Search, Adverse Selection and Market Clearing

This paper demonstrates that adverse selection can cause the coexistence of involuntary unemployment and involuntary vacancy in a dynamic decentralized trading model, even without search friction. Our model is built on a simple version of Mortensen and Pissarides (1994) with three important changes. First, a seller has private information about the quality of the goods to be traded, while a buyer has to make a decision without observing the true quality (Chang (2012)). Second, the matching technology is efficient in the sense that an agent in the short side of the matching pool is matched with probability 1 and the long side is rationed (Rubinstein and Wolinsky (1985)). Third, to consummate the matching, the two parties must agree upon the price at which the good is delivered. We model the bargaining process as a random proposal model in which a price is randomly drawn by a third party, and each party responds to the price either by accepting or rejecting the offer (Burdett and Wright (1998)). If both parties agree, then the matching is consummated. Otherwise, each party returns to the respective pool, waiting for another round of matching. We quantify the amount of search friction by the time span of each round. We compute a sequence of stationary equilibria as search friction vanishes. We prove that the mass of high quality sellers, the mass of low quality sellers and the mass of buyers are uniformly bounded away from 0, as search friction vanishes.