Efficiency in Search and Matching Models: A Generalized Hosios Condition

This paper generalizes the well-known Hosios (1990) efficiency condition to dynamic search and matching environments where the expected match output depends on the market tightness. Such environments give rise to a novel externality – the output externality – which may be either positive or negative. The generalized Hosios condition is simple: entry is constrained efficient when buyers’ surplus share equals the matching elasticity plus the surplus elasticity (i.e. the elasticity of the expected joint match surplus with respect to buyers). This intuitive condition captures both the standard externalities generated by the frictional matching process and the output externality.