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Learning equilibria

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Author Info
James Bullard

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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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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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
  2. Grandmont Jean-michel, 1988. "Nonlinear difference equations bifurcations and chaos : an introduction," CEPREMAP Working Papers (Couverture Orange) 8811, CEPREMAP.
  3. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December. [Downloadable!] (restricted)
  4. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September. [Downloadable!] (restricted)
  5. Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. Grandmont Jean-michel & Laroque Guy, 1987. "Stability, expectations, and predetermined variables," CEPREMAP Working Papers (Couverture Orange) 8714, CEPREMAP.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2003. "Bifurcation Routes to Volatility Clustering under Evolutionary Learning," CeNDEF Working Papers 03-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  2. Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    Other versions:
  3. John Duffy, 1998. "Monetary theory in the laboratory," Review, Federal Reserve Bank of St. Louis, issue Sep, pages 9-26. [Downloadable!]
  4. James B. Bullard & Alvin L. Marty, 1998. "What has become of the "stability-through-inflation" argument?," Review, Federal Reserve Bank of St. Louis, issue Jan, pages 37-45. [Downloadable!]
  5. William Brock & Cars Hommes & Florian Wagener, 2006. "More Hedging Instruments may destablize Markets," Tinbergen Institute Discussion Papers 06-080/1, Tinbergen Institute, revised 30 Apr 2008. [Downloadable!]
    Other versions:
  6. Carl Chiarella & Xue-Zhong He, 2000. "Stability of Competitive Equilibria with Heterogeneous Beliefs and Learning," Research Paper Series 37, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  7. Lettau, Martin & Van Zandt, Timothy, 2001. "Robustness of Adaptive Expectations as an Equilibrium Selection Device," CEPR Discussion Papers 2882, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  8. Atanas Christev, 2007. "Learning Hyperinflations," Money Macro and Finance (MMF) Research Group Conference 2006 126, Money Macro and Finance Research Group. [Downloadable!]
    Other versions:
  9. James Bullard & John Duffy, 1993. "Learning in a large square economy," Working Papers 1994-013, Federal Reserve Bank of St. Louis. [Downloadable!]
  10. Brock, W.A. & Dindo, P.D.E. & Hommes, C.H., 2005. "Adaptive Rational Equilibrium with Forward Looking Agents, fortcoming in International Journal of Economic Theory (IJET) 2006, special issue in honor of Jean-Michel Grandmont," CeNDEF Working Papers 05-15, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  11. Thomas J. Sargent & Noah William, 2005. "Impacts of Priors on Convergence and Escapes from Nash Inflation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 360-391, April. [Downloadable!] (restricted)
    Other versions:
  12. Stefano Eusepi, 2005. "Central bank transparency under model uncertainty," Staff Reports 199, Federal Reserve Bank of New York. [Downloadable!]
  13. Tuinstra, J. & Wagener, F.O.O., 2003. "On Learning Equilibria (Revised June 2003)," CeNDEF Working Papers 03-07, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  14. George W. Evans, 2003. "Comment on "Imperfect Knowledge, Inflation Expectations and Monetary Policy" by Athanasios Orphanides and John C. Williams," University of Oregon Economics Department Working Papers 2003-29, University of Oregon Economics Department, revised 31 Mar 2003. [Downloadable!]
  15. Hommes, C.H., 2007. "Bounded Rationality and Learning in Complex Markets," CeNDEF Working Papers 07-01, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  16. James Bullard & John Duffy, 1998. "Learning and excess volatility," Working Papers 1998-016, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  17. Florian Wagener & Jan Tuinstra, 2004. "On Learning Equilibria," Computing in Economics and Finance 2004 217, Society for Computational Economics. [Downloadable!]
    Other versions:
  18. Carl Chiarella & Xue-Zhong He, 2000. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model with a Market Maker," Research Paper Series 35, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  19. César L. Guerrero-Luchtenberg, 2004. "Alternative Dynamics and Stability Results in a Standard OLG Model: An Interpretation," Economia Mexicana NUEVA EPOCA, , vol. 0(2), pages 191-208, July-Dece. [Downloadable!]
  20. Stefano Eusepi, 2004. "Does Central Bank Transparency Matter for Economic Stability," Computing in Economics and Finance 2004 176, Society for Computational Economics. [Downloadable!]
  21. Wilfredo Leiva, 1999. "Adaptive Learning in Models with Lagged Variables," Economics Working Papers 413, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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