IDEAS home Printed from https://ideas.repec.org/p/man/cgbcrp/242.html
   My bibliography  Save this paper

Discrete beliefs space and equilibrium: a cautionary note

Author

Listed:
  • Michele Berardi

Abstract

Bounded rationality requires assumptions about ways in which rationality is constrained and agents form their expectations. Evolutionary schemes have been used to model beliefs dynamics, with agents choosing endogenously among a limited number of beliefs heuristics according to their relative performance. This work shows that arbitrarily constraining the beliefs space to a finite (small) set of possibilities can generate artificial equilibria that can be stable under evolutionary dynamics. Only when "enough" heuristics are available, beliefs in equilibrium are not arti?cially constrained. I discuss these findings in light of an alternative approach to modelling beliefs dynamics, namely adaptive learning.

Suggested Citation

  • Michele Berardi, 2018. "Discrete beliefs space and equilibrium: a cautionary note," Centre for Growth and Business Cycle Research Discussion Paper Series 242, Economics, The University of Manchester.
    • Handle: RePEc:man:cgbcrp:242
    as

    Download full text from publisher

    File URL: http://hummedia.manchester.ac.uk/schools/soss/cgbcr/discussionpapers/dpcgbcr242.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Berardi, Michele, 2015. "On the fragility of sunspot equilibria under learning and evolutionary dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 251-265.
    2. Branch, William & McGough, Bruce, 2016. "Heterogeneous beliefs and trading inefficiencies," Journal of Economic Theory, Elsevier, vol. 163(C), pages 786-818.
    3. 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.
    4. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    5. Diks, C.G.H. & Weide, R. van der, 2003. "Heterogeneity as a natural source of randomness," CeNDEF Working Papers 03-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    6. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
    7. George W. Evans & Seppo Honkapohja, 2003. "Expectations and the Stability Problem for Optimal Monetary Policies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(4), pages 807-824.
    8. 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.
    9. Anna Agliari & Domenico Massaro & Nicolò Pecora & Alessandro Spelta, 2017. "Inflation Targeting, Recursive Inattentiveness, and Heterogeneous Beliefs," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(7), pages 1587-1619, October.
    10. Berardi, Michele, 2007. "Heterogeneity and misspecifications in learning," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3203-3227, October.
    11. Diks, C.G.H. & Weide, R. van der, 2002. "Continuous Beliefs Dynamics," CeNDEF Working Papers 02-11, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    12. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    13. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    14. 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.
    15. Aoki, Masanao, 2002. "Open models of share markets with two dominant types of participants," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 199-216, October.
    16. Berardi, Michele, 2009. "Heterogeneous expectations, sunspot equilibria and their fragility," Economics Letters, Elsevier, vol. 105(3), pages 276-279, December.
    17. Branch, William A. & Evans, George W., 2006. "Intrinsic heterogeneity in expectation formation," Journal of Economic Theory, Elsevier, vol. 127(1), pages 264-295, March.
    18. Igor Evstigneev & Thorsten Hens & Klaus Schenk-Hoppé, 2006. "Evolutionary stable stock markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 449-468, January.
    19. George W. Evans, 2001. "Expectations in Macroeconomics. Adaptive versus Eductive Learning," Revue Économique, Programme National Persée, vol. 52(3), pages 573-582.
    20. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    21. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    22. 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.
    23. Cees Diks & Roy van der Weide, 2003. "Heterogeneity as a Natural Source of Randomness," Tinbergen Institute Discussion Papers 03-073/1, Tinbergen Institute.
    24. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
    25. 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.
    26. Paul Grauwe, 2011. "Animal spirits and monetary policy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 423-457, June.
    27. Branch, William A., 2002. "Local convergence properties of a cobweb model with rationally heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 63-85, November.
    28. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February.
    29. Marimon, Ramon, 1993. "Adaptive learning, evolutionary dynamics and equilibrium selection in games," European Economic Review, Elsevier, vol. 37(2-3), pages 603-611, April.
    30. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    31. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    32. Anufriev, Mikhail & Assenza, Tiziana & Hommes, Cars & Massaro, Domenico, 2013. "Interest Rate Rules And Macroeconomic Stability Under Heterogeneous Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 17(8), pages 1574-1604, December.
    33. 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.
    34. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk‐Hoppé, 2002. "Market Selection Of Financial Trading Strategies: Global Stability," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 329-339, 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. Michele Berardi, 2015. "Expectations formation under adaptive learning and evolutionary dynamics," Centre for Growth and Business Cycle Research Discussion Paper Series 206, Economics, The University of Manchester.
    2. Berardi, Michele, 2015. "On the fragility of sunspot equilibria under learning and evolutionary dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 251-265.
    3. Michele Berardi, 2011. "Heterogeneous sunspots solutions under learning and replicator dynamics," Centre for Growth and Business Cycle Research Discussion Paper Series 160, Economics, The University of Manchester.
    4. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    5. Schmitt, Noemi & Westerhoff, Frank, 2015. "Managing rational routes to randomness," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 157-173.
    6. Hommes, C.H., 2005. "Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006," CeNDEF Working Papers 05-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    7. Berardi, Michele, 2022. "Beliefs asymmetry and price stability in a cobweb model," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 401-415.
    8. Cars Hommes & Florian Wagener, 2008. "Complex Evolutionary Systems in Behavioral Finance," Tinbergen Institute Discussion Papers 08-054/1, Tinbergen Institute.
    9. Tiziana Assenza & William A. Brock & Cars H. Hommes, 2017. "Animal Spirits, Heterogeneous Expectations, And The Amplification And Duration Of Crises," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 542-564, January.
    10. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    11. Mele, Antonio & Molnár, Krisztina & Santoro, Sergio, 2020. "On the perils of stabilizing prices when agents are learning," Journal of Monetary Economics, Elsevier, vol. 115(C), pages 339-353.
    12. Hommes, Cars & Lustenhouwer, Joep, 2019. "Managing unanchored, heterogeneous expectations and liquidity traps," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 1-16.
    13. Massaro, Domenico, 2013. "Heterogeneous expectations in monetary DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 680-692.
    14. Hommes, C.H. & Lustenhouwer, J., 2016. "Managing Heterogeneous and Unanchored Expectations: A Monetary Policy Analysis," CeNDEF Working Papers 16-01, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    15. Goy, Gavin & Hommes, Cars & Mavromatis, Kostas, 2022. "Forward guidance and the role of central bank credibility under heterogeneous beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 1240-1274.
    16. Debes, Sebastian & Gareis, Johannes & Mayer, Eric & Rüth, Sebastian, 2014. "Towards a consumer sentiment channel of monetary policy," W.E.P. - Würzburg Economic Papers 91, University of Würzburg, Department of Economics.
    17. Anufriev, Mikhail & Assenza, Tiziana & Hommes, Cars & Massaro, Domenico, 2013. "Interest Rate Rules And Macroeconomic Stability Under Heterogeneous Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 17(8), pages 1574-1604, December.
    18. Hommes, Cars & Lustenhouwer, Joep, 2019. "Inflation targeting and liquidity traps under endogenous credibility," Journal of Monetary Economics, Elsevier, vol. 107(C), pages 48-62.
    19. Anufriev, M. & Assenza, T. & Hommes, C.H. & Massaro, D., 2008. "Interest Rate Rules with Heterogeneous Expectations," CeNDEF Working Papers 08-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    20. Anna Agliari & Domenico Massaro & Nicolò Pecora & Alessandro Spelta, 2017. "Inflation Targeting, Recursive Inattentiveness, and Heterogeneous Beliefs," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(7), pages 1587-1619, October.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    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:man:cgbcrp:242. 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: Marianne Sensier (email available below). General contact details of provider: https://edirc.repec.org/data/semanuk.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.