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Convergence for difference equations with vanishing time-dependence, with applications to adaptive learning

Author

Listed:
  • George W. Evans

    (Department of Economics, University of Oregon, Eugene, OR 97403-1285, USA)

  • Seppo Honkapohja

    (Department of Economics, University of Helsinki, P.O.Box 54,FIN-00014 University of Helsinki, FINLAND)

Abstract

We provide conditions for local stability and instability of an equilibrium point in certain systems of nonautonomous nonstochastic difference equations. In the systems under study the influence of time is present through a positive scalar "gain" parameter which converges in the limit to zero. These systems have recently been used to study the dynamics of adaptive learning in economic models, and we provide two economic illustrations of the formal results.

Suggested Citation

  • George W. Evans & Seppo Honkapohja, 2000. "Convergence for difference equations with vanishing time-dependence, with applications to adaptive learning," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 717-725.
    • Handle: RePEc:spr:joecth:v:15:y:2000:i:3:p:717-725
    Note: Received: October 7, 1997; revised version: February 8, 1999
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    Citations

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    Cited by:

    1. Atanas Christev, 2006. "Learning Hyperinflations," Computing in Economics and Finance 2006 475, Society for Computational Economics.
    2. Honkapohja, Seppo & Mitra, Kaushik, 2003. "Learning with bounded memory in stochastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1437-1457, June.
    3. Damjanovic, Tatiana & Girdėnas, Šarūnas & Liu, Keqing, 2015. "Stationarity of econometric learning with bounded memory and a predicted state variable," Economics Letters, Elsevier, vol. 130(C), pages 93-96.
    4. Bao, Te & Duffy, John, 2016. "Adaptive versus eductive learning: Theory and evidence," European Economic Review, Elsevier, vol. 83(C), pages 64-89.
    5. Van Zandt, Timothy & Lettau, Martin, 2003. "Robustness Of Adaptive Expectations As An Equilibrium Selection Device," Macroeconomic Dynamics, Cambridge University Press, vol. 7(1), pages 89-118, February.
    6. Damjanovic, Tatiana & Girdėnas, Šarūnas & Liu, Keqing, 2015. "Stationarity of econometric learning with bounded memory and a predicted state variable," Economics Letters, Elsevier, vol. 130(C), pages 93-96.

    More about this item

    Keywords

    Learning; Stability; Instability; Rational expectations.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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