
41.8 32.3
Additional change in Quarter 2 ⫺
335.7 49.6
⫺ 197.5
45.9 43.8
33.7 Additional change in Quarter 3
⫺ 149.7
⫺ 25.0
⫺ 120.5
46.1 44.0
33.8 Additional change in Quarter 4
⫺ 61.4
⫺ 100.3
⫺ 77.1
43.9 41.6
32.1 Trend in loss after Quarter 4
⫺ 133.6
⫺ 72.2
⫺ 113.0
12.2 11.3
8.9 Tenure ⬉ 6 months
Change in injury Quarter 1 562.1
360.1 522.1
42.2 44.6
32.0 Additional change in Quarter 2
106.4 57.3
89.5 44.3
47.1 33.6
Additional change in Quarter 3 ⫺
226.5 ⫺
165.4 ⫺
214.6 44.3
47.1 33.7
Additional change in Quarter 4 ⫺
10.1 39.2
7.5 42.2
44.6 32.0
Trend in loss after Quarter 4 11.8
18.9 14.9
9.1 9.5
7.0 Tenure 6.1 months to 1 year
Change in injury Quarter 1 ⫺
296.0 ⫺
288.0 ⫺
254.8 43.6
43.4 32.3
Additional change in Quarter 2 181.5
125.1 165.9
46.9 47.1
34.8 Additional change in Quarter 3
⫺ 232.8
⫺ 167.6
⫺ 222.1
46.9 47.1
34.8 Additional change in Quarter 4
⫺ 117.5
⫺ 61.3
⫺ 97.8
44.9 44.9
33.4 Trend in loss after Quarter 4
⫺ 4.0
⫺ 24.1
⫺ 10.4
18.4 18.3
13.7
Table 3 continued
Men Women
All n ⫽ 36,283
n ⫽ 18,026 n ⫽ 54,309
Selected Variables Coefficient
Coefficient Coeffcient
Tenure 1.1 to 5 years Change in injury Quarter 1
70.9 57.3
101.9 38.8
40.2 29.2
Additional change in Quarter 2 132.3
⫺ 29.4
78.7 42.1
44.1 31.8
Additional change in Quarter 3 ⫺
231.5 ⫺
181.6 ⫺
277.1 42.1
44.2 31.8
Additional change in Quarter 4 ⫺
30.3 ⫺
50.3 ⫺
35.2 40.4
42.2 30.5
Trend after Quarter 4 ⫺
2.8 ⫺
29.0 ⫺
8.8 18.2
19.3 13.8
Tenure 5.1 to 10 years Change in injury Quarter 1
119.2 76.1
145.6 46.6
45.2 34.2
Additional change in Quarter 2 133.3
⫺ 111.7
44.3 50.9
50.0 37.6
Additional change in Quarter 3 ⫺
196.4 ⫺
55.8 ⫺
162.9 50.9
50.0 37.6
Additional change in Quarter 4 65.1
24.3 48.0
48.9 47.9
36.1 Trend after Quarter 4
1.6 ⫺
33.1 ⫺
9.9 23.4
23.3 17.5
Tenure more than 10 years base case
base case base case
Employment ⬍ 50 Change in injury Quarter 1
32.6 17.3
⫺ 1.9
36.9 41.4
27.7 Additional change in Quarter 2
199.3 217.0
209.4 38.9
43.9 29.1
Additional change in Quarter 3 ⫺
79.2 ⫺
193.3 ⫺
100.0 38.9
43.9 29.1
Additional change in Quarter 4 ⫺
98.4 ⫺
35.2 ⫺
92.3 37.0
41.5 27.7
Trend after Quarter 4 7.7
7.6 10.0
8.0 8.8
6.0 Employment 51–250
Change in injury Quarter 1 ⫺
13.1 41.5
⫺ 19.4
34.5 31.2
24.9 Additional change in Quarter 2
152.6 110.3
145.4 36.8
33.0 26.2
Additional change in Quarter 3 ⫺
52.2 ⫺
111.4 ⫺
71.2 36.8
33.0 26.2
Table 3 continued
Men Women
All n ⫽ 36,283
n ⫽ 18,026 n ⫽ 54,309
Selected Variables Coefficient
Coefficient Coeffcient
Additional change in Quarter 4 ⫺
59.7 ⫺
44.2 ⫺
55.9 35.1
31.3 24.9
Trend after Quarter 4 ⫺
8.3 8.5
2.0 7.6
6.6 5.4
Employment 251–1,000 Change in injury Quarter 1
39.4 68.5
45.7 3.9
30.4 25.1
Additional change in Quarter 2 222.6
86.8 168.5
37.7 32.2
26.5 Additional change in Quarter 3
⫺ 82.9
⫺ 76.9
⫺ 83.8
37.7 32.2
26.5 Additional change in Quarter 4
⫺ 20.9
26.0 ⫺
1.3 36.0
30.5 25.2
Trend after Quarter 4 ⫺
3.1 3.8
0.25 7.7
6.5 5.4
Employment more than 1,000 base case
base case base case
Coefficient of variation in pre- injury earnings
Change in injury Quarter 1 663.2
447.1 593.6
26.8 25.7
19.7 Additional change in Quarter 2
⫺ 381.2
⫺ 226.5
⫺ 326.7
29.0 28.2
21.4 Additional change in Quarter 3
⫺ 233.5
⫺ 105.9
⫺ 194.6
29.0 28.1
21.4 Additional change in Quarter 4
⫺ 0.7
⫺ 30.3
⫺ 6.3
27.9 26.9
20.5 Trend after Quarter 4
1.2 ⫺
21.8 ⫺
5.7 12.6
12.5 9.4
Significant, p ⬍ .05 Significant, p ⬍ .10
Note: The omitted categories used imply that the estimates of injury impacts displayed in this table are for the base case of a 25–54 year old unskilled blue-collar worker in a durable manufacturing industry
with ten years of tenure in a firm with over 1,000 employees. This worker had constant earnings in the pre-injury period and the injury did not involve low back pain or carpal tunnel syndrome. Each person is
observed for 24 time periods. Because we use first differences, this results in 23 observations per person, or 1,249,107 observations overall. The estimations also included coefficients representing changes in in-
come related to a second injury and dummy variables for each time period with the first observed quarter omitted. We omit from this table the coefficients of variables affecting uninjured earnings: age
2
, age
3
; job tenure at the time of the injury ⱕ6 months, 6.1 months to 1 year, 1.1 to 5 years, 5.1 to 10 years, greater
than 10 years; two-digit SIC dummies; one-digit Census occupational categories; log number of the em- ployees 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. Age is omitted because its effect is captured by the
constant in this differenced data set. Standard errors are in parentheses.
Table 4 Estimated Average Percentage of Earnings Lost, Men and Women
Injured at Work
Quarters from Injury Men’s Losses
Women’s Losses 1–2
21.2 21.7
3–16 6.5
9.2 1–16
8.2 10.7
the equivalent estimate is 2 per quarter more p ⬎ 0.85. In neither case is the difference large. This implies that we cannot reject the hypothesis of equality in the
trend of uninjured earnings between the comparison group and the injured group of women; for men, the difference is on the margin of statistical significance, although
the amount is not large. Similar pre-injury earnings growth suggests that the choice of comparison group is reasonable.
Given this estimation of Equation 3, we calculate expected uninjured earnings for each individual and time period by setting to zero the coefficients of the interac-
tions measuring the impact of injuries δ
kI
⫽ 0 and
η
k
⫽ 0. Next, for each person
in the sample, we calculate expected losses, that is, actual earnings minus expected uninjured earnings. To obtain total losses, we also add each worker’s average pre-
injury daily wage multiplied by nine days, the average duration of lost time in the comparison group. Then, the expected average percentage of earnings lost is ex-
pected losses divided by expected uninjured earnings. They are displayed in Table 4 and Figure 3.
9
The results are consistent with the pattern we had detected originally in the raw data in Figure 1. In Table 4 and Figure 3, women’s losses in the quarter of injury
and in the next quarter average 21.7 percent of expected uninjured earnings, a little more than men’s, which average 21.2 percent. However, shortly after the injury, the
disparity increases sharply, and women’s losses become greater than men’s, averag- ing 2.7 percentage points higher than men’s for the remainder of the observed period
women lose an average of 9.2 percent of earnings, while men lose only 6.5 percent. From another perspective, women’s proportionate losses average 42 percent higher
than men’s over this period.
9. Our estimates of losses are based on the assumption that losses in the comparison group are limited to the period of their temporary disability benefits. Estimates would be biased downward if some workers
in the comparison group experience injury-related losses after this period. Actual losses of the compar- ison group would then be larger than we have calculated, as would calculated losses for workers
with more than ten days off work because their losses are based in part on calculated comparison group losses. This would only have a small impact on our male-female comparisons of losses unless
the unmeasured losses for the eight-to-ten day group are more than a small fraction of measured losses for the more than ten-day group. This seems unlikely to the authors, but we cannot test to see if it
holds.
Figure 3 Estimated Percent of Earnings Lost, Wisconsin Injuries, 1989–1990
IV. The Impact of Differential Characteristics on Gender Differences in Losses
