Simultaneous Choice Models: The Sandwich Approach to Nonparametric Analysis

Abstract

We study simultaneous choice models from a revealed preference approach given limited data. By limited data we mean that we observe a single equilibrium from the equilibrium set for a collection of related models or games. The objective of our analysis is twofold: We first use monotone and exclusion restrictions to provide out-of-sample predictions of equilibrium points. The predictions we offer take the form of intervals in lattices whose sharp bounds are characterized via monotone comparative statics. We then propose conditions on the data so that the empirical evidence can be rationalized as the Nash equilibria of a supermodular game. The approach we propose is nonparametric, allows for unobserved heterogeneity, and does not rely on any equilibrium selection mechanism.

Keywords: Simultaneous choice models, supermodular games, partial identification, out-of-sample predictions, monotone comparative statics, revealed preferences

JEL Classification: C31, D01