IDEAS home Printed from https://ideas.repec.org/a/aea/aejmac/v17y2025i2p101-33.html
   My bibliography  Save this article

A Unified Model of Learning to Forecast

Author

Listed:
  • George W. Evans
  • Christopher G. Gibbs
  • Bruce McGough

Abstract

We propose a model of boundedly rational and heterogeneous expectations that unifies adaptive learning, k-level reasoning, and replicator dynamics. Level-0 forecasts evolve over time via adaptive learning. Agents revise over time their depth of reasoning in response to forecast errors, observed and counterfactual. The unified model makes sharp predictions for when and how quickly markets converge in Learning-to-Forecast Experiments, including novel predictions for individual and market behavior in response to announced events. We present experimental results that support these predictions. We apply our unified approach in the New Keynesian model to study forward guidance policy.

Suggested Citation

  • George W. Evans & Christopher G. Gibbs & Bruce McGough, 2025. "A Unified Model of Learning to Forecast," American Economic Journal: Macroeconomics, American Economic Association, vol. 17(2), pages 101-133, April.
    • Handle: RePEc:aea:aejmac:v:17:y:2025:i:2:p:101-33
    DOI: 10.1257/mac.20220205
    as

    Download full text from publisher

    File URL: https://www.aeaweb.org/doi/10.1257/mac.20220205
    Download Restriction: Access to full text is restricted to AEA members and institutional subscribers.
    File URL: https://doi.org/10.3886/E198204V1
    Download Restriction: no
    File URL: https://www.aeaweb.org/articles/materials/22736
    Download Restriction: no
    File URL: https://www.aeaweb.org/articles/materials/22737
    Download Restriction: no
    File URL: https://libkey.io/10.1257/mac.20220205?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. George-Marios Angeletos & Chen Lian, 2018. "Forward Guidance without Common Knowledge," American Economic Review, American Economic Association, vol. 108(9), pages 2477-2512, September.
    2. Mikhail Anufriev & John Duffy & Valentyn Panchenko, "undated". "Planar Beauty Contests," Discussion Papers 2019-06, School of Economics, The University of New South Wales.
    3. Hommes, Cars & Sonnemans, Joep & Tuinstra, Jan & Van De Velden, Henk, 2007. "Learning In Cobweb Experiments," Macroeconomic Dynamics, Cambridge University Press, vol. 11(S1), pages 8-33, November.
    4. Mariana García-Schmidt & Michael Woodford, 2019. "Are Low Interest Rates Deflationary? A Paradox of Perfect-Foresight Analysis," American Economic Review, American Economic Association, vol. 109(1), pages 86-120, January.
    5. Khaw, Mel Win & Stevens, Luminita & Woodford, Michael, 2017. "Discrete adjustment to a changing environment: Experimental evidence," Journal of Monetary Economics, Elsevier, vol. 91(C), pages 88-103.
    6. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    7. Antoni Bosch-Domènech & José G. Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, Two, (Three), Infinity, ...: Newspaper and Lab Beauty-Contest Experiments," American Economic Review, American Economic Association, vol. 92(5), pages 1687-1701, December.
    8. 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.
    9. Ben Greiner, 2015. "Subject pool recruitment procedures: organizing experiments with ORSEE," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 1(1), pages 114-125, July.
    10. Ernst Fehr & Jean-Robert Tyran, 2008. "Limited Rationality and Strategic Interaction: The Impact of the Strategic Environment on Nominal Inertia," Econometrica, Econometric Society, vol. 76(2), pages 353-394, March.
    11. Arifovic, Jasmina & Schmitt-Grohé, Stephanie & Uribe, Martín, 2018. "Learning to live in a liquidity trap," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 120-136.
    12. Evans, George W. & Honkapohja, Seppo & Mitra, Kaushik, 2009. "Anticipated fiscal policy and adaptive learning," Journal of Monetary Economics, Elsevier, vol. 56(7), pages 930-953, October.
    13. Emmanuel Farhi & Iván Werning, 2019. "Monetary Policy, Bounded Rationality, and Incomplete Markets," American Economic Review, American Economic Association, vol. 109(11), pages 3887-3928, November.
    14. Bao, Te & Hommes, Cars & Sonnemans, Joep & Tuinstra, Jan, 2012. "Individual expectations, limited rationality and aggregate outcomes," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1101-1120.
    15. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    16. Bao, Te & Duffy, John, 2016. "Adaptive versus eductive learning: Theory and evidence," European Economic Review, Elsevier, vol. 83(C), pages 64-89.
    17. Guesnerie, Roger, 1992. "An Exploration of the Eductive Justifications of the Rational-Expectations Hypothesis," American Economic Review, American Economic Association, vol. 82(5), pages 1254-1278, December.
    18. Duffy, John & Nagel, Rosemarie, 1997. "On the Robustness of Behaviour in Experimental "Beauty Contest" Games," Economic Journal, Royal Economic Society, vol. 107(445), pages 1684-1700, November.
    19. Evans, George W & Ramey, Garey, 1992. "Expectation Calculation and Macroeconomic Dynamics," American Economic Review, American Economic Association, vol. 82(1), pages 207-224, March.
    20. Branch, William A. & McGough, Bruce, 2008. "Replicator dynamics in a Cobweb model with rationally heterogeneous expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 65(2), pages 224-244, February.
    21. repec:fth:iniesr:487 is not listed on IDEAS
    22. repec:hhs:iuiwop:487 is not listed on IDEAS
    23. Gaballo, Gaetano, 2013. "Eductive learning and the rationalizability of oligopoly games," Economics Letters, Elsevier, vol. 120(3), pages 401-404.
    24. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
    25. 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.
    26. Sethi, Rajiv & Franke, Reiner, 1995. "Behavioural Heterogeneity under Evolutionary Pressure: Macroeconomic Implications of Costly Optimisation," Economic Journal, Royal Economic Society, vol. 105(430), pages 583-600, May.
    27. Olivier Coibion & Yuriy Gorodnichenko & Saten Kumar & Jane Ryngaert, 2021. "Do You Know that I Know that You Know…? Higher-Order Beliefs in Survey Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(3), pages 1387-1446.
    28. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    29. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    30. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    31. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
    32. Chen, Daniel L. & Schonger, Martin & Wickens, Chris, 2016. "oTree—An open-source platform for laboratory, online, and field experiments," Journal of Behavioral and Experimental Finance, Elsevier, vol. 9(C), pages 88-97.
    33. Paul De Grauwe, 2012. "Lectures on Behavioral Macroeconomics," Economics Books, Princeton University Press, edition 1, volume 1, number 9891.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:zbw:bofrdp:2021_011 is not listed on IDEAS
    2. Eusepi, Stefano & Gibbs, Chris & Preston, Bruce, 2021. "Forward guidance with unanchored expectations," Research Discussion Papers 11/2021, Bank of Finland.

    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. Mauersberger, Felix & Nagel, Rosemarie & Bühren, Christoph, 2020. "Bounded rationality in Keynesian beauty contests: A lesson for central bankers?," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 14, pages 1-38.
    2. Bao, Te & Duffy, John, 2016. "Adaptive versus eductive learning: Theory and evidence," European Economic Review, Elsevier, vol. 83(C), pages 64-89.
    3. Hommes, Cars, 2018. "Behavioral & experimental macroeconomics and policy analysis: a complex systems approach," Working Paper Series 2201, European Central Bank.
    4. Assenza, T. & Heemeijer, P. & Hommes, C.H. & Massaro, D., 2021. "Managing self-organization of expectations through monetary policy: A macro experiment," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 170-186.
    5. Mariana García-Schmidt & Michael Woodford, 2019. "Are Low Interest Rates Deflationary? A Paradox of Perfect-Foresight Analysis," American Economic Review, American Economic Association, vol. 109(1), pages 86-120, January.
    6. Sergeyev, Dmitriy & Iovino, Luigi, 2018. "Central Bank Balance Sheet Policies Without Rational Expectations," CEPR Discussion Papers 13100, C.E.P.R. Discussion Papers.
    7. Tiziana Assenza & Te Bao & Cars Hommes & Domenico Massaro, 2014. "Experiments on Expectations in Macroeconomics and Finance," Research in Experimental Economics, in: Experiments in Macroeconomics, volume 17, pages 11-70, Emerald Group Publishing Limited.
    8. Hanaki, Nobuyuki & Koriyama, Yukio & Sutan, Angela & Willinger, Marc, 2019. "The strategic environment effect in beauty contest games," Games and Economic Behavior, Elsevier, vol. 113(C), pages 587-610.
    9. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    10. Bao, Te & Hommes, Cars & Pei, Jiaoying, 2021. "Expectation formation in finance and macroeconomics: A review of new experimental evidence," Journal of Behavioral and Experimental Finance, Elsevier, vol. 32(C).
    11. Xavier Gabaix, 2017. "Behavioral Inattention," NBER Working Papers 24096, National Bureau of Economic Research, Inc.
    12. Bulutay, Muhammed & Cornand, Camille & Zylbersztejn, Adam, 2022. "Learning to deal with repeated shocks under strategic complementarity: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 1318-1343.
    13. Bao, Te & Hommes, Cars, 2019. "When speculators meet suppliers: Positive versus negative feedback in experimental housing markets," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    14. Guse, Eran A., 2010. "Heterogeneous expectations, adaptive learning, and evolutionary dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 74(1-2), pages 42-57, May.
    15. Bianchi-Vimercati, Riccardo & Eichenbaum, Martin & Guerreiro, Joao, 2024. "Fiscal stimulus with imperfect expectations: Spending vs. tax policy," Journal of Economic Theory, Elsevier, vol. 217(C).
    16. George-Marios Angeletos & Chen Lian, 2018. "Forward Guidance without Common Knowledge," American Economic Review, American Economic Association, vol. 108(9), pages 2477-2512, September.
    17. Bersson, Betsy & Hürtgen, Patrick & Paustian, Matthias, 2019. "Expectations formation, sticky prices, and the ZLB," Discussion Papers 34/2019, Deutsche Bundesbank.
    18. Eran Guse, 2004. "Learning with Heterogeneous Expectations in an Evolutionary World," Computing in Economics and Finance 2004 99, Society for Computational Economics.
    19. Kopányi, Dávid & Rabanal, Jean Paul & Rud, Olga A. & Tuinstra, Jan, 2019. "Can competition between forecasters stabilize asset prices in learning to forecast experiments?," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    20. Pfajfar, Damjan & Žakelj, Blaž, 2014. "Experimental evidence on inflation expectation formation," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 147-168.

    More about this item

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • E12 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Keynes; Keynesian; Post-Keynesian; Modern Monetary Theory
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E71 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on the Macro Economy

    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:aea:aejmac:v:17:y:2025:i:2:p:101-33. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Michael P. Albert (email available below). General contact details of provider: https://edirc.repec.org/data/aeaaaea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.