Cupid's Invisible Hand: Social Surplus and Identification in Matching Models

TL;DR

This paper develops a general model of matching with unobserved heterogeneity, providing new identification formulas, efficient algorithms, and revisiting empirical applications to enhance understanding of social surplus in matching markets.

Contribution

It introduces a generalized model that identifies joint surplus and utilities in matching markets with unobserved heterogeneity, extending prior work with closed-form formulas and estimation methods.

Findings

Closed-form formulas for joint surplus and utilities

Efficient algorithms for stable matching computation

Successful empirical application revisiting previous models

Abstract

We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006), we first show that the equilibrium matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow's empirical application to illustrate the potential of our more general approach.