An Equilibrium Theory of Declining Reservation Wages and Learning

In this paper we consider learning from search as a mechanism to understand the relationship between unemployment duration and search outcomes as a labor market equilibrium. We rely on the assumption that workers do not have precise knowledge of their job finding probabilities and therefore, learn about them from their search histories. Embedding this assumption in a model of the labor market with directed search, we provide an equilibrium theory of declining reservation wages over unemployment spells. After each period of search, unemployed workers update their beliefs about the market matching efficiency. We characterize situations where reservation wages decline with unemployment duration. Consequently, the wage distribution is non-degenerate, despite the facts that matches are homogeneous and search is directed. Moreover, aggregate matching probability decreases with unemployment duration, in contrast to individual workers' matching probability, which increases over individual unemployment spells. The difficulty in establishing these results is that learning generates non-differentiable value functions and multiple solutions to a worker's optimization problem. We overcome this difficulty by exploiting a connection between convexity of a worker's value function and the property of supermodularity.