Wage Dispersion in the Search and Matching Model with Intra-Firm Bargaining

Matched employer-employee data exhibits both wage and productivity dispersion across firms and suggest that a linear relationship holds between the average wage paid and a firm productivity. The purpose of this paper is to demonstrate that these facts can be explained by a search and matching model when firms are heterogenous with respect to productivity, are composed of many workers, and face diminishing returns to labor given the wage paid to identical workers is the solution to the Stole-Zwiebel bilateral bargaining problem. Helpman and Iskhoki (2008) show that a unique single wage (degenerate) equilibrium solution to the model exists in this environment. In this paper, I demonstrate that another equilibrium exists that can be characterized by a non-degenerate distribution of wages in which more productive firms pay more if employed workers are able to search. Generically this dispersed wage equilibrium is unique and exists if and only if firms are heterogenous with respect to factor productivity. Finally, employment is lower in the dispersed wage equilibrium than in the single wage equilibrium but this fact does not imply that welfare is higher in the single wage equilibrium