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Determinacy and Stability under Learning of Rational Expectations Equilibria

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  • Stéphane Gauthier

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, ERMES - Equipe de recherche sur les marches, l'emploi et la simulation - UP2 - Université Panthéon-Assas - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper studies relationships between the local determinacy of a stationary equilibrium in the perfect foresight dynamics, and its local stability in dynamics arising from econometric learning procedures. Attention is focused on linear scalar economies where agents forecast only one period ahead, and with an arbitrary, but fixed, number of predetermined variables. In such a framework, it is well known that there are no clear links between the determinacy of the stationary state in the perfect foresight dynamics on the levels of the state variable, and its stability under learning. The paper emphasizes, however, that this is not the right perfect foresight dynamics to look at whenever agents try to learn the coefficients of the perfect foresight dynamics restricted to an eigenspace of lower dimension. Indeed the paper introduces a growth rate perfect foresight dynamics on these coefficients and proves equivalence between determinacy in that dynamics and stability under learning provided that a simple sign condition is satisfied.

Suggested Citation

  • Stéphane Gauthier, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Post-Print hal-00731065, HAL.
    • Handle: RePEc:hal:journl:hal-00731065
    DOI: 10.1006/jeth.2000.2768
    Note: View the original document on HAL open archive server: https://hal.science/hal-00731065v1
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    Cited by:

    1. Hippolyte d'Albis & Jean-Pierre Drugeon, 2020. "On Investment and Cycles in Explicitely Solved Vintage Capital Models," PSE Working Papers halshs-02570648, HAL.
    2. Seonghoon Cho & Antonio Moreno, 2008. "Expectational Stability in Multivariate Models," Faculty Working Papers 06/08, School of Economics and Business Administration, University of Navarra.
    3. Desgranges, Gabriel & Negroni, Giorgio, 2003. "Expectations Coordination On A Sunspot Equilibrium: An Eductive Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 7(1), pages 7-41, February.
    4. Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.
    5. Roger Guesnerie, 2009. "Macroeconomic and Monetary Policies from the Eductive Viewpoint," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 6, pages 171-202, Central Bank of Chile.
    6. Roger Guesnerie & Pedro Jara-Moroni, 2011. "Expectational coordination in simple economic contexts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 205-246, June.
    7. Roger Guesnerie & Pedro Jara-Moroni, 2009. "Expectational coordination in simple economic contexts: concepts and analysis with emphasis on strategic substitutabilities," PSE Working Papers halshs-00574957, HAL.
    8. McCallum, Bennett T., 2004. "On the relationship between determinate and MSV solutions in linear RE models," Economics Letters, Elsevier, vol. 84(1), pages 55-60, July.
    9. Gauthier, Stephane, 2004. "Determinacy in linear rational expectations models," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 815-830, November.
    10. Evans, George W. & Guesnerie, Roger, 2005. "Coordination on saddle-path solutions: the eductive viewpoint--linear multivariate models," Journal of Economic Theory, Elsevier, vol. 124(2), pages 202-229, October.

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    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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