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Stochastic Gradient Learning in the Cobweb Model

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Abstract

We consider the effects of replacing least squares learning by stochastic gradient learning in the multivariate "Cobweb" model. Are the stability conditions altered? For this model, we show global convergence of stochastic gradient learning to the unique rational expectations equilibrium provided the E-stability condition is satisfied.

Suggested Citation

  • Evans, G.W. & Honkapohja, S., 1998. "Stochastic Gradient Learning in the Cobweb Model," University of Helsinki, Department of Economics 438, Department of Economics.
  • Handle: RePEc:fth:helsec:438
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    1. George W. Evans & Seppo Honkapohja, 1998. "Economic Dynamics with Learning: New Stability Results," Review of Economic Studies, Oxford University Press, vol. 65(1), pages 23-44.
    2. 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.
    3. Kuan, Chung-Ming & White, Halbert, 1994. "Adaptive Learning with Nonlinear Dynamics Driven by Dependent Processes," Econometrica, Econometric Society, vol. 62(5), pages 1087-1114, September.
    4. 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.
    5. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
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    Cited by:

    1. Berardi, Michele & Galimberti, Jaqueson K., 2013. "A note on exact correspondences between adaptive learning algorithms and the Kalman filter," Economics Letters, Elsevier, vol. 118(1), pages 139-142.
    2. Colucci, Domenico & Valori, Vincenzo, 2005. "Error learning behaviour and stability revisited," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 371-388, March.
    3. Atanas Christev, 2006. "Learning Hyperinflations," Computing in Economics and Finance 2006 475, Society for Computational Economics.
    4. Michele Berardi & Jaqueson K Galimberti, 2017. "Smoothing-based Initialization for Learning-to-Forecast Algorithms," KOF Working papers 17-425, KOF Swiss Economic Institute, ETH Zurich.
    5. Seppo Honkapohja & Kaushik Mitra, 2006. "Learning Stability in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 284-309, April.
    6. Gauthier, Stephane, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, vol. 102(2), pages 354-374, February.
    7. Davies, Ronald B. & Shea, Paul, 2010. "Adaptive learning with a unit root: An application to the current account," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 179-190, February.
    8. Michele Berardi & Jaqueson K. Galimberti, 2012. "On the plausibility of adaptive learning in macroeconomics: A puzzling conflict in the choice of the representative algorithm," Centre for Growth and Business Cycle Research Discussion Paper Series 177, Economics, The Univeristy of Manchester.
    9. George W. Evans & Seppo Honkapohja & Noah Williams, 2010. "Generalized Stochastic Gradient Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 237-262, February.
    10. repec:eee:dyncon:v:78:y:2017:i:c:p:26-53 is not listed on IDEAS
    11. Domenico Colucci & Vincenzo Valori, 2005. "Ways of learning in a simple economic setting: a comparison," Working Papers - Mathematical Economics 2005-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    12. Berardi, Michele & Galimberti, Jaqueson K., 2017. "On the initialization of adaptive learning in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 26-53.
    13. Berardi, Michele & Galimberti, Jaqueson K., 2014. "A note on the representative adaptive learning algorithm," Economics Letters, Elsevier, vol. 124(1), pages 104-107.
    14. Michele Berardi & Jaqueson K. Galimberti, 2012. "On the initialization of adaptive learning algorithms: A review of methods and a new smoothing-based routine," Centre for Growth and Business Cycle Research Discussion Paper Series 175, Economics, The Univeristy of Manchester.

    More about this item

    Keywords

    ECONOMETRICS ; ECONOMIC MODELS ; BOUNDED RATIONALITY;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General

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