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VALID HETEROSKEDASTICITY ROBUST TESTING

Published online by Cambridge University Press:  11 September 2023

Benedikt M. Pötscher  and
David Preinerstorfer
Benedikt M. Pötscher*
Affiliation:
University of Vienna
David Preinerstorfer
Affiliation:
University of St. Gallen
*
Address correspondence to Benedikt Pötscher, Department of Statistics, University of Vienna, A-1090 Oskar-Morgenstern Platz 1, Vienna, Austria; e-mail: benedikt.poetscher@univie.ac.at.
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Abstract

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Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to severe size distortions, and so do existing adjustments including the bootstrap. To avoid these issues, we suggest to use smallest size-controlling critical values, the generic existence of which we prove in this article for the commonly used test statistics. Furthermore, sufficient and often also necessary conditions for their existence are given that are easy to check. Granted their existence, these critical values are the canonical choice: larger critical values result in unnecessary power loss, whereas smaller critical values lead to overrejections under the null hypothesis, make spurious discoveries more likely, and thus are invalid. We suggest algorithms to numerically determine the proposed critical values and provide implementations in accompanying software. Finally, we numerically study the behavior of the proposed testing procedures, including their power properties.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 53
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

Financial support of the second author by the Program of Concerted Research Actions (ARC) of the Université libre de Bruxelles in an early stage of this project is gratefully acknowledged. We thank two referees, a Co-Editor, and the Editor for helpful comments.

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