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Testing for a Valid Normalization of Cointegrating Vectors in Vector Autoregressive Processes


  • Luukkonen, Ritva
  • Ripatti, Antti
  • Saikkonen, Pentti


This article develops test procedures for checking the validity of general normalizing restrictions imposed on cointegrating vectors in vector autoregressive processes. Such test procedures are of importance because normalizing restrictions, possibly combined with overidentifying restrictions, are often necessary for a proper interpretation of cointegrating vectors. The null hypothesis of the authors' tests assumes that the employed normalization is valid or, alternatively, that certain linear combinations of the considered series are not cointegrated. The asymptotic distribution theory of these tests agrees with that of likelihood ratio tests for cointegration. The practical usefulness of the proposed tests is demonstrated by Monte Carlo simulation and an empirical application to interest-rate data.

Suggested Citation

  • Luukkonen, Ritva & Ripatti, Antti & Saikkonen, Pentti, 1999. "Testing for a Valid Normalization of Cointegrating Vectors in Vector Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(2), pages 195-204, April.
  • Handle: RePEc:bes:jnlbes:v:17:y:1999:i:2:p:195-204

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    References listed on IDEAS

    1. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 119-136, Suppl. De.
    2. repec:adr:anecst:y:1991:i:20-21:p:06 is not listed on IDEAS
    3. Balke, Nathan S & Fomby, Thomas B, 1994. "Large Shocks, Small Shocks, and Economic Fluctuations: Outliers in Macroeconomic Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(2), pages 181-200, April-Jun.
    4. Peracchi, Franco, 1991. "Robust M-Tests," Econometric Theory, Cambridge University Press, vol. 7(01), pages 69-84, March.
    5. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207, June.
    6. Hoek, Henk & Lucas, Andre & van Dijk, Herman K., 1995. "Classical and Bayesian aspects of robust unit root inference," Journal of Econometrics, Elsevier, vol. 69(1), pages 27-59, September.
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    Cited by:

    1. Bertocco Giancarlo, 2006. "Are banks special? A note on Tobin’s theory of financial intermediaries," Economics and Quantitative Methods qf0605, Department of Economics, University of Insubria.
    2. Paolo Paruolo, 2006. "The Likelihood Ratio Test for the Rank of a Cointegration Submatrix," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 921-948, December.
    3. Jaroslava Hlouskova & Martin Wagner, 2009. "Finite Sample Correction Factors for Panel Cointegration Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 851-881, December.
    4. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    5. Kerry Patterson & Michael A. Thornton, 2013. "A review of econometric concepts and methods for empirical macroeconomics," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 2, pages 4-42 Edward Elgar Publishing.
    6. Holtemöller, Oliver, 2002. "Money and banks: Some theory and empirical evidence for Germany," SFB 373 Discussion Papers 2002,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Markku Lanne, 2000. "Near unit roots, cointegration, and the term structure of interest rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 513-529.
    8. Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004. "Bayesian Approaches to Cointegration," Discussion Papers in Economics 04/27, Department of Economics, University of Leicester.
    9. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    10. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.

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