In this note we consider the asymptotic power functions of some
bootstrap unit root tests under local alternatives and show that they
are in fact the same as for ordinary unit root tests. This is
regardless of whether the differences of the observations, i.e., the
so-called restricted residuals, or the ordinary least squares residuals
are used to construct the resampled observations. We also consider
models containing a constant and a linear trend and the DF-GLS tests
proposed by Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813–836). A
small Monte Carlo experiment is included.I
thank the associate editor, Bruce E. Hansen, and three anonymous referees
for very constructive comments on the previous versions of the
manuscript.