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

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  • Le-Yu Chen

    (Institute for Fiscal Studies and Academia Sinica)

  • Sokbae (Simon) Lee

    (Institute for Fiscal Studies and Columbia University)

Abstract

This paper studies inference of preference parameters in semiparametric discrete choice models when these parameters are not point-identi?ed and the identi?ed set is characterized by a class of conditional moment inequalities. Exploring the semiparametric modeling restrictions, we show that the identi?ed 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.

Suggested Citation

  • Le-Yu Chen & Sokbae (Simon) Lee, 2015. "Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models," CeMMAP working papers CWP26/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:26/15
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    References listed on IDEAS

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    Cited by:

    1. Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
    2. Adam M. Rosen & Takuya Ura, 2019. "Finite Sample Inference for the Maximum Score Estimand," Papers 1903.01511, arXiv.org, revised May 2020.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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