The screening role of market tightness in a competitive search with adverse selection

This paper revisits Guerrieri, Shimer, and Wright (2010) (GSW) to study screening in a competitive search market with adverse selection. GSW show that there exists a unique separating equilibrium in which each type applies to a different contract, and their key sorting assumption involves a single-crossing property on agents' preferences. We show that GSW's main results hold under a weaker assumption on preference heterogeneity, called generalized sorting, and weakening the sorting assumption relies on explicitly considering the screening role of market tightness. The assumption can be weakened further if we assume that agents' matching probability strictly increases in market tightness. In addition to providing theoretical insights, we study examples to demonstrate how generalized sorting facilitates the study of market imperfections under search and informational frictions. In our examples, indivisibility, price limits, and the minimum wage violate GSW's sorting assumption but remain tractable under generalized sorting. Thus, an additional contribution of this paper is the expansion in applicability of GSW's approach.