Identifying Labor Market Sorting with Firm Dynamics

Studying wage inequality requires understanding how workers and firms match. I propose a novel strategy to identify the complementarities in production between unobserved worker and firm attributes, based on the idea that positive (negative) sorting implies that firms upgrade (downgrade) their workforce quality when they grow in size. I use German matched employer-employee data to estimate a search and matching model with worker-firm complementarities, job-to-job transitions, and firm dynamics. The relationship between changes in workforce quality and firm growth rates in the data informs the strength of complementarities in the model. Thus, this strategy bypasses the lack of identification inherent to environments with constant firm types. I find evidence of negative sorting and a significant dampening effect of worker-firm complementarities on wage inequality. Worker and firm heterogeneity, differential bargaining positions, and sorting contribute 71%, 20%, 32% and -23% to wage dispersion, respectively. Reallocating workers across firms to the first-best allocation without mismatch yields an output gain of less than one percent.