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

Liang Chen (1) , Eugene Choo (2) , Alfred Galichon (3, 4, 5) , Simon Weber (6)

1 Wuhan University [China]
2 Yale-NUS College
3 NYU - NYU System
4 CIMS - Courant Institute of Mathematical Sciences [New York]
5 ECON - Département d'économie (Sciences Po)
6 University of York [York, UK]

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.

Mots clés: Matching function; Maximum likelihood estimation; Counterfactuals; Matching; Transferable utility; Imperfectly transferable utility

Domaines: Economies et finances

Liang Chen, Eugene Choo, Alfred Galichon, Simon Weber. Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation. 2021. ⟨hal-03936296⟩