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

Inequality Using the Employment

Cost Index

Michael K. Lettau

a b s t r a c t

The Employment Cost Index measures the change in wage rates for a Žxed set of jobs over time. The separate indices for industry and occupa-tion groups grew at varying rates during the 1980s. However, their growth rates have been much more similar since then, which implies that the increase in the wage rates of low-wage workers relative to middle-wage workers during the 1990s was due to changes in the mix of jobs. Had all workers remained in their jobs, the relative wage of low-wage to middle-wage workers would have remained constant.

I. Introduction

Many authors document a widening of the wage distribution in the United States over the last 25 years, especially during the 1980s.1 _{These studies} typically use household surveys as their data source, such as the decennial Census or the Current Population Survey (CPS). Wage rates in these data sets uctuate for many reasons: Workers move in and out of the labor force, workers change their Michael K. Lettau is an economist with the U.S. Bureau of Labor Statistics. He thanks an anonymous referee and members of the Compensation Research and Program Development Group and the OfŽce of Employment Research and Program Development of the U.S. Bureau of Labor Statistics for their comments. The views expressed in this paper are those of the author and do not necessarily reect the view of the Bureau of Labor Statistics or any of its staff. The publicly available data used in this arti-cle can be obtained beginning April 2004 through March 2007 from Michael Lettau, U.S. Bureau of Labor Statistics, 2 Massachusetts Ave. NE, Washington, DC 20212. The author can provide advice on the application process for the conŽdential data used in this article. Application details can be ob-tained by contacting the OfŽce of the Commissioner at the same address.

[Submitted March 1999; accepted May 2002]

ISSN 022-166XÓ2003 by the Board of Regents of the University of Wisconsin System

1. For example, see Bound and Johnson (1992), Levy and Murnane (1992), Katz and Autor (1999), and Pierce (2001).

Žrms, workers are promoted within the same Žrm, and wages grow at different rates for workers remaining in their jobs. Trends in wage rates over time are an amalgam of these dynamics.

Acknowledging the need for an alternative, the Bureau of Labor Statistics devel-oped the Employment Cost Index (ECI) in the 1970s. By following a panel of jobs over three-month periods, the ECI would focus more narrowly on how much a Žrm must raise compensation to retain its labor input. It would be unaffected by shifts in the mix of jobs in the labor market.2_{Indeed, since its inception, the Employment} Cost Indices for all civilian workers has generally grown at a different rate than the averages from other wage series.3

The broad indices for all workers are watched most closely, but the ECI program also reports several subindices, notably for industry and occupations groups. This paper compares the ECI’s wage growth for these groups with average wage rates for the same groups in the CPS. If their growth rates are similar, trends in average wage rates are not just an artifact of workers moving into the labor force and upgrad-ing their jobs. They represent differential wage increases for workers who remain in their jobs. Viewed from the Žrm’s perspective, they represent the different cost increases employers must absorb to retain the different groups of workers. On the other hand, if the variation in the ECI over time does not match the trends among average wage rates in the CPS, the variation among industry/occupation groups re-sults from the upgrading of jobs alone, not any differential adjustment to compensa-tion within jobs.

After a comparison of their growth rates, the ECI and CPS estimates are combined to create a hypothetical wage distribution. This distribution shows what wage rates would have been had workers remained in stable job situations, in contrast to the CPS, which is inuenced by all dynamics of the labor market. Summary measures of wage dispersion are calculated for both distributions.

The results are the following. During the 1980s, the variation in wage growth among industry/occupation groups in the ECI was quite similar to the corresponding change in average wage rates in the CPS. Since then, however, the ECI has shown little systematic variation in wage growth among the groups. This translates into a different pattern of wage dispersion between the CPS and the hypothetical distribu-tion. In the CPS, the wage rates of low-wage workers fell relative to the middle workers during the early to middle 1980s, but they have increased since then. The hypothetical distribution shows the same pattern for the 1980s, but a more stable ratio between low- and middle-wage workers since then. Thus, the gains low-wage workers have made in the more recent years were due to the creation and movement of workers between jobs, not the more passive circumstance of higher wage increases for low-wage workers remaining in their job.

2. Another way to understand the ECI as a distinct measure of wage movement is to consider the Job Quality Index (JQI), which the Center for National Policy reports every three months. Frumkin (2000) describes the JQI as the obverse of the ECI. The JQI measures changes in wage rates due solely to shifts in the types of jobs held by workers. It is not affected by changes to compensation within jobs. Conceptually then, movement in the ECI is a subset of movement in average wage rates, with movement in the JQI as its complement.

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 industry/occupation groups is the following, wherewit is the log wage rate for jobiin monthtandDindicates the three-month change.

(1) Dwit5q¢itg1x¢itd1vit

The vectorqitcontains dummy variables for each month, while the vectorxitcontains dummy variables for each industry/occupation group. Thevit 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 industry/occupation 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 industry/occupation coefŽcients to pick up more systematic variation in wage growth among the groups.

One context in which to consider the industry/occupation 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 zit, which had been removed by the Žrst difference.

(2) wit5z¢itb1q¢ita1x¢itp1t×x¢itd1uit

The vectorqitstill 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 industry/occupation group is now additionally multiplied by a time trendt, which increments by one for successive three-month periods, starting at zero for three months prior to the Žrst current month. The residual termuitrefers 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 inzit 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) wCPS

it 5z¢itbˆCPS1q¢itaˆCPS1x¢itpˆCPS1t×x¢itdˆCPS1uˆCPSit

The hypothetical log wage rate for individual iin period t is constructed with a combination of the ECI and CPS estimates, as shown in Equation 4.

(4) wwithin-job

it 5z¢itbˆCPS1q¢itaˆCPS1x¢itpˆCPS1t×x¢itdˆECI1uˆCPSit

Equation 4 substitutes the ECI estimates for the wage growth by industry/occupation 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

The paper uses microdata from the Employment Cost Index and the Current Population Survey. The ECI data are available for four months of the year: March, June, September, and December. The CPS data are from outgoing-rotation groups, and they are restricted to March, June, September, and December to match the ECI. The data run from June 1981 through December 1998. As mentioned above, authors using the CPS generally deŽne the skill groups based on demographic infor-mation such as age and education, but this paper deŽnes categories of workers by the intersection of nine major industries and nine major occupations because the ECI program does not collect demographic information about workers. Appendix 1 discusses further details of the CPS and ECI data.

The nine industries and nine occupations deŽne the industry/occupation groups, so the parameter vectordcontains 81 elements. The Žrst element is deŽned arbitrarily as zero. The regressions use the sample weights from the CPS and the ECI. The next section reports the standard deviation across the 81 estimates for the wage growth parameters ind, so a correction is made for the expected variation due to sampling error. This adjustment is based on the variance matrix for the estimate of d. No corresponding adjustment is made for the covariance between the ECI and CPS estimates, as the sampling error is assumed independent across surveys. As a conse-quence, when the correlation between the estimates is calculated using the covariance and the adjusted standard errors, it can exceed one if the expected sampling error is large relative to the actual variation. Appendix 2 discusses the adjustment in detail.

IV. Empirical Results

A. Comparison of Wage Growth

Table 1 compares the industry/occupation growth parametersdbetween 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 2.39₃1023_{and 2.51}

31023_{, 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 industry/occupation 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 industry/occupation 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

Industries/occupations

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 Industries/occupations

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 Industries/occupations

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 103_{. 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 industry/occupation 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

Equation 4 shows the construction of individual log wage rates using the ECI wage growth estimates. The demographic component, the initial level for the industry/ occupation group, and the residual are the same as for the CPS log wage rates in Equation 3. The wage rates differ because the group’s growth since the initial period is at the ECI rate, not the CPS rate. They will tend to diverge because the growth rates are multiplied by the time since the initial period. The divergence potentially changes with the introduction of the new growth parameters for the second sub-period.6

6. The within-job wage rates are based on the spline regression described in the appendix instead of the separate regressions by subperiod. The spline would be equivalent to the separate regressions if it addition-ally included dummy variables for the industry/occupation groups in the second subperiod. The advantage to the spline is that it allows for new growth rates in the second subperiod without resetting the difference

Figure 3

Wage Dispersion Ratios: June 1981– December 1998

Though the measures of wage dispersion are invariant to a shift in the month-speciŽc mean, the within-job log wage rates are adjusted to make their mean equal to the CPS mean for each month. The growth for the ECI has generally outpaced the growth for the CPS during the sample period. For the earlier subperiod, the average annual growth rates for the ECI and CPS are 4.4 percent and 4.1 percent, respectively. By the end of 1998, the trend actually reversed, with a 3.4 percent growth rate for the CPS and a 3.2 percent for the ECI in the later subperiod, but this is due to particularly strong growth in the CPS for 1998.7_{For March 1990 through the} December 1997, the ECI growth rate exceeded the CPS growth rate, 3.2 percent to 3.1 percent. The trend from the dynamics of the labor market has been to reduce average wage rates during most of the sample period.

It helps to keep this in mind in light of the results in Figure 3, which compares measures of dispersion between the CPS and within-job wage rates. The Žgure shows the ratio of the 90th percentile to the 50th percentile and the ratio of the 50th percen-tile to the 10th percenpercen-tile for the CPS and the within-job wage rates.8 _{The ratios} equal the exponential of the log difference. For the high-wage workers relative to the middle workers, the ratios for the two series stay fairly similar. By the end of

between the CPS and within-job wage rates to zero at the break month. The results in Table 1 are similar when the growth parameters from the separate regressions are used.

7. Although the CPS wage rates use the correction for top coding suggested by West (1986), an increase in the topcode value for weekly earnings might explain some of the strong wage growth in 1998. However, the growth is not concentrated in the change from December 1997 to March 1998, when the new topcode would have taken effect.

8. The quantile statistics are calculated using the interpolating procedure, outlined in West (1986). It is the procedure used for the published CPS quantile statistics.

the period, the ratio for the within-job wages is slightly higher, which suggests slightly more dispersion at the higher end. The difference is more substantial at the other end of the distribution, however. According to the CPS wage rates, low-wage workers gained relative to the middle workers beginning in the last few years of the 1980s. In contrast, the ratio has held more or less steady for the within-job wage rates. During the 1990s, wage increases were about the same for workers remaining in stable job situations, regardless of their skill group. The trend from the labor force dynamics has been toward a slight downgrading of jobs. However, workers at the lower end of the distribution appear to have been less adversely affected, which produced a relative gain. By the end of 1998, when the trend appears to have reversed toward an upgrading of jobs, low-wage workers also beneŽted more. Using the stan-dard deviation of the log wage rates rather than the 90–50 and 50–10 ratios also suggests that wage dispersion would have been higher during the 1990s had workers never changed jobs.9

Card and DiNardo (2002) evaluate the most common explanation for the change in wage inequality over the past 25 years—skill-biased technological change. They Žnd it to be a plausible explanation for some aspects of the increase in wage inequal-ity during the early and middle 1980s. However, wage inequalinequal-ity stabilized during the 1990s, and may have even turned down slightly. There has been no obvious slowdown in the adaptation of technology into the workplace. They argue that re-searchers must look in other directions to explain the time pattern of inequality. The stabilization in wage inequality during the 1990s is doubtless a mixture of many intertwined factors, but the results in Figure 3 point to job dynamics as one of them. Opportunities that arose during the extended expansion, either through job-change opportunities within a Žrm or through job opportunities in other Žrms, disproportion-ately aided workers at the bottom of the wage distribution when they took advantage of them. The relative wage rates of workers who remained in their jobs were more stable.

V. Summary

The empirical results in this paper summarize wage growth in the ECI for industry and occupation groups, with parallel results from the CPS. For the 1980s, when the dispersion of wage rates for the U.S. increased dramatically, the CPS and ECI results align closely. More recently, however, when the upward trend in wage dispersion has been less dramatic, wage growth from the ECI does not differ signiŽcantly among the industry/occupation groups. Workers remaining in a job received about the same wage increases regardless of their skill group.

The ECI growth parameters are then incorporated into the CPS wage rates to create a hypothetical wage distribution for workers had they remained in the same job. The measures of wage dispersion for the resulting distribution are higher than for the CPS distribution in the 1990s. Thus, generous wage increases to existing

9. The earnings questions in the CPS were redesigned beginning in the 1994 survey. See Polivka and Rothgeb (1993) for details. The redesign seems to have caused a jump in wage dispersion between 1993 and 1994, which affects both the CPS and within-job wage rates.

low-wage workers did not reduce wage dispersion in the 1990s. Instead, labor force dynamics, such as the creation of and movement into new jobs, caused the decline in wage inequality during this period.

Appendix 1

CPS and ECI Data

The ECI is a survey of jobs within establishments. For each establishment in the survey, a small number of jobs are sampled randomly, usually between four and eight. Because the unit of observation is a job, the microdata equal the average value of compensation per hour among the workers in the job. A job is deŽned by the most detailed classiŽcation recognized by each establishment, so the ECI essentially defers to the establishment to ensure that workers in the job represent the same labor input from month to month.

The CPS and the ECI samples are restricted to workers and jobs in private, non-agricultural industries. To match the ECI, the CPS sample is restricted to wage and salaried workers and excludes workers in private household occupations. The regres-sions use the CPS earnings weights and the ECI sample weights. The weights are normalized to one for each month.

The nine industries are mining; construction; durable manufacturing; nondurable manufacturing; transportation, communication, and public utilities; wholesale trade; retail trade; Žnance, insurance, and real estate; and services. The nine occupations are professional and technical; executive and managerial; sales occupations; adminis-trative support occupations; precision and craft occupations; operators and assem-blers; transportation occupations; handlers and laborers; and service occupations.

For the CPS, the four education categories are less than high school, high school, some college, and at least a college degree. See Frazis and Stewart (1999). The Žve age categories are 16 to 24, 25 to 34, 35 to 44, 45 to 54, and 55 or older. Although the ECI imposes no age restriction for the jobs in its sample, the CPS data are restricted to workers at least 16 years old. The dummy variable for whether a worker is covered by a collective bargaining agreement is not available before 1983, so it is set to zero for all workers in years prior to then. This is arbitrary because the month dummy variables would subsume an additional dummy variable for whether the collective bargaining information is missing.

For years prior to the CPS redesign in 1994, the wage rate in the CPS equals usual hourly earnings for workers paid hourly and usual weekly earnings divided by usual weekly hours for other workers. I use the same procedure for 1994 and subsequent years, although I follow Polivka (1997) for workers who report that their hours vary. I also use her procedure to account for the topcoding of earnings. Details on this procedure are available from the author upon request. Results reported in the paper are similar when I use usual weekly earnings divided by usual weekly hours for all workers, which is generally interpreted as including overtime pay in wage rates.

Workers in the CPS and jobs in the ECI with a wage rate less than $1 per hour or more than $200 per hour in March 1979 dollars are excluded as outliers. The ECI

for wages and salaries for workers in private industries is used as the index for the outlier threshold. For both the CPS and the ECI, the weighted proportion of outliers stays below one percent.

Prior to 1986, the ECI data are only available as averages for the current and previous quarter by month/industry/occupation cells. This presents three complica-tions. First, for each cell, the log difference between the average wage rates for the current month and three months prior replaces for the average log difference between the current and previous wage rates. The regression results do not change much, however, when the same replacement is made for months in which the microdata are available. Second, the sum of the sample weights for each cell is not available. Therefore, the cells’ relative frequencies from the CPS are used. Third, the weighted sum of the squared residuals, the sum of the weights, and the sum of the squared weights for each cell are all needed to calculate the standard errors. Because the residual is assumed homoskedastic across all months, the estimated residual variance from months in which the microdata are available is applied to all months. Further, the sum of the weights and the sum of the squared weights for the cells are assumed to be the same for months in which the microdata are and are not available, so their values from months in which they are available are inated accordingly.

Appendix 2

Estimation Procedures

The wage growth parameters in vectordare estimated by weighted least squares. The variance matrixVis estimated under the assumption of homoskedasticity, al-though the results do not change much when the ECI regressions use a block form of White’s (1980) procedure, which allows for heteroskedasticity and general forms of covariation among jobs from the same establishment in the same month.

The standard deviation among the parameters indis calculated as follows. DeŽne an 81381 matrixHas follows.

(5) H5F1/2_[I

2m(m¢Fm)21_m¢F]

The matrixFis an 81₃81 diagonal matrix with a vector fon its main diagonal;f gives the weighted frequency for each industry/occupation group, which is calculated using data pooled across all months. The matrixIis an 81 ₃81 identity matrix. The vectorm is an 8131 vector of ones.

DeŽne the Žrst element ofdequal to zero, and deŽne the Žrst row and column ofVequal to zero. The following holds.

(6) E(dˆ¢H¢Hdˆ)₅d¢H¢Hd₁trace(HVH¢)

The Žrst term on the right-hand side of Equation 6 equals the variance among the parameters ind, so the second term on the right-hand side is the adjustment to the variance estimate due to sampling variation. The standard deviation across occupa-tions is calculated using a similar procedure, althoughHis more complicated because the dparameters must Žrst be averaged across industries. The same procedure is used for industries.

Equations 7 and 8 show the speciŽcations for the ECI and CPS used for the calcu-lation of the within-job wage rates. For the ECI in Equation 7, the subscriptjis the index for the subperiods,tj equals three months prior to Žrst current month in the subperiod, and the indicator function 1[t _.tj] equals one if the current month is later thantj, zero otherwise.

(7) Dwit5q¢itg1

^

j

1[t.tj] ×x¢itd1vit

For example, the expected change for an industry/occupation group in a month from the subperiodjequals the month’s coefŽcient ingplus the sum of the group’s coefŽ-cients in d1 through dj. Equation 7 uses the accumulation of coefŽcients for the previous subperiods, rather than a separate coefŽcient for each subperiod, because it makes the mapping to the log-wage speciŽcation easier. Equation 7 translates into a spline function for the log wage rate.

(8) wit5z¢itb1q¢ita1x¢itp1

^

j

1[t.tj] ×(t2tj)×x¢itd1uit

Equation 8 is used for the CPS. The parameters inbare also allowed to differ be-tween the Žrst and second subperiods.

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West, Sandra A. 1986. ‘‘Measures of Central Tendency for Censored Earnings Data from the Current Population Survey.’’Proceedings of the Section on Business and Economics Statistics: 751– 756. Alexandria, Va.: American Statistical Association.

White, Halbert. 1980. ‘‘A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.’ ’Econometrica 48(4):817– 38.

Figure 3

Wage Dispersion Ratios: June 1981– December 1998

Though the measures of wage dispersion are invariant to a shift in the month-speciŽc mean, the within-job log wage rates are adjusted to make their mean equal to the CPS mean for each month. The growth for the ECI has generally outpaced the growth for the CPS during the sample period. For the earlier subperiod, the average annual growth rates for the ECI and CPS are 4.4 percent and 4.1 percent, respectively. By the end of 1998, the trend actually reversed, with a 3.4 percent growth rate for the CPS and a 3.2 percent for the ECI in the later subperiod, but this is due to particularly strong growth in the CPS for 1998.7_{For March 1990 through the} December 1997, the ECI growth rate exceeded the CPS growth rate, 3.2 percent to 3.1 percent. The trend from the dynamics of the labor market has been to reduce average wage rates during most of the sample period.

It helps to keep this in mind in light of the results in Figure 3, which compares measures of dispersion between the CPS and within-job wage rates. The Žgure shows the ratio of the 90th percentile to the 50th percentile and the ratio of the 50th percen-tile to the 10th percenpercen-tile for the CPS and the within-job wage rates.8 _{The ratios} equal the exponential of the log difference. For the high-wage workers relative to the middle workers, the ratios for the two series stay fairly similar. By the end of between the CPS and within-job wage rates to zero at the break month. The results in Table 1 are similar when the growth parameters from the separate regressions are used.

7. Although the CPS wage rates use the correction for top coding suggested by West (1986), an increase in the topcode value for weekly earnings might explain some of the strong wage growth in 1998. However, the growth is not concentrated in the change from December 1997 to March 1998, when the new topcode would have taken effect.

8. The quantile statistics are calculated using the interpolating procedure, outlined in West (1986). It is the procedure used for the published CPS quantile statistics.

the period, the ratio for the within-job wages is slightly higher, which suggests slightly more dispersion at the higher end. The difference is more substantial at the other end of the distribution, however. According to the CPS wage rates, low-wage workers gained relative to the middle workers beginning in the last few years of the 1980s. In contrast, the ratio has held more or less steady for the within-job wage rates. During the 1990s, wage increases were about the same for workers remaining in stable job situations, regardless of their skill group. The trend from the labor force dynamics has been toward a slight downgrading of jobs. However, workers at the lower end of the distribution appear to have been less adversely affected, which produced a relative gain. By the end of 1998, when the trend appears to have reversed toward an upgrading of jobs, low-wage workers also beneŽted more. Using the stan-dard deviation of the log wage rates rather than the 90–50 and 50–10 ratios also suggests that wage dispersion would have been higher during the 1990s had workers never changed jobs.9

Card and DiNardo (2002) evaluate the most common explanation for the change in wage inequality over the past 25 years—skill-biased technological change. They Žnd it to be a plausible explanation for some aspects of the increase in wage inequal-ity during the early and middle 1980s. However, wage inequalinequal-ity stabilized during the 1990s, and may have even turned down slightly. There has been no obvious slowdown in the adaptation of technology into the workplace. They argue that re-searchers must look in other directions to explain the time pattern of inequality. The stabilization in wage inequality during the 1990s is doubtless a mixture of many intertwined factors, but the results in Figure 3 point to job dynamics as one of them. Opportunities that arose during the extended expansion, either through job-change opportunities within a Žrm or through job opportunities in other Žrms, disproportion-ately aided workers at the bottom of the wage distribution when they took advantage of them. The relative wage rates of workers who remained in their jobs were more stable.

V. Summary

The empirical results in this paper summarize wage growth in the ECI for industry and occupation groups, with parallel results from the CPS. For the 1980s, when the dispersion of wage rates for the U.S. increased dramatically, the CPS and ECI results align closely. More recently, however, when the upward trend in wage dispersion has been less dramatic, wage growth from the ECI does not differ signiŽcantly among the industry/occupation groups. Workers remaining in a job received about the same wage increases regardless of their skill group.

The ECI growth parameters are then incorporated into the CPS wage rates to create a hypothetical wage distribution for workers had they remained in the same job. The measures of wage dispersion for the resulting distribution are higher than for the CPS distribution in the 1990s. Thus, generous wage increases to existing

9. The earnings questions in the CPS were redesigned beginning in the 1994 survey. See Polivka and Rothgeb (1993) for details. The redesign seems to have caused a jump in wage dispersion between 1993 and 1994, which affects both the CPS and within-job wage rates.

low-wage workers did not reduce wage dispersion in the 1990s. Instead, labor force dynamics, such as the creation of and movement into new jobs, caused the decline in wage inequality during this period.

Appendix 1

CPS and ECI Data

The ECI is a survey of jobs within establishments. For each establishment in the survey, a small number of jobs are sampled randomly, usually between four and eight. Because the unit of observation is a job, the microdata equal the average value of compensation per hour among the workers in the job. A job is deŽned by the most detailed classiŽcation recognized by each establishment, so the ECI essentially defers to the establishment to ensure that workers in the job represent the same labor input from month to month.

The CPS and the ECI samples are restricted to workers and jobs in private, non-agricultural industries. To match the ECI, the CPS sample is restricted to wage and salaried workers and excludes workers in private household occupations. The regres-sions use the CPS earnings weights and the ECI sample weights. The weights are normalized to one for each month.

The nine industries are mining; construction; durable manufacturing; nondurable manufacturing; transportation, communication, and public utilities; wholesale trade; retail trade; Žnance, insurance, and real estate; and services. The nine occupations are professional and technical; executive and managerial; sales occupations; adminis-trative support occupations; precision and craft occupations; operators and assem-blers; transportation occupations; handlers and laborers; and service occupations.

For the CPS, the four education categories are less than high school, high school, some college, and at least a college degree. See Frazis and Stewart (1999). The Žve age categories are 16 to 24, 25 to 34, 35 to 44, 45 to 54, and 55 or older. Although the ECI imposes no age restriction for the jobs in its sample, the CPS data are restricted to workers at least 16 years old. The dummy variable for whether a worker is covered by a collective bargaining agreement is not available before 1983, so it is set to zero for all workers in years prior to then. This is arbitrary because the month dummy variables would subsume an additional dummy variable for whether the collective bargaining information is missing.

For years prior to the CPS redesign in 1994, the wage rate in the CPS equals usual hourly earnings for workers paid hourly and usual weekly earnings divided by usual weekly hours for other workers. I use the same procedure for 1994 and subsequent years, although I follow Polivka (1997) for workers who report that their hours vary. I also use her procedure to account for the topcoding of earnings. Details on this procedure are available from the author upon request. Results reported in the paper are similar when I use usual weekly earnings divided by usual weekly hours for all workers, which is generally interpreted as including overtime pay in wage rates.

Workers in the CPS and jobs in the ECI with a wage rate less than $1 per hour or more than $200 per hour in March 1979 dollars are excluded as outliers. The ECI

for wages and salaries for workers in private industries is used as the index for the outlier threshold. For both the CPS and the ECI, the weighted proportion of outliers stays below one percent.

Prior to 1986, the ECI data are only available as averages for the current and previous quarter by month/industry/occupation cells. This presents three complica-tions. First, for each cell, the log difference between the average wage rates for the current month and three months prior replaces for the average log difference between the current and previous wage rates. The regression results do not change much, however, when the same replacement is made for months in which the microdata are available. Second, the sum of the sample weights for each cell is not available. Therefore, the cells’ relative frequencies from the CPS are used. Third, the weighted sum of the squared residuals, the sum of the weights, and the sum of the squared weights for each cell are all needed to calculate the standard errors. Because the residual is assumed homoskedastic across all months, the estimated residual variance from months in which the microdata are available is applied to all months. Further, the sum of the weights and the sum of the squared weights for the cells are assumed to be the same for months in which the microdata are and are not available, so their values from months in which they are available are inated accordingly.

Appendix 2

Estimation Procedures

The wage growth parameters in vectordare estimated by weighted least squares. The variance matrixVis estimated under the assumption of homoskedasticity, al-though the results do not change much when the ECI regressions use a block form of White’s (1980) procedure, which allows for heteroskedasticity and general forms of covariation among jobs from the same establishment in the same month.

The standard deviation among the parameters indis calculated as follows. DeŽne an 81381 matrixHas follows.

(5) H5F1/2_[I

2m(m¢Fm)21_m¢F]

The matrixFis an 81₃81 diagonal matrix with a vector fon its main diagonal;f

gives the weighted frequency for each industry/occupation group, which is calculated using data pooled across all months. The matrixIis an 81 ₃81 identity matrix. The vectorm is an 8131 vector of ones.

DeŽne the Žrst element ofdequal to zero, and deŽne the Žrst row and column ofVequal to zero. The following holds.

(6) E(dˆ¢H¢Hdˆ)₅d¢H¢Hd₁trace(HVH¢)

The Žrst term on the right-hand side of Equation 6 equals the variance among the parameters ind, so the second term on the right-hand side is the adjustment to the variance estimate due to sampling variation. The standard deviation across occupa-tions is calculated using a similar procedure, althoughHis more complicated because the dparameters must Žrst be averaged across industries. The same procedure is used for industries.

Equations 7 and 8 show the speciŽcations for the ECI and CPS used for the calcu-lation of the within-job wage rates. For the ECI in Equation 7, the subscriptjis the index for the subperiods,tj equals three months prior to Žrst current month in the

subperiod, and the indicator function 1[t _.tj] equals one if the current month is

later thantj, zero otherwise.

(7) Dwit5q¢itg1

^

j

1[t.tj] ×x¢itd1vit

For example, the expected change for an industry/occupation group in a month from the subperiodjequals the month’s coefŽcient ingplus the sum of the group’s coefŽ-cients in d1 through dj. Equation 7 uses the accumulation of coefŽcients for the

previous subperiods, rather than a separate coefŽcient for each subperiod, because it makes the mapping to the log-wage speciŽcation easier. Equation 7 translates into a spline function for the log wage rate.

(8) wit5z¢itb1q¢ita1x¢itp1

^

j

1[t.tj] ×(t2tj)×x¢itd1uit

Equation 8 is used for the CPS. The parameters inbare also allowed to differ be-tween the Žrst and second subperiods.

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