arXiv 13 Nov 2023 · Econometrics · publishedJournal of Econometrics (2025)
arXiv:2311.07067 · PDF · DOI · OpenAlex · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Xue, S., T. T. Yang, and Q. Zhou (2018) Binary choice model with interactive effects self | 1.000 | 6 | 4 | 100% |
| 2 | Cheng, X. and Z. Liao (2015) Select the valid and relevant moments: An information-based LASSO for GMM with many moments | 0.950 | 14 | 4 | 86% |
| 3 | Hall, P., J. Racine, and Q. Li (2004) Cross-validation and the estimation of conditional probability densities | 0.930 | 41 | 6 | 80% |
| 4 | Lin, Z., Y. Xiang, and C. Zhang (2009) Adaptive Lasso in high-dimensional settings | 0.916 | 13 | 3 | 77% |
| 5 | Fan, J. and J. Lv (2008) Sure independence screening for ultrahigh dimensional feature space | 0.874 | 5 | 2 | 100% |
| 6 | Liao, Z (2013) Adaptive GMM shrinkage estimation with consistent moment selection | 0.874 | 5 | 2 | 100% |
| 7 | Lewbel, A (2000) Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables | 0.794 | 14 | 8 | 50% |
| 8 | Székely, G. J., M. L. Rizzo, and N. K. Bakirov (2007) Measuring and testing dependence by correlation of distances | 0.794 | 12 | 3 | 50% |
| 9 | Li, R., W. Zhong, and L. Zhu (2012) Feature screening via distance correlation learning | 0.693 | 5 | 1 | 100% |
| 10 | Dong, Y. and A. Lewbel (2015) A simple estimator for binary choice models with endogenous regressors | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 52 scored citations.