Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models

TL;DR

This paper introduces a method to simplify the inference of preference parameters in semiparametric discrete choice models by reducing the dimensionality of conditional moment inequalities, overcoming the curse of dimensionality.

Contribution

It shows that the identified set can be characterized by moment inequalities conditional on only two continuous variables, regardless of covariate dimension.

Findings

Dimension reduction of conditional moment inequalities to two variables

Applicable to monotone single index and other semiparametric models

Breaks the curse of dimensionality in nonparametric inference

Abstract

This paper studies inference of preference parameters in semiparametric discrete choice models when these parameters are not point-identified and the identified set is characterized by a class of conditional moment inequalities. Exploring the semiparametric modeling restrictions, we show that the identified set can be equivalently formulated by moment inequalities conditional on only two continuous indexing variables. Such formulation holds regardless of the covariate dimension, thereby breaking the curse of dimensionality for nonparametric inference based on the underlying conditional moment inequalities. We further apply this dimension reducing characterization approach to the monotone single index model and to a variety of semiparametric models under which the sign of conditional expectation of a certain transformation of the outcome is the same as that of the indexing variable.