On the Long-Run Variance Ratio Test for a Unit Root

This paper investigates the effects of consistent and inconsistent long-run variance estimation on a unit root test based on the generalization of the von Neumann ratio. The results from the Monte Carlo experiments suggest that the tests based on an inconsistent estimator have less size distortion and more stability of size across different autocorrelation speciÞcations as compared to the tests based on a consistent estimator. This improvement in size property, however, comes at the cost of a loss in power. The Þnite sample power, as well as the local asymptotic power, of the tests with an inconsistent estimator is shown to be much lower than that of conventional tests. This Þnding resembles the case of the autocorrelation robust test in the standard regression context. The paper also points out that combining consistent and inconsistent estimators in the long-run variance ratio test for a unit root is one possibility of balancing the size and power.