Ranking Firms Using Revealed Preference∗

Firms account for a substantial share of earnings inequality. Although the standard explanation for why is that search frictions support an equilibrium with rents, this paper finds that compensating differentials are at least as important. To reach this finding, this paper develops a structural search model and estimates it on U.S. administrative data with 1.5 million firms and 100 million workers. The model analyzes the revealed preference information contained in how workers move between firms. Compensating differentials are revealed when workers systematically move to lower-paying firms, while rents are revealed when workers systematically move to higher-paying firms. With the number of parameters proportional to the number of firms (1.5 million), standard estimation approaches are infeasible. The paper develops an estimation approach that is feasible for data on this scale. The approach uses tools from numerical linear algebra to measure central tendency of worker flows, which is closely related to the ranking of firms revealed by workers’ choices. ∗[email protected]. Thanks to Matthew D. Shapiro, John Bound, Daniel Ackerberg and Josh Hausman for patient advising and support. Thanks also to John Abowd, Audra Bowlus, Charles Brown, Jediphi Cabal, Varanya Chaubey, Tim Conley, Cynthia Doniger, Matthew Fiedler, Eric French, Paul Goldsmith-Pinkham, Henry Hyatt, Patrick Kline, Pawel Krolikowski, Margaret Levenstein, Kristin McCue, Erika McEntarfer, Andreas Mueller, Michael Mueller-Smith, Justin Wolfers, Mary Wootters, Eric Zwick and seminar and conference participants at University of Michigan, U.S. Census Bureau, UWO/MSU/UM Labo(u)r Day, European Search and Matching Conference, Barcelona GSE Summer Forum: Search, Matching and Sorting, SOLE/EALE, Census RDC Conference and the Chicago Fed for helpful comments and conversations. Thanks to Kristin McCue for help with the disclosure process. Thanks to David Gleich for making Matlab BGL publicly available. This research uses data from the U.S. Census Bureau’s Longitudinal Employer Household Dynamics Program, which was partially supported by the following National Science Foundation Grants SES-9978093, SES-0339191 and ITR-0427889; National Institute on Aging Grant AG018854; and grants from the Alfred P. Sloan Foundation. This research was supported in part by an NICHD training grant to the Population Studies Center at the University of Michigan (T32 HD007339) and the Robert V. Roosa Dissertation Fellowship. This research was also supported by a grant from the Sloan Foundation to the University of Michigan and by the Michigan Node of the NSF-Census Research Data Network (NSF-SES 1131500). Any opinions and conclusions expressed herein are those of the author and do not necessarily represent the views of the the Federal Reserve Bank of Chicago, the Federal Reserve System, or the U.S. Census Bureau. All results have been reviewed to ensure no confidential information is disclosed. Firms play a central role in explaining worker earnings. Conditional on person fixed effects, firms account for over 20% of the variance of worker earnings (e.g., Abowd, Kramarz, and Margolis (1999) and Card, Heining, and Kline (2013)).1 But there is little work asking why firms play such a central role. There are two main explanations that differ in whether high-paying firms are high-value firms: rents and compensating differentials. Rents is the leading explanation in the literature (e.g., Postel-Vinay and Robin (2002)). In the rents explanation, frictions prevent workers from bidding away the rents at high-paying firms. In this explanation, workers are lucky to end up at high-paying firms. As a result, high-paying firms are high-value firms. In contrast, in the compensating differentials explanation (e.g., Rosen (1986)), firms differ both in how much they pay and in nonpay characteristics. In this explanation, higher pay compensates for variation in unpleasant nonpay characteristics. As a result, high-paying firms are not high-value firms. Thus, measuring the relative importance of rents and compensating differentials means figuring out whether high-paying firms are high-value firms. To distinguish between high-paying and high-value firms, this paper estimates the value of working at a firm without using information in pay. Specifically, I use information in quantities. To do so, I exploit the revealed preference idea embedded in search models that workers move to firms with higher value. Using U.S. matched employer-employee data with 1.5 million firms, I map the 1.5 million by 1.5 million matrix of worker flows across firms into the value of working at each firm. By comparing the firm-level values to firm-level pay, I find that both rents and compensating differentials explanations are operative, but compensating differentials are more important. This finding has four (closely related) implications. First it shows that in many cases the conventional interpretation of high-paying firms as “good” firms is not warranted. Second, it contrasts with the conventional wisdom that compensating differentials are unimportant in explaining the variance of worker earnings. Third, it resolves a puzzle that benchmark search models are unable to reproduce the extent of earnings dispersion while also yielding plausible values of nonemployment. Fourth, the distribution of compensating differentials across firms means that the variance of earnings is larger than it would be if all jobs were equally pleasant. In the first part of the paper, I write down a simple model of the labor market that contains both the rents explanation and the compensating differentials explanation and develop tools to estimate it using only quantity information. The model is a benchmark partial equilibrium utility-posting model in the spirit of Burdett and Mortensen (1998). The nonstandard ingredients in the model are first, that firms post a utility offer that consists of both earnings and a nonpecuniary bundle and second, that workers receive idiosyncratic utility draws (taste shocks) each period. On the one hand, the rents explanation is contained in the model because there is the possibility of equilibrium See also Andersson et al. (2012), Barth et al. (2014), and Song et al. (2015) for analyses of the role of employers and firms in the growth of earnings inequality in the U.S. In this paper, I use the word firm and employer interchangeably.