Firm productivity, wages, and sorting

Increasing wage inequality is associated with changes in the degree of labor market sorting, i.e. the allocation of workers to firms. To measure sorting, we propose a new method which disentangles the respective contributions of worker and firm heterogeneity to wage inequality. Inspired by sorting theory, we infer firm productivity from estimating firm-level production functions, taking into account that worker ability and firm productivity may interact at the match level. Using German data, we find that highly productive firms display low labor shares, dominate concentrated markets, and pay lower wages than less productive firms. Sorting is positive, but lower than what wage-based measures suggest. It increases over time, driven by new matches between low-productivity firms and low-ability workers. At the top, sorting decreases, reflected in worker transitions away from high-productivity firms that pay relatively low wages. We discuss implications of our findings for the interpretation of increasing wage inequality.