II. Empirical Specication
The Employment Cost Index is the aggregation of wage rates for the sample of jobs matched between the current month and three months prior. The
aggregation occurs in two steps. In the rst step, the change in the wage rate is estimated for about 650 categories of labor, which are dened by the intersection
of industry and occupation groups. The change equals the average wage rate in the current month divided by the average wage rate three months prior among the same
jobs. Each job gets the same sample weight in both months. In the second step, following a Laspeyres index formula, the change in compensation for the categories
are combined using xed employment weights from a base period.
4
When the ECI microdata from multiple months are pooled, a natural specication to compare the growth rates among industryoccupation groups is the following,
where w
it
is the log wage rate for job i in month t and D indicates the three-month change.
1 Dw
it
5 q¢
it
g 1 x¢
it
d 1 v
it
The vector q
it
contains dummy variables for each month, while the vector x
it
contains dummy variables for each industryoccupation group. The v
it
term adds a residual. If the log change in the wage rate were regressed on the month dummy variables
only, the coefcient estimates would essentially give the three-month change in the ECI for each period.
5
Adding the industryoccupation variables picks up the tendency for the groups’ wage rates to grow at different rates. Data from multiple months are
pooled because the three-month change in wage rates is quite noisy. Many of the jobs show no change while others show large changes. Pooling the data allows the
industryoccupation coefcients to pick up more systematic variation in wage growth among the groups.
One context in which to consider the industryoccupation parameters in Equation 1 is to relate them to more general patterns in the wage distribution. Rewrite Equation
1 in its log form instead of its rst difference. In the log form, the equation includes dummy variables for each job in adjacent three-month periods, denoted by vector
z
it
, which had been removed by the rst difference. 2
w
it
5 z¢
it
b 1 q¢
it
a 1 x¢
it
p 1 t × x¢
it
d 1 u
it
The vector q
it
still contains dummy variables for each month, although its parameter vector is redened for logs rather than rst differences of logs. The vector of dummy
variables for each industryoccupation group is now additionally multiplied by a time trend t, which increments by one for successive three-month periods, starting
at zero for three months prior to the rst current month. The residual term u
it
refers to logs rather than rst differences.
Equation 2 is a general specication for the log wage rate. Its parameters can be
4. For more information, see U.S. Department of Labor 1997 and Lettau, Loewenstein, and Cushner 1997a.
5. There are slight differences. Because of the log functional form, the regression uses differences in geometric means rather than ratios of arithmetic means. Also, the xed employment weights are not ap-
plied. However, the growth in the ECI has been quite invariant to such minor modications. See Lettau, Loewenstein, and Cushner 1997a.
estimated using data on individuals from the Current Population Survey, which will provide a direct comparison for the ECI estimates. For the CPS regressions, the
control variables in z
it
are dummy variables for ve age categories, four education categories, four census region categories, and dummy variables for whether the
worker is white, male, married, part-time, and covered by a collective bargaining agreement.
Beyond the comparison of growth rates, the dual estimates also allow the construc- tion of an alternative set of individual wage rates with features of both the ECI and
the CPS. As a preliminary step, Equation 3 divides the CPS log wage rates into the explanatory variables, parameter estimates, and the estimated residual.
3 w
CPS it
5 z¢
it
bˆ
CPS
1 q¢
it
aˆ
CPS
1 x¢
it
pˆ
CPS
1 t × x¢
it
dˆ
CPS
1 uˆ
CPS it
The hypothetical log wage rate for individual i in period t is constructed with a combination of the ECI and CPS estimates, as shown in Equation 4.
4 w
within-job it
5 z¢
it
bˆ
CPS
1 q¢
it
aˆ
CPS
1 x¢
it
pˆ
CPS
1 t × x¢
it
dˆ
ECI
1 uˆ
CPS it
Equation 4 substitutes the ECI estimates for the wage growth by industryoccupation group. The empirical section reports measures of wage dispersion based on the CPS
individual wage rates and the individual wage rates calculated using Equation 4, which will be referred to as the within-job rates. Dispersion measures based on the
within-job rates show, at least to the extent possible, how inequality would have changed had workers remained in the same job.
III. Data