Ranking Firms Using Revealed Preference Ranking Firms Using Revealed Preference∗

This paper estimates workers’ preferences for firms by studying the structure of employer-toemployer transitions in U.S. administrative data. The paper uses a tool from numerical linear algebra to measure the central tendency of worker flows, which is closely related to the ranking of firms revealed by workers’ choices. There is evidence for compensating differential when workers systematically move to lower-paying firms in a way that cannot be accounted for by layoffs or differences in recruiting intensity. The estimates suggest that compensating differentials account for over half of the firm component of the variance of earnings. ∗[email protected]. An earlier version of this paper was the first chapter of my dissertation at the University of Michigan: thanks to Matthew D. Shapiro, John Bound, Daniel Ackerberg and Josh Hausman for patient advising and support. Thanks also to Larry Katz, anonymous referees, John Abowd, Audra Bowlus, Charles Brown, Jediphi Cabal, Varanya Chaubey, Raj Chetty, Tim Conley, Cynthia Doniger, Matthew Fiedler, Eric French, Matt Gentzkow, Paul Goldsmith-Pinkham, Henry Hyatt, Gregor Jarosch, Patrick Kline, Pawel Krolikowski, Margaret Levenstein, Ilse Lindenlaub, Kristin McCue, Erika McEntarfer, Andreas Mueller, Michael Mueller-Smith, Matt Notowidigdo, Luigi Pistaferri, Giovanni Righi, Justin Wolfers, Mary Wootters, Eric Zwick and numerous seminar and conference participants for helpful comments and conversations. Thanks to Giovanni Righi for research assistance, Kristin McCue for help with the disclosure process, and 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 ITR0427889; 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 the CenHRS project, funded by a Sloan Foundation grant to the University of Michigan, and by the Michigan Node of the NSF-Census Research Network (NSF SES 1131500). Work on this paper took place at the Michigan, Chicago and Stanford Federal Statistical Research Data Centers. Part of the work on this paper was completed while I was employed by the Federal Reserve Bank of Chicago. Any opinions and conclusions expressed herein are those of the author and do not necessarily represent the views of 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. Dating back to at least Smith (1776/2003, Book 1, Chapter 10) (see also Rosen (1986)), economists have argued that differences in the nonpay characteristics of jobs explain some of earnings inequality. To find evidence for these compensating differentials, the literature has typically taken a bottom-up, hedonic approach. In the classic hedonic approach, the researcher considers a cross-sectional regression of earnings on one (or a few) nonpay characteristics and interprets the coefficient on each nonpay characteristic as the market price of that characteristic. For stark case studies such as fatality risk or whether or not a PhD scientist has control over their research agenda, this approach has identified compensating differentials.1 But these findings are typically viewed as somewhat special leading to the conclusion that compensating differentials are not relevant for understanding the structure of earnings.2 This conclusion is potentially unwarranted because the hedonic approach can lead to an incomplete picture of the importance of compensating differentials for at least two reasons. First, it assumes that a researcher knows—and can measure—all the nonpay characteristics that workers value. Even among the characteristics a researcher can measure, if the unobserved characteristics are negatively correlated with the observed characteristics, then estimated prices can be biased down. Second, it assumes that the labor market is perfectly competitive and so utility is equalized across jobs. If there is dispersion in utility, then higher-paying jobs might also have more desirable nonpay characteristics, also biasing estimates down. This paper develops and implements an empirical framework to measure the role of compensating differentials that addresses these two critiques via two building blocks. First, the framework uses a revealed preference argument. As opposed to measuring and valuing one nonpay characteristic at a time, revealed preference takes a top-down approach and relies on worker choices to tell the researcher which bundle of characteristics they value. Second, the framework allows for differences in utility across jobs. As opposed to assuming that the labor market is perfectly competitive, the framework quantifies the extent of utility dispersion across jobs. To see how these two building blocks could lead to an estimate of the role of compensating differentials, suppose there are two firms: A and B. Suppose that the firms do not tailor their offers to specific workers, and workers have common preferences (up to an idiosyncratic utility draw). Suppose also that both firms are initially the same size and make the same number of offers to workers at the other firm at random. If more workers accept A’s offer than B’s offer, then we can infer that workers prefer firm A to firm B. If it also turns out that B is higher-paying than A, then we infer that B offers worse nonpay characteristics than A (since workers prefer A to B despite the lower pay). Hence, compensating differentials explains why B pays more than A.3 This For recent work on fatality risk see Lavetti and Schmutte (2016) and Lavetti (2017). For PhD scientists and their research agenda, see Stern (2004). See Mas and Pallais (2017) for an interesting recent study of alternative work arrangements. For example, Hornstein, Krusell, and Violante (2011, pg. 2883) survey some literature on the hedonic approach and write that compensating differentials “does not show too much promise” in explaining earnings dispersion. With exactly two firms, this idea will find that compensating differentials explains either all or none of the pay gap. With three or more firms, however, this idea can find that it is a mix: suppose the ranking based on choices is A then B then C, while the ranking based on pay is B then A then C. Then the A and B pay gap is compensating differentials, while the B and C pay gap is not.