of Equation 1b. But differencing the observations transforms the term α
4
t to
α
4
. That is, in the differenced form, the time trend term is transformed into a constant. Again,
if the time trend α
4
is additive and the same in the pre-injury and post-injury periods, differencing will have eliminated this type of selection on unobservables
and the difference-in-differences estimator will no longer be biased Imbens, Lieb- man, and Eissa 1997.
C. The Comparison Group
We choose for a comparison group workers with short-duration injuries. These work- ers meet three criteria: 1 they had a single workplace injury from April 1, 1989
through September 30, 1990 and no subsequent injuries through 1993, 2 they lost eight to ten days from work and then returned,
6
and 3 they received no permanent disability payments.
Because workers’ compensation data provide information on several important personal characteristics, including gender, age, occupation, and job tenure, we can
condition our estimates on these covariates. The matched unemployment insurance data allow us to condition on other factors, including industry, employer size, and
workers’ pre-injury employment patterns.
We considered using uninjured workers as a comparison group, but our source of data on uninjured workers, the unemployment compensation wage files, does not
provide information about gender as well as age, occupation, and tenure. Because this information is critical to a study of gender discrimination, uninjured workers
are problematic as a comparison group for this study. In addition, we expect that workers with short-term injuries are more like other injured workers on both ob-
served and unobserved characteristics than are uninjured workers.
Table 2 presents for male and female workers the distribution of worker, employer, and injury characteristics for the comparison group and workers with longer-term
injuries by gender. Workers in the comparison group tend to be younger, have less tenure, and earn less than those in the injured group. Occupation distribution is gener-
ally similar between the two groups, although the comparison group for women has more service workers and fewer unskilled blue-collar workers. Workers in the
comparison group are also more likely to be in wholesale, retail, or service industries, less likely to be in durable manufacturing, and less likely to work in larger firms.
These differences between the comparison group and the injured group suggest that there is selection into the injured population. However, when we estimate losses
controlling for observed covariates, the trend in earnings of the injured group closely tracks the trend of the comparison group in the pre-injury period. This suggests that
selection is predominately based on observed covariates.
Figure 2 is based on our raw data and displays quarterly earnings in both the pre- injury and post-injury periods. For both male and female workers, it shows that the
younger, lower-tenure comparison group workers have lower average wages than
6. Wisconsin compensates and keeps records on injuries with more than three days’ lost time and lacks data on workers with claims involving no lost-time. Some other states only track injuries with at least
eight days’ lost time. For interstate comparability with future studies in other states, we use injuries with eight to ten days’ lost time for the comparison group.
Table 2 Summary of Statistics for Wisconsin 1989–1990 Injuries: Comparison and
Injured Groups
Men Women
Comparison Injured
Comparison Injured
Group Group
Group Group
Individual characteristics Age in years
34.48 36.59
35.44 37.46
11.76 11.46
11.91 11.82
Tenure in years 5.52
6.42 4.49
5.09 7.62
8.35 6.09
6.46 Median
2 2
1 2
Occupation type proportion Managerial or professional
0.03 0.03
0.11 0.09
0.16 0.16
0.31 0.28
Clerical 0.04
0.04 0.17
0.14 0.20
0.19 0.37
0.35 Service
0.09 0.07
0.35 0.28
0.29 0.26
0.48 0.45
Skilled blue collar 0.29
0.29 0.06
0.08 0.45
0.46 0.24
0.27 Unskilled blue collar
0.52 0.55
0.30 0.40
0.50 0.50
0.46 0.49
Agricultural, military, or other 0.03
0.02 0.01
0.01 0.16
0.15 0.09
0.09 Industry type proportion
Agricultural, domestic service, or other 0.07
0.07 0.06
0.05 0.26
0.25 0.24
0.22 Mining or construction
0.14 0.15
0.01 0.01
0.35 0.36
0.07 0.08
Durable manufacturing 0.28
0.32 0.17
0.24 0.45
0.47 0.38
0.42 Nondurable manufacturing
0.12 0.13
0.15 0.18
0.32 0.33
0.36 0.38
Transportation, communication, or 0.08
0.09 0.02
0.02 utilities
0.28 0.29
0.13 0.15
Wholesale trade or retail sales 0.19
0.16 0.20
0.17 0.39
0.37 0.40
0.37 Finance, insurance, real estate, or other
0.12 0.10
0.39 0.34
services 0.32
0.30 0.49
0.47 Employer characteristics
Number of employees 902
1,001 1,428
1,548 2,108
2,105 2,671
2,678 Median
141 166
359 430
Proportion of employees in firms with 0.30
0.29 0.13
0.12 50 or fewer employees
0.46 0.45
0.34 0.32
Proportion in public sector 0.09
0.08 0.14
0.11 0.29
0.27 0.34
0.32
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
