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Bayesian Inference of General Linear Restrictions on the Cointegration Space

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Author Info
Villani, Mattias () (Research Department, Central Bank of Sweden)

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Abstract

The degree of empirical support of a priori plausible structures on the cointegration vectors has a central role in the analysis of cointegration. Villani (2000) and Strachan and van Dijk (2003) have recently proposed finite sample Bayesian procedures to calculate the posterior probability of restrictions on the cointegration space, using the existence of a uniform prior distribution on the cointegration space as the key ingredient. The current paper extends this approach to the empirically important case with different restrictions on the individual cointegration vectors. Prior distributions are proposed and posterior simulation algorithms are developed. Consumers' expenditure data for the US is used to illustrate the robustness of the results to variations in the prior. A simulation study shows that the Bayesian approach performs remarkably well in comparison to other more established methods for testing restrictions on the cointegration vectors.

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Publisher Info
Paper provided by Sveriges Riksbank (Central Bank of Sweden) in its series Working Paper Series with number 189.

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Length: 22 pages
Date of creation: 01 Sep 2005
Date of revision:
Handle: RePEc:hhs:rbnkwp:0189

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Postal: Sveriges Riksbank, SE-103 37 Stockholm, Sweden
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Related research
Keywords: Bayesian inference; Cointegration; Posterior probability; Restrictions.;

Other versions of this item:

Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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  1. Johansen, S ren, 2000. "A Bartlett Correction Factor For Tests On The Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 16(05), pages 740-778, October. [Downloadable!]
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  2. Gredenhoff, Mikael & Jacobson, Tor, 2001. "Bootstrap Testing Linear Restrictions on Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 63-72, January.
  3. Johansen, Soren, 1995. "Identifying restrictions of linear equations with applications to simultaneous equations and cointegration," Journal of Econometrics, Elsevier, vol. 69(1), pages 111-132, September. [Downloadable!] (restricted)
  4. Villani, Mattias, 2005. "Bayesian Reference Analysis Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(02), pages 326-357, April. [Downloadable!]
  5. Rodney W. Strachan & Herman K. Dijk, 2003. "Bayesian Model Selection with an Uninformative Prior," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 863-876, December. [Downloadable!] (restricted)
    Other versions:
  6. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
  7. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October. [Downloadable!] (restricted)
  8. Gael M. Martin, 2000. "US deficit sustainability: a new approach based on multiple endogenous breaks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(1), pages 83-105. [Downloadable!]
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  9. Rodney W Strachan & Herman K van Dijik, 2005. "Valuing Structure, Model Uncertainty and Model Averaging in Vector Autoregressive Process," Money Macro and Finance (MMF) Research Group Conference 2005 30, Money Macro and Finance Research Group. [Downloadable!]
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  10. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November. [Downloadable!] (restricted)
  11. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  12. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
    Other versions:
  13. 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. [Downloadable!] (restricted)
    Other versions:
  14. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January. [Downloadable!] (restricted)
  15. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December. [Downloadable!] (restricted)
  16. Kleibergen, F.R. & Van Dijk, H.K., 1993. "On the Shape of the Likelyhood/Posterior in Cointegration Models," Papers 9315-a, Erasmus University of Rotterdam - Econometric Institute.
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  17. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March. [Downloadable!] (restricted)
  18. Jukka Corander & Mattias Villani, 2004. "Bayesian assessment of dimensionality in reduced rank regression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 255-270. [Downloadable!] (restricted)
  19. Strachan, Rodney W, 2003. "Valid Bayesian Estimation of the Cointegrating Error Correction Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 185-95, January.
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  20. Villani, Mattias, 2001. "Bayesian prediction with cointegrated vector autoregressions," International Journal of Forecasting, Elsevier, vol. 17(4), pages 585-605. [Downloadable!] (restricted)
  21. Paap, Richard & van Dijk, Herman K, 2003. "Bayes Estimates of Markov Trends in Possibly Cointegrated Series: An Application to U.S. Consumption and Income," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 547-63, October.
    Other versions:
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