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The Power of Single Equation Tests for Cointegration when the Cointegrating Vector is Prespecified

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  • Eric Zivot

    (The University of Washington)

Abstract

In this paper I present an alternative derivation of the asymptotic distribution of Kremers, Ericsson and Dolado's (1992) conditional ECM- based t-test for no-cointegration with a single prespecified cointegrating vector. This alternative distribution, which is identical to the distribution of Hansen's (1995) covariate augmented t-test for a unit root, is valid for weakly exogenous regressors and depends on a consistently estimable nuisance parameter that takes on values in the unit interval. I show analytically, using asymptotic power functions based on near cointegrated alternatives, that the ECM t-test with a prespecified cointegrating vector can have much higher power than single equation tests for cointegration based on estimating the cointegrating vector. I also characterize situations in which the ECM t-test computed with a misspecified cointegrating vector will have high power.

Suggested Citation

  • Eric Zivot, 1996. "The Power of Single Equation Tests for Cointegration when the Cointegrating Vector is Prespecified," Econometrics 9612001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:9612001
    Note: Type of Document - Adobe .pdf file; prepared on IBM-PC; pages: 25; figures: 25, in separate file ecmfigs.pdf
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    References listed on IDEAS

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    1. repec:cup:etheor:v:11:y:1995:i:5:p:984-1014 is not listed on IDEAS
    2. Kremers, Jeroen J M & Ericsson, Neil R & Dolado, Juan J, 1992. "The Power of Cointegration Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 325-348, August.
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    9. Inder, Brett, 1993. "Estimating long-run relationships in economics : A comparison of different approaches," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 53-68.
    10. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    11. Peter Boswijk, H., 1994. "Testing for an unstable root in conditional and structural error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 37-60, July.
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    13. Horvath, Michael T.K. & Watson, Mark W., 1995. "Testing for Cointegration When Some of the Cointegrating Vectors are Prespecified," Econometric Theory, Cambridge University Press, vol. 11(5), pages 984-1014, October.
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    15. repec:cup:etheor:v:11:y:1995:i:5:p:1148-71 is not listed on IDEAS
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    Cited by:

    1. Miguel Arranz & Alvaro Escribano, 2006. "Bootstrapping cointegration tests under structural co-breaks: A robust extended ECM test," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 179-208, June.
    2. Christoffersen, Peter F & Diebold, Francis X, 1998. "Cointegration and Long-Horizon Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 450-458, October.
    3. Joakim Westerlund, 2007. "Testing for Error Correction in Panel Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(6), pages 709-748, December.
    4. Neil R. Ericsson & James G. MacKinnon, 2002. "Distributions of error correction tests for cointegration," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 285-318, June.
    5. Ming Chien Lo & Eric Zivot, 1999. "Threshold Cointegration and Nonlinear Adjustment to the Law of One Price," Discussion Papers in Economics at the University of Washington 0030, Department of Economics at the University of Washington.
    6. Allan W. Gregory & Alfred A. Haug & Nicoletta Lomuto, 2004. "Mixed signals among tests for cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(1), pages 89-98.
    7. Berben, R-P. & van Dijk, D.J.C., 1998. "Does the absence of cointegration explain the typical findings in long horizon regressions?," Econometric Institute Research Papers EI 9814, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Jing Li & Junsoo Lee, 2010. "ADL tests for threshold cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 241-254, July.
    9. Bingcheng Yan & Eric Zivot, 2007. "A Structural Analysis of Price Discovery Measures," Working Papers UWEC-2006-08-FC, University of Washington, Department of Economics, revised Apr 2007.

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    More about this item

    Keywords

    cointegration; common factor; error correction model; local power; misspecification; near-cointegration; strong exogeneity; weak exogeneity.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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