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Minimality of State Space Solutions of DSGE Models and Existence Conditions for Their VAR Representation

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  • Massimo Franchi
  • Paolo Paruolo

Abstract

Standard solution methods of DSGE models do not necessarily deliver minimal state space forms. When the ABCD form is non-minimal, the conditions in the literature are not necessary for the existence of a VAR representation of the observables. In this paper we present necessary and sufficient conditions that are valid in general, and hence can be applied to minimal and non-minimal ABCD forms. If the state space form is minimal, our conditions coincide with those in the literature. These results also clarify that it is possible to have unstable eigenvalues together with a (possibly finite) VAR representation of the observables. Copyright European Union 2015

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  • Massimo Franchi & Paolo Paruolo, 2015. "Minimality of State Space Solutions of DSGE Models and Existence Conditions for Their VAR Representation," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 613-626, December.
    • Handle: RePEc:kap:compec:v:46:y:2015:i:4:p:613-626
    DOI: 10.1007/s10614-014-9465-4
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    Cited by:

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    2. Soccorsi, Stefano, 2016. "Measuring nonfundamentalness for structural VARs," Journal of Economic Dynamics and Control, Elsevier, vol. 71(C), pages 86-101.
    3. Iskrev, Nikolay, 2018. "Are asset price data informative about news shocks? A DSGE perspective," Working Paper Series 2161, European Central Bank.
    4. Franchi, Massimo, 2018. "Testing for cointegration in I(1) state space systems via a finite order approximation," Economics Letters, Elsevier, vol. 165(C), pages 73-76.
    5. Enrique Martínez García, 2020. "A Matter of Perspective: Mapping Linear Rational Expectations Models into Finite-Order VAR Form," Globalization Institute Working Papers 389, Federal Reserve Bank of Dallas.
    6. Enrique Martínez García, 2016. "Finite-Order VAR Representation of Linear Rational Expectations Models: With Some Lessons for Monetary Policy," Globalization Institute Working Papers 285, Federal Reserve Bank of Dallas.
    7. Maddalena Cavicchioli, 2020. "Invertibility and VAR Representations of Time-Varying Dynamic Stochastic General Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 61-86, January.
    8. Iskrev, Nikolay, 2019. "On the sources of information about latent variables in DSGE models," European Economic Review, Elsevier, vol. 119(C), pages 318-332.
    9. Alessandro SACCAL, 2021. "A Note On Gensys’ Minimality," Theoretical and Practical Research in the Economic Fields, ASERS Publishing, vol. 12(1), pages 57-60.
    10. Mario Forni & Luca Gambetti & Luca Sala, 2016. "VAR Information and the Empirical Validation of DSGE Models," Center for Economic Research (RECent) 119, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    11. Angelini, Giovanni & Sorge, Marco M., 2021. "Under the same (Chole)sky: DNK models, timing restrictions and recursive identification of monetary policy shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    12. Nikolay Iskrev, 2021. "Spectral decomposition of the information about latent variables in dynamic macroeconomic models," Working Papers w202105, Banco de Portugal, Economics and Research Department.
    13. Angelini, Giovanni, 2020. "Bootstrap lag selection in DSGE models with expectations correction," Econometrics and Statistics, Elsevier, vol. 14(C), pages 38-48.
    14. Saccal, Alessandro, 2020. "A note on minimality in Dynare," MPRA Paper 103656, University Library of Munich, Germany.

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    More about this item

    Keywords

    DGSE models; VAR models; Fundamentalness; Finite order VAR; Minimal state space representation; C18; C32; E32;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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