Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 2015, Volume 83, Issue 3

Large Matching Markets as Two‐Sided Demand Systems

https://doi.org/10.3982/ECTA12299
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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Supplemental Material

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.

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

This zip file contains the replication files for the manuscript.

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