Bilateral Worker-Firm Training Decisions and an Application to Discrimination

A large part of group differences in wages comes from unobserved or unverifiable characteristics such as the intensity of human capital investments on-the-job. This is notably the classical argument to account for gender differentials. We build a framework in which training decisions are bilateral, in the presence of frictions in the labor market generated by a flow-matching model. Workers make learning efforts while firm invest by paying direct training costs. Under complementarity of the learning function of these two inputs (effort and direct costs), the outcome of training decisions requires coordination between the firm and the worker. We exhibit cases in which a high investment in training/high effort Nash equilibrium is a dominant strategy, which makes discrimination between groups difficult, and cases in which there is a coordination failure. We define coordination discrimination as a case in which observed characteristics of workers (gender, race, diploma) help to coordinate on an equilibrium. We explore the case of unobservable types of workers, and study under which conditions the (common knowledge) priors of firms do not affect the equilibrium strategies, and under which conditions they play a crucial role instead.