This paper develops the nonparametric identification of models with production complementarities, worker-firm specific disutility of labor and search frictions. Mobility in the model is subject to preference shocks, and we assume that firms can write wage contracts. We develop a constructive proof for the nonparametric identification of the model primitives from matched employer-employee data. We use the estimated model to decompose the sources of wage dispersion into worker heterogeneity, compensating differentials, and search frictions that generate between-firm and within-firm dispersion. We find that compensating differentials are substantial on average, but the contribution differs greatly between the lowest and highest types of workers. Finally, we use the model to provide an economic interpretation of several empirical regularities.