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Learning with Bounded Memory in Stochastic Models

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  • Seppo Honkapohja
  • Kaushik Mitra

Abstract

Learning with bounded memory in stochastic frameworks is incomplete in the sense that the learning dynamics cannot converge to an rational expectations equilibrium (REE). The properties of the dynamics arising from such rules are studied for models with steady states. If in standard linear models the REE is in a certain sense expectationally stable (E-stable), then the dynamics are asymptotically stationary and forecasts are unbiased. We also provide similar local results for a class of nonlinear models with small noise and their approximations.

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Paper provided by Department of Economics, University of York in its series Discussion Papers with number 00/42.

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Handle: RePEc:yor:yorken:00/42

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Keywords: Bounded memory; expectational stability; unbiased.;

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  1. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
  2. Albert Marcet & Juan P. Nicolini, 2003. "Recurrent Hyperinflations and Learning," American Economic Review, American Economic Association, vol. 93(5), pages 1476-1498, December.
  3. Kaushik Mitra, 2004. "Is more data better?," Royal Holloway, University of London: Discussion Papers in Economics 04/19, Department of Economics, Royal Holloway University of London, revised Jul 2004.
  4. Evans George W. & Honkapohja Seppo, 1994. "On the Local Stability of Sunspot Equilibria under Adaptive Learning Rules," Journal of Economic Theory, Elsevier, vol. 64(1), pages 142-161, October.
  5. Balasko, Yves & Royer, Daniel, 1996. "Stability of Competitive Equilibrium with Respect to Recursive and Learning Processes," Journal of Economic Theory, Elsevier, vol. 68(2), pages 319-348, February.
  6. George W. Evans & Seppo Honkapohja, 1993. "Adaptive forecasts, hysteresis, and endogenous fluctuations," Economic Review, Federal Reserve Bank of San Francisco, pages 3-13.
  7. Evans, G.W. & Guesnerie, R., 1992. "Rationalizability, Strong Rationality and Expectational Stability," DELTA Working Papers 92-03, DELTA (Ecole normale supérieure).
  8. Grandmont Jean-michel & Laroque Guy, 1985. "Stability of cycles and expectations," CEPREMAP Working Papers (Couverture Orange) 8519, CEPREMAP.
  9. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  10. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
  11. Lucas, Robert E, Jr, 1973. "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review, American Economic Association, vol. 63(3), pages 326-34, June.
  12. Evans, George W & Honkapohja, Seppo, 1995. "Local Convergence of Recursive Learning to Steady States and Cycles in Stochastic Nonlinear Models," Econometrica, Econometric Society, vol. 63(1), pages 195-206, January.
  13. 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).
  14. Grandmont Jean-michel, 1983. "On endogenous competitive business cycles," CEPREMAP Working Papers (Couverture Orange) 8316, CEPREMAP.
  15. Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
  16. 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.
  17. George W. Evans & Seppo Honkapohja, 2000. "Convergence for difference equations with vanishing time-dependence, with applications to adaptive learning," Economic Theory, Springer, vol. 15(3), pages 717-725.
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