Nonparametric Estimation of Matching Games With Endogenous Prices

In two-sided and coalition matching games, agents must all agree for a match to be formed, and agents can make only a finite number of matches. I examine the nonparametric identification and estimation of match production functions in matching games with endogenous prices and transferable utility. Inequalities derived from necessary conditions for equilibrium underly a nonparametric maximum score estimator of match production functions. The inequalities do not require data on prices, quotas, or production levels. The estimator does not suffer from a computational or data curse of dimensionality in the number of agents in a matching market as it avoids solving for an equilibrium and estimating first-stage match probabilities. Further, using only a subset of the possible inequalities preserves consistency. The estimator allows markets with one-to-one, one-to-many, many-to-many and coalition formation matching.