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The Size and Power of Bootstrap Tests

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Author Info

  • Russell Davidson
  • James G. MacKinnon

Abstract

Bootstrap tests are tests for which the significance level is calculated by some sort of bootstrap procedure, which may be parametric or nonparametric. 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 distortion 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 of magnitude as the size distortion, and of arbitrary sign. Monte Carlo results are presented for two cases of interest: tests for serial correlation and nonnested hypothesis tests. These results confirm and illustrate the utility of our theoretical results, and they also suggest that bootstrap tests will often work extremely well in practice.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_932.pdf
File Function: First version 1996
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 932.

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Length: 41 pages
Date of creation: Feb 1996
Date of revision:
Handle: RePEc:qed:wpaper:932

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Keywords: bootstrapping; hypothesis testing; Non-nested hypothesis tests; P values; tests for serial correlation;

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References

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  1. 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.
  2. 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.
  3. Horowitz, J.L., 1995. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Working Papers 95-10, University of Iowa, Department of Economics.
  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.
  5. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  6. 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.
  7. 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.
  8. Weber, N. C., 1984. "On resampling techniques for regression models," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 275-278, October.
  9. 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.
  10. repec:wop:humbsf:1995-63 is not listed on IDEAS
  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. 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.
  13. Davidson , R. & Mackinnon, J.G., 1985. "Implicit alternatives and the local power of test statistics," CORE Discussion Papers 1985025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. 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.
  15. 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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Citations

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Cited by:
  1. Siani, Carole & de Peretti, Christian, 2007. "Analysing the performance of bootstrap neural tests for conditional heteroskedasticity in ARCH-M models," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2442-2460, February.
  2. Coakley, Jerry & Fuertes, Ana-Maria, 2006. "Testing for sign and amplitude asymmetries using threshold autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 30(4), pages 623-654, April.
  3. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
  4. Davidson, Russell & MacKinnon, James G., 2002. "Bootstrap J tests of nonnested linear regression models," Journal of Econometrics, Elsevier, vol. 109(1), pages 167-193, July.
  5. Harris, R. I. D. & Judge, G., 1998. "Small sample testing for cointegration using the bootstrap approach," Economics Letters, Elsevier, vol. 58(1), pages 31-37, January.
  6. Alessandra Canepa & Raymond O'Brien, 2000. "The Size and Power of Bootstrap Tests for Linear Restrictions in Misspecified Cointegrating Relationships," Econometric Society World Congress 2000 Contributed Papers 1807, Econometric Society.
  7. Li, Hongyi & Xiao, Zhijie, 2000. "On bootstrapping regressions with unit root processes," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 261-267, July.
  8. Pinkse, Joris & Slade, Margaret E., 1998. "Contracting in space: An application of spatial statistics to discrete-choice models," Journal of Econometrics, Elsevier, vol. 85(1), pages 125-154, July.
  9. Jeong, Jinook & Chung, Seoung, 2001. "Bootstrap tests for autocorrelation," Computational Statistics & Data Analysis, Elsevier, vol. 38(1), pages 49-69, November.
  10. Dennis Philip & Chihwa Kao & Giovanni Urga, 2007. "Testing for Instability in Factor Structure of Yield Curves," Center for Policy Research Working Papers 96, Center for Policy Research, Maxwell School, Syracuse University.
  11. Martin, Michael A., 2007. "Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6321-6342, August.

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