We adapt the Oaxaca-Blinder-Neumark method to decompose injury related losses. Therefore, we apply it to injury-related losses estimated from Equation 3, and not to
wages. We allow the loss coefficients to vary in the quarter of injury and in each of the four subsequent quarters and to have a long-term trend. Therefore, our new specification
differs from Equation 4 in having the gender difference in losses as the dependent variable and in allowing losses to change with time after injury:
4a L¯
mk
⫺ L¯
fk
⫽
冱
k⫽ 1,5
F
k
{X¯
mk
⫺ X
¯
fk
b
k
⫹ [X¯
mk
b
mk
⫺ b
k
⫺ X¯
fk
b
fk
⫺ b
k
]} Here, L
k
is the estimate of the injury-induced change in earnings in period k relative to the quarter of injury derived from the results of Table 3; X¯
k
is a vector of mean characteristics in period k, and b
k
is a vector of coefficients for the period k relative to the injury. Of course, the m and f subscripts represent male and female. Variables
without subscripts refer to the entire population. As in Equation 3, the impact of injury on wages in a given quarter is the sum of the F
k
for that quarter and the preceding ones.
B. Results of Decomposition
Our original estimates of losses had shown that in the quarter of injury and in the following quarter, men’s and women’s percentage losses were very similar: both
average a little more than 20 percent of expected uninjured earnings. Over the next three and a half years, however, women’s losses averaged 2.7 points more than
men’s. We use the loss decomposition in a 4a to determine the amount of the difference accounted for by gender disparities in characteristics b
k
, calculating expected losses from the full-sample parameter estimates at the means of the co-
variates for both men and women Figure 4 and Table 5. During the first two
Figure 4 Estimated Nondiscriminatory Losses, Wisconsin Injuries, 1989–1990
Table 5 Decomposition of Estimates of Gender Differences in Injury-Related Losses
Women’s Losses minus Men’s Losses
percent of injured earnings
Quarters from Injury 1–2
3–16 1. Male advantage due to characteristic
3.5 ⫺
1.1 2. Male advantage due to behavior
⫺ 0.8
0.9 3. Female advantage due to behavior
2.3 ⫺
3.0 4. Overall male advantage due to behavior 2. ⫺ 3.
⫺ 3.1
4.0
a
5. Overall difference 1. ⫹ 4. 0.4
2.8
a
a. Numbers do not sum exactly because of rounding.
quarters after injury, the full-sample nondiscriminatory parameter estimates generate men’s losses that are 3.5 points less than women’s Table 5, Row 1.
After this initial period, the result reverses and women’s expected nondiscrimin- atory losses average 1.1 points less than those of men. This suggests that, if there
were no discrimination or gender differences in behavior, women would initially have lost more, but in the longer term they would have lost a smaller proportion of
earnings.
We next calculate the difference, given men’s covariates, between expected losses based on the full sample estimates and on men’s parameter estimates Figure 5 and
Table 5, Row 2. This is the estimate of men’s advantage, X¯
mk
b
mk
⫺ b
k
, given their characteristics. It appears that, relative to ‘‘nondiscriminatory’’ losses, men are at a
slight disadvantage in the two post-injury quarters, while afterward they benefit a little. The story is quite different for women. Women’s parameter estimates at the
mean of their covariates show different results for the first two quarters after injury and the long term. In the first two quarters, women’s parameter estimates produce
substantially lower expected losses than the full-sample parameter estimates—by an average of 2.3 points. However, in the three and a half years observed after that
point, losses based on women’s parameter estimates are 3.0 points greater than based on the full-sample parameter estimates. Figure 6 and Table 5, Row 3. This measures
possible post-injury gender discrimination. Combining estimates of men’s advantage and women’s disadvantage gives men a 3.1 percentage point disadvantage in the
first two post-injury periods and a 4.0 point earnings advantage thereafter Table 5, Row 4. Women’s advantage in the first two quarters is erased shortly after the end
of the fourth quarter, and following that their disadvantage continues at least until the end of the observed period.
Figure 5 Estimated Percent of Earnings Lost Men Injured in Wisconsin, 1989–1990
Figure 6 Estimated Percent of Earnings Lost Women Injured in Wisconsin, 1989–1990
To test the hypothesis that characteristics alone explain the difference between the losses of men and of women, we calculate bootstrapped standard errors of the
overall male advantage due to behavior in each period. We use 50 bootstrapped samples from the overall data to calculate the mean overall male advantage, which
is our measure of women’s losses attributable to discrimination. For all quarters, the 95 percent confidence interval for the impact of behavior on proportionate earnings
losses does not include zero. This leads us to reject the hypothesis that the observed disparity in long-term losses is caused only by differences in observed personal,
employer, job, or injury characteristics.
V. The Impact of Nonemployment on Gender Differences in Losses
