Matching with Trade-offs: Revealed Preferences over Competing Characteristics

TL;DR

This paper develops a theoretical and econometric framework for analyzing optimal matchings with multiple competing criteria, such as income and education, accounting for unobserved characteristics and trade-offs.

Contribution

It introduces a flexible surplus function model, characterizes feasible and optimal matchings, and provides methods to test and estimate social preferences using observed matching data.

Findings

Characterizes properties of feasible and optimal matchings.

Provides a method to test if observed matches are socially optimal.

Offers estimation techniques for social preference parameters.

Abstract

We investigate in this paper the theory and econometrics of optimal matchings with competing criteria. The surplus from a marriage match, for instance, may depend both on the incomes and on the educations of the partners, as well as on characteristics that the analyst does not observe. Even if the surplus is complementary in incomes, and complementary in educations, imperfect correlation between income and education at the individual level implies that the social optimum must trade off matching on incomes and matching on educations. Given a flexible specification of the surplus function, we characterize under mild assumptions the properties of the set of feasible matchings and of the socially optimal matching. Then we show how data on the covariation of the types of the partners in observed matches can be used to test that the observed matches are socially optimal for this specification, and to estimate the parameters that define social preferences over matches.