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Bayesian Approaches to Cointegration


  • Gary Koop


  • Rodney Strachan
  • Herman van Dijk
  • Mattias Villani


The purpose of this paper is to survey and critically assess the Bayesian cointegration literature. In one sense, Bayesian analysis of cointegration is straightforward. The researcher can combine the likelihood function with a prior and do Bayesian inference with the resulting posterior. However, interesting and empirically important issues of global and local identification (and, as a result, prior elicitation) arise from the fact that the matrix of long run parameters is potentially of reduced rank. As we shall see, these identification problems can cause serious problems for Bayesian inference. For instance, a common noninformative prior can lead to a posterior distribution which is improper (i.e. is not a valid p.d.f. since it does not integrate to one) thus precluding valid statistical inference. This issue was brought forward by Kleibergen and Van Dijk (1994, 1998). The development of the Bayesian cointegration literature reflects an increasing awareness of these issues and this paper is organized to reflect this development. In particular, we begin by discussing early work, based on VAR or Vector Moving Average (VMA) representations which ignored these issues. We then proceed to a discussion of work based on the ECM representation, beginning with a simple specification using the linear normalization and normal priors before moving onto the recent literature which develops methods for sensible treatment of the identification issues.
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Suggested Citation

  • Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004. "Bayesian Approaches to Cointegration," Discussion Papers in Economics 04/27, Division of Economics, School of Business, University of Leicester.
  • Handle: RePEc:lec:leecon:04/27

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    References listed on IDEAS

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    Cited by:

    1. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    2. Andrea Silvestrini, 2010. "Testing fiscal sustainability in Poland: a Bayesian analysis of cointegration," Empirical Economics, Springer, vol. 39(1), pages 241-274, August.
    3. Gareth W. Peters & Balakrishnan Kannan & Ben Lasscock & Chris Mellen, 2010. "Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model," Papers 1004.3830,
    4. Fuentes-Albero, Cristina & Melosi, Leonardo, 2013. "Methods for computing marginal data densities from the Gibbs output," Journal of Econometrics, Elsevier, vol. 175(2), pages 132-141.
    5. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
    6. Kociecki, Andrzej, 2012. "Orbital Priors for Time-Series Models," MPRA Paper 42804, University Library of Munich, Germany.
    7. Villani, Mattias, 2005. "Bayesian Inference of General Linear Restrictions on the Cointegration Space," Working Paper Series 189, Sveriges Riksbank (Central Bank of Sweden).

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