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Economists wish to use data on matches to learn about the structural primitives that govern sorting. The author shows how to use equilibrium data on who matches with whom for semi parametric estimation 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 estimator 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 equilibrium and estimating first-stage match probabilities. The author presents an empirical application to automotive suppliers and assemblers.
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