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The Power of Bootstrap and Asymptotic Tests

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Author Info
Russell Davidson () (McGill University)
James G. MacKinnon () (Queen's University)

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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.

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File URL: http://www.econ.queensu.ca/working_papers/papers/qed_wp_1035.pdf
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File Function: First version 2004
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Publisher Info
Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1035.

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Length: 22 pages
Date of creation: Jul 2004
Date of revision:
Publication status: Forthcoming in Journal of Econometrics
Handle: RePEc:qed:wpaper:1035

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Related research
Keywords: bootstrap test; bootstrap discrepancy; Pitman drift; drifting DGP; Monte Carlo; test power; power; asymptotic test;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, Blackwell Publishing, vol. 66(1), pages 1-26, January.
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  2. Davidson, Russell & MacKinnon, James G, 1987. "Implicit Alternatives and the Local Power of Test Statistics," Econometrica, Econometric Society, vol. 55(6), pages 1305-29, November. [Downloadable!] (restricted)
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  3. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June. [Downloadable!]
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  4. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April. [Downloadable!] (restricted)
  5. Russell Davidson & James G. MacKinnon, 2001. "Bootstrap Tests: How Many Bootstraps?," Working Papers 1036, Queen's University, Department of Economics. [Downloadable!]
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  6. Davidson, Russell & MacKinnon, James G., 1984. "Convenient specification tests for logit and probit models," Journal of Econometrics, Elsevier, vol. 25(3), pages 241-262, July. [Downloadable!] (restricted)
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  7. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jamel Jouini, 2006. "Bootstrap Tests in Bivariate VAR Process with Single Structural Change : Power versus Corrected Size and Empirical Illustration," Working Papers halshs-00410759_v1, HAL. [Downloadable!]
  2. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics. [Downloadable!]
  3. Ahlgren, Niklas & Antell, Jan, 2009. "The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series," Working Papers 541, Hanken School of Economics. [Downloadable!]
  4. Russell Davidson & James G. MacKinnon, 2006. "Improving the Reliability of Bootstrap Tests with the Fast Double Bootstrap," Working Papers 1044, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
  5. Carsten Trenkler, 2006. "Bootstrapping Systems Cointegration Tests with a Prior Adjustment for Deterministic Terms," SFB 649 Discussion Papers SFB649DP2006-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  6. James G. MacKinnon, 2006. "Bootstrap Methods in Econometrics," Working Papers 1028, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
  7. Claude Lopez, 2005. "A Panel Unit Root Test with Good Power in Small Samples," University of Cincinnati, Economics Working Papers Series 2005-01, University of Cincinnati, Department of Economics, revised 2007. [Downloadable!]
    Other versions:
  8. Russell Davidson & James G. MacKinnon, 2006. "Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables," Working Papers 1024, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
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