Empirical SpeciŽcation Manajemen | Fakultas Ekonomi Universitas Maritim Raja Ali Haji 792.full_2

II. Empirical SpeciŽcation

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 Žrst step, the change in the wage rate is estimated for about 650 categories of labor, which are deŽned 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 Žxed employment weights from a base period. 4 When the ECI microdata from multiple months are pooled, a natural speciŽcation 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 coefŽcient 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 coefŽcients 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 Žrst 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 Žrst 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 redeŽned for logs rather than Žrst 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 Žrst current month. The residual term u it refers to logs rather than Žrst differences. Equation 2 is a general speciŽcation 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 Žxed employment weights are not ap- plied. However, the growth in the ECI has been quite invariant to such minor modiŽcations. 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 Žve 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