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Identification Restrictions and Posterior Densities in Cointegrated Gaussian VAR Systems
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Identification Restrictions and Posterior Densities in Cointegrated Gaussian VAR Systems

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  • BAUWENS, Luc

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • LUBRANO , Michel

    (GREQE, CNRS)

Abstract

We derive the postenor density of the cointegrating coetficients in a Gaussian VAR system. The density does not belong in general to a family of densities with known properties. If there is one cointegrating vector, the density belongs to the class of poly-t densities. It is integrable if the coefficients are identified and it has finite moments to the order of overidentification. The identifying restrictions we consider are linear restrictions on the cointegrating vectors. The structure or the posterior density is exploited to implement Monte Carlo integTi\tion nwthods that are needed when there is more than one cointegrating veetor. The paper contains two empirical illustrations.

Suggested Citation

  • 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).
    • Handle: RePEc:cor:louvco:1994018
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    1. Efthymios Tsionas, 2003. "Inflation and Productivity in Europe: An Empirical Investigation," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 30(1), pages 39-62, March.
    2. Rodney Strachan & Herman K. van Dijk, "undated". "Bayesian Model Averaging in Vector Autoregressive Processes with an Investigation of Stability of the US Great Ratios and Risk of a Liquidity Trap in the USA, UK and Japan," MRG Discussion Paper Series 1407, School of Economics, University of Queensland, Australia.
    3. Luca Benati & Thomas A. Lubik, 2021. "Searching for Hysteresis," Working Paper 21-03, Federal Reserve Bank of Richmond.
    4. Jan Klacso, 2015. "The Effects of the Euro Area Entrance on the Monetary Transmission Mechanism in Slovakia in Light of the Global Economic Recession," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 65(1), pages 55-83, January.
    5. Villani, Mattias, 2005. "Bayesian Inference of General Linear Restrictions on the Cointegration Space," Working Paper Series 189, Sveriges Riksbank (Central Bank of Sweden).
    6. Rault, Christophe, 2005. "Further Results on Weak Exogeneity in Vector Error Correction Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 25(2), November.
    7. Urbain, Jean-Pierre, 1995. "Partial versus full system modelling of cointegrated systems an empirical illustration," Journal of Econometrics, Elsevier, vol. 69(1), pages 177-210, September.
    8. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    9. Ossama Mikhail, 2005. "What Happens After A Technology Shock? A Bayesian Perspective," Macroeconomics 0510016, University Library of Munich, Germany.
    10. Jim Malley & Ulrich Woitek, 2011. "Productivity Shocks and Aggregate Fluctuations in an Estimated Endogenous Growth Model with Human Capital," CESifo Working Paper Series 3567, CESifo.
    11. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2019. "Priors for the Long Run," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 565-580, April.
    12. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
    13. Villani, Mattias, 2001. "Bayesian prediction with cointegrated vector autoregressions," International Journal of Forecasting, Elsevier, vol. 17(4), pages 585-605.
    14. Sugita, Katsuhiro, 2002. "Testing For Cointegration Rank Using Bayes Factors," The Warwick Economics Research Paper Series (TWERPS) 654, University of Warwick, Department of Economics.
    15. Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 217-234.
    16. 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.
    17. 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.
    18. Warne, Anders, 2006. "Bayesian inference in cointegrated VAR models: with applications to the demand for euro area M3," Working Paper Series 692, European Central Bank.
    19. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
    20. Villani, Mattias, 2003. "Bayes Estimators of the Cointegration Space," Working Paper Series 150, Sveriges Riksbank (Central Bank of Sweden).
    21. Andrea Silvestrini, 2010. "Testing fiscal sustainability in Poland: a Bayesian analysis of cointegration," Empirical Economics, Springer, vol. 39(1), pages 241-274, August.
    22. Kleibergen, Frank, 2004. "Invariant Bayesian inference in regression models that is robust against the Jeffreys-Lindley's paradox," Journal of Econometrics, Elsevier, vol. 123(2), pages 227-258, December.
    23. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October.
    24. 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, arXiv.org.
    25. Sugita, Katsuhiro, 2008. "Bayesian analysis of a Markov switching temporal cointegration model," Japan and the World Economy, Elsevier, vol. 20(2), pages 257-274, March.

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