Comparison of Wage Growth

IV. Empirical Results

A. Comparison of Wage Growth

Table 1 compares the industryoccupation growth parameters d between the ECI and CPS. It shows estimates of the standard deviation among the groups, both before and after an adjustment for sampling variation. The estimates for the correlation between the CPS and ECI parameters use the adjusted standard deviation. The Žnal column shows the test statistic for the joint hypothesis that all groups have the same growth rate. The top of the table has results for the entire period, which runs from June 1981 through December 1998. The middle and bottom of the table has results for two subperiods, with March 1990 used as the break. March 1990 is chosen be- cause many of the previous results from the CPS refer to the 1980s. A comparison is easier with the ECI likewise restricted. The two subperiods correspond roughly in terms of the business cycle. Both begin with recessionary periods, followed by a longer period of expansion. Appendix 2 shows how Equations 1 and 2 are modiŽed to allow the parameters to differ by subperiod. Focusing Žrst on results for the earlier subperiod in the middle of the table, the wage growth parameters for the ECI and CPS line up quite closely. The adjusted standard deviations are 2.39 3 10 23 and 2.51 3 10 23 , respectively. To give an idea for the magnitude of these estimates, the average three-month change in the log wage rate for the ECI during the subperiod is 0.011, which translates into about a 4.4 percent annual growth rate. Therefore, the ECI’s standard deviation for an industry occupation group is about 22 percent of the overall growth rate. The adjusted correla- tion between the ECI and CPS is also high at 0.73. Table 1 also shows dispersion statistics across the nine industries and the nine occupations. The nine industry parameters equal the weighted average of the 81 industryoccupation parameters across occupations. The corresponding procedure is used for the nine occupation parameters. Again, they line up closely for the earlier subperiod. The ECI is higher than the CPS for the nine industries, though lower for the nine occupation groups. Figure 1 shows the individual estimates for the nine occupations to illustrate their magnitude more clearly. The parameter estimates are differenced from their weighted average to set the mean to zero, then converted to an annual rate. The Žgure makes apparent the high correlation and similar variance between the ECI and the CPS parameter estimates. Only the estimates for sales occupations differ in sign. Thus, for the 1980s, the variation in the growth of average wage rates among the groups from the CPS does not substantially overstate nor misrepresent the variation in wage growth incurred by employers to retain the various types of workers. The high correlation between the ECI and the CPS breaks down in the later sub- period, however. For March 1990 through December 1998, the standard deviation estimates for the ECI are small in magnitude, both relative to the CPS in the same period and the ECI in the earlier period. Moreover, although the growth rates for the various groups continue to be jointly signiŽcant for the CPS, the hypothesis that the wage rates for various groups all grew at the same rate cannot be rejected at the 5 percent level for the ECI. In fact, for the industryoccupation groups, the estimate for the adjusted standard deviation is negative. The adjustment uses the variance- Table 1 Variation Among Growth Rates for ECI and CPS Adjusted Adjusted Standard Standard Correlation Joint Test Deviation Deviation with CPS Statistic June 1981– December 1998 Industriesoccupations ECI wage rates 1.55 1.33 0.69 231.7 CPS wage rates 1.36 1.34 — 2,878.9 Industries: ECI wage rates 1.14 1.10 0.68 112.3 CPS wage rates 1.10 1.09 — 1,881.7 Occupations: ECI wage rates 1.04 1.00 0.78 104.5 CPS wage rates 1.09 1.08 — 1,834.1 June 1981– March 1990 Industriesoccupations ECI wage rates 2.66 2.39 0.73 297.8 CPS wage rates 2.58 2.51 — 1,432.5 Industries ECI wage rates 1.92 1.87 0.83 131.1 CPS wage rates 1.53 1.51 — 499.7 Occupations ECI wage rates 1.72 1.66 0.86 124.1 CPS wage rates 2.17 2.16 — 1,007.0 March 1990– December 1998 Industriesoccupations ECI wage rates 0.79 — — 47.7 CPS wage rates 1.43 1.28 — 395.7 Industries: ECI wage rates 0.44 0.27 20.10 12.8 CPS wage rates 1.03 1.01 — 205.7 Occupations: ECI wage rates 0.45 0.22 20.51 11.7 CPS wage rates 0.81 0.78 — 128.1 Notes: The estimates for the standard deviation and adjusted standard deviation are multiplied by 10 3 . The test statistic refers to the hypothesis that all groups have the same growth rate. An asterisk indicates statisti- cal signiŽcance at 5 percent. Figure 1 Occupation Growth Rates: June 1981– March 1990 covariance matrix for the parameter estimates to remove the expected upward bias in the standard deviation because it is measured among estimates rather than the true parameters. For the industryoccupation groups in the ECI, the adjustment actu- ally exceeds the overall variation among the estimates, which leads to the negative value. To the extent that the growth rates do vary among groups for the ECI, they do not particularly line up with the CPS. Figure 2 shows the individual estimates for the nine occupations. In contrast to Figure 1, the ECI and the CPS parameter esti- mates often differ in sign. Also apparent is the smaller variation among the growth rates for the ECI in the 1990s compared to the 1980s. Thus, since 1990, employers have not incurred substantially different rates of wage growth for some workers relative to others, at least with the workers deŽned by industry and occupation groups. The difference in the results for the two subperiods leads to the question of how the results vary over time under a less structured speciŽcation, one that neither forces the differentials in wage growth for the groups to be constant within the subperiods nor chooses a break month arbitrarily. Therefore, a speciŽcation was tried that allows a separate ECI change parameter for each occupation group in each month, and a separate CPS level parameter for each occupation group in each month. DeŽning groups by industry and occupation leads to a prohibitive number of parameters. The variation in growth rates over time was assumed to be continuous, so the parameters were smoothed using a kernel estimator. The results, not shown but available from Figure 2 Occupation Growth Rates: March 1990– December 1998 the author, suggest that the correlation between wage growth in the ECI and CPS is close to one when the variation is large in magnitude during the 1980s. But when the variation becomes smaller during the 1990s, the correlation becomes erratic and has been negative at times. Thus, like the subperiod results, the more exible esti- mates imply that, during the 1980s, wage growth in the ECI was highly correlated with the change in average wage rates in the CPS for the industry and occupation groups, until the 1990s when the high correlation broke down. Wage growth in the ECI no longer seems to differ substantially among the groups.

B. Comparison of Wage Dispersion