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Bayesian Inference of General Linear Restrictions on the Cointegration Space

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  • Villani, Mattias

    (Research Department, Central Bank of Sweden)

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.

Suggested Citation

  • Villani, Mattias, 2005. "Bayesian Inference of General Linear Restrictions on the Cointegration Space," Working Paper Series 189, Sveriges Riksbank (Central Bank of Sweden).
    • Handle: RePEc:hhs:rbnkwp:0189
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. 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 185-195, January.
    3. 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.
    4. Darryl Holden & Roger Perman, 1994. "Unit Roots and Cointegration for the Economist," Palgrave Macmillan Books, in: B. Bhaskara Rao (ed.), Cointegration, chapter 3, pages 47-112, Palgrave Macmillan.
    5. Johansen, Søren, 2000. "A Bartlett Correction Factor For Tests On The Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 16(5), pages 740-778, October.
    6. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    7. 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 547-563, October.
    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.
    9. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    10. BAUWENS, Luc & LUBRANO , Michel, 1994. "Identification Restrictions and Posterior Densities in Cointegrated Gaussian VAR Systems," LIDAM Discussion Papers CORE 1994018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. 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.
    12. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    13. 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.
    14. Rodney W. Strachan & Herman K. van 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.
    15. 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.
    16. 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, August.
    17. 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.
    18. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October.
    19. 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.
    20. 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.
    21. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    22. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    23. 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.
    24. Villani, Mattias, 2001. "Bayesian prediction with cointegrated vector autoregressions," International Journal of Forecasting, Elsevier, vol. 17(4), pages 585-605.
    25. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    26. Villani, Mattias, 2005. "Bayesian Reference Analysis Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(2), pages 326-357, April.
    27. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
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    More about this item

    Keywords

    Bayesian inference; Cointegration; Posterior probability; Restrictions.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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