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A finite, empirically useless and almost sure VAR representation for all minimal transition equations

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  • Saccal, Alessandro

Abstract

Does there exist a systematic manner to derive a finite vector autoregression (VAR) representation for any minimal transition equation? While the good news be that any transition equation of a minimal linear time invariant (LTI) state space representation in discrete time admits a VAR representation of finite order of the non-minimal states in the (minimal) measurement equation’s outputs, the bad news are that such a representation, on account of the procedure underlying its derivation, is both the probabilistically surest and empirically useless, ranging from linear combinations of non-minimal states in principle, equal to shifted white noises, to output nullity, thereby presenting negative repercussions with particular regard to first order linear rational expectations (LRE) models of optimising representative agents.

Suggested Citation

  • Saccal, Alessandro, 2023. "A finite, empirically useless and almost sure VAR representation for all minimal transition equations," MPRA Paper 116435, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:116435
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    File URL: https://mpra.ub.uni-muenchen.de/116435/1/MPRA_paper_116435.pdf
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    References listed on IDEAS

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    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Thomas J. Sargent & Mark W. Watson, 2007. "ABCs (and Ds) of Understanding VARs," American Economic Review, American Economic Association, vol. 97(3), pages 1021-1026, June.
    2. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-1026, November.
    3. Ravenna, Federico, 2007. "Vector autoregressions and reduced form representations of DSGE models," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2048-2064, October.
    4. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    5. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
    6. Massimo Franchi, 2013. "Comment on: Ravenna, F., 2007. Vector autoregressions and reduced form representations of DSGE models. Journal of Monetary Economics 54, 2048-2064," DSS Empirical Economics and Econometrics Working Papers Series 2013/2, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    7. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    8. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
    9. Franchi, Massimo & Vidotto, Anna, 2013. "A check for finite order VAR representations of DSGE models," Economics Letters, Elsevier, vol. 120(1), pages 100-103.
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    Cited by:

    1. Saccal, Alessandro, 2023. "A role for confidence: volition regimes and news," MPRA Paper 117484, University Library of Munich, Germany.

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    More about this item

    Keywords

    DSGE models; LRE models; minimality; state space; VMA representation; VAR representation.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • 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

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