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.

Notes

1 Given our Monte Carlo analysis is based on random N(0,1) errors, the lagged level term in the Dickey Fuller regression Δy_t = βy_t-1 + η_i may take negative values. For this reason, our heteroscedastic form relates σ_t to . rather than . as in Long and Ervin. See Section 4.1.

2 The papers of Wichern, Miller and Hsu (1976), Hsu (1977), Inclan (1993) and Inclan and Tiao (1994) can be considered as the rare exceptions to this where a break in innovation variance is considered in more general circumstances. Kim et al. (2002) cite Hamori and Tokihisa (1997) as the only case where the impact of a variance break upon an integrated series is examined.

3 This ranking is evident for each break point considered independently.

4 Note that the recently proposed tF test of Kim et al. (2002) has similar size properties to the DF tests employing the four heteroscedasticity consistent covariance matrices considered here, but has superior power.

5 The use of resampling methods has been suggested by a referee as a potential solution to the problem of inference in the presence of heteroscedasticity.