Partial commitment in models of on-the-job search with an application to minimum wage spillovers

This paper studies the role of partial commitment in models with on-the-job search. Commitment is modeled as the frequency at which wages are renegotiated. The formulation nests earlier models in the literature as special cases in which the frequency of renegotiation goes to zero (full commitment) or infinity (no commitment). I show that the equilibrium wage distribution and the bargaining outcomes are unique. The degree of commitment is important for the share of the surplus captured by the worker. With no commitment, the worker value only reflects her bargaining power. With commitment, the worker receives a higher share of the surplus because a higher wage increases the total surplus by increasing the length of the match. The length of the match is more responsive to the agreed wage when the commitment is higher. When the model is calibrated, the values of the model primitives, e.g. the bargaining power of workers and the productivity distribution, differ starkly depending on the assumed degree of commitment. Further, there is only a positive spillover from an increase in the minimum wage if there is a high degree of commitment. Lastly, when the degree of commitment is endogenous, the two corner cases analyzed in the literature only arise under particular parameter values.