Search equilibrium with unobservable investment

Abstract

This article studies a wage posting game in which workers invest in human capital so as to reduce the disutility of labor. If investment were observable, then no workers would invest in skills due to the holdup problem, and all employers would offer the monopsony wage as in the Diamond paradox. With unobservable investment, however, the equilibrium wage and skill distributions are nondegenerate, despite agents being ex ante identical. An asymptotic efficiency result is obtained in which investment converges to the efficient level as the arrival rate of job offers tends to infinity, with firms receiving all the surplus in the market. The model generates distinctive comparative statics predictions, and the theory can rationalize any wage distribution that satisfies a few regularity conditions. The analysis is robust to the inclusion of some forms of direct search costs.