Large Matching Markets as Two-sided Demand Systems

Author(s): Konrad Menzel
Date: July 2014
Type: CRATE Working Papers, CRATE-2014-3
doi: download pdf

Abstract

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. Fur- thermore, 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 charac- teristics at the level of pairs resulting from a stable matching.