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Dynamic equivalence principle in linear rational expectations models

Author

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  • Stéphane Gauthier

    () (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - 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, CREST-INSEE - Centre de Recherche en Economie et en Statistique - Institut national de la statistique et des études économiques (INSEE))

Abstract

Linear models with infinite horizon generally admit infinitely many rational expectations solutions. Consequently, some additional selection devices are needed to narrow the set of relevant solutions. The viewpoint of this paper is that a solution will be more likely to arise if it is locally determinate (i.e., locally isolated), locally immune to sunspots, and locally stable under learning. These three criteria are applied to solutions of linear univariate models along which the level of the state variable evolves through time. In such models the equilibrium behavior of the level of the state variable is described by a linear recursive equation characterized by the set of its coefficients. The main innovation of this paper is to define new perfect-foresight dynamics whose fixed points are these sets of coefficients, thus allowing us to study the property of determinacy of these sets, or, equivalently, of the associated solutions. It is shown that only one solution is locally determinate in the new dynamics. It is also locally immune to sunspots and locally stable under myopic learning. This solution corresponds to the saddle path in the saddle-point case.

Suggested Citation

  • Stéphane Gauthier, 2003. "Dynamic equivalence principle in linear rational expectations models," Post-Print halshs-00069499, HAL.
  • Handle: RePEc:hal:journl:halshs-00069499
    DOI: 10.1017/S1365100502010301
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00069499
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    Cited by:

    1. Bennett T. McCallum, 2002. "Consistent Expectations, Rational Expectations, Multiple-Solution Indeterminacies, and Least-Squares Learnability," NBER Working Papers 9218, National Bureau of Economic Research, Inc.
    2. 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.
    3. Roger Guesnerie, 2005. "Strategic substitutabilities versus strategic complementarities: Towards a general theory of expectational coordination?," Working Papers halshs-00590856, HAL.
    4. 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.
    5. Bennett T. McCallum, 2002. "The Unique Minimum State Variable RE Soluiton is E-Stable in All Well Formulated Linear Models," GSIA Working Papers 2003-25, Carnegie Mellon University, Tepper School of Business.
    6. Roger Guesnerie, 2006. "General equilibrium, coordination and multiplicity on spot markets," Working Papers halshs-00590540, HAL.

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