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Solutions of Multivariate Rational Expectations Models

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  • Laurence Broze
  • Christian Gourieroux
  • Ariane Szafarz

Abstract

The aim of this paper is the study of the path solutions of a multivariate rational expectations model. We describe several procedures for solving such dynamic systems based on either the adjoint operator method or the Smith form. As a by-product, we derive the dimension of the set of solutions in terms of martingale differences and the dimension of the set of linear stationary solutions when we restrict ourselves to the linear case. These dimensions are functions of the number of equations in the system, of the maximum lead, and of the orders of some eigenvalues of the characteristic equation associated with the system. © 1995, Cambridge University Press. All rights reserved.

Suggested Citation

  • Laurence Broze & Christian Gourieroux & Ariane Szafarz, 1995. "Solutions of Multivariate Rational Expectations Models," ULB Institutional Repository 2013/701, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/701
    Note: SCOPUS: ar.j
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    Cited by:

    1. Ariane Szafarz, 2015. "Market Efficiency and Crises:Don’t Throw the Baby out with the Bathwater," Bankers, Markets & Investors, ESKA Publishing, issue 139, pages 20-26, November-.
    2. Bernd Funovits, 2014. "Implications of Stochastic Singularity in Linear Multivariate Rational Expectations Models," Vienna Economics Papers 1405, University of Vienna, Department of Economics.
    3. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    4. Jones, John Bailey, 2002. "Has fiscal policy helped stabilize the postwar U.S. economy?," Journal of Monetary Economics, Elsevier, vol. 49(4), pages 709-746, May.
    5. John Bailey Jones & Sohini Sahu, 2017. "Transition accounting for India in a multi-sector dynamic general equilibrium model," Economic Change and Restructuring, Springer, vol. 50(4), pages 299-339, November.
    6. Al-Sadoon, Majid M., 2018. "The Linear Systems Approach To Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 34(3), pages 628-658, June.
    7. Ariane Szafarz, 2009. "How Did Financial-Crisis-Based Criticisms of Market Efficiency Get It So Wrong?," Working Papers CEB 09-048.RS, ULB -- Universite Libre de Bruxelles.
    8. Onatski, Alexei, 2006. "Winding number criterion for existence and uniqueness of equilibrium in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 323-345, February.
    9. Binder, Michael & Pesaran, Hashem, 2000. "Solution of finite-horizon multivariate linear rational expectations models and sparse linear systems," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 325-346, March.
    10. Bernd Funovits, 2014. "Implications of Stochastic Singularity in Linear Multivariate Rational Expectations Models," Vienna Economics Papers vie1405, University of Vienna, Department of Economics.
    11. Gary Anderson, 2008. "Solving Linear Rational Expectations Models: A Horse Race," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 95-113, March.
    12. Bernd Funovits, 2020. "The Dimension of the Set of Causal Solutions of Linear Multivariate Rational Expectations Models," Papers 2002.04369, arXiv.org.
    13. John G. Thistle, 2018. "The Origin and the Resolution of Nonuniqueness in Linear Rational Expectations," Papers 1806.06657, arXiv.org, revised Apr 2019.
    14. Zadrozny, Peter A., 1998. "An eigenvalue method of undetermined coefficients for solving linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1353-1373, August.
    15. Timmermann, Allan, 1995. "Cointegration Tests of Present Value Models with a Time-Varying Discount Factor," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(1), pages 17-31, Jan.-Marc.
    16. Tan, Fei & Walker, Todd B., 2015. "Solving generalized multivariate linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 95-111.
    17. Majid M. Al-Sadoon, 2020. "The Spectral Approach to Linear Rational Expectations Models," Papers 2007.13804, arXiv.org, revised Jun 2023.

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