The Revealed Preference Theory of Stable and Extremal Stable Matchings

Abstract

We investigate the testable implications of the theory of stable matchings. We provide a characterization of the data that are rationalizable as a stable matching when agents' preferences are unobserved. The characterization is a simple nonparametric test for stability, in the tradition of revealed preference tests. We also characterize the observed stable matchings when monetary transfers are allowed, and the stable matchings that are best for one side of the market (extremal stable matchings). We find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching, or that the matching be consistent with unrestricted monetary transfers. We also present results on rationalizing a matching as the median stable matching.

Keywords: Aggregate matching, stability, rationalizability, revealed preference tests

JEL Classification: C71, C78