Heteroskedasticity-Robust Inference in Linear Regressions

Abstract

The assumption that all errors share the same variance (homoskedasticity) is commonly violated in empirical analyses carried out using the linear regression model. A widely adopted modeling strategy is to perform point estimation by ordinary least squares and then perform testing inference based on these point estimators and heteroskedasticity-consistent standard errors. These tests, however, tend to be size-distorted when the sample size is small and the data contain atypical observations. Furno (1996) suggested performing point estimation using a weighted least squares mechanism in order to attenuate the effect of leverage points on the associated inference. In this article, we follow up on her proposal and define heteroskedasticity-consistent covariance matrix estimators based on residuals obtained using robust estimation methods. We report Monte Carlo simulation results (size and power) on the finite sample performance of different heteroskedasticity-robust tests. Overall, the results favor inference based on HC0 tests constructed using robust residuals.

Keywords:

• Heteroskedasticity
• Leverage point
• Linear regression
• Quasi-t test
• Robust estimation

Mathematics Subject Classification:

• 62J05
• 62F35
• 62F03

Acknowledgments

This work was supported by FAPESB (research grant number 7547/2006) and CNPq. We thank an anonymous referee for comments and suggestions.