Firming Up Inequality (1)

David J Price, University of Toronto

The dramatic rise in U.S. earnings inequality from the 1970s to today has been well documented. An enormous body of theoretical and empirical research has been conducted over the past two decades in an attempt to understand the causes of these trends. Until recently, the analysis of the role of employers has been largely absent from this literature, chiefly because of the lack of a comprehensive, matched employer-employee data set in the United States covering the period of rising inequality.
A long literature in economics has recognized that some firms pay workers with similar skills more than others . Controlling for differences in the composition of observed and unobserved worker characteristics between firms, an increasing number of studies have shown that these differences in firm pay premiums contribute substantially to the distribution of earnings.
Important questions are to what extent the differences in firm pay premiums have widened and to what extent this widening can explain the observed rise in earnings inequality. In a recent paper, Card, Heining, and Kline (2013) show that a rise in the dispersion of firm pay premiums has contributed substantially to recent increases in wage inequality in Germany. They also show that inequality rose in equal measure because of large changes in worker composition—high-wage workers became increasingly likely to work in high-wage firms (i.e., sorting increased), and high-wage workers became increasingly likely to work with each other (i.e., segregation rose).
Similar phenomena of changes in firm pay premiums and worker composition could explain some of the shifts in inequality in the United States, which has experienced a stronger and more persistent increase in inequality than have Germany and many other continental European countries. Indeed, as we will discuss, many of the mechanisms considered in the U.S. literature on inequality have potential implications for the contribution of firms and worker sorting to inequality, but so far these have not been evaluated. The firm dimension is also particularly interesting because it may help us better understand the rise in earnings at the very top, which many attribute to an increase in executive compensation, a phenomenon contributing to rising inequality within firms.
In this article, we study the contribution of firms and the role of worker composition between firms in the rise in earnings inequality in the United States using a longitudinal data set covering workers and firms for the entire U.S. labor market from 1978 to 2013. Our data set has several key advantages for studying firms and inequality: it is the only U.S. data set covering 100% of workers and firms for the entire period of the rise in inequality, it has uncapped W-2 earnings capturing a large share of earnings even at the very top, it has no lower earnings limit, and it has information on firms rather than establishments. Using this data set, in a first step we analyze the overall contribution of a rise in the variance of average earnings between firms in explaining the evolution of U.S. earnings inequality from 1978 to today.
Our first main result is that the rise in the dispersion between firms in firm average annual earnings accounts for the majority of the increase in total earnings inequality. We show that the 19 log point increase in total variance between 1981 and 2013 is driven by a 13-point increase in the between-firm component and a 6-point increase within firms. This between-firm component captures all three components of firm-related changes in inequality—changes in firm pay premiums, changes in worker sorting, and changes in worker segregation. The importance of increases in between-firm inequality in explaining pay is also seen in very fine industry, location, and demographic subsets of the economy and is robust to different measures of inequality. Using a counterfactual analysis, we find that changes in the distribution of firm average earnings explain almost all of the rise in inequality below the 80th percentile, while changes in the within-firm distribution of earnings explain some of the increase in inequality above that point.
Three factors could account for the rising variance of firm average earnings. First, the dispersion of firm pay premiums could increase; that is, high-paying firms would pay more, adjusting for worker composition, and the opposite would be true for low-paying firms. (We infer the dispersion of firm-wage premiums by measuring the variance of firm fixed effects, as described later.) Second, there could be a rise in the covariance between high-earnings workers and high-pay firms (which we refer to as “sorting”). Third, similar workers could be increasingly likely to work together (which we refer to as “segregation”). Although a rise in segregation by itself does not raise earnings inequality (because of a corresponding reduction in within-firm inequality), it leads to a higher contribution of firms in explaining earnings dispersion in a descriptive sense and could reflect important underlying economic forces.
To distinguish among these factors, we follow the modeling approach of Abowd, Kramarz, and Margolis (1999) (AKM) and Card, Heining, and Kline (2013) (CHK) to estimate unobserved permanent worker and firm components of each worker’s annual earnings. With this approach, we can decompose rising overall inequality into the portion due to the changing dispersion of worker effects, the changing dispersion of firm effects, and the changing covariance between the two.2 Based on this approach, our second main finding is that the rising variance of worker effects—potentially due to rising returns to skill—explains 68% of rising inequality, while the rising covariance between worker and firm effects explains 35%. In contrast, the third component, the variance of firm effects, declined slightly during this time, making a small, negative contribution to rising inequality.
Although this last finding may appear surprising in light of our first result—that the rising dispersion of firm-wide average earnings explains more than two-thirds of the rise in the variance of total earnings—these results are perfectly consistent, which is our third main finding. Using the estimated worker and firm fixed effects, we show that the rise in between-firm inequality can be completely explained by changes in the composition of workers between firms. Increases in sorting (a rise in the covariance between worker and firm effects) and segregation (a rise in the variance of average worker fixed effects at a firm) explain the entire increase in between-firm inequality in our data. The increased variance in individual fixed effects can itself lead to increases in such sorting and segregation; we show that rising returns to skill, absent any firm-level changes, could account for about a third of rising segregation but almost none of the increase in sorting.
Our fourth result is that of the 31% of the increase in the total variance of annual earnings that occurs within firms, most comes from large firms. The increase in the total variance of log earnings in firms with 10,000+ employees—which we call “mega firms,” a group comprising about 750 firms employing about 23% of U.S. workers in 2013—is 58% between firms and 42% within firms. In contrast, the change in the variance of log earnings in firms with 20 to 1,000 workers is 92% between and 8% within firms. This rise in within-firm inequality in mega firms comes from substantial changes at both the bottom and the top of the within-firm earnings distribution. For example, between 1981 and 2013, median workers at mega firms saw their earnings fall by an average of 7%, those at the 10th percentile saw an average drop of 17%, and those at the 90th percentile saw an average rise of 11%. Overall, we calculate that the bottom half of the distribution is responsible for 35% of the rise in within-firm dispersion from 1981 to 2013 in mega firms. Changes in the 90th percentile and above explain 46% of the rise in dispersion.

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