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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

  • Massimo Franchi


    (Universita' di Roma "La Sapienza")

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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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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  1. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
  2. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Thomas J. Sargent, 2005. "A,B,C's (and D's)'s for Understanding VARS," Levine's Bibliography 172782000000000096, UCLA Department of Economics.
  3. 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.
  4. 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.
  5. Eric M. Leeper & Todd B. Walker & Shu‐Chun Susan Yang, 2013. "Fiscal Foresight and Information Flows," Econometrica, Econometric Society, vol. 81(3), pages 1115-1145, 05.
  6. Lippi, Marco & Reichlin, Lucrezia, 1994. "VAR analysis, nonfundamental representations, blaschke matrices," Journal of Econometrics, Elsevier, vol. 63(1), pages 307-325, July.
  7. Franchi, Massimo & Vidotto, Anna, 2013. "A check for finite order VAR representations of DSGE models," Economics Letters, Elsevier, vol. 120(1), pages 100-103.
  8. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
  9. Eric R. Sims, 2012. "News, Non-Invertibility, and Structural VARs," Working Papers 013, University of Notre Dame, Department of Economics, revised Jun 2012.
  10. 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.
  11. Ravenna, Federico, 2007. "Vector autoregressions and reduced form representations of DSGE models," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2048-2064, October.
  12. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
  13. Lars Peter Hansen & Thomas J. Sargent, 1979. "Formulating and estimating dynamic linear rational expectations models," Working Papers 127, Federal Reserve Bank of Minneapolis.
  14. Fabio Canova & Filippo Ferroni & Christian Matthes, 2014. "Choosing The Variables To Estimate Singular Dsge Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1099-1117, November.
  15. 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. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  17. Javier García-Cicco & Roberto Pancrazi & Martín Uribe, 2006. "Real Business Cycles in Emerging Countries?," NBER Working Papers 12629, National Bureau of Economic Research, Inc.
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