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A Note on Johansen's Cointegration Procedure When Trends Are Present

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  • Perron, Pierre
  • Campbell, John Y

Abstract

This note discusses some issues that arise when Johansen's (1991) framework is used to analyze cointegrating relationships among variables with deterministic linear time trends. We distinguish "stochastic" and "deterministic" cointegration, arguing that stochastic cointegration is sufficient for the existence of an error correction representation and that it is often the hypothesis of interest in empirical applications. We show that Johansen's (1991) method, which includes only a constant term in the estimated regression system, does not allow for stochastic cointegration. We propose to modify Johansen's method by including a vector of deterministic linear trends in the estimated model. We present tabulated critical values of the maximal eigen value and trace statistics appropriate for this case. We discuss the circumstances under which our modification may be useful.

Suggested Citation

  • Perron, Pierre & Campbell, John Y, 1993. "A Note on Johansen's Cointegration Procedure When Trends Are Present," Empirical Economics, Springer, vol. 18(4), pages 777-789.
  • Handle: RePEc:spr:empeco:v:18:y:1993:i:4:p:777-89
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    Cited by:

    1. Celine Gauthier & David Tessier, 2002. "Supply Shocks and Real Exchange Rate Dynamics: Canadian Evidence," Staff Working Papers 02-31, Bank of Canada.
    2. Pesaran, M. Hashem & Shin, Yongcheol & Smith, Richard J., 2000. "Structural analysis of vector error correction models with exogenous I(1) variables," Journal of Econometrics, Elsevier, vol. 97(2), pages 293-343, August.
    3. Robinson, P.M. & Iacone, F., 2005. "Cointegration in fractional systems with deterministic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 263-298.
    4. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
    5. Deschamps, Philippe J., 1998. "Full maximum likelihood estimation of dynamic demand models," Journal of Econometrics, Elsevier, vol. 82(2), pages 335-359, February.
    6. Matei Demetrescu & Helmut Lütkepohl & Pentti Saikkonen, 2009. "Testing for the cointegrating rank of a vector autoregressive process with uncertain deterministic trend term," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 414-435, November.
    7. Guillaume Chevillon, 2017. "Robust cointegration testing in the presence of weak trends, with an application to the human origin of global warming," Econometric Reviews, Taylor & Francis Journals, vol. 36(5), pages 514-545, May.
    8. Maurice Kugler & Reza Ofoghi, 2005. "Does Insurance Promote Economic Growth? Evidence from the UK," Money Macro and Finance (MMF) Research Group Conference 2005 8, Money Macro and Finance Research Group.
    9. Harris, David & Leybourne, Stephen J. & Taylor, A.M. Robert, 2016. "Tests of the co-integration rank in VAR models in the presence of a possible break in trend at an unknown point," Journal of Econometrics, Elsevier, vol. 192(2), pages 451-467.
    10. Pierre Perron & Gabriel Rodríguez, "undated". "Residuals-based Tests for Cointegration with GLS Detrended Data," Boston University - Department of Economics - Working Papers Series wp2015-017, Boston University - Department of Economics, revised 19 Oct 2015.
    11. Lutkepohl, Helmut & Saikkonen, Pentti, 1999. "A lag augmentation test for the cointegrating rank of a VAR process," Economics Letters, Elsevier, vol. 63(1), pages 23-27, April.
    12. Qu, Zhongjun & Perron, Pierre, 2007. "A Modified Information Criterion For Cointegration Tests Based On A Var Approximation," Econometric Theory, Cambridge University Press, vol. 23(04), pages 638-685, August.
    13. Carsten Trenkler*, 2005. "The Effects of Ignoring Level Shifts on Systems Cointegration Tests," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 89(3), pages 281-301, August.
    14. Lee, Hahn S. & Siklos, Pierre L., 1995. "A note on the critical values for the maximum likelihood (seasonal) cointegration tests," Economics Letters, Elsevier, vol. 49(2), pages 137-145, August.
    15. Gerdesmeier, Dieter, 1996. "Die Rolle des Vermögens in der Geldnachfrage," Discussion Paper Series 1: Economic Studies 1996,05, Deutsche Bundesbank.
    16. Fukuda, Kosei, 2007. "Joint detection of unit roots and cointegration: Data-based simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(1), pages 28-36.
    17. repec:hal:journl:hal-00914830 is not listed on IDEAS
    18. Chau-Jung Kuo & Su-Lien Lu, 2005. "Taiwan's financial holding companies: an empirical investigation based on Markov regime-switching model," Applied Economics, Taylor & Francis Journals, vol. 37(5), pages 593-605.
    19. Lutkepohl, Helmut & Saikkonen, Pentti, 2000. "Testing for the cointegrating rank of a VAR process with a time trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 177-198, March.
    20. Niklas Ahlgren & Mikael Juselius, 2012. "Tests for cointegration rank and the initial condition," Empirical Economics, Springer, vol. 42(3), pages 667-691, June.
    21. Byeongseon, Seo, 1998. "Statistical inference on cointegration rank in error correction models with stationary covariates," Journal of Econometrics, Elsevier, vol. 85(2), pages 339-385, August.

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