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Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes

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  • Pentti Saikkonen

Abstract

This paper develops test procedures for testing the validity of general linear identifying restrictions imposed on cointegrating vectors in the context of a vector autoregressive model. In addition to overidentifying restrictions the considered restrictions may also involve normalizing restrictions. Tests for both types of restrictions are developed and their asymptotic properties are obtained. Under the null hypothesis tests for normalizing restrictions have an asymptotic "multivariate unit root distribution", similar to that obtained for the likelihood ratio test for cointegration, while tests for overidentifying restrictions have a standard chi-square limiting distribution. Since these two types of tests are asymptotically independent they are easy to cotnbine to an overall test for the spccifed identifying restrictions. An overall test of this kind can consistently reveal the failure of the identifying restrictions in a wider class of cases than previous tests which only test for overidentifying restrictions.

Suggested Citation

  • Pentti Saikkonen, 1999. "Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 235-257.
    • Handle: RePEc:taf:emetrv:v:18:y:1999:i:3:p:235-257
    DOI: 10.1080/07474939908800444
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    Cited by:

    1. Karaman Örsal, Deniz Dilan & Droge, Bernd, 2014. "Panel cointegration testing in the presence of a time trend," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 377-390.
    2. Santos, João & Domingos, Tiago & Sousa, Tânia & St. Aubyn, Miguel, 2018. "Useful Exergy Is Key in Obtaining Plausible Aggregate Production Functions and Recognizing the Role of Energy in Economic Growth: Portugal 1960–2009," Ecological Economics, Elsevier, vol. 148(C), pages 103-120.
    3. 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.
    4. Martin Wagner & Jaroslava Hlouskova, 2010. "The Performance of Panel Cointegration Methods: Results from a Large Scale Simulation Study," Econometric Reviews, Taylor & Francis Journals, vol. 29(2), pages 182-223, April.
    5. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    6. She, Rui & Ling, Shiqing, 2020. "Inference in heavy-tailed vector error correction models," Journal of Econometrics, Elsevier, vol. 214(2), pages 433-450.
    7. 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.
    8. Jorg Breitung, 2005. "A Parametric approach to the Estimation of Cointegration Vectors in Panel Data," Econometric Reviews, Taylor & Francis Journals, vol. 24(2), pages 151-173.
    9. 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.
    10. In Choi, 2012. "Panel Cointegration," Working Papers 1208, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    11. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.
    12. Droge, Bernd & Örsal, Deniz Dilan Karaman, 2009. "Panel cointegration testing in the presence of a time trend," SFB 649 Discussion Papers 2009-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. 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.
    14. 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.
    15. repec:hum:wpaper:sfb649dp2009-005 is not listed on IDEAS
    16. 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.
    17. Kurita, Takamitsu, 2020. "Normalising cointegrating relationships subject to long-run exclusion," Economics Letters, Elsevier, vol. 192(C).

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