Labor market efficiency, wages and employment when search frictions interact with intrafirm bargaining

In search of a macroeconomic theory of wage determination, the agnostic reader should be puzzled by the apparent contradiction between two influential theories. On one hand, in the standard search-matching theory with wage bargaining, hiring cost and constant returns of labor, the bargaining power of employees allows them to get rents and gives rise either to overemployment or to under-employment compared with the first-best. On the other hand, in Stole and Zwiebel's theory of intrafirm bargaining with no hiring cost and decreasing returns of labor, the bargaining power of employees does not allow them to get rent and always gives rise to over-employment. In this paper, we try to reconcile the approaches. A simple matching model with large firms and diminishing marginal productivity of labor allows us to show that the two limit cases described above yield a mix of robust and non robust results: In the most general case, employees get rents and there is more frequently over employment compared to the efficient allocation than in the standard search-matching model.