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Determinacy in linear rational expectations models

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  • Gauthier, Stephane

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

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 40 (2004)
Issue (Month): 7 (November)
Pages: 815-830

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Handle: RePEc:eee:mateco:v:40:y:2004:i:7:p:815-830

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  1. 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.
  2. Gauthier, S., 1999. "Determinacy and Stability under Learning of Rational Expectations Equilibria," DELTA Working Papers 1999-22, DELTA (Ecole normale supérieure).
  3. Timothy J. Kehoe & David K. Levine, 1982. "Comparitive Statics and Perfect Foresight in Infinite Horizon Economies," UCLA Economics Working Papers 259, UCLA Department of Economics.
  4. 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.
  5. 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.
  6. G. Desgranges & Stéphane Gauthier, 2003. "Uniqueness of bubble-free solution in linear rational expectations models," Post-Print halshs-00069498, HAL.
  7. 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.
  8. Guesnerie, Roger, 1993. "Successes and failures in coordinating expectations," European Economic Review, Elsevier, vol. 37(2-3), pages 243-268, April.
  9. 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.
  10. 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.
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Cited by:
  1. Roger Guesnerie, 2008. "Macroeconomic and monetary policies from the "eductive" viewpoint," Working Papers halshs-00586749, HAL.

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