Estimating Matching Games with Transfers

Abstract

I explore the estimation of transferable utility matching games, encompassing many-to-many matching, marriage and matching with trading networks (trades). I introduce a matching maximum score estimator that does not suffer from a computational curse of dimensionality in the number of agents in a matching market. I apply the estimator to data on the car parts supplied by automotive suppliers to estimate the returns from different portfolios of parts to suppliers and automotive assemblers.

The formation of physician patient sharing networks in medicare: Exploring the effect of hospital affiliation

“…A physician is defined as affiliated with a given hospital if they provided services there to at least three different patients, on at least three different occasions, occurring within the last year. In line 9 Early work on the maximum score estimator was done by Manski (1975); however, more recent work by Fox (2018Fox ( , 2010 has applied the maximum score estimator toward the estimation of pairwise-stable two-sided matching problems. 10 For a complete list of physicians specialties, see the Supporting Information.…”

Bank Capital and Lending Relationships

“…Next, to obtain a more structured characterization of the matching equilibrium, I estimate the Fox (2016) semiparametric matching model. This model allows me to quantify trade-offs across match characteristics and to generate counterfactual matching assignments, which I use to derive quantitative implications of matching for credit provision.…”

“…This model allows me to quantify trade-offs across match characteristics and to generate counterfactual matching assignments, which I use to derive quantitative implications of matching for credit provision. I employ the Fox (2016) model rather than alternative matching models (e.g., Sorensen (2007)) or models of differentiated product demand (e.g., Berry, Levinsohn, and Pakes (2004)) because…”

“…it allows agents to split the match surplus with transfer payments, but treats these transfers as unobservable, which avoids the need for counterfactual loan spreads and valuation of nonprice contract terms. Chen and Song (2013) also use the Fox (2016) model to study the syndicated loan market. They find that firms and banks match by size, but they do not explore matching by bank capital structure.…”

Dynamic Marriage Matching: An Empirical Framework

“…There is a growing body of structural empirical papers on matching applied to a variety of matching markets. Recent papers include Chen (2013), who looked at matching of CEOs and firms; Agrawal (2013), who looked at placement of medical residents; and Fox (2010), who proposed a maximum-score estimator to analyze firm-level car parts matching data. A number of papers have proposed generalizations to the CS empirical framework.…”