Combinatorial approach to inference in partially identified incomplete structural models

Abstract

We propose a computationally feasible inference method in finite games of complete information. Galichon and Henry, 2011 and Beresteanu, Molchanov, and Molinari, 2011 show that the empirical content in such models is characterized by a collection of moment inequalities whose number increases exponentially with the number of discrete outcomes. We propose an equivalent characterization based on classical combinatorial optimization methods that allows the construction of confidence regions with an efficient bootstrap procedure that runs in linear computing time. The method can be applied to the empirical analysis of cooperative and noncooperative games, instrumental variable models of discrete choice, and revealed preference analysis. We propose an application to the determinants of long term elderly care choices.