Long-run expectations in a learning-to-forecast experiment: a simulation approach

  • Annarita Colasante
  • Simone Alfarano
  • Eva Camacho-Cuena
  • Mauro Gallegati
Regular Article


In this paper, we elicit short-run as well as long-run expectations on the evolution of the price of a financial asset in a Learning-to-Forecast Experiment (LtFE). Subjects, in each period, have to forecast the the asset price for each one of the remaining periods. The aim of this paper is twofold: first, we fill the gap in the experimental literature of LtFEs where great effort has been devoted to investigate short-run expectations, i.e. one step-ahead predictions, while there are no contributions that elicit long-run expectations. Second, we propose a new computational algorithm to replicate the main properties of short and long-run expectations observed in the experiment. This learning algorithm, called Exploration-Exploitation Algorithm, is based on the idea that agents anchor their expectations around the last realized price rather than on the fundamental value, with a range proportional to the past observed price volatility. When compared to the Heuristic Switching Model, our algorithm performs equally well in describing the dynamics of short-run expectations and the realized price dynamics. The EEA, additionally, is able to reproduce the dynamics long-run expectations.


Long-run expectations Experiment Evolutionary learning 

JEL Classification

D03 G12 C91 



The authors are grateful for funding the Universitat Jaume I under the project P11B2015-63 and the Spanish Ministry Science and Technology under the project ECO2015-68469-R. We thank the anonymous reviewers for their careful reading of our manuscript and their insightful comments and suggestions.

Compliance with Ethical Standards

Funding: This study is funded by the Universitat Jaume I under the project P11B2015-63 and the Spanish Ministry Science and Technology under the project ECO2015-68469-R. The authors declare that they have no conflict of interest.


  1. Anufriev M, Hommes CH (2012) Evolutionary selection of individual expectations and aggregate outcomes in asset pricing experiments. American Economic Journal: Microeconomics 4(4):35–64Google Scholar
  2. Anufriev M, Assenza T, Hommes CH, Massaro D (2013a) Interest rate rules and macroeconomic stability under heterogeneous expectations. Macroecon Dyn 17(8):1574–1604CrossRefGoogle Scholar
  3. Anufriev M, Hommes CH, Philipse RH (2013) Evolutionary selection of expectations in positive and negative feedback markets. J Evol Econ 23(3):663–688CrossRefGoogle Scholar
  4. Arifovic J, Masson P (2004) Heterogeneity and evolution of expectations in a model of currency crisis. Nonlinear Dynamics Psychol Life Sci. 8(2):231–58Google Scholar
  5. Ashiya M (2003) Testing the rationality of Japanese gdp forecasts: the sign of forecast revision matters. J Econ Behav Organ 50(2):263–269CrossRefGoogle Scholar
  6. Assenza T, Heemeijer P, Hommes CH, Massaro D (2011) Individual expectations and aggregate macro behavior. Technical report ceNDEF Working Papers 11-01, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and FinanceGoogle Scholar
  7. Assenza T, Bao T, Hommes CH, Massaro D (2014) Experiments on expectations in Macroeconomics and Finance in John Duffy (ed.) Experiments in Macroeconomics (Research in Experimental Economics, Volume 17) Emerald Group Publishing Limited, pp 11 – 70Google Scholar
  8. Auer P, Cesa-Bianchi N, Fischer P (2002) Finite-time analysis of the multiarmed bandit problem. Mach Learn 47(2-3):235–256CrossRefGoogle Scholar
  9. Bao T, Ding L (2016) Non-recourse mortgage and housing price boom, bust, and rebound. Real Estate Econ 44(3):584–605CrossRefGoogle Scholar
  10. Bao T, Hommes CH, Sonnemans J, Tuinstra J (2012) Individual expectations, limited rationality and aggregate outcomes. J Econ Dyn Control 36 (8):1101–1120CrossRefGoogle Scholar
  11. Bao T, Duffy J, Hommes CH (2013) Learning, forecasting and optimizing: an experimental study. Eur Econ Rev 61:186–204CrossRefGoogle Scholar
  12. Brock WA, Hommes CH (1997) A rational route to randomness. Econometrica 65(5):1059–1096CrossRefGoogle Scholar
  13. Brock WA, Hommes CH (1998) Heterogeneous beliefs and routes to chaos in a simple asset pricing model. J Econ Dyn Control 22(8-9):1235–1274CrossRefGoogle Scholar
  14. Campbell SD, Sharpe SA (2009) Anchoring bias in consensus forecasts and its effect on market prices. J Financ Quant Anal 44(02):369–390CrossRefGoogle Scholar
  15. Cœuré B (2013) Monetary policy in the crisis – confronting short-run challenges while anchoring long-run expectations. Tech. rep., Speech by Benoit cœuré, Member of the Executive Board of the ECB at the Journées de l’ AFSE 2013Google Scholar
  16. Colasante A, Alfarano S, Camacho-Cuena E, Gallegati M (2018) Long-run expectations in a learning-to-forecast experiment. Appl Econ Lett 25(10):681–687CrossRefGoogle Scholar
  17. Cornand C, Kader M’baye C (2013) Does inflation targeting matter? An experimental investigation. Macroeconomic Dynamics, forthcomingGoogle Scholar
  18. Diks C, Van Der Weide R (2005) Herding, a-synchronous updating and heterogeneity in memory in a CBS. J Econ Dyn Control 29(4):741–763CrossRefGoogle Scholar
  19. Draghi M (2008) Monetary policy, expectations and financial markets, Speech delivered at the Central Bank Whitaker Lecture in Dublin 18Google Scholar
  20. Fujiwara I, Ichiue H, Nakazono Y, Shigemi Y (2013) Financial markets forecasts revisited: Are they rational, stubborn or jumpy? Econ Lett 118(3):526–530CrossRefGoogle Scholar
  21. Galati G, Heemeijer P, Moessner R (2011) How do inflation expectations form? New insights from a high-frequency survey. BIS Working Papers No 349Google Scholar
  22. Gurkaynak RS, Sack B, Swanson E (2005) The sensitivity of long-term interest rates to economic news: evidence and implications for macroeconomic models. The American Economic Review 95(1):425–436CrossRefGoogle Scholar
  23. Hanaki N, Akiyama E, Ishikawa R (2016) A methodological note on eliciting price forecasts in asset market experiments. Working paper halshs-01263661Google Scholar
  24. Haruvy E, Lahav Y, Noussair CN (2007) Traders’ expectations in asset markets: experimental evidence. The American Economic Review 97(5):1901–1920CrossRefGoogle Scholar
  25. Heemeijer P, Hommes CH, Sonnemans J, Tuinstra J (2009) Price stability and volatility in markets with positive and negative expectations feedback: an experimental investigation. J Econ Dyn Control 33(5):1052–1072CrossRefGoogle Scholar
  26. Hommes CH (2001) Financial markets as nonlinear adaptive evolutionary systems. Quant Finan 1(1):149–167CrossRefGoogle Scholar
  27. Hommes CH, Huang H, Wang D (2005a) A robust rational route to randomness in a simple asset pricing model. J Econ Dyn Control 29(6):1043–1072CrossRefGoogle Scholar
  28. Hommes CH, Sonnemans J, Tuinstra J, van de Velden H (2005b) A strategy experiment in dynamic asset pricing. J Econ Dyn Control 29(4):823–843CrossRefGoogle Scholar
  29. Hommes CH (2013) Behavioral rationality and heterogeneous expectations in complex economic systems. Cambridge University PressGoogle Scholar
  30. Hommes CH, Lux T (2013) Individual expectations and aggregate behavior in learning-to-forecast experiments. Macroecon Dyn 17(2):373–401CrossRefGoogle Scholar
  31. Joyce M, Relleen J, Sorensen S (2008) Measuring monetary policy expectations from financial market instruments. Bank of England working papers 356, Bank of EnglandGoogle Scholar
  32. Koulouriotis DE, Xanthopoulos A (2008) Reinforcement learning and evolutionary algorithms for non-stationary multi-armed bandit problems. Appl Math Comput 196(2):913–922Google Scholar
  33. Lucas RE Jr (1978) Asset prices in an exchange economy. Econometrica 46 (6):1429–1445CrossRefGoogle Scholar
  34. Marimon R, Sunder S (1993) Indeterminacy of equilibria in a hyperinflationary world: Experimental evidence. Econometrica 61(5):1073–1107CrossRefGoogle Scholar
  35. Manski CF (2004) Measuring expectations. Econometrica 72:1329–1376CrossRefGoogle Scholar
  36. Nakazono Y (2012) Heterogeneity and anchoring in financial markets. Appl Financ Econ 22(21):1821–1826CrossRefGoogle Scholar
  37. Tversky A, Kahneman D (1974) Judgment under uncertainty: Heuristics and biases. Science 185(4157):1124–1131CrossRefGoogle Scholar
  38. Woodford M (2001) Monetary policy in the information economy. In: Economic Policy for the Information Economy. Kansas City: Federal Reserve Bank of Kansas City, pp 97–370Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University Jaume ICastellónSpain
  2. 2.Polytechnic University of MarcheAnconaItaly

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