Firming Up Inequality (2)

David J Price, University of Toronto

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.
We also find that in these mega firms, the top 50 managers have seen robust earnings increases. For example, the 50th highest-paid manager in mega firms—who would typically be a senior executive—has, on average, seen a 47% rise in earnings between 1981 and 2013. The top-paid employee (presumably the chief executive officer) has seen earnings rise by 137% over the same period. However, because there are few of these top-50 employees relative to the size of total employment at these mega firms (about 35,000 of them versus about 20 million total employees in these firms), we find that rising top executive earnings explain little of the increase in the variance in overall earnings.
For example, the t op 50 employees account for about 3% of the total increase i n t he within-firm dispersion of earnings from 1981 to 2013 at mega firms, whereas the t op five employees account for
less than 1% of the increase. Turning to smaller firms, we find that top paid employees have seen their earnings rise more in line with the rise in the average earnings at their firm. Consequently,
the numerical contribution of taxable earnings of top executives to the rise i n overall inequality i n earnings during this period appears limited.
To summarize, our findings imply that the large rise in earnings inequality i n t he United States can be formally decomposed into three equally important components—a rise in the sorting of
higher-paid workers into higher-paying firms, a rise in segregation of higher-paid workers to the same firms, and a rise in earnings inequality within firms. The rise in within-firm inequality was largely driven by mega firms, which saw a four times larger rise in within-firm inequality relative to all other firms, while accounting f or only a quarter of total employment i n t he economy.
These findings highlight several potential mechanisms underlying rising earnings inequality. For example, it has long been hypothesized that persistent differences in firm pay premiums reflect rent-sharing (e.g., Dickens and Katz 1987; Katz and Summers 1989; AKM). Our finding of increasing sorting suggests that the distribution of rents may have become increasingly skewed, with an increasing share going to high-wage workers.
A complementary explanation is the rise in domestic outsourcing and temporary work (e.g., Abraham and Taylor 1996; Segal and Sullivan 1997; Weil 2014). Indeed, Katz and Krueger (forthcoming) find that contingent workers, such as independent contractors and freelancers, make up an increasing part of the workforce.
Similarly, Goldschmidt and Schmieder (2017) show that domestic outsourcing in Germany can explain a rise in sorting and a rise in inequality. These alternative work arrangements could help explain rising segregation and sorting, as a previously diverse workforce splits into a homogeneous well-paying lead firm and a range of homogeneous lower-paying suppliers and service providers.
Our results are consistent with a substantial literature documenting that technological changes have increased inequality by shifting the demand for different skill groups (e.g., Acemoglu and Autor 2011 for a survey). Rising returns to skill, even with a stable distribution of skill across firms, could mechanically lead to increased sorting and segregation if more skilled employees tend to be clustered together in typically higher-paying firms. Then rising returns to skill would cause top workers to have even higher-paid coworkers (which we would see as part of higher segregation) and top firms to have even higher-paid employees (which we would see as part of sorting). Although this point is relatively straightforward, it is an important one in light of the empirical evidence on rising returns to skill during this period, so we discuss it further in Section V.A. Finally, the reduction in earnings for low-wage workers within large firms that we document corroborates the view that low-wage workers may have experienced a decline in access to high-paying jobs for institutional reasons, such as a decline in unionization or changes in company culture.
Our findings complement a growing body of work that documents that the variance of firm earnings or wages explains an increasing share of total inequality in a range of countries.
In the United States, Davis and Haltiwanger (1991) were among the first to draw attention to the fact that rising inequality among workers was closely mirrored in rising inequality among establishments. However, these papers lacked data on wages within firms, which limited the scope of their analysis to between-firm data. This finding was confirmed by Barth et al. (2016), who also report that a large share (about two-thirds in their analysis) of the rise in earnings inequality can be attributed to the rise in between-establishment inequality, concentrating on the period 1992 to 2007, for which they have both worker and establishment data for a subset of U.S. states. Our matched worker-firm data include information back to the 1970s and after 2007 for all workers in the United States. As a result, we can consistently examine the contribution of firms throughout the entire earnings distribution—including for the top end of the distribution, which has attracted a lot of attention—for the whole period of key changes in inequality.

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