Valid Heteroskedasticity Robust Testing

TL;DR

This paper introduces a method for selecting the smallest size-controlling critical values for heteroskedasticity robust tests, ensuring accurate size control and improving reliability in econometric practice.

Contribution

It provides a theoretical foundation and practical algorithms for determining minimal size-controlling critical values, addressing size distortions in heteroskedasticity robust testing.

Findings

Proved the existence of smallest size-controlling critical values.

Provided easy-to-check conditions for their existence.

Demonstrated the effectiveness of the proposed methods through numerical studies.

Abstract

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 over-rejections 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.