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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 autore- gressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. Our proposal is to use prior infor- mation on observables systematically. We show how this kind of prior can be used 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 large number of parameters. We prove various convergence theorems for the algorithm. Using examples from the VAR literature, we show how priors on observables can address a priori weaknesses of standard priors, serving as a cross check and an alternative formulation.

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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 684.

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Date of creation: Mar 2013
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Handle: RePEc:bge:wpaper:684
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  1. Stéphane Bonhomme & Jean-Marc Robin, 2008. "Generalized nonparametric deconvolution with an application to earnings dynamics," CeMMAP working papers CWP03/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. 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.
  3. Robert B. Litterman, 1985. "Forecasting with Bayesian vector autoregressions five years of experience," Working Papers 274, Federal Reserve Bank of Minneapolis.
  4. 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.
  5. Marek Jarocinski & Albert Marcet, 2011. "Autoregressions in Small Samples, Priors about Observables and Initial Conditions," CEP Discussion Papers dp1061, Centre for Economic Performance, LSE.
  6. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-68, November.
  7. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  8. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
  9. 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.
  10. 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.
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