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Determinacy in Linear Rational Expectations Models

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  • Stéphane Gauthier

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

Abstract

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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Bibliographic Info

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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Related research

Keywords: Rational expectations; Selection; Determinacy; Saddle point property;

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  1. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 433-53, March.
  2. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, American Economic Association, vol. 69(2), pages 114-18, May.
  3. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, Econometric Society, vol. 48(5), pages 1305-11, July.
  4. Desgranges, Gabriel & Gauthier, St phane, 2003. "Uniqueness Of Bubble-Free Solution In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 7(02), pages 171-191, April.
  5. Sargent, Thomas J & Wallace, Neil, 1973. "The Stability of Models of Money and Growth with Perfect Foresight," Econometrica, Econometric Society, Econometric Society, vol. 41(6), pages 1043-48, November.
  6. 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, Econometric Society, vol. 60(5), pages 1097-126, September.
  7. Stéphane Gauthier, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Post-Print, HAL hal-00731065, HAL.
  8. Guesnerie, R., 1993. "Successes and Failures in Coordinating Expectations," DELTA Working Papers, DELTA (Ecole normale supérieure) 93-08, DELTA (Ecole normale supérieure).
  9. Gourieroux, C & Laffont, J J & Monfort, Alain, 1982. "Rational Expectations in Dynamic Linear Models: Analysis of the Solutions," Econometrica, Econometric Society, Econometric Society, vol. 50(2), pages 409-25, March.
  10. Bennett T. McCallum, . "Role of the minimal state variable criterion in rational expectations models," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 1999-13, Carnegie Mellon University, Tepper School of Business.
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