IDEAS home Printed from https://ideas.repec.org/p/fip/fedlwp/88664.html
   My bibliography  Save this paper

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

Author

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://s3.amazonaws.com/real.stlouisfed.org/wp/2020/2020-027.pdf
    File Function: Full Text
    Download Restriction: no

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Azariadis, Costas & Stachurski, John, 2005. "Poverty Traps," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.),Handbook of Economic Growth, edition 1, volume 1, chapter 5, Elsevier.
    2. Ennis, Huberto M. & Keister, Todd, 2005. "Government policy and the probability of coordination failures," European Economic Review, Elsevier, vol. 49(4), pages 939-973, May.
    3. Kelly, David L. & Shorish, Jamsheed, 2000. "Stability of Functional Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, vol. 95(2), pages 215-250, December.
    4. Bin Ye & Jingjing Jiang & Lixin Miao & Ji Li & Yang Peng, 2015. "Innovative Carbon Allowance Allocation Policy for the Shenzhen Emission Trading Scheme in China," Sustainability, MDPI, Open Access Journal, vol. 8(1), pages 1-1, December.
    5. Rami Zwick & Amnon Rapoport, 2002. "Tacit Coordination in a Decentralized Market Entry Game with Fixed Capacity," Experimental Economics, Springer;Economic Science Association, vol. 5(3), pages 253-272, December.
    6. Van der Heijden, Eline C. M. & Nelissen, Jan H. M. & Potters, Jan J. M. & Verbon, Harrie A. A., 1998. "The poverty game and the pension game: The role of reciprocity," Journal of Economic Psychology, Elsevier, vol. 19(1), pages 5-41, February.
    7. Tim Taylor & Richard Harrison, 2008. "Misperceptions, heterogeneous expectations and macroeconomic dynamics," 2008 Meeting Papers 710, Society for Economic Dynamics.
    8. Huang, Weihong, 2010. "On the hidden hazards of adaptive behavior," Journal of Economic Dynamics and Control, Elsevier, vol. 34(8), pages 1442-1455, August.
    9. John Duffy, 1998. "Monetary theory in the laboratory," Review, Federal Reserve Bank of St. Louis, issue Sep, pages 9-26.
    10. Sergey Slobodyan, 1999. "Sunspot Fluctuations: A Way Out of a Development Trap?," Computing in Economics and Finance 1999 922, Society for Computational Economics.
    11. Robert Deacon & Charles Kolstad & Allen Kneese & David Brookshire & David Scrogin & Anthony Fisher & Michael Ward & Kerry Smith & James Wilen, 1998. "Research Trends and Opportunities in Environmental and Natural Resource Economics," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 11(3), pages 383-397, April.
    12. Gauthier, Stephane, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, vol. 102(2), pages 354-374, February.
    13. Theresa Lant & Zur Shapira, 2009. "Managerial Reasoning about Aspirations and Expectations," Discussion Paper Series dp498, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    14. John Duffy & Frank Heinemann, 2016. "Central Bank Reputation, Cheap Talk and Transparency as Substitutes for Commitment: Experimental Evidence," SFB 649 Discussion Papers SFB649DP2016-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Beltrametti, Luca & Fiorentini, Riccardo & Marengo, Luigi & Tamborini, Roberto, 1997. "A learning-to-forecast experiment on the foreign exchange market with a classifier system," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1543-1575, June.
    16. Felipe Pérez, 1998. "- Private Experience In Adaptive Learning Models," Working Papers. Serie AD 1998-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    17. Dávila Julio, 2016. "The Rationality of Expectations Formation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(2), pages 515-543, June.
    18. Smith, V. Kerry & Mansfield, Carol, 1998. "Buying Time: Real and Hypothetical Offers," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 209-224, November.
    19. Hommes, Cars, 2011. "The heterogeneous expectations hypothesis: Some evidence from the lab," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 1-24, January.
    20. Huberto Ennis & Todd Keister, 2000. "Government Policy and Probabilistic Equilibrium Selection," Econometric Society World Congress 2000 Contributed Papers 1148, Econometric Society.

    More about this item

    Keywords

    rational expectations equilibrium; learning algorithm; convergence; gain function;

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedlwp:88664. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://edirc.repec.org/data/frbslus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.