The results from the formal decomposition of total variance into between- and within-plant components based upon equations (1) and (2) are reported in Table 1 and Figure 1. Table 1 includes just selected years while Figure 1 depicts the patterns of the components for all years from 1975-92. While the formal decomposition is in terms of levels of hourly wages we are concerned about the possible effects of changes in scale. Therefore, the components in Figure 1 are depicted in terms of coefficients of variation. Continue reading
III. Between-Plant and Within-Plant Components of Wage Dispersion
In this section, we combine data from household and establishment surveys to decompose the variance of hourly manufacturing wages into between-plant and within-plant components. The decomposition methodology is from Davis and Haltiwanger (1991, 1996). The analysis in this section extends their results over a longer time period and incorporates nonproduction workers who work in auxiliary establishments such as central administrative offices, research facilities, and warehouses. The variance of hourly wages across hours worked in the manufacturing sector can be written as:
where a denotes production workers’ share of hours worked, Vp denotes the variance of wages across hours worked by production workers, V” denotes the variance of wages across hours worked by nonproduction workers, Wp is the hours-weighted mean of the production worker wage, and W” is the hours-weighted mean of the nonproduction worker wage. Equation (1) expresses the total variance of hourly wages as the hours-weighted sum of the variances of production and nonproduction workers along with a term reflecting the contribution of differences in the mean wages across production and nonproduction workers. For each worker type, the variance can be further decomposed as:
where V^p represents the between plant component and V^p the within plant component for worker type j.
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To estimate the components of the decompositions in (1) and (2) for the manufacturing sector we proceed as follows. We utilize household data from the 1975 through 1993 March Current Population Survey (CPS) and establishment data from the Longitudinal Research Database (LRD). From the individual-level wage observations in the CPS files, we calculate α, V, Vp, Vn, Wp, W” for all workers employed in manufacturing in each of the years under consideration (1975-1992). We also generate the production and nonproduction variances at the two-digit SIC industry level. From the plant-level observations in the LRD, we calculate the between-plant component for each worker type for each of the corresponding years at the two-digit level. For each worker type, we generate the within-plant component in equation (2) by taking the difference between the total variance calculated from the CPS and the between-plant variance calculated from the LRD at the two-digit level. Appropriately aggregating the between and within plant components across industries yields the decomposition at the total manufacturing level. As part of this aggregation, we decompose the overall between-plant component for each worker type into a between-plant, within-industry component and a between-industry component.
Kremer and Maskin (1996) also provide a theoretical structure for our empirical analysis. Their model can account for the simultaneous existence of increased wage inequality and increased segregation of workers of different skill levels into different plants. These forces are set in motion by changes in the skill distribution, which can be due to a skill-biased technical change, but need not be. The main features of their model are imperfect substitution among workers of different skills, complementary tasks within a plant, differences in worker skill effects which vary by task, and an exogenous distribution of worker skills. Intuitively, there are two competing forces at work in determining the equilibrium matching patterns at plants. The asymmetry of tasks in the production function favors cross-matching (less segregation) but the complementarity between tasks favors self-matching (more segregation). Unequally skilled workers will be cross-matched up to the point in which the differences in skills is so great that the second effect overwhelms the first and the plant moves to self-matching. With a diffuse skill distribution, an increase in the mean skill-level exacerbates wage inequality across plants. Continue reading
II Review of Theoretical Literature
The two theoretical papers that form the basis for our analysis are the papers by Caselli (1999) and Kremer and Maskin (1996). In this section we briefly outline the two models and present the most relevant predictions of the models. Caselli (1999) models the effect of a technical revolution on the dispersion of wages and productivity. In the Caselli model a technology is a matching of workers of type i who have the appropriate set of skills to operate machines of type I. An important feature of this technology assumption for our purposes is that workers are completely segregated by skill across plants. Continue reading