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The Size and Power of Bootstrap Tests for Linear Restrictions in Misspecified Cointegrating Relationships

  • Alessandra Canepa

    (University of Southampton)

  • Raymond O'Brien

    (University of Southampton)

This paper considers computer intensive methods for inference on cointegrating vectors in maximum likelihood analysis. It investigates the robustness of LR , Wald tests and an F-type test for linear restrictions on cointegrating space to misspecification on the number of cointegrating relations. In addition, since all the distributional results within the maximum likelihood cointegration model rely on asymptotic considerations, it is important to consider the sensitivity of inference procedures to the sample size. In this paper we use bootstrap hypothesis testing as a way to improve inference for linear restriction on the cointegrating space. We find that the resampling procedure is a very useful device for tests that lack the invariance property such as the Wald test, where the size distortion of the bootstrap test converges to zero even for a sample size T=50. Moreover, it turns out that when the number of cointegrating vectors are correctly specified the bootstrap succeeds where the asymptotic approximation is not satisfactory, that is, for a sample size T

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1807.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1807
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  1. O'Brien, R.J., 1997. "Further curiosa in 'spurious' cointegration," Discussion Paper Series In Economics And Econometrics 9704, Economics Division, School of Social Sciences, University of Southampton.
  2. Davidson, R. & Mackinnon, J.G., 1996. "The Size and Power of Bootstrap Tests," G.R.E.Q.A.M. 96a03, Universite Aix-Marseille III.
  3. O'Brien, R. J., 1996. "The curious case of spurious cointegration," Discussion Paper Series In Economics And Econometrics 9638, Economics Division, School of Social Sciences, University of Southampton.
  4. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
  5. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  6. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
  7. Bent Nielsen, . "On the distribution of tests of cointegration rank," Economics Papers 1997-W10, Economics Group, Nuffield College, University of Oxford.
  8. Fachin, Stefano, 2000. " Bootstrap and Asymptotic Tests of Long-Run Relationships in Cointegrated Systems," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(4), pages 543-51, September.
  9. Podivinsky, Jan M., 1998. "Testing misspecified cointegrating relationships," Economics Letters, Elsevier, vol. 60(1), pages 1-9, July.
  10. Johansen, Soren, 2002. "A small sample correction for tests of hypotheses on the cointegrating vectors," Journal of Econometrics, Elsevier, vol. 111(2), pages 195-221, December.
  11. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
  12. Andrade, I.C. & O'Brien, R. & Podivinsky, J.M., 1994. "Cointegration tests and mean shifts," Discussion Paper Series In Economics And Econometrics 9405, Economics Division, School of Social Sciences, University of Southampton.
  13. Harris, R I D, 1992. "Small Sample Testing for Unit Roots," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(4), pages 615-25, November.
  14. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
  15. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  16. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
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