Nonparametric identification of static multinomial choice models

This paper proposes a new nonparametric identification strategy for static multiple choice models with random heterogeneity in unobservables. The strategy relies on functional properties of the sub-utilities and the distribution of the unobservables, a known payoff function for the “outside option” and exclusion restrictions for all but one alternative. This new strategy does not transform the multiple choice model into a set of binary models, does not need “special regressors”, additive separability on observables or differentiability conditions. Some ideas for this new identification strategy are borrowed from Theorem 2 in Matzkin (1993) that intends to identify all the sub-utility functions but one and also the distribution of the shocks in differences. However, the proof of this published theorem is incorrect and this paper is the first literature pointing this out and providing a new proof of a different version of the theorem after modifications of its assumptions.