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A NONPARAMETRIC TEST OF HETEROGENEITY IN CONDITIONAL QUANTILE TREATMENT EFFECTS

Published online by Cambridge University Press:  07 March 2024

Zongwu Cai Open the ORCID record for Zongwu Cai [Opens in a new window] ,
Ying Fang Open the ORCID record for Ying Fang [Opens in a new window] ,
Ming Lin  and
Shengfang Tang
Zongwu Cai
Affiliation:
University of Kansas
Ying Fang
Affiliation:
Xiamen University
Ming Lin*
Affiliation:
Xiamen University
Shengfang Tang
Affiliation:
Jiangxi University of Finance and Economics
*
Address correspondence to Ming Lin, Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian, China, [email protected]; Shengfang Tang, School of Finance, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, China, [email protected].
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Abstract

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This paper proposes a nonparametric test to assess whether there exist heterogeneous quantile treatment effects (QTEs) of an intervention on the outcome of interest across different sub-populations defined by covariates of interest. Specifically, a consistent test statistic based on the Cramér–von Mises type criterion is developed to test if the treatment has a constant quantile effect for all sub-populations defined by covariates of interest. Under some regularity conditions, the asymptotic behaviors of the proposed test statistic are investigated under both the null and alternative hypotheses. Furthermore, a nonparametric Bootstrap procedure is suggested to approximate the finite-sample null distribution of the proposed test; then, the asymptotic validity of the proposed Bootstrap test is theoretically justified. Through Monte Carlo simulations, we demonstrate the power properties of the test in finite samples. Finally, the proposed testing approach is applied to investigate whether there exists heterogeneity for the QTE of maternal smoking during pregnancy on infant birth weight across different age groups of mothers.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 28
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

The authors are grateful to the editor (Peter C. B. Phillips), the co-editor, and the two anonymous referees for their insightful comments which substantially improved the paper. This research is supported by the National Science Foundation of China (Grant Nos. 72033008, 72301119, 72133002, and 71988101).

References

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