Unit Root Testing Using Heteroscedasticity Consistent Covariance Matrix Estimators: Finite- Sample Evidence

Abstract

Based upon Monte Carlo experiments mimicking cross-sectional analysis, Long and Ervin (2000) have suggested the routine application of heteroscedasticity consistent covariance matrix (HCCM) estimators, irrespective of whether heteroscedasticity is detected or expected. In this paper the use of HCCM estimators is re-examined in the context of testing the unit root hypothesis. The properties of Dickey-Fuller tests based on alternative HCCM estimators are considered in the presence of innovation variance breaks and heteroscedasticity in the square root of a regressor variable. The results show that for variance breaks, size correction comes at the expense of dramatic reduction in power. When heteroscedasticity is related to the square root of the lagged level in a Dickey-Fuller regression, the test does not have nominal size when the covariance matrix is either conventional or heteroscedasticity consistent. Furthermore, when HCCM estimators are used, the resultant tests can be expected to possess very little power against the null in most practical applications. Throughout, the more favoured HCCM estimator is subject to the greatest loss in power.