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Michael Keane is affiliated with the University of Minnesota and the Federal Reserve Bank of Minneapolis. Eswar Prasad is an economist in the North American Division of the Western Hemisphere Department. We would like to thank Finn Kydland for helpful discussions and Ana Stevens for help in preparing the manuscript. The views expressed in this paper do not necessarily reflect the views of the University of Minnesota, the Federal Reserve Bank of Minneapolis, or the International Monetary Fund.
The magnitude of this bias in measuring the cyclicality of the average real wage may be substantial, as shown by Keane, Moffitt and Runkle (1988).
The standard measure of labor input is aggregate hours worked, which is the product of the number of persons employed and the average weekly hours worked (or whatever the appropriate frequency).
At the industry level, we find that the wage premium for skills is strongly procyclical in durable and nondurable manufacturing and is countercyclical in retail trade and services. In durable manufacturing, workers with a college degree have much more procyclical variation in wages than other workers. Educated workers in durable manufacturing have relatively less procyclical variation in employment probabilities and are actually found to have countercyclical variation in weekly hours.
Notice that firm-specific and industry-specific capital are not necessarily identical. However, when issues of labor reallocation and wage dispersion etc. are examined in the context of business cycles, the typical unit of analysis is the industry (for example, see Lilien (1982)). This is partly driven by the fact that industry level data contain less measurement error. Also, the concept of a ‘firm’ is much less well defined than that of an industry. Given these facts and the constraints of our dataset, we will refer to industry-specific and firm-specific capital interchangeably. Alternatively, we could use the notion of a representative firm in each industry as the unit of our analysis.
Oi (1962) uses a similar notion of fixed hiring costs to model skilled labor as a quasi-fixed factor input.
Further, if a firm received the entire return from a worker’s specific capital, it would be even more willing to assure him or her a relatively smooth wage in order to prevent a separation and the consequent loss of such specific capital. The precise extent of wage and employment smoothing would depend on the degree of the firm’s risk-aversion, the cost of specific capital investment, the persistence of the shock etc.
This argument implicitly assumes that temporary and permanent separations between a firm and a worker are equivalent in that they cause specific capital to depreciate fully. This is the limiting case of a more general argument that would go through if there was a sufficiently large depreciation in specific capital resulting from a temporary separation.
Length of tenure is also a good measure of the quality of the match between a worker and a firm. Given the uncertainty inherent in job-matching, workers and firms would both be reluctant to terminate a good match when faced with a temporary decline in demand or productivity. For our purposes, the quality of a job match may be considered as part of a worker’s specific capital.
Our results were not significantly affected by the choice of the business cycle indicator. See the discussion in the next section.
Industry-specific fixed effects are a potential problem only in the case of workers switching industries over the sample period. Workers who stay in one industry over the entire sample period would have their industry-specific fixed effects eliminated by the transformation described in (3).
It might appear, from the specification in (2), that individual fixed effects could be eliminated by first-differencing the data. However, such a procedure may exacerbate this selectivity bias if there were any missing data, except under a set of restrictive conditions. This is because differencing would require selecting only those pairwise adjacent periods for both of which an individual has an observed wage. See Keane et al. (1988) pp. 1,238-44 for a detailed discussion.
Estimating a single, multinomial model with selection corrections would require sector-specific regressors in order to identify cross-correlations among the error terms in the choice equations. We do not have such regressors in our data set. See Keane (1990) on this.
In the fixed effects selection model, estimates of the choice equation fixed effects are inconsistent for small T. Monte-Carlo experiments by Heckman (1981) show that this inconsistency is small for T>8. In our data set, T is on average 6 (with a maximum value of 12), indicating that inconsistency is a potential problem. However, the estimated ρ in the model with fixed effects in both the wage and employment equations always went to 1 or -1. Hence, the results we will report are from a model with fixed effects in the wage equation alone. This obviates the problem of inconsistency of the estimated fixed effects in the choice equation. Besides, consistent estimation of the choice equation parameters is not important for our main results. Further, in our estimates reported below, we obtain values of ρ close to zero. Hence, any transfer of inconsistency from the choice equation to the wage equation would be negligible.
An alternative two-stage procedure developed by Heckman (1979) yields estimates that are consistent but not efficient. This motivates our use of full-information maximum likelihood.
Keane et al (1988) pp. 1,245-46 discuss the other sorts of bias that may result from using annual survey data on wage income rather than the point-in-time measure used here.
For the survey years in which both of these hours variables were available, the correlation between them was about 0.6. About 45 percent of the observations for the HOURS variable used in this study lie in the range of thirty seven to forty hours a week.
In this and all the tables that follow, we run separate regressions for each of the interaction terms. We do this to compare the effects of different proxies for human capital. Further, it is instructive (and much less tedious) to examine and interpret the magnitude of fixed effects and selection corrections for each of the human capital variables separately.
TENURE was not used as a regressor in the employment choice equations in table 1. The estimated equations in that table are essentially reduced form equations for employment choice and, obviously, TENURE would be endogenous in the choice equation.
The URATE coefficient is an estimate of the percentage change in weekly hours for workers without a degree, associated with a one percentage point rise in the unemployment rate. For workers with a degree, this is given by the sum of the coefficients on URATE and URATE*DEGREE.
The mean value of the DEGREE variable in our sample is 0.23. Multiplying this by the coefficient on URATE*DEGREE and adding the product to the URATE coefficient yields an estimate of the percentage change in average weekly hours associated with a one percentage point increase in the unemployment rate (.23*.0082 - .0061 = -.0042).
For the average wage measure from aggregate data to be countercyclically biased, it is sufficient that the interaction coefficient in the hours regression be significantly positive.
Note that 23 percent of the observations in our sample have a degree. Weekly hours are a cyclical for workers without a degree and, for workers without a degree, hours decline by 0.6 percent when the unemployment rate goes up by one percentage point. Thus, when the unemployment rate goes up, for instance, by 5 percent, uneducated workers face a 3 percent decline in hours. Assume that a college degree yields a wage premium of 50 percent (i.e. workers with a degree are 50 percent more productive). Then, after controlling for employment variation, an unweighted total hours measure would overstate the decline in quality-corrected hours (and, thereby, lead us to understate the decline in mean offer wages) by less than a quarter of a percent.
When unemployment goes up by one percentage point and hours fall by 0.4 percent, the reduction in total hours is roughly 1.4 percent. Hence, it can be inferred that the decline in hours accounts for about 30 percent (0.4/1.4) of the fall in total hours.
Using postwar quarterly data for the U.S., Hansen (1985) examined the following decomposition:
where Ht is aggregate hours worked, ht is average hours worked, and Nt is the number of persons employed, with all variables expressed as deviations from trend. He found that 55X of the variance in Ht was due to variance in Nt and only 20% was attributable to variation in ht, with the remainder due to the covariance term.
Panels containing selection corrected fixed effects estimates do not report estimates from the probit employment choice equations that were estimated jointly with the wage equations. The full effect of changes in the aggregate unemployment rate on unemployment probabilities must be read off from the OLS employment probability models in table 1.
The coefficient on URATE measures the percentage change in the average real wage, for workers without a degree, associated with a one percentage point rise in the aggregate unemployment rate. For example, a coefficient of -.0050 implies that a one percentage point increase in the aggregate unemployment rate causes a 0.5 percent decline in the real wage for unskilled workers (in the aggregate or in a particular industry, as the case may be). A positive coefficient on URATE, on the other hand, implies a countercyclical unskilled wage, i.e., an increase in the unskilled wage when the unemployment rate rises.
The bias in the OLS URATE and URATE*DEGREE coefficients offset each other to some extent. At the mean of the data, the OLS estimate of overall wage cyclicality is weakly countercyclically biased.
The variable URATE trends upward over our sample period. Hence, workers who take longer to get a degree and enter our sample towards the end have larger mean URATE*DEGREE values. Such workers also tend to have lower wages. This leads to a downward bias in the OLS interaction coefficient. The fixed effects estimates obviate this problem by considering only the effects of deviations of variables from their individual means.
This implies that the absolute offer wage differential is, in fact, procyclical. We focus on relative wage differentials since the emphasis of this paper is on the relative variability of wages across skill levels.
Industry-specific individual fixed effects are a potential source of bias only if (i) they are correlated with the regressors in the model and (ii) individuals in the sample switch industries. Employing the same dataset as in this paper, Jovanovic and Moffitt (1990) find that gross flows across sectors average as much as 17.2 percent of the sample between two-year survey waves. Moreover, their three-sector classification probably understates the gross flows relative to the finer industry classification used in this paper. Such high mobility is partly attributable to the young age of the sample.
Fixed effects models estimated separately for each industry yielded point estimates close to the SCFE industry estimates. Rather than present yet another set of estimates, we chose to report only the SCFE industry estimates since they correct for all the sources of bias that we discussed earlier.
As noted earlier, TENURE would be endogenous in the employment choice equation. Hence, we are unable to estimate the selection corrected fixed effects model using this variable.
The cyclicality of the average real wage is given by the sum of (i) the coefficient on URATE and (ii) the URATE*EXPERIENCE coefficient multiplied by the mean level of EXPERIENCE in the sample (7.9 for all workers). In the four industries mentioned here, the URATE coefficient is positive and more than 12 times the magnitude of the respective URATE*EXPERIENCE coefficient (which is negative in all four cases).
These estimates indicate that the average offer wage in our sample is weakly procyclical (.0122 - .0026*7.9 = -.0083).
For instance, using data from the Panel Study of Income Dynamics, Kydland and Prescott (1988) estimate average real wages to be strongly procyclical after adjusting for observed measures of worker quality.
In this context, it would also be of interest to examine the role of noncompetitive factors such as union membership. Unfortunately, except in a couple of years, our data set does not have a variable that would enable us to distinguish between union and nonunion workers.