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Abstract
Bootstrap tests are tests for which the signicance level is calculated using some variant of the bootstrap which may be parametric or nonparametric We show that the power of a bootstrap test will generally be very close to the power of the asymptotic test on which it is based provided that both tests are properly adjusted to have the correct size We also discuss the loss of power that can occur when the number of bootstrap samples is relatively small Some Monte Carlo results for two forms of omitted variable test in logit models are presented These illustrate the theoretical results of the paper and demonstrate that the sizeadjusted power of asymptotic tests can vary greatly depending on the method used for size adjustment