Econometrica: May 2015, Volume 83, Issue 3

Large Matching Markets as Two‐Sided Demand Systems
p. 897-941

K. Menzel

This paper studies two‐sided matching markets with non‐transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed‐point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.

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Supplement to "Large Matching Markets as Two-Sided Demand Systems"

This appendix contains the proofs for Lemmas and Theorems that were omitted in the main paper.  Equation numbers refer to formulae and expressions in the main text.

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Supplement to "Large Matching Markets as Two-Sided Demand Systems"

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