Constrained efficiency with adverse selection and directed search

This paper studies constrained efficiency in Guerrieri et al.'s (2010) model of adverse selection and directed search. Buyers post contracts, and sellers with private information about their type direct their search toward their preferred contract. Buyers and sellers then match bilaterally and trade. If the Guerrieri-Shimer-Wright equilibrium fails to achieve the first best, then the planner subject to the frictions of the environment achieves strictly higher welfare than the equilibrium, i.e., the equilibrium is not ex-ante constrained efficient. Under certain conditions, the planner achieves an allocation that even Pareto dominates the equilibrium, i.e., the equilibrium is not interim constrained efficient. Under other conditions, the planner can completely undo the effects of adverse selection and achieves the first best. Cross-subsidization is the key to these results.