Determinacy and Stability under Learning of Rational Expectations Equilibria
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.
|Date of creation:||Feb 2002|
|Publication status:||Published in Journal of Economic Theory, Elsevier, 2002, 102 (2), pp.354-374. <10.1006/jeth.2000.2768>|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00731065|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 297-317, March.
- 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.
- Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, vol. 59(4), pages 401-426, October.
- Evans, George W. & Honkapohja, S., 1998.
"Stochastic gradient learning in the cobweb model,"
Elsevier, vol. 61(3), pages 333-337, December.
- Evans, G.W. & Honkapohja, S., 1998. "Stochastic Gradient Learning in the Cobweb Model," University of Helsinki, Department of Economics 438, Department of Economics.
- Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
- Woodford, Michael, 1986. "Learning to Believe in Sunspots," Working Papers 86-16, C.V. Starr Center for Applied Economics, New York University.
- Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
- Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
- Jean-Michel Grandmont, 1997. "Expectations Formation and Stability of Large Socioeconomic Systems," Working Papers 97-27, Centre de Recherche en Economie et Statistique.
- GRANDMONT, Jean-Michel, 1997. "Expectations formation and stability of large socioeconomic systems," CORE Discussion Papers 1997088, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
- Grandmont, Jean-Michel & Laroque, Guy, 1986. "Stability of cycles and expectations," Journal of Economic Theory, Elsevier, vol. 40(1), pages 138-151, October.
- Grandmont Jean-michel & Laroque Guy, 1985. "Stability of cycles and expectations," CEPREMAP Working Papers (Couverture Orange) 8519, CEPREMAP.
- 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. Full references (including those not matched with items on IDEAS)