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Learning equilibria

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  • James Bullard

Abstract

This paper employs the Hopf bifurcation theorem to prove the existence of complicated equilibrium trajectories under least squares learning in a standard version of the overlapping generations model. The periodic and quasiperiodic learning equilibria exist when the locally unique perfect foresight equilibrium is the monetary steady state, and thus are induced by the introduction of learning alone. Learning equilibria can be stable or unstable depending on higher order derivatives of the underlying utility function not specified by economic theory; examples of both attracting and repelling invariant dosed curves are provided. This research confirms the intuition of some previous authors, who have suggested that stationary equilibrium trajectories under learning may differ from those under rational expectations. I would like to thank Robert Becker and members of my dissertation committee for helpful comments on this and related work. Suggestions made by Michael Woodford materially improved this paper. I also thank Albert Marcet, Mark Salmon, George Evans, Seppo Honkapohja, and participants at the June 1991 Meetings of the Society for Economic Dynamics and Control in Capri, Italy, and the May 1991 Midwest Mathematical Economics meeting at Northwestern University, for helpful discussions. All errors are the author's responsibility.

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Bibliographic Info

Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 1991-004.

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Date of creation: 1991
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Publication status: Published in Journal of Economic Theory, v. 64, no. 2 (December 1994) pp. 468-485
Handle: RePEc:fip:fedlwp:1991-004

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Keywords: Econometrics;

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  1. Marcet, Albert & Sargent, Thomas J, 1988. "The Fate of Systems with "Adaptive" Expectations," American Economic Review, American Economic Association, vol. 78(2), pages 168-72, May.
  2. Evans, George, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, MIT Press, vol. 100(4), pages 1217-33, November.
  3. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
  4. Marcet, Albert & Sargent, Thomas J, 1989. "Convergence of Least-Squares Learning in Environments with Hidden State Variables and Private Information," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1306-22, December.
  5. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  6. Grandmont Jean-michel & Laroque Guy, 1987. "Stability, expectations, and predetermined variables," CEPREMAP Working Papers (Couverture Orange) 8714, CEPREMAP.
  7. Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
  8. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  9. Sargent, Thomas J., 1991. "Equilibrium with signal extraction from endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 245-273, April.
  10. 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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