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This paper studies the behavior of recently proposed bootstrap tests for the null hypothesis of stationarity when the data are generated under the alternative hypothesis of a unit root. Using Monte Carlo experiments and empirical examples, it is shown that the power of these tests critically depends on the type of bootstrap employed. Specifically, while tests based on the stationary bootstrap have power functions that are increasing with respect to sample size, those based on the sieve bootstrap have non-monotonic power functions. We argue that this difference arises from the fact that the latter procedure does not impose the null hypothesis when generating the bootstrap samples while the former ensures that the bootstrap samples are stationary, conditional on the original data. Our results therefore suggest that while both forms of bootstrap are effective at providing improved distributional approximations …