The Balance Condition in Search-and-Matching Models

Most of the literature that studies frictional search-and-matching models with heterogeneous agents and random search investigates steady state equilibria. Steady state equilibrium requires, in particular, that the flows of agents into and out of the population of unmatched agents balance. We investigate the structure of this balance condition, taking agents' matching behavior as given. Building on the "fundamental matching lemma" for quadratic search technologies in Shimer and Smith (2000), we establish existence, uniqueness, and comparative statics properties of the solution to the balance condition for any search technology satisfying minimal regularity conditions. Implications for the existence and structure of steady state equilibria in the Shimer-Smith model and extensions thereof are noted. These reinforce the point that much of the structure of search-and-matching models with quadratic search technologies carries over to more general search technologies.