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Determinacy in Linear Rational Expectations Models

  • Stéphane Gauthier

    (CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique)

The purpose of this paper is to assess the relevance of rational expectations solutions to the class of linear univariate models where both the number of leads in expectations and the number of lags in predetermined variables are arbitrary. It recommends to rule out all the solutions that would fail to be locally unique, or equivalently, locally determinate. So far, this determinacy criterion has been applied to particular solutions, in general some steady state or periodic cycle. However solutions to linear models with rational expectations typically do not conform to such simple dynamic patterns but express instead the current state of the economic system as a linear difference equation of lagged states. The innovation of this paper is to apply the determinacy criterion to the sets of coefficients of these linear difference equations. Its main result shows that only one set of such coefficients, or the corresponding solution, is locally determinate. This solution is commonly referred to as the fundamental one in the literature. In particular, in the saddle point configuration, it coincides with the saddle stable (pure forward) equilibrium trajectory.

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Paper provided by HAL in its series Post-Print with number hal-00731138.

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Date of creation: Nov 2004
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Publication status: Published, Journal of Mathematical Economics, 2004, 40, 7, 815-830
Handle: RePEc:hal:journl:hal-00731138
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00731138
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  1. G. Desgranges & Stéphane Gauthier, 2003. "Uniqueness of bubble-free solution in linear rational expectations models," Post-Print halshs-00069498, HAL.
  2. Bennett T. McCallum, . "Role of the minimal state variable criterion in rational expectations models," GSIA Working Papers 1999-13, Carnegie Mellon University, Tepper School of Business.
  3. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  4. Timothy J Kehoe & David K Levine, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Levine's Working Paper Archive 1873, David K. Levine.
  5. Gauthier, S., 1999. "Determinacy and Stability under Learning of Rational Expectations Equilibria," DELTA Working Papers 1999-22, DELTA (Ecole normale supérieure).
  6. Sargent, Thomas J & Wallace, Neil, 1973. "The Stability of Models of Money and Growth with Perfect Foresight," Econometrica, Econometric Society, vol. 41(6), pages 1043-48, November.
  7. Guesnerie, R., 1993. "Successes and Failures in Coordinating Expectations," DELTA Working Papers 93-08, DELTA (Ecole normale supérieure).
  8. Chiappori, Pierre-Andre & Geoffard, Pierre-Yves & Guesnerie, Roger, 1992. "Sunspot Fluctuations around a Steady State: The Case of Multidimensional, One-Step Forward Looking Economic Models," Econometrica, Econometric Society, vol. 60(5), pages 1097-126, September.
  9. Gourieroux, C & Laffont, J J & Monfort, Alain, 1982. "Rational Expectations in Dynamic Linear Models: Analysis of the Solutions," Econometrica, Econometric Society, vol. 50(2), pages 409-25, March.
  10. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, vol. 69(2), pages 114-18, May.
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