Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation

52 Pages Posted: 3 Jun 2019 Last revised: 3 Feb 2021

See all articles by Liang Chen

Liang Chen

Wuhan University

Eugene Siang Yew Choo

University of Toronto - Department of Economics

Alfred Galichon

NYU, Department of Economics and Courant Institute

Simon Weber

University of York - Department of Economics and Related Studies

Date Written: May 13, 2019

Abstract

In this paper, we argue that models coming from a variety of fields share a common structure that we call matching function equilibria with partial assignment. This structure revolves around an aggregate matching function and a system of nonlinear equations. This encompasses search and matching models, matching models with transferable, non-transferable and imperfectly transferable utility, and matching with peer effects. We provide a proof of existence and uniqueness of an equilibrium as well as an efficient algorithm to compute it. We show how to estimate parametric versions of these models by maximum likelihood. We also propose an approach to construct counterfactuals without estimating the matching functions for a subclass of models. We illustrate our estimation approach by analyzing the impact of the elimination of the Social Security Student Benefit Program in 1982 on the marriage market in the United States.

Keywords: matching function, maximum likelihood estimation, counterfactuals, matching, transferable utility, imperfectly transferable utility

JEL Classification: C1, C78, I2, J12

Suggested Citation

Chen, Liang and Choo, Eugene Siang Yew and Galichon, Alfred and Weber, Simon, Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation (May 13, 2019). Available at SSRN: https://ssrn.com/abstract=3387335 or http://dx.doi.org/10.2139/ssrn.3387335

Liang Chen

Wuhan University ( email )

Wuhan
China

Eugene Siang Yew Choo

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S 3G7
Canada
416-978-5146 (Phone)
416-978-6713 (Fax)

HOME PAGE: http://www.chass.utoronto.ca/~eugechoo/

Alfred Galichon

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Simon Weber (Contact Author)

University of York - Department of Economics and Related Studies ( email )

Heslington
York, YO1 5DD
United Kingdom

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