Unique equilibria and substitution effects in a stochastic model of the marriage market

Colin Decker, Elliott H. Lieb, Robert J. McCann and Benjamin K. Stephens

Journal of Economic Theory, 2013, vol. 148, issue 2, 778-792

Abstract: Choo and Siow (2006) [7] proposed a model for the marriage market which allows for random identically distributed McFadden-type noise in the preferences of each of the participants. In this note we exhibit a strictly convex function whose derivatives vanish precisely at the equilibria of their model. This implies uniqueness of the resulting equilibrium marriage distribution, simplifies the argument for its existence, and gives a representation of it in closed form. We go on to derive smooth dependence of this distribution on exogenous preference and population parameters, and establish sign, symmetry, and size of the various substitution effects. This leads to the testable but unexpected prediction that the percentage change of type i unmarrieds with respect to fluctuations in the total number of type j men or women turns out to form a symmetric positive-definite matrix rij=rji, and thus to satisfy bounds such as |rij|⩽(riirjj)1/2.

Keywords: Choo–Siow; Marriage market; Matching; Random; Unique equilibrium; Comparative statics; Convex analysis (search for similar items in EconPapers)
JEL-codes: C62 C78 C81 D03 J12 Z13 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (33)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:148:y:2013:i:2:p:778-792

DOI: 10.1016/j.jet.2012.12.005

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