Estimating matching games with transfers

Economists wish to use data on matches to learn about the structural primitives that govern sort-ing. I show how to use equilibrium data on who matches with whom for semiparametric estima-tion of match production functions in many-to-many, two-sided matching games with transferable utility. Inequalities derived from equilibrium necessary conditions underlie a maximum score es-timator of match production functions. The inequalities do not require data on transfers, quotas, production levels, or unmatched agents. 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. I present an empirical application to automotive suppliers and assemblers. ∗Thanks to SupplierBusiness as well as Thomas Klier for help with the empirical application. I thank the Nationa