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Error learning behaviour and stability revisited

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  • Domenico Colucci

    (University of Florence)

  • V. Valori

Abstract

We study the implications of error learning behaviour on the global dynamic properties of stationary equilibria in discrete time deterministic models under bounded rationality. We assume agents' ability to learn from the past performance of their expectations formation mechanism, so that such mechanism itself is made endogenous. We determine sufficient conditions under which this type of error learning behaviour enhances the stability properties of the economy. Also, we show that the set of error learning rules compatible with these conditions is not small in a topological sense and that this set can be used to approximate, with arbitrary precision, alternative learning rules that have been considered in the literature. We focus on the consequences of these results on a class of models in which agents possess fading memory, along the lines of a thread of recent literature. In particular, in this framework we treat adaptive expectations as a special case. We propose a generalisation of this expectation mechanism with fading memory which tries to capture the attitude of agents in the presence of exogenous shocks or structural breaks.

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Bibliographic Info

Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Workshop Papers, January 2001 with number 1A.1.

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Date of creation: 04 Jan 2001
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Handle: RePEc:ams:cdws01:1a.1

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Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
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References

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  1. Evans, George W & Ramey, Garey, 1992. "Expectation Calculation and Macroeconomic Dynamics," American Economic Review, American Economic Association, vol. 82(1), pages 207-24, March.
  2. Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
  3. Slonim, Robert L., 1999. "Learning rules of thumb or learning more rational rules," Journal of Economic Behavior & Organization, Elsevier, vol. 38(2), pages 217-236, February.
  4. repec:att:wimass:9530 is not listed on IDEAS
  5. Hommes, Cars H., 1991. "Adaptive learning and roads to chaos : The case of the cobweb," Economics Letters, Elsevier, vol. 36(2), pages 127-132, June.
  6. 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.
  7. Schonhofer, Martin, 2001. "Can agents learn their way out of chaos?," Journal of Economic Behavior & Organization, Elsevier, vol. 44(1), pages 71-83, January.
  8. Tuinstra, Jan, 2003. "Beliefs equilibria in an overlapping generations model," Journal of Economic Behavior & Organization, Elsevier, vol. 50(2), pages 145-164, February.
  9. Barucci, Emilio, 2000. "Exponentially fading memory learning in forward-looking economic models," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 1027-1046, June.
  10. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 2(03), pages 287-321, September.
  11. 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.
  12. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
  13. Domenico Colucci & V. Valori, 2001. "Error learning behaviour and stability revisited," CeNDEF Workshop Papers, January 2001 1A.1, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  14. Fuchs, Gerard & Laroque, Guy, 1976. "Dynamics of Temporary Equilibria and Expectations," Econometrica, Econometric Society, vol. 44(6), pages 1157-78, November.
  15. Fuchs, Gerard, 1979. "Is error learning behaviour stabilizing?," Journal of Economic Theory, Elsevier, vol. 20(3), pages 300-317, June.
  16. Evans, George W. & Honkapohja, S., 1998. "Stochastic gradient learning in the cobweb model," Economics Letters, Elsevier, vol. 61(3), pages 333-337, December.
  17. 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.
  18. Evans, George W. & Ramey, Garey, 1998. "Calculation, Adaptation And Rational Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 2(02), pages 156-182, June.
  19. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  20. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
  21. Barucci, Emilio & Landi, Leonardo, 1997. "Least mean squares learning in self-referential linear stochastic models," Economics Letters, Elsevier, vol. 57(3), pages 313-317, December.
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Citations

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Cited by:
  1. Domenico Colucci & V. Valori, 2001. "Error learning behaviour and stability revisited," CeNDEF Workshop Papers, January 2001 1A.1, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  2. Domenico Colucci & Vincenzo Valori, 2004. "Generalised Fading Memory Learning in a Cobweb Model: some evidence," Computing in Economics and Finance 2004 272, Society for Computational Economics.
  3. Carvalho, Fabia A. & Minella, André, 2012. "Survey forecasts in Brazil: A prismatic assessment of epidemiology, performance, and determinants," Journal of International Money and Finance, Elsevier, vol. 31(6), pages 1371-1391.

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