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Tests for Long-Run Granger Non-Causality in Cointegrated Systems


  • Yamamoto, Taku
  • Kurozumi, Eiji


In this paper, we propose a new approach to test the hypothesis of long-run Granger non-causality in cointegrated systems. We circumvent the problem of singularity of the variance-covariance matrix associated with the usual Wald type test by proposing a generalized inverse procedure, and an alternative simple procedure which can be approximated by a suitable chi-square distribution. A test for the ranks of submatrices of the cointegration matrix and its orthogonal matrix plays a vital role in the former. The relevant small sample experiments indicate that the proposed method performs reasonably well in finite samples. As empirical applications, we examine long-run causal relations among long-term interest rates of three and five nations.

Suggested Citation

  • Yamamoto, Taku & Kurozumi, Eiji, 2003. "Tests for Long-Run Granger Non-Causality in Cointegrated Systems," Discussion Papers 2003-12, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2003-12 Note: February 2001; First Revision, February 2002; Second Revision, February 2003; Third Revision, June 2003

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    References listed on IDEAS

    1. Osterwald-Lenum, Michael, 1992. "A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 461-472, August.
    2. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, June.
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    Cited by:

    1. Yiannis Kamarianakis & Vagelis Kaslis, 2005. "Geographical competition-complementarity relationships between Greek regional economies," ERSA conference papers ersa05p552, European Regional Science Association.
    2. Majid M. Al-Sadoon, 2015. "Testing subspace Granger causality," Economics Working Papers 1495, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Ingianni, Andrea, 2012. "Intra-European Union trade openness and new members’ output convergence: A time-series analysis," Economics Discussion Papers 2012-5, School of Economics, Kingston University London.
    4. Al-Sadoon, Majid M., 2014. "Geometric and long run aspects of Granger causality," Journal of Econometrics, Elsevier, vol. 178(P3), pages 558-568.
    5. Ghysels, Eric & Hill, Jonathan B. & Motegi, Kaiji, 2016. "Testing for Granger causality with mixed frequency data," Journal of Econometrics, Elsevier, vol. 192(1), pages 207-230.
    6. Bilge Kagan Ozdemir, 2009. "Banking Sector Stability During The Process Of Euro Adoption," Anadolu University Journal of Social Sciences, Anadolu University, vol. 9(1), pages 123-1236, June.
    7. Stephanie-Carolin Grosche, 2014. "What Does Granger Causality Prove? A Critical Examination of the Interpretation of Granger Causality Results on Price Effects of Index Trading in Agricultural Commodity Markets," Journal of Agricultural Economics, Wiley Blackwell, vol. 65(2), pages 279-302, June.
    8. 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.
    9. Fanelli, Luca & Paruolo, Paolo, 2010. "Speed of adjustment in cointegrated systems," Journal of Econometrics, Elsevier, vol. 158(1), pages 130-141, September.
    10. repec:dau:papers:123456789/1483 is not listed on IDEAS

    More about this item


    Vector autoregression; Cointegration; Long-run causality; Hypothesis testing;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General


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