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The Size Distortion of Bootstrap Tests

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  • Davidson, Russell
  • MacKinnon, James G.

Abstract

Bootstrap tests are tests for which the signicance level is calculated by some sort of bootstrap procedure which may be parametric or nonparametric We provide a theoretical framework in which to study the size distortions of bootstrap P values We show that in many circumstances the size distortion of a bootstrap test will be one whole order of magnitude smaller than that of the corresponding asymptotic test 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 Monte Carlo results are presented for the case of nonnested hypothesis tests These results conrm and illustrate the utility of our theoretical results and they also suggest that bootstrap tests may often work extremely well in practice This research was supported in part by grants from the Social Sciences and Humanities Research Council of Canada An earlier version was presented at Universidad Carlos III de Madrid Universidad Complutense de Madrid Cambridge University INSEECREST Paris CORE LouvainlaNeuve the Tinbergen Institute Amsterdam the University of Geneva the European University Institute Florence the ESRC Econometrics Conference Bristol and the Berkeley Symposium on the Bootstrap We are grateful to many seminar participants and to two anonymous referees for comments on the earlier version We are especially grateful to Joel Horowitz not only for comments but also for his probing questions that led us to clarify the paper The paper was written while the second author was visiting GREQAM

Suggested Citation

  • Davidson, Russell & MacKinnon, James G., 1996. "The Size Distortion of Bootstrap Tests," Queen's Institute for Economic Research Discussion Papers 273347, Queen's University - Department of Economics.
    • Handle: RePEc:ags:queddp:273347
    DOI: 10.22004/ag.econ.273347
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    References listed on IDEAS

    as
    1. 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.
    2. Davidson, Russell & MacKinnon, James G, 1987. "Implicit Alternatives and the Local Power of Test Statistics," Econometrica, Econometric Society, vol. 55(6), pages 1305-1329, November.
    3. MacKinnon, James G. & White, Halbert & Davidson, Russell, 1983. "Tests for model specification in the presence of alternative hypotheses : Some further results," Journal of Econometrics, Elsevier, vol. 21(1), pages 53-70, January.
    4. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    6. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    7. Horowitz, J., 1996. "Bootstrap Critical Values For Tests Based On The Smoothed Maximum Score Estimator," SFB 373 Discussion Papers 1996,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    9. 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.
    10. Joel L. Horowitz, 1996. "Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator," Econometrics 9603003, University Library of Munich, Germany.
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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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