Empirical methods for transferable-utility matching games have previously been developed using the key outcome of the matches formed in equilibrium. In the first chapter, we explore the identification and estimation of match production functions and agent valuation functions using data on two additional outcomes of such matching games: monetary transfers (prices) and profits. We provide identification results for nonparametric models for the case of data on profits and more parametric models for the case of data on prices. We provide estimators paralleling the identification results for both profit data and price data. Importantly, our identification results allow for agents to have valuations defined over the unmeasured characteristics of potential partners. Further, using data on CEO compensation of large public firms in the U.S., we estimate the effects of the CEO’s experience, the scope of the firm’s operations, and the firm’s size on the match valuations of CEOs and firms.

In the second chapter, we investigate how data on firms’ profits allow the identification of the distribution of unobserved heterogeneity under a specific equilibrium selection rule in a two-sided matching model with a finite number of firms. We prove an extension of Theorem 9 in Heckman and Honoré (1990) where we show data on market-wide profits identify the joint distribution of total unobserved match productions. Finally, under an equilibrium selection rule that relies on the core structure in assignment games, we show that data on equilibrium matching, individual firm profits, and match-level measured characteristics of all agents identify the joint distribution of match-level unmeasured characteristics.