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The Size and Power of Bootstrap Tests

  • Davidson, R.
  • Mackinnon, J.G.

We show that, in many circumstances, the size distortion of a bootstrap P value for a test will be one whole order of magnitude smaller than that of the corresponding asymptotic P value. We also show that, at least in the parametric case, the magnitude of the distorsion will depend on the shape of what we call the P value function. As regards the power of bootstrap tests, we show that the size-corrected power of a bootstrap test differs from that of the corresponding asymptotic test only by an amount of the same order magnitude as the size distortion, and of arbitrary sign.

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Paper provided by Universite Aix-Marseille III in its series G.R.E.Q.A.M. with number 96a03.

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Length: 33 pages
Date of creation: 1996
Date of revision:
Handle: RePEc:fth:aixmeq:96a03
Contact details of provider: Postal: G.R.E.Q.A.M., (GROUPE DE RECHERCHE EN ECONOMIE QUANTITATIVE D'AIX MARSEILLE), CENTRE DE VIEILLE CHARITE, 2 RUE DE LA CHARITE, 13002 MARSEILLE.
Phone: 04.91.14.07.70
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Web page: http://www.greqam.fr/
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  1. Horowitz, J.L., 1995. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Working Papers 95-10, University of Iowa, Department of Economics.
  2. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-21, May.
  3. Russell Davidson & James G. MacKinnon, 1980. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Working Papers 378, Queen's University, Department of Economics.
  4. Godfrey, L. G. & Pesaran, M. H., 1983. "Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence," Journal of Econometrics, Elsevier, vol. 21(1), pages 133-154, January.
  5. 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.
  6. Godfrey, Leslie G, 1978. "Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1303-10, November.
  7. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  8. Kiviet, Jan F, 1986. "On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships," Review of Economic Studies, Wiley Blackwell, vol. 53(2), pages 241-61, April.
  9. J. L. Horowitz, 1995. "Bootstrap Methods In Econometrics: Theory And Numerical Performance," SFB 373 Discussion Papers 1995,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  10. Attfield, C. L. F., 1995. "A Bartlett adjustment to the likelihood ratio test for a system of equations," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 207-223.
  11. Davidson, Russell & MacKinnon, James G., 1992. "Regression-based methods for using control variates in Monte Carlo experiments," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 203-222.
  12. Weber, N. C., 1984. "On resampling techniques for regression models," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 275-278, October.
  13. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
  14. Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-42, July.
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