Numerical evaluation of tests based on different heteroskedasticity-consistent covariance matrix estimators

Abstract

This article considers the issue of performing tests in linear heteroskedastic models when the test statistic employs a consistent variance estimator. Several different estimators are considered, namely: HC0, HC1, HC2, HC3, and their bias-adjusted versions. The numerical evaluation is performed using numerical integration methods; the Imhof algorithm is used to that end. The results show that bias-adjustment of variance estimators used to construct test statistics delivers more reliable tests when they are performed for the HC0 and HC1 estimators, but the same does not hold for the HC3 estimator. Overall, the most reliable test is the HC3-based one.

Keywords:

• Bias correction
• Covariance matrix estimation
• Heteroskedasticity
• Leverage points
• Numerical integration
• Quasi-t test

Acknowledgements

We gratefully acknowledge partial financial support from CAPES, CNPq, FAPESP, and FINEP. We also thank an anonymous referee for comments and suggestions.