On the Identification of Models of Uncertainty, Learning, and Human Capital Acquisition with Sorting

We consider a general class of models of the labor market with human capital acquisition, learning about worker ability, job assignment, and imperfect competition among firms. We prove that these models are identified based on information on workers’ jobs and wages under standard assumptions. We show that accounting for differences in workers’ opportunities for human capital acquisition and learning about productivity across jobs and firms helps explain why the measured degree of labor market sorting can be low even in the presence of a high degree of complementarity between firms and workers, for two reasons. First, the wage contains a compensating differential term for the lost opportunity to acquire human capital and information at other jobs and firms, which attenuates the importance of firm and worker effects for wages. Second, as the process of information acquisition takes place gradually over time, information is noisy so at any point in time, say, a high-productivity worker can be matched with a low-productivity firm. We offer a novel decomposition of the determinants of cross-sectional wage inequality and estimate them based on U.S. matched employer-employee data (LEHD).