Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models
研究了半参数离散选择模型中偏好参数的推断问题，利用模型结构将识别集等价转化为仅依赖于两个连续索引变量的条件矩不等式，从而打破维度诅咒，适用于高维协变量场景。
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.