Figure 1 shows that, in the first two quarters after injury, men experience an aver- age percentage loss in earnings relative to the comparison group that is about the
same as for women. Yet, the unadjusted means suggest that over the next 3 12 years, men lost an average of 8.3 percent of pre-injury earnings while women lost
10.1 percent—about 14 higher than men. Figure 1 motivated this study and also helped us to specify the statistical model.
III. Methods
A. Basic Model of Earnings
We define injury-related lost earnings as the difference between workers’ actual post- injury earnings and what they would have earned if they had not been injured. We
call these observed injured earnings and uninjured earnings respectively. Of course, we do not observe uninjured earnings but must estimate them from data that we
do observe. This estimation problem is parallel to those addressed by literature on nonexperimental program evaluation, where there is a substantial literature on esti-
mating the impact of for example public-sector training programs. Here, the ‘‘treat- ment’’ is the injury, not a training program and the comparison group should ideally
consist of workers who have not suffered the injury.
If we observe worker i before and after injury, we can write the model of that worker’s earnings as:
1 y
i
⫽ α
1i
⫹ γ
t
⫹ X
i
∗ α
2
⫹ β
1
T ⫹
ε
i
where y is earnings, α
1i
is an individual-specific fixed effect, γ
t
is a time-specific fixed effect capturing general economic conditions affecting all workers, T ⫽ 0 before the
injury and T ⫽ 1 after the injury, and X
i
is a vector of observed and unobserved covariates. As long as noninjury factors do not affect the earnings path differentially
in the pre-injury and post-injury periods, Equation 1 is a reasonable framework within which to estimate losses, with
β
1
measuring the impact of the injury on earn- ings.
However, because of the way our data were collected, even uninjured earnings are affected by their timing relative to the date of injury. This occurs because we
assembled the data for people with a workplace injury in a given quarter. Because by definition 100 percent of people injured at work must have been employed when
they were injured, employment rates will generally be lower in quarters before and after the injury, rising as the date of injury approaches and falling after the injury.
This data-collection artifact would make it look as if losses occurred even for people whose earnings were unaffected by their injuries. As a consequence, the estimates
of losses based on Equation 1 would be biased away from zero.
This is the type of situation that the difference-in-differences approach is designed to handle. Because it compares post-injury changes in earnings of the injured with
changes in a suitably chosen uninjured comparison population, it can produce unbi- ased estimates of the impact of injuries under suitable conditions. This approach can
be summarized by representing earnings as:
1a y
i
⫽ α
1i
⫹ γ
t
⫹ X
i
∗ α
2
⫹ α
3
∗ I ⫹ β
1
T ⫹ β
2
T ∗ I ⫹ ε
i
Here I ⫽ 1 for the injured group and I ⫽ 0 otherwise. The impact on the comparison group’s uninjured earnings of measured and unmeasured factors is captured by
α
2
. Differences in uninjured earnings between the injured and comparison groups are
measured by α
3
. β
1
captures the data-collection artifact just described, and β
2
mea- sures the average effect of injury on earnings.
B. Selection Issues
