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Priors about Observables in Vector Autoregressions

  • Marek Jarocinski

    ()

  • Albert Marcet

Standard practice in Bayesian VARs is to formulate priors on the autoregres- sive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how this kind of prior can be used in a VAR under strict probability theory principles. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical situations with a very large number of parameters. We prove various convergence theorems for the algorithm. As an application, we first show that the results in Christiano et al. (1999) are very sensitive to the introduction of various priors that are widely used. These priors turn out to be associated with undesirable priors on observables. But an empirical prior on observables helps clarify the relevance of these estimates: we find much higher persistence of out- put responses to monetary policy shocks than the one reported in Christiano et al. (1999) and a significantly larger total effect.

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Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 929.13.

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Length: 36
Date of creation: 18 Mar 2013
Date of revision:
Handle: RePEc:aub:autbar:929.13
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  1. Marek Jarocinski & Albert Marcet, 2011. "Autoregressions in Small Samples, Priors about Observables and Initial Conditions," CEP Discussion Papers dp1061, Centre for Economic Performance, LSE.
  2. Christopher A. Sims & Tao Zha, 1996. "Bayesian methods for dynamic multivariate models," Working Paper 96-13, Federal Reserve Bank of Atlanta.
  3. Adjemian, Stéphane & Bastani, Houtan & Karamé, Fréderic & Juillard, Michel & Maih, Junior & Mihoubi, Ferhat & Perendia, George & Pfeifer, Johannes & Ratto, Marco & Villemot, Sébastien, 2011. "Dynare: Reference Manual Version 4," Dynare Working Papers 1, CEPREMAP, revised Jul 2014.
  4. Christiano, Lawrence J. & Trabandt, Mathias & Walentin, Karl, 2007. "Introducing Financial Frictions and Unemployment into a Small Open Economy Model," Working Paper Series 214, Sveriges Riksbank (Central Bank of Sweden), revised 01 Jun 2011.
  5. Stéphane Bonhomme & Jean-Marc Robin, 2010. "Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 491-533.
  6. Robert B. Litterman, 1985. "Forecasting with Bayesian vector autoregressions five years of experience," Working Papers 274, Federal Reserve Bank of Minneapolis.
  7. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
  8. Kadane, Joseph B. & Chan, Ngai Hang & Wolfson, Lara J., 1996. "Priors for unit root models," Journal of Econometrics, Elsevier, vol. 75(1), pages 99-111, November.
  9. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
  10. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2013. "On the Testability of Identification in Some Nonparametric Models With Endogeneity," Econometrica, Econometric Society, vol. 81(6), pages 2535-2559, November.
  11. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
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