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Bayesian Inference of General Linear Restrictions on the Cointegration Space

  • Villani, Mattias

    ()

    (Research Department, Central Bank of Sweden)

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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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
Contact details of provider: Postal: Sveriges Riksbank, SE-103 37 Stockholm, Sweden
Phone: 08 - 787 00 00
Fax: 08-21 05 31
Web page: http://www.riksbank.com/
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  1. Strachan, R., 2000. "Valid Bayesian Estimation of the Cointegrating Error Correction Model," Monash Econometrics and Business Statistics Working Papers 6/00, Monash University, Department of Econometrics and Business Statistics.
  2. Rodney W. Strachan & Herman K. van Dijk, 2004. "Bayesian Model Selection with an Uninformative Prior," Keele Economics Research Papers KERP 2004/01, Centre for Economic Research, Keele University.
  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. 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.
  5. John F. Geweke, 1995. "Bayesian reduced rank regression in econometrics," Working Papers 540, Federal Reserve Bank of Minneapolis.
  6. Paap, R. & van Dijk, H.K., 2002. "Bayes estimates of Markov trends in possibly cointegrated series: an application to US consumption and income," Econometric Institute Research Papers EI 2002-42, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  7. Villani, Mattias, 2001. "Bayesian prediction with cointegrated vector autoregressions," International Journal of Forecasting, Elsevier, vol. 17(4), pages 585-605.
  8. 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.
  9. Strachan, R.W. & van Dijk, H.K., 2004. "Valuing structure, model uncertainty and model averaging in vector autoregressive processes," Econometric Institute Research Papers EI 2004-23, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  10. 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.
  11. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
  12. 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.
  13. 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.
  14. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
  15. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  16. Villani, Mattias, 2005. "Bayesian Reference Analysis Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(02), pages 326-357, April.
  17. Bauwens, L. & Lubrano, M., . "Identification restrictions and posterior densities in cointegrated Gaussian VAR system," CORE Discussion Papers RP -1206, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. 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.
  19. Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004. "Bayesian Approaches to Cointegration," Discussion Papers in Economics 04/27, Department of Economics, University of Leicester.
  20. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October.
  21. 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.
  22. 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.
  23. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  24. 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.
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