The Power of Bootstrap and Asymptotic Tests

Russell Davidson and James MacKinnon ()

No 1035, Working Papers from Queen's University, Department of Economics

Abstract: We introduce the concept of the bootstrap discrepancy, which measures the difference in rejection probabilities between a bootstrap test based on a given test statistic and that of a (usually infeasible) test based on the true distribution of the statistic. We show that the bootstrap discrepancy is of the same order of magnitude under the null hypothesis and under non-null processes described by a Pitman drift. However, complications arise in the measurement of power. If the test statistic is not an exact pivot, critical values depend on which data-generating process (DGP) is used to determine the distribution under the null hypothesis. We propose as the proper choice the DGP which minimizes the bootstrap discrepancy. We also show that, under an asymptotic independence condition, the power of both bootstrap and asymptotic tests can be estimated cheaply by simulation. The theory of the paper and the proposed simulation method are illustrated by Monte Carlo experiments using the logit model.

Keywords: bootstrap test; bootstrap discrepancy; Pitman drift; drifting DGP; Monte Carlo; test power; power; asymptotic test (search for similar items in EconPapers)
JEL-codes: C12 C15 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: Written
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Forthcoming in Journal of Econometrics

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Related works:
Journal Article: The power of bootstrap and asymptotic tests (2006)
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