Bargaining with renegotiation in models with on-the-job search

Abstract

This paper studies a model with wage bargaining, random on-the-job search and renegotiation. Wages are determined by a bargaining process in which the firm and the worker alternate in making offers and there is a probability that this process breaks down. In the model, a given wage contract ends at a Poisson rate, and then the firm and the worker bargain over a new wage. In this setting, a higher wage decreases the firm's markup, but this effect is partly offset by lowering turnover, which increases match surplus. This increase in match surplus enables the worker to capture a higher share of the surplus. This positive effect of a higher wage on match surplus diminishes when they renegotiate more frequently. Eventually, as the contract length tends to zero, the equilibrium of the model converges to the equilibrium payoffs discussed by Pissarides (1994). My model thereby justifies using the Nash bargaining solution with perfectly transferable values in models with on-the-job search. In contrast, when the Poisson rate goes to zero, the equilibrium in the model, which I show to be unique, converges to one of the equilibria found by Shimer (2006)