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Determinacy and Stability under Learning of Rational Expectations Equilibria

  • Stéphane Gauthier

    (CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique, ERMES - Equipe de recherche sur les marches, l'emploi et la simulation - CNRS : UMR7017 - Université Paris II - Panthéon-Assas)

This paper studies relationships between the local determinacy of a stationary equilibrium in the perfect foresight dynamics, and its local stability in dynamics arising from econometric learning procedures. Attention is focused on linear scalar economies where agents forecast only one period ahead, and with an arbitrary, but fixed, number of predetermined variables. In such a framework, it is well known that there are no clear links between the determinacy of the stationary state in the perfect foresight dynamics on the levels of the state variable, and its stability under learning. The paper emphasizes, however, that this is not the right perfect foresight dynamics to look at whenever agents try to learn the coefficients of the perfect foresight dynamics restricted to an eigenspace of lower dimension. Indeed the paper introduces a growth rate perfect foresight dynamics on these coefficients and proves equivalence between determinacy in that dynamics and stability under learning provided that a simple sign condition is satisfied.

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Paper provided by HAL in its series Post-Print with number hal-00731065.

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Date of creation: Feb 2002
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Publication status: Published, Journal of Economic Theory, 2002, 102, 2, 354-374
Handle: RePEc:hal:journl:hal-00731065
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00731065
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  1. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
  2. Jean-Michel Grandmont, 1997. "Expectations Formation and Stability of Large Socioeconomic Systems," Working Papers 97-27, Centre de Recherche en Economie et Statistique.
  3. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
  4. Grandmont Jean-michel & Laroque Guy, 1985. "Stability of cycles and expectations," CEPREMAP Working Papers (Couverture Orange) 8519, CEPREMAP.
  5. Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 297-317, March.
  6. Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, vol. 59(4), pages S401-26, October.
  7. Duffy John, 1994. "On Learning and the Nonuniqueness of Equilibrium in an Overlapping Generations Model with Fiat Money," Journal of Economic Theory, Elsevier, vol. 64(2), pages 541-553, December.
  8. Evans, George W. & Honkapohja, S., 1998. "Stochastic gradient learning in the cobweb model," Economics Letters, Elsevier, vol. 61(3), pages 333-337, December.
  9. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
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