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Convergence to Rational Expectations in Learning Models: A Note of Caution

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Abstract

This paper illustrates a challenge in analyzing the learning algorithms resulting in second-order difference equations. We show in a simple monetary model that the learning dynamics do not converge to the rational expectations monetary steady state. We then show that to guarantee convergence, the gain parameter used in the learning rule has to be restricted based on economic fundamentals in the monetary model.

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  • YiLi Chien & In-Koo Cho & B. Ravikumar, 2020. "Convergence to Rational Expectations in Learning Models: A Note of Caution," Working Papers 2020-027, Federal Reserve Bank of St. Louis, revised 19 Sep 2020.
    • Handle: RePEc:fip:fedlwp:88664
    DOI: 10.20955/wp.2020.027
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    1. Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, vol. 59(4), pages 401-426, October.
    2. Klaus Adam & Albert Marcet & Johannes Beutel, 2017. "Stock Price Booms and Expected Capital Gains," American Economic Review, American Economic Association, vol. 107(8), pages 2352-2408, August.
    3. George W. Evans, 2001. "Expectations in Macroeconomics. Adaptive versus Eductive Learning," Revue Économique, Programme National Persée, vol. 52(3), pages 573-582.
    4. Evans, George W. & Honkapohja, Seppo & Marimon, Ramon, 2001. "Convergence In Monetary Inflation Models With Heterogeneous Learning Rules," Macroeconomic Dynamics, Cambridge University Press, vol. 5(1), pages 1-31, February.
    5. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
    6. 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. YiLi Chien & In-Koo Cho & B. Ravikumar, 2021. "Stability and Equilibrium Selection in Learning Models: A Note of Caution," Review, Federal Reserve Bank of St. Louis, vol. 103(4), pages 477-488, October.
    2. Basse, Tobias & Wegener, Christoph, 2022. "Inflation expectations: Australian consumer survey data versus the bond market," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 416-430.

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    More about this item

    Keywords

    rational expectations equilibrium; learning algorithm; convergence; gain function;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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