Estimating Matching Games with Transfers

In matching games, agents are rivals to match with the most attractive partners. I examine the nonparametric identification and estimation of match production functions in matching games with endogenous transfers. Inequalities derived from single-agent best responses underly a nonparametric maximum score estimator of match production functions. The inequalities do not require data on transfers, 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 the estimator 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, as well as externalities from agents outside a given match. For games with multiple equilibrium sets of matches, there is no need to estimate an equilibrium selection rule or computationally itemize the equilibria. ∗Thanks to helpful comments from many colleagues as well as workshop participants at Bar-Ilan, Chicago, Haifa, Minnesota, the New York Fed, North Carolina, Northwestern, Stanford, Tel Aviv, and Virginia, as well as the Society of Economic Dynamics and the Econometric Society World Congress. Email: [email protected].