Isaac Sorkin is a job candidate from the University of Michigan, and he has some fascinating new research on that question. Here is the abstract:
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.
The paper is here.
Here is Adam Ozimek on the research. I would put it this way: very often when workers switch jobs, they take a pay cut, voluntarily, in return for better amenities. In this regard “true inequality” is lower than measured income inequality would suggest.