IDEAS home Printed from
   My bibliography  Save this paper

Bayesian Testing in Cointegration Models using the Jeffreys' Prior


  • Richard Kleijn

    (Erasmus University Rotterdam)


We develop a Bayesian cointegration test statistic that can be used under a Jeffreys' prior. The test statistic is equal to the posterior expectation of the classical score statistic. Under the assumption of a full rank value of the long run multiplier the test statistic is a random variable with a chi-squared distribution. We evaluate whether the value of the test statistic under the restriction of cointegration is a plausible realization from its distribution under the encompassing, full rank model. We provide the posterior simulator that is needed to compute the test statistic. The simulator utilizes the invariance properties of the Jeffreys' prior such that the parameter drawings from a suitably rescaled model can be used. The test statistic can straightforwardly be extended to a more general model setting. For example, we show that structural breaks in the constant or trend and general mixtures of normal disturbances can be modelled, because conditional on some latent parameters all derivations still hold. We apply the Bayesian cointegration statistic to the Danish dataset of Johansen and Juselius (1990) and to four artificial examples to illustrate the use of the statistic as a diagnostic tool.

Suggested Citation

  • Richard Kleijn, 2000. "Bayesian Testing in Cointegration Models using the Jeffreys' Prior," Econometric Society World Congress 2000 Contributed Papers 1445, Econometric Society.
  • Handle: RePEc:ecm:wc2000:1445

    Download full text from publisher

    File URL:
    File Function: main text
    Download Restriction: no

    References listed on IDEAS

    1. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    2. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
    3. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December.
    4. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    5. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:wc2000:1445. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.