IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v172y2025ics0165188924001726.html

Least squares learning? Evidence from the laboratory

Author

Listed:
  • Bao, Te
  • Dai, Yun
  • Duffy, John

Abstract

We report on an experiment testing the empirical relevance of least squares (LS) learning, a common way of modelling how individuals learn a rational expectations equilibrium (REE). Subjects are endowed with the correct perceived law of motion (PLM) for a price level variable they are seeking to forecast, but do not know the true parameterization of that PLM. Instead, they must choose and can adjust the parameters of this PLM over 50 periods. Consistent with the E-stability of the REE in the model studied, 97.8% of subjects achieve weak convergence to the REE in terms of their price level predictions. However, the number of participants that can be characterized as least squares learners via the adjustments they make to the parameterization of the PLM over time depends on properties of the data generating process of the dependent and independent variables. Participants learn the REE faster, and behave more like least squares learners when there is greater variance in the independent variable of the model. We consider several alternatives to least squares learning and find evidence that many subjects employ a simple satisficing approach.

Suggested Citation

  • Bao, Te & Dai, Yun & Duffy, John, 2025. "Least squares learning? Evidence from the laboratory," Journal of Economic Dynamics and Control, Elsevier, vol. 172(C).
  • Handle: RePEc:eee:dyncon:v:172:y:2025:i:c:s0165188924001726
    DOI: 10.1016/j.jedc.2024.104980
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188924001726
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jedc.2024.104980?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    2. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    3. Luis Armona & Andreas Fuster & Basit Zafar, 2019. "Home Price Expectations and Behaviour: Evidence from a Randomized Information Experiment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(4), pages 1371-1410.
    4. Petersen, Luba & Rholes, Ryan, 2022. "Macroeconomic expectations, central bank communication, and background uncertainty: A COVID-19 laboratory experiment," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    5. Branch, William & McGough, Bruce, 2016. "Heterogeneous beliefs and trading inefficiencies," Journal of Economic Theory, Elsevier, vol. 163(C), pages 786-818.
    6. Cornand, Camille & Hubert, Paul, 2020. "On the external validity of experimental inflation forecasts: A comparison with five categories of field expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 110(C).
    7. Mikhail Anufriev & Cars Hommes, 2012. "Evolutionary Selection of Individual Expectations and Aggregate Outcomes in Asset Pricing Experiments," American Economic Journal: Microeconomics, American Economic Association, vol. 4(4), pages 35-64, November.
    8. Luba Petersen, 2014. "Forecast Error Information and Heterogeneous Expectations in Learning-to-Forecast Experiments," Discussion Papers dp14-05, Department of Economics, Simon Fraser University.
    9. repec:spo:wpmain:info:hdl:2441/7t8isspkbs8hk8kol9kk9sjdl6 is not listed on IDEAS
    10. Bullard, James & Suda, Jacek, 2016. "The stability of macroeconomic systems with Bayesian learners," Journal of Economic Dynamics and Control, Elsevier, vol. 62(C), pages 1-16.
    11. Hommes, Cars & Sonnemans, Joep & Tuinstra, Jan & van de Velden, Henk, 2005. "A strategy experiment in dynamic asset pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 823-843, April.
    12. Olivier Coibion & Yuriy Gorodnichenko & Michael Weber, 2022. "Does Policy Communication during COVID Work?," International Journal of Central Banking, International Journal of Central Banking, vol. 18(1), pages 3-39, March.
    13. Hommes, Cars & Huber, Stefanie J. & Minina, Daria & Salle, Isabelle, 2024. "Learning in a complex world: Insights from an OLG lab experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 220(C), pages 813-837.
    14. Evans, George W. & Hommes, Cars & McGough, Bruce & Salle, Isabelle, 2022. "Are long-horizon expectations (de-)stabilizing? Theory and experiments," Journal of Monetary Economics, Elsevier, vol. 132(C), pages 44-63.
    15. Kryvtsov, Oleksiy & Petersen, Luba, 2021. "Central bank communication that works: Lessons from lab experiments," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 760-780.
    16. Luba Petersen, 2014. "Forecast Error Information and Heterogeneous Expectations in Learning-to-Forecast Macroeconomic Experiments," Research in Experimental Economics, in: Experiments in Macroeconomics, volume 17, pages 109-137, Emerald Group Publishing Limited.
    17. 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.
    18. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    19. Pfajfar, Damjan & Santoro, Emiliano, 2010. "Heterogeneity, learning and information stickiness in inflation expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 426-444, September.
    20. Fourgeaud, Claude & Gourieroux, Christian & Pradel, Jacqueline, 1986. "Learning Procedures and Convergence to Rationality," Econometrica, Econometric Society, vol. 54(4), pages 845-868, July.
    21. 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).
    22. 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.
    23. Michael Woodford, 2013. "Macroeconomic Analysis Without the Rational Expectations Hypothesis," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 303-346, May.
    24. George W Evans & Roger Guesnerie & Bruce McGough, 2019. "Eductive Stability in Real Business Cycle Models," The Economic Journal, Royal Economic Society, vol. 129(618), pages 821-852.
    25. Bao, Te & Duffy, John & Hommes, Cars, 2013. "Learning, forecasting and optimizing: An experimental study," European Economic Review, Elsevier, vol. 61(C), pages 186-204.
    26. 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.
    27. Jess Benhabib & Chetan Dave, 2014. "Learning, Large Deviations and Rare Events," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(3), pages 367-382, July.
    28. Bao, Te & Duffy, John, 2016. "Adaptive versus eductive learning: Theory and evidence," European Economic Review, Elsevier, vol. 83(C), pages 64-89.
    29. William A. Branch, 2004. "The Theory of Rationally Heterogeneous Expectations: Evidence from Survey Data on Inflation Expectations," Economic Journal, Royal Economic Society, vol. 114(497), pages 592-621, July.
    30. George W. Evans & Seppo Honkapohja, 2003. "Adaptive learning and monetary policy design," Proceedings, Federal Reserve Bank of Cleveland, pages 1045-1084.
    31. Coibion, Olivier & Gorodnichenko, Yuriy & Weber, Michael, 2020. "Does Policy Communication during COVID-19 Work?," IZA Discussion Papers 13355, IZA Network @ LISER.
    32. Hommes, Cars & Zhu, Mei, 2014. "Behavioral learning equilibria," Journal of Economic Theory, Elsevier, vol. 150(C), pages 778-814.
    33. George W. Evans, 2001. "Expectations in Macroeconomics. Adaptive versus Eductive Learning," Revue Économique, Programme National Persée, vol. 52(3), pages 573-582.
    34. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(2), pages 179-214, October.
    35. Preston, Bruce, 2006. "Adaptive learning, forecast-based instrument rules and monetary policy," Journal of Monetary Economics, Elsevier, vol. 53(3), pages 507-535, April.
    36. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 2(3), pages 287-321, September.
    37. 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.
    38. Evans, George W. & Guesnerie, Roger, 2005. "Coordination on saddle-path solutions: the eductive viewpoint--linear multivariate models," Journal of Economic Theory, Elsevier, vol. 124(2), pages 202-229, October.
    39. Carola Binder & Alex Rodrigue, 2018. "Household Informedness and Long‐Run Inflation Expectations: Experimental Evidence," Southern Economic Journal, John Wiley & Sons, vol. 85(2), pages 580-598, October.
    40. Hommes,Cars, 2015. "Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems," Cambridge Books, Cambridge University Press, number 9781107564978, November.
    41. Mikhail Anufriev & Cars Hommes & Tomasz Makarewicz, 2019. "Simple Forecasting Heuristics that Make us Smart: Evidence from Different Market Experiments," Journal of the European Economic Association, European Economic Association, vol. 17(5), pages 1538-1584.
    42. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    43. Te Bao & Cars Hommes & Tomasz Makarewicz, 2017. "Bubble Formation and (In)Efficient Markets in Learning‐to‐forecast and optimise Experiments," Economic Journal, Royal Economic Society, vol. 127(605), pages 581-609, October.
    44. Camille Cornand & Paul Hubert, 2020. "On the external validity of experimental inflation forecasts: A comparison with five categories of field expectations," Post-Print halshs-02285233, HAL.
    45. Olivier Coibion & Yuriy Gorodnichenko & Michael Weber, 2022. "Monetary Policy Communications and Their Effects on Household Inflation Expectations," Journal of Political Economy, University of Chicago Press, vol. 130(6), pages 1537-1584.
    46. George W. Evans & Seppo Honkapohja, 2009. "Learning and Macroeconomics," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 421-451, May.
    47. Olivier Coibion & Yuriy Gorodnichenko & Rupal Kamdar, 2018. "The Formation of Expectations, Inflation, and the Phillips Curve," Journal of Economic Literature, American Economic Association, vol. 56(4), pages 1447-1491, December.
    48. Hassan Afrouzi & Spencer Y Kwon & Augustin Landier & Yueran Ma & David Thesmar, 2023. "Overreaction in Expectations: Evidence and Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(3), pages 1713-1764.
    49. 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.
    50. David Gill & Victoria Prowse, 2016. "Cognitive Ability, Character Skills, and Learning to Play Equilibrium: A Level-k Analysis," Journal of Political Economy, University of Chicago Press, vol. 124(6), pages 1619-1676.
    51. Rholes, Ryan & Petersen, Luba, 2021. "Should central banks communicate uncertainty in their projections?," Journal of Economic Behavior & Organization, Elsevier, vol. 183(C), pages 320-341.
    52. Mikhail Anufriev & Jasmina Arifovic & John Ledyard & Valentyn Panchenko, 2013. "Efficiency of continuous double auctions under individual evolutionary learning with full or limited information," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 539-573, July.
    53. Arifovic, Jasmina & Hommes, Cars & Salle, Isabelle, 2019. "Learning to believe in simple equilibria in a complex OLG economy - evidence from the lab," Journal of Economic Theory, Elsevier, vol. 183(C), pages 106-182.
    54. Thomas J. Sargent, 2008. "Evolution and Intelligent Design," American Economic Review, American Economic Association, vol. 98(1), pages 5-37, March.
    55. Anufriev, Mikhail & Duffy, John & Panchenko, Valentyn, 2022. "Learning in two-dimensional beauty contest games: Theory and experimental evidence," Journal of Economic Theory, Elsevier, vol. 201(C).
    56. Jasmina Arifovic & Cars Hommes & Anita Kopányi-Peuker & Isabelle Salle, 2023. "Ten Isn't Large! Group Size and Coordination in a Large-Scale Experiment," American Economic Journal: Microeconomics, American Economic Association, vol. 15(1), pages 580-617, February.
    57. Cars Hommes, 2021. "Behavioral and Experimental Macroeconomics and Policy Analysis: A Complex Systems Approach," Journal of Economic Literature, American Economic Association, vol. 59(1), pages 149-219, March.
    58. Branch, William A. & Evans, George W., 2006. "A simple recursive forecasting model," Economics Letters, Elsevier, vol. 91(2), pages 158-166, May.
    59. Gary Charness & Dan Levin, 2009. "The Origin of the Winner's Curse: A Laboratory Study," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 207-236, February.
    60. Olivier Coibion & Yuriy Gorodnichenko & Tiziano Ropele, 2020. "Inflation Expectations and Firm Decisions: New Causal Evidence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(1), pages 165-219.
    61. Marimon Ramon & Spear Stephen E. & Sunder Shyam, 1993. "Expectationally Driven Market Volatility: An Experimental Study," Journal of Economic Theory, Elsevier, vol. 61(1), pages 74-103, October.
    62. Cars Hommes & Joep Sonnemans & Jan Tuinstra & Henk van de Velden, 2005. "Coordination of Expectations in Asset Pricing Experiments," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 955-980.
    63. Branch, William A. & Davig, Troy & McGough, Bruce, 2013. "Adaptive Learning In Regime-Switching Models," Macroeconomic Dynamics, Cambridge University Press, vol. 17(5), pages 998-1022, July.
    64. Benjamin Enke & Florian Zimmermann, 2019. "Correlation Neglect in Belief Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 313-332.
    65. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
    66. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695.
    67. 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.
    68. Cars Hommes & Domenico Massaro & Isabelle Salle, 2019. "Monetary And Fiscal Policy Design At The Zero Lower Bound: Evidence From The Lab," Economic Inquiry, Western Economic Association International, vol. 57(2), pages 1120-1140, April.
    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. 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).
    2. Mauersberger, Felix, 2021. "Monetary policy rules in a non-rational world: A macroeconomic experiment," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Hommes, Cars, 2018. "Behavioral & experimental macroeconomics and policy analysis: a complex systems approach," Working Paper Series 2201, European Central Bank.
    4. Kronick, Jeremy & Petersen, Luba, 2025. "Is monetary and fiscal policy conflict that dire?," Journal of Economic Dynamics and Control, Elsevier, vol. 172(C).
    5. Kresta Aleš & Sedláková Michaela, 2025. "How initial price history influences expectation formation in multi-asset experimental markets: An exploratory case study," Economics and Business Review, Sciendo, vol. 11(2), pages 7-37.
    6. Bao, Te & Füllbrunn, Sascha & Pei, Jiaoying & Zong, Jichuan, 2024. "Reading the market? Expectation coordination and theory of mind," Journal of Economic Behavior & Organization, Elsevier, vol. 219(C), pages 510-527.
    7. Mikhail Anufriev & Frieder Neunhoeffer & Jan Tuinstra, 2024. "Time pressure reduces financial bubbles: Evidence from a forecasting experiment," Working Papers REM 2024/0351, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    8. Anufriev, Mikhail & Lamantia, Fabio & Radi, Davide & Tichy, Tomas, 2025. "Leaning against the wind in the New Keynesian model with heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 172(C).
    9. John Duffy, 2022. "Why macroeconomics needs experimental evidence," The Japanese Economic Review, Springer, vol. 73(1), pages 5-29, January.
    10. Simone Alfarano & Eva Camacho-Cuena & Annarita Colasante & Alba Ruiz-Buforn, 2024. "The effect of time-varying fundamentals in learning-to-forecast experiments," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 19(4), pages 619-647, October.
    11. Leonid Serkov & Sergey Krasnykh, 2023. "The Specific Behavior of Economic Agents with Heterogeneous Expectations in the New Keynesian Model with Rigid Prices and Wages," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    12. 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.
    13. Colasante, Annarita & Palestrini, Antonio & Russo, Alberto & Gallegati, Mauro, 2017. "Adaptive expectations versus rational expectations: Evidence from the lab," International Journal of Forecasting, Elsevier, vol. 33(4), pages 988-1006.
    14. Gerunov, Anton, 2014. "Критичен Преглед На Основните Подходи За Моделиране На Икономическите Очаквания [A Critical Review of Major Approaches for Modeling Economic Expectations]," MPRA Paper 68797, University Library of Munich, Germany.
    15. Anufriev, Mikhail & Chernulich, Aleksei & Tuinstra, Jan, 2022. "Asset price volatility and investment horizons: An experimental investigation," Journal of Economic Behavior & Organization, Elsevier, vol. 193(C), pages 19-48.
    16. Hommes, Cars & Massaro, Domenico & Weber, Matthias, 2019. "Monetary policy under behavioral expectations: Theory and experiment," European Economic Review, Elsevier, vol. 118(C), pages 193-212.
    17. Anufriev, Mikhail & Duffy, John & Panchenko, Valentyn, 2022. "Learning in two-dimensional beauty contest games: Theory and experimental evidence," Journal of Economic Theory, Elsevier, vol. 201(C).
    18. Ahrens, Steffen & Lustenhouwer, Joep & Tettamanzi, Michele, 2023. "The Stabilizing Effects of Publishing Strategic Central Bank Projections," Macroeconomic Dynamics, Cambridge University Press, vol. 27(3), pages 826-868, April.
    19. Cars Hommes & Kostas Mavromatis & Tolga Özden & Mei Zhu, 2023. "Behavioral learning equilibria in New Keynesian models," Quantitative Economics, Econometric Society, vol. 14(4), pages 1401-1445, November.
    20. Makarewicz, Tomasz, 2021. "Traders, forecasters and financial instability: A model of individual learning of anchor-and-adjustment heuristics," Journal of Economic Behavior & Organization, Elsevier, vol. 190(C), pages 626-673.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

    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:eee:dyncon:v:172:y:2025:i:c:s0165188924001726. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.