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 also extend this dimension reducing characterization result to a variety of semi-parametric models under which the sign of conditional expectation of a certain transformation of the outcome is the same as that of the indexing variable.
Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models
18 June 2015
Working Paper (CWP26/15)