Heterogeneity and Learning in Labor Markets∗

I develop a matching model with heterogeneous workers, firms, and worker-firm matches, and apply it to longitudinal linked data on employers and employees. Workers vary in their marginal product when employed. Firms vary in their marginal product and cost of maintaining a vacancy. The marginal product of a worker-firm match also depends on a match-specific interaction between worker and firm that I call match quality. Agents have complete information about worker and firm heterogeneity, and symmetric but incomplete information about match quality. They learn its value slowly by observing production outcomes. There are two key results. First, under a Nash bargain, the equilibrium wage is linear in a person-specific component, a firm-specific component, and the posterior mean of beliefs about match quality. Second, in each period the optimal separation policy is characterized by a reservation level of beliefs about match quality. The reservation value varies across workers and firms, and is monotone in job tenure. These results have several implications for empirical work. The first implies that residuals within a worker-firm match are a martingale; the second implies the distribution of earnings is truncated. I test predictions from the matching model using data from the Longitudinal Employer-Household Dynamics (LEHD) Program at the US Census Bureau. I present both fixed and mixed model specifications of the equilibrium wage function, taking account of structural aspects implied by the learning process. In the most general specification, earnings residuals have a completely unstructured covariance within a worker-firm match. I estimate structural parameters of the matching model, and test the martingale structure implied by the learning process. I find considerable support for the matching model in these data.