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On learnability of E–stable equilibria

Author

Listed:
  • Sergey Slobodyan

    (CERGE-EI, Czech Republic)

  • Atanas Christev

    (Heriot Watt University, UK)

Abstract

While under recursive least squares learning the dynamics of the economy converges to rational expectations equilibria (REE) which are E–stable, some recent examples propose that E–stability is not a sufficient condition for learnability. In this paper, we provide some further evidence on the conditions under which E–stability of a particular equilibrium might fail to imply its stochastic gradient (SG) or generalized SG learnability. We also claim that the requirement on the speed of convergence of the learning process imposed by [4] also implies that E–stable equilibria are likely to be GSG learnable. We show this in a simple †New Keneysian†model of optimal monetary policy design in which the stability of REE under SG learning. In this case, the paper gives the conditions which are necessary for reversal of learnability

Suggested Citation

  • Sergey Slobodyan & Atanas Christev, 2006. "On learnability of E–stable equilibria," Computing in Economics and Finance 2006 451, Society for Computational Economics.
    • Handle: RePEc:sce:scecfa:451
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    References listed on IDEAS

    as
    1. Giuseppe Ferrero, 2004. "Monetary Policy and the Transition to Rational Expectations," Econometric Society 2004 North American Summer Meetings 101, Econometric Society.
    2. Giannitsarou, Chryssi, 2005. "E-Stability Does Not Imply Learnability," Macroeconomic Dynamics, Cambridge University Press, vol. 9(2), pages 276-287, April.
    3. 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.
    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.
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    Cited by:

    1. Araújo, Eurilton, 2016. "Determinacy and learnability of equilibrium in a small-open economy with sticky wages and prices," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 16-32.
    2. Berardi, Michele, 2015. "Learning and coordination with dispersed information," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 19-33.

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    More about this item

    Keywords

    Adaptive learning; E–stability; stochastic gradient; learnability;
    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
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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