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A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

Published online by Cambridge University Press:  20 November 2020

Feng Yao  and
Taining Wang
Feng Yao
Affiliation:
Shenzhen University West Virginia University Guangdong University of Foreign Studies
Taining Wang*
Affiliation:
Capital University of Economics and Business
*
Address correspondence to Taining Wang, International School of Economics and Management, Capital University of Economics and Business, Beijing, China; e-mail: [email protected].
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Abstract

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 5 , October 2021 , pp. 959 - 1003
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

We would like to express our sincere thanks to the Editor, Peter C. B. Phillips, the Co-Editor, Liangjun Su, and three anonymous referees for their constructive suggestions and comments that improved the paper substantially. We also thank Carlos Martins-Filho, the participants in the 2017 Asian Meeting of the Econometric Society and the 4th Econometric Workshop in Dongbei University of Finance and Economics (DUFE) for valuable comments. Any remaining errors are the authors’ responsibility.

References

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