This paper investigates the effects of consistent and inconsistent
long-run variance estimation on a test for a unit root, based on the
generalization of the von Neumann ratio. The results from the Monte Carlo
experiments suggest that the unit root tests based on an inconsistent
estimator have less size distortion and more stability of size across
different autocorrelation specifications 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 finite-sample power, in addition to
the local asymptotic power, of the tests with an inconsistent estimator is
shown to be much lower than that of conventional tests. This finding can
be well generalized to the test for cointegration in a multivariate
system. The paper also points out that combining consistent and
inconsistent estimators in the long-run variance ratio test is one
possibility of balancing the size and power.The authors thank two anonymous referees, Pentti Saikkonen,
and participants of the 2004 Midwest Econometrics Group meetings, 2005
Spring Meetings of The Japanese Economic Association, and a workshop at
Vanderbilt University for helpful comments and suggestions.