Agent Heterogeneity and Learning: An Application to 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 and their value of leisure when unemployed. Firms vary in their marginal product and cost of maintaining a vacancy. The marginal product of a worker-firm match depends on worker and firm marginal productivities, as well as 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, the optimal separation policy is of the reservation wage type. Specifically, the match persists as long as the posterior mean of beliefs about match quality remains above a threshold value. I show the reservation level of beliefs is linear in person and firm specific components, and monotone in tenure. These theoretical results have several implications for an empirical model of earnings with person and firm effects. The first result implies that residuals within a worker-firm match are a martingale; the second result 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 and test a variety of more parsimonious error structures, including the martingale hypothesis implied by the learning process. I find considerable support for the matching model in these data.