Aggregate Matchings

This paper characterizes the testable implications of stability for aggregate matchings. We consider data on matchings where individuals are aggregated, based on their observable characteristics, into types, and we know how many agents of each type match. We derive stability conditions for an aggregate matching, and, based on these, provide a simple necessary and sufficient condition for an observed aggregate matching to be rationalizable (i.e. such that preferences can be found so that the observed aggregate matching is stable). Subsequently, we derive moment inequalities based on the stability conditions, and provide an empirical illustration using the cross-sectional marriage distributions across the US states.