Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation
52 Pages Posted: 3 Jun 2019 Last revised: 3 Feb 2021
Date Written: May 13, 2019
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
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