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Comment on: Ravenna, F., 2007. Vector autoregressions and reduced form representations of DSGE models. Journal of Monetary Economics 54, 2048-2064

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  • Massimo Franchi

    ()
    (Universita' di Roma "La Sapienza")

Abstract

Solutions of DSGE models are usually represented by state space forms. This note shows that if one wishes to determine whether the observables of the model admit a finite order VAR representation, minimality of the state space representation of the solution matters. More specifically, we first provide a counterexample to Proposition 2.1 and Corollary 2.2 in Ravenna (2007), which state that in the square casea finite order VAR exists if and only if a `unimodularity condition' holds. Our counterexample shows that the proposed condition is not necessary for the existence of a finite order VAR representation. That is, if the state space representation of the solution is non-minimal, the observables of the DSGE may admit a finite order VAR representation even though the unimodularity condition fails. It is further shown that if the state space representation of the solution is minimal, then the unimodularity condition is necessary. Given that a minimal state space representation always exists, before applying the unimodularity condition one simply needs to check whether the state space representation of the solution is minimal and if not transform it into an equivalent minimal form. A discussion of how to perform such reduction is presented and further it is shown that the economic interpretation of the system is not affected by this transformation. An interpretation of the results in terms of the eigenvalues of the matrix defined in Fernandez-Villaverde et al. (2007) for the poor man's invertibility condition is also provided. The analysis is then applied to the Smets and Wouters (2007) model.

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Bibliographic Info

Paper provided by Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome in its series DSS Empirical Economics and Econometrics Working Papers Series with number 2013/2.

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Length: 17 pages
Date of creation: May 2013
Date of revision:
Handle: RePEc:sas:wpaper:20132

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Keywords: VAR; DSGE; invertibility condition.;

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References

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  1. Smets, Frank & Wouters, Rafael, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," CEPR Discussion Papers 6112, C.E.P.R. Discussion Papers.
  2. Jesus Fernandez-Villaverde & Juan Rubio-Ramirez & Thomas J. Sargent, 2005. "A, B, C's (and D)'s for Understanding VARs," NBER Technical Working Papers 0308, National Bureau of Economic Research, Inc.
  3. Javier Garcia-Cicco & Roberto Pancrazi & Martin Uribe, 2010. "Real Business Cycles in Emerging Countries?," American Economic Review, American Economic Association, vol. 100(5), pages 2510-31, December.
  4. Christopher Otrok & Andre Kurmann, 2011. "News Shocks and the Term Structure of Interest Rates: A Challenge for DSGE Models," 2011 Meeting Papers 426, Society for Economic Dynamics.
  5. Marco Lippi & Lucrezia Reichlin, 1994. "VAR analysis, non-fundamental representations, Blashke matrices," ULB Institutional Repository 2013/10151, ULB -- Universite Libre de Bruxelles.
  6. Eric M. Leeper & Todd B. Walker & Shu-Chun Susan Yang, 2009. "Fiscal Foresight and Information Flows," NBER Working Papers 14630, National Bureau of Economic Research, Inc.
  7. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
  8. Federico Ravenna, 2005. "Vector Autoregressions and Reduced Form Representations of DSGE Models," 2005 Meeting Papers 841, Society for Economic Dynamics.
  9. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
  10. Canova, Fabio & Ferroni, Filippo & Matthes, Christian, 2013. "Choosing the variables to estimate singular DSGE models," CEPR Discussion Papers 9381, C.E.P.R. Discussion Papers.
  11. Franchi, Massimo & Vidotto, Anna, 2013. "A check for finite order VAR representations of DSGE models," Economics Letters, Elsevier, vol. 120(1), pages 100-103.
  12. Eric R. Sims, 2012. "News, Non-Invertibility, and Structural VARs," Working Papers 013, University of Notre Dame, Department of Economics, revised Jun 2012.
  13. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  14. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  15. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2006. "Assessing structural VARs," International Finance Discussion Papers 866, Board of Governors of the Federal Reserve System (U.S.).
    • Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2007. "Assessing Structural VARs," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 1-106 National Bureau of Economic Research, Inc.
  16. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
  17. Eric M. Leeper & Todd B. Walker & Shu-Chun Susan Yang, 2011. "Foresight and Information Flows," NBER Working Papers 16951, National Bureau of Economic Research, Inc.
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