A New Test of Linear Hypotheses in OLS Regression Under Heteroscedasticity of Unknown Form

Abstract

When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM) estimator. However, many HCCM estimators do not perform well when the sample size is small or when there exist points of high leverage in the design matrix. Prompted by a connection between MacKinnon and White’s HC2 HCCM estimator and the heterogeneous-variance two-sample t statistic, the authors provide a new statistic for testing linear hypotheses in an OLS regression model that does not assume homoscedasticity. The authors report simulation results showing that their new test maintains better Type I error rate control than existing methods in both the presence and absence of heteroscedasticity.