We develop the theory of stability for aggregate matchings used in empirical studies and establish fundamental properties of stable matchings including the result that the set of stable matchings is a non-empty, complete, and distributive lattice. Aggregate matchings are relevant as matching...

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...

Stability is often the goal for clearinghouses in matching markets, such as those matching residents to hospitals, students to schools, etc. Stable outcomes absent transfers need not be utilitarian efficient, suggesting the potential value of transfers. We study the wedge between stability and...