Testing inference in heteroskedastic linear regressions: a comparison of two alternative approaches

Abstract

We consider the issue of performing testing inferences on the parameters that index the linear regression model under heteroskedasticity of unknown form. Quasi-t test statistics use asymptotically correct standard errors obtained from heteroskedasticity-consistent covariance matrix estimators. An alternative approach involves making an assumption about the functional form of the response variances and jointly modeling mean and dispersion effects. In this dissertation we compare the accuracy of testing inferences made using the two approaches. We consider several different quasi-t tests and also z tests performed after generalized least squares estimation which was carried out using three different estimation strategies. Our numerical evaluations were performed using different models, different sample sizes, and different heteroskedasticity strengths. The numerical evidence shows that some quasi-t tests are considerably less size distorted in small samples than the tests carried out after the jointly modeling mean and dispersion effects. Finally, we present and discuss two empirical applications.