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

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Abstract

We show in a simple monetary model that the learning dynamics do not converge to the rational expectations monetary steady state. We then show it is necessary to restrict the learning rule to obtain convergence. We derive an upper bound on the gain parameter in the learning rule, based on economic fundamentals in the monetary model, such that gain parameters above the upper bound would imply that the learning dynamics would diverge from the rational expectations monetary steady state.

Suggested Citation

  • YiLi Chien & In-Koo Cho & B. Ravikumar, 2021. "Convergence to Rational Expectations in Learning Models: A Note of Caution," Review, Federal Reserve Bank of St. Louis, vol. 103(3), pages 351-366, July.
    • Handle: RePEc:fip:fedlrv:92881
    DOI: 10.20955/r.103.351-65
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    1. George William Evans, 2001. "Expectations in Macroeconomics Adaptive versus Eductive Learning," Revue économique, Presses de Sciences-Po, vol. 52(3), pages 573-582.
    2. 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.
    3. 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.
    4. 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.
    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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    Keywords

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    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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