Heterogeneous workers and occupations: inequality, unemployment, and crowding out.

• Author: Khalifa, Sherif

1. Introduction

   This article attempts to determine the factors behind the cyclical behavior of the skill premium. Previous studies attempted to explain the observation that the skill premium is uncorrelated with contemporaneous output and lags the business cycle. However, these studies encountered several problems that rendered this observation a puzzle remaining to be properly addressed. To this purpose, the article derives a set of stylized facts that demonstrate not only the cyclical behavior of the skill premium but also that of other variables that capture the cyclical allocation of labor input in a labor market with heterogeneous agents across educational levels. These additional observations reflect a lagged cyclical upgrading of jobs by the college educated, or a lagged cyclical increase in their labor input from jobs that do not require college education to ones that do. This causes the gap between the wage of the high educated and that of the low educated to widen with a lag and accordingly can provide a possible explanation to the lagged procyclical skill premium. This intuition is used to develop a mode! that is capable of reproducing the observation of interest.

   Using the Outgoing Rotation Group of the Current Population Survey for the period from 1979 to 2004, the participants are divided into those who are employed and those who are unemployed. The two groups are further divided into those who are high and low educated, where the former are those with at least some college education. The employed types are further divided into those working in complex and in simple occupations, where the former are those jobs that require at least some college education. Therefore, a monthly data set is compiled including measures of the skill premium, the total hours of the high educated in complex and in simple occupations, the total hours of the low educated in simple occupations, the unemployment ratios of the high and the low educated, and a measure of the crowding out of the low educated by the high educated in occupying simple jobs. The observations suggest that the skill premium is uncorrelated with contemporaneous output and lags the business cycle. In addition, an economic expansion is accompanied contemporaneously by an increase in the total hours of all labor types employed in simple occupations, followed with a lag by an increase in the total hours of those employed in complex occupations and a decrease in the crowding-out effect. These observations reflect a possible lagged cyclical upgrading of jobs by the high educated through increasing their level of employment or their hours of work in complex occupations. This causes the gap between their wage and that of the low educated to widen and accordingly can explain the lagged procyclical skill premium.

   The article develops a model to identify the underlying market interactions that are critical in generating the observed behavior along the lines of this intuition. These interactions are captured in a dynamic stochastic general equilibrium model that features search frictions. The households are divided into those high and low educated, and firms post two types of vacancies: the complex, which can be matched with the high educated, and the simple, which can be matched with both the high and the low educated. The high educated in simple occupations are allowed to search on the job for a complex occupation. An aggregate technological shock induces firms to increase their posting of simple and complex vacancies. As complex vacancies are more costly to create compared to simple ones, the increase in the former lags that of the latter. The lagged increase in the number of complex vacancies is accompanied by an increase in on-the-job search intensity. As the high educated in simple occupations increase the portion of time spent to search for a complex vacancy, their hours of work decline. On the other hand, because of the lagged increase in the employment and hours of work of the high educated in complex occupations, the total hours of this type increase. The wage of the high educated is a weighted average of the wage of those employed in complex and in simple occupations. The weights are given by the total hours in these occupations. Accordingly, these two factors cause the weight of the hours of work of the high educated in complex occupations to increase and the weighted average wage of the high educated to increase as well. This causes the gap between the wage of the high educated and that of the low educated to increase with a lag, causing the skill premium to increase with a lag as well.

   This article adopts a different approach compared to previous studies that focused on the features of capital skill complementarity and variable utilization of capital to explain the cyclical pattern of the skill premium. For instance, Lindquist (2004) argued that capital skill complementarity allows the model to reproduce the cyclical pattern of the skill premium. However, Young (2003) argued that the success of the model in Lindquist (2004) is attributed to its abstraction from variable utilization of capital, whose introduction implies strong procyclical skill premium. Another criticism to the Lindquist (2004) framework is its inability to replicate the cyclical behavior of the underlying wages. Both Lindquist (2004) and Young (2003) argued that the Walrasian aspects of the model cause the wages, which are equal to the marginal product of labor, to be strongly correlated with output. They suggested the introduction of implicit contracts to resolve this problem. Pourpourides (2007) developed a model with implicit contracts and demonstrated that the feature of variable utilization of capital, rather than capital skill complementarity, is essential in reproducing the observation that the skill premium is uncorrelated with contemporaneous output. The model, however, cannot explain the lagged procyclicality of the premium.

   The remainder of the article is organized as follows: Section 2 presents the stylized facts, section 3 develops the model, section 4 includes the calibration, section 5 analyzes the results, and section 6 concludes. Data and derivations can be found in the Appendix.

2. Observations

   To derive the business cycle patterns of selected labor market variables that reflect agent heterogeneity in educational levels and the educational requirements of jobs they are occupying, a time series is compiled from the Outgoing Rotation Group of the Current Population Survey. (1) The survey provides monthly information from January 1979 until December 2004 on the participants' employment status, level of education, type of occupation, weekly earnings, and weekly hours of work.

   To compile a time series out of this survey, the labor market participants in each monthly file are divided into those employed and those unemployed. Each group is further divided into those high and low educated, where the former are those who obtained at least some college education. Each of the two employed groups is further divided into those working in a complex occupation and those working in a simple occupation, where the former is a job that requires at least some college education. This provides four employed and two unemployed types: the high educated employed in a complex occupation, the high educated employed in a simple occupation, the high educated unemployed, the low educated employed in a complex occupation, the low educated employed in a simple occupation, and the low educated unemployed. The low educated employed in a complex occupation are dropped from the sample because of their insignificant proportion out of all the low educated and out of all those employed in complex occupations. For the remainder of the employed types, weighted average hourly wages are calculated as the ratio of the weighted average weekly earnings to the weighted average weekly hours for each type. Using the hourly wages of the three employed types, the skill premium is defined as the ratio of the weighted average wage of the two high educated types to that of the low educated in simple occupations. Levels of employment are calculated for the three employed types, and levels of unemployment are calculated for the two unemployed types. Using the weighted average weekly hours of work of each group and the level of employment, the total hours of each group is derived. The proportion of each type out of the total sample is also calculated. Finally, a crowding-out variable is defined as the proportion of the total hours of the high educated among the total hours of all those employed in simple occupations, such that its increase reflects an increase in the crowding-out process of the low educated by the high educated in occupying this type of job.

   Therefore, the variables compiled and used in the analysis are (i) the skill premium, (ii) the total hours of the high educated employed in complex occupations, (iii) the total hours of the high educated employed in simple occupations, (iv) the total hours of the low educated employed in simple occupations, (v) the proportion of the high educated unemployed, (vi) the proportion of the low educated unemployed, and (vii) the crowding-out effect. This monthly time series are transformed into quarterly data by taking three month averages.

   The cross-correlation coefficients between real gross domestic product (GDP) in period t and each of these variables in lag and lead periods are displayed in Table 5. These patterns demonstrate that the skill premium has an insignificant correlation coefficient with contemporaneous output but is procyclical with a lag where the fourth lagged cross-correlation coefficient is statistically significant with a p-value of 0.0049. In addition, the total hours of the high educated in complex occupations is procyclical and lags the cycle by three quarters, as the cross-correlation coefficient with output reaches 0.4147, which...