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Dynamic equivalence principle in linear rational expectations models

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  • Stéphane Gauthier

    (CREM - Centre de Recherche en Economie et Management - CNRS : UMR6211 - Université de Rennes I - Université de Caen Basse-Normandie, ERMES - Equipe de recherche sur les marches, l'emploi et la simulation - CNRS : UMR7017 - Université Paris II - Panthéon-Assas, 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.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00069499.

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Date of creation: Feb 2003
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Publication status: Published, Macroeconomic Dynamics, 2003, 7, 3, 63-88
Handle: RePEc:hal:journl:halshs-00069499

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Keywords: linear rational expectations models; dynamic equivalence principle;

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Cited by:
  1. repec:hal:wpaper:halshs-00590856 is not listed on IDEAS
  2. Bennett McCallum, 2004. "On the Relationship Between Determinate and MSV Solutions in Linear RE Models," NBER Technical Working Papers 0297, National Bureau of Economic Research, Inc.
  3. Bennett T. McCallum, 2003. "The Unique Minimum State Variable RE Solution is E-Stable in All Well Formulated Linear Models," NBER Working Papers 9960, National Bureau of Economic Research, Inc.
  4. 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.
  5. repec:hal:wpaper:halshs-00590540 is not listed on IDEAS

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