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SEMIPARAMETRIC ESTIMATION OF QUANTILE REGRESSION WITH BINARY QUANTILE SELECTION

Published online by Cambridge University Press:  29 September 2025

Songnian Chen  and
Hanghui Zhang
Songnian Chen
Affiliation:
Zhejiang University
Hanghui Zhang*
Affiliation:
Shanghai University of Finance and Economics
*
Address correspondence to Hanghui Zhang, School of Economics, Shanghai University of Finance and Economics; Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai 200433, China e-mail: zhang.hanghui@mail.shufe.edu.cn
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Abstract

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This article proposes a novel method for estimating quantile regression models that account for sample selection. Unlike the approach by Arellano and Bonhomme (2017, Econometrica 85(1), 1–28; hereafter referred to as AB17), which employs a parametric selection equation, our method utilizes a standard binary quantile regression model to handle the selection issue, thereby accommodating general heterogeneity in both the selection and outcome equations. We adopt a semiparametric estimation technique for the outcome quantile regression by integrating local moment conditions, resulting in $\sqrt {n}$-consistent estimators for the quantile coefficients and copula parameter. Monte Carlo simulation results demonstrate that our estimator performs well in finite samples. Additionally, we apply our method to examine the wage distribution among women using a randomly simulated sample from the US General Social Survey. Our key finding is the presence of significant positive selection among women in the US, which is notably more pronounced than the estimates produced by the AB17’s model.

Information

Type
ARTICLE
Information
Econometric Theory , Volume 42 , Issue 4 , August 2026 , pp. 1034 - 1077
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Footnotes

We are very grateful for the insightful comments and suggestions from the editor, co-editor, and two anonymous referees, which greatly help to enhance the quality of this article.

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