EconBase
← All papers

High Dimensional Binary Choice Model with Unknown Heteroskedasticity or Instrumental Variables

Fu Ouyang, Thomas Tao Yang

arXiv 13 Nov 2023 · Econometrics · publishedJournal of Econometrics (2025)

arXiv:2311.07067 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous regressors. Our approaches extend the special regressor estimator originally proposed by Lewbel (2000). This estimator becomes impractical in high-dimensional settings due to the curse of dimensionality associated with high-dimensional conditional density estimation. To overcome this challenge, we introduce an innovative data-driven dimension reduction method for nonparametric kernel estimators, which constitutes the main contribution of this work. The method combines distance covariance-based screening with cross-validation (CV) procedures, making special regressor estimation feasible in high dimensions. Using this new feasible conditional density estimator, we address variable and moment (instrumental variable) selection problems for these models. We apply penalized least squares (LS) and generalized method of moments (GMM) estimators with an L1 penalty. A comprehensive analysis of the oracle and asymptotic properties of these estimators is provided. Finally, through Monte Carlo simulations and an empirical study on the migration intentions of rural Chinese residents, we demonstrate the effectiveness of our proposed methods in finite sample settings.

Citation extraction

52
references
191
in-text mentions
52
distinct cited
2
self-citations
16,792
main-text words

appendix boundary found by appendix_command · 35% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Xue, S., T. T. Yang, and Q. Zhou (2018) Binary choice model with interactive effects self1.00064100%
2Cheng, X. and Z. Liao (2015) Select the valid and relevant moments: An information-based LASSO for GMM with many moments0.95014486%
3Hall, P., J. Racine, and Q. Li (2004) Cross-validation and the estimation of conditional probability densities0.93041680%
4Lin, Z., Y. Xiang, and C. Zhang (2009) Adaptive Lasso in high-dimensional settings0.91613377%
5Fan, J. and J. Lv (2008) Sure independence screening for ultrahigh dimensional feature space0.87452100%
6Liao, Z (2013) Adaptive GMM shrinkage estimation with consistent moment selection0.87452100%
7Lewbel, A (2000) Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables0.79414850%
8Székely, G. J., M. L. Rizzo, and N. K. Bakirov (2007) Measuring and testing dependence by correlation of distances0.79412350%
9Li, R., W. Zhong, and L. Zhu (2012) Feature screening via distance correlation learning0.69351100%
10Dong, Y. and A. Lewbel (2015) A simple estimator for binary choice models with endogenous regressors0.64422100%

Showing the top 10 of 52 scored citations.