Using data on who matches with whom and outcomes of matches, we build a structural model to make causal inference by differentiating the partner's direct influence on outcomes from the sorting on agents or firms during the matching process.

In the first chapter, we apply this new methodology to study the effect of research alliances on drug innovation, which controls for the potential endogeneity generated by the sorting of firms in the alliance formation process. We find that biotechnology firms are more likely to collaborate with pharmaceutical firms with higher research abilities despite benefiting more from the pharmaceutical firm's drug development experience in drug innovation. After controlling for the sorting on drug qualities, pharmaceutical firms' direct influence promotes the passing of Phase I clinical trials by 10%. A policy aiming to lower drug prices may discourage pharmaceutical firms' participation in collaborative projects, which would decrease the success rate of passing Phase I clinical trials by 4%.

In the second chapter, we show that the joint distribution of unobservables determining who matches with whom and counterfactual outcomes is nonparametrically identified by postulating a factor structure. We discuss different specifications of factor structure, such as market-specific factor, agent-specific factor, and match-specific factor. Our model controls for the endogeneity generated by sorting on unobserved characteristics without the instrumental variable and exclusion restriction. We also show results on partial identification without a factor structure.

In the third chapter, we generalize a lemma in Kotlarski (1967) to fit the empirical applications in economics where outcomes of matches are determined by multiple mutual factors. Kotlarski (1967) establishes a fundamental result on identification of marginal distributions of independent random variables X, Y, and Z from the joint distribution of random variables (U,V), where (U,V)=(X+Z,Y+Z). We extend this result to the case (U,V)=(X+aZ_1+bZ_2,Y+cZ_1+dZ_2), where Z_1 and Z_2 are identically distributed, and a, b, c, and d are different weights. As an outgrowth of the proof, we also present a complete solution to a generalized version of Cauchy functional equation.