IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-00586045.html
   My bibliography  Save this paper

Bubbles and crashes with partially sophisticated investors

Author

Listed:
  • Milo Bianchi

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Philippe Jehiel

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UCL - University College of London [London])

Abstract

We consider a purely speculative market with finite horizon and complete information. We introduce partially sophisticated investors, who know the average buy and sell strategies of other traders, but lack a precise understanding of how these strategies depend on the history of trade. In this setting, it is common knowledge that the market is overvalued and bound to crash, but agents hold different expectations about the date of the crash. We define conditions for the existence of equilibrium bubbles and crashes, characterize their structure, and show how bubbles may last longer when the amount of fully rational traders increases.

Suggested Citation

  • Milo Bianchi & Philippe Jehiel, 2008. "Bubbles and crashes with partially sophisticated investors," Working Papers halshs-00586045, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00586045
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00586045
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00586045/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bruno Biais & Peter Bossaerts, 1998. "Asset Prices and Trading Volume in a Beauty Contest," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(2), pages 307-340.
    2. Peter Temin & Hans-Joachim Voth, 2004. "Riding the South Sea Bubble," American Economic Review, American Economic Association, vol. 94(5), pages 1654-1668, December.
    3. De Long, J Bradford, et al, 1990. "Positive Feedback Investment Strategies and Destabilizing Rational Speculation," Journal of Finance, American Finance Association, vol. 45(2), pages 379-395, June.
    4. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
    5. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    6. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    7. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    8. Stephen Morris, 1996. "Speculative Investor Behavior and Learning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(4), pages 1111-1133.
    9. Milo Bianchi & Philippe Jehiel, 2008. "Bubbles and crashes with partially sophisticated investors," Working Papers halshs-00586045, HAL.
    10. Cutler, David M & Poterba, James M & Summers, Lawrence H, 1990. "Speculative Dynamics and the Role of Feedback Traders," American Economic Review, American Economic Association, vol. 80(2), pages 63-68, May.
    11. Harrison Hong & José Scheinkman & Wei Xiong, 2006. "Asset Float and Speculative Bubbles," Journal of Finance, American Finance Association, vol. 61(3), pages 1073-1117, June.
    12. Gennotte, Gerard & Leland, Hayne, 1990. "Market Liquidity, Hedging, and Crashes," American Economic Review, American Economic Association, vol. 80(5), pages 999-1021, December.
    13. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    14. Greenwood, Robin & Nagel, Stefan, 2009. "Inexperienced investors and bubbles," Journal of Financial Economics, Elsevier, vol. 93(2), pages 239-258, August.
    15. Stiglitz, Joseph E, 1990. "Symposium on Bubbles," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 13-18, Spring.
    16. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February.
    17. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    18. Allen F. & Morris S. & Postlewaite A., 1993. "Finite Bubbles with Short Sale Constraints and Asymmetric Information," Journal of Economic Theory, Elsevier, vol. 61(2), pages 206-229, December.
    19. repec:bla:jfinan:v:59:y:2004:i:5:p:2013-2040 is not listed on IDEAS
    20. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    21. Brad M. Barber & Terrance Odean, 2008. "All That Glitters: The Effect of Attention and News on the Buying Behavior of Individual and Institutional Investors," The Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 785-818, April.
    22. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    23. Ernan Haruvy & Yaron Lahav & Charles N. Noussair, 2007. "Traders' Expectations in Asset Markets: Experimental Evidence," American Economic Review, American Economic Association, vol. 97(5), pages 1901-1920, December.
    24. David Hirshleifer, 2001. "Investor Psychology and Asset Pricing," Journal of Finance, American Finance Association, vol. 56(4), pages 1533-1597, August.
    25. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695.
    26. David H. Cutler & James M. Poterba & Lawrence H. Summers, 1988. "What Moves Stock Prices?," Working papers 487, Massachusetts Institute of Technology (MIT), Department of Economics.
    27. Bhattacharya, Utpal & Galpin, Neal & Ray, Rina & Yu, Xiaoyun, 2009. "The Role of the Media in the Internet IPO Bubble," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(3), pages 657-682, June.
    28. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-1181, September.
    29. Harrison Hong & Jeremy C. Stein, 2007. "Disagreement and the Stock Market," Journal of Economic Perspectives, American Economic Association, vol. 21(2), pages 109-128, Spring.
    30. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    31. Garber, Peter M, 1990. "Famous First Bubbles," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 35-54, Spring.
    32. Richard T. Baillie & Tim Bollerslev, 1991. "Intra-Day and Inter-Market Volatility in Foreign Exchange Rates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 565-585.
    33. Paul C. Tetlock, 2007. "Giving Content to Investor Sentiment: The Role of Media in the Stock Market," Journal of Finance, American Finance Association, vol. 62(3), pages 1139-1168, June.
    34. John H. Cochrane, 2002. "Stocks as Money: Convenience Yield and the Tech-Stock Bubble," NBER Working Papers 8987, National Bureau of Economic Research, Inc.
    35. 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.
    36. Daniel Kahneman, 2003. "Maps of Bounded Rationality: Psychology for Behavioral Economics," American Economic Review, American Economic Association, vol. 93(5), pages 1449-1475, December.
    37. Veldkamp, Laura L., 2005. "Slow boom, sudden crash," Journal of Economic Theory, Elsevier, vol. 124(2), pages 230-257, October.
    38. Allen, Franklin & Gale, Douglas, 1994. "Limited Market Participation and Volatility of Asset Prices," American Economic Review, American Economic Association, vol. 84(4), pages 933-955, September.
    39. Ariel Rubinstein, 1997. "Modeling Bounded Rationality," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262681005, April.
    40. David Porter & Vernon Smith, 1994. "Stock market bubbles in the laboratory," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(2), pages 111-128.
    41. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
    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. Jakub Steiner & Colin Stewart, 2012. "Price Distortions in High-Frequency Markets," Discussion Papers 1549, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Milo Bianchi & Philippe Jehiel, 2008. "Bubbles and crashes with partially sophisticated investors," Working Papers halshs-00586045, HAL.
    3. Antler, Yair, 2018. "Multilevel Marketing: Pyramid-Shaped Schemes or Exploitative Scams?," CEPR Discussion Papers 13054, C.E.P.R. Discussion Papers.
    4. Antler, Yair, 2023. "Multilevel marketing: pyramid-shaped schemes or exploitative scams?," Theoretical Economics, Econometric Society, vol. 18(2), May.
    5. Steiner, Jakub & Stewart, Colin, 2015. "Price distortions under coarse reasoning with frequent trade," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 574-595.
    6. repec:dau:papers:123456789/5361 is not listed 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. repec:dau:papers:123456789/5361 is not listed on IDEAS
    2. Brunnermeier, Markus K. & Oehmke, Martin, 2013. "Bubbles, Financial Crises, and Systemic Risk," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1221-1288, Elsevier.
    3. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    4. David Hirshleife, 2015. "Behavioral Finance," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 133-159, December.
    5. Wei Xiong, 2013. "Bubbles, Crises, and Heterogeneous Beliefs," NBER Working Papers 18905, National Bureau of Economic Research, Inc.
    6. Fotini Economou & Konstantinos Gavriilidis & Bartosz Gebka & Vasileios Kallinterakis, 2022. "Feedback trading: a review of theory and empirical evidence," Review of Behavioral Finance, Emerald Group Publishing Limited, vol. 15(4), pages 429-476, February.
    7. Kaizoji, Taisei (kaizoji@icu.ac.jp), 2010. "A Behavioral Model of Bubbles and Crashes," MPRA Paper 20352, University Library of Munich, Germany.
    8. Baghestanian, S. & Lugovskyy, V. & Puzzello, D., 2015. "Traders’ heterogeneity and bubble-crash patterns in experimental asset markets," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 82-101.
    9. Zhou, Hang, 2022. "Informed speculation with k-level reasoning," Journal of Economic Theory, Elsevier, vol. 200(C).
    10. Hirota, Shinichi & Sunder, Shyam, 2007. "Price bubbles sans dividend anchors: Evidence from laboratory stock markets," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1875-1909, June.
    11. 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.
    12. John R. Conlon, 2015. "Should Central Banks Burst Bubbles? Some Microeconomic Issues," Economic Journal, Royal Economic Society, vol. 125(582), pages 141-161, February.
    13. Peter Temin & Hans-Joachim Voth, 2004. "Riding the South Sea Bubble," American Economic Review, American Economic Association, vol. 94(5), pages 1654-1668, December.
    14. Dirk-Jan Janssen & Sascha Füllbrunn & Utz Weitzel, 2019. "Individual speculative behavior and overpricing in experimental asset markets," Experimental Economics, Springer;Economic Science Association, vol. 22(3), pages 653-675, September.
    15. Bianchi, Milo & Jehiel, Philippe, 2015. "Financial reporting and market efficiency with extrapolative investors," Journal of Economic Theory, Elsevier, vol. 157(C), pages 842-878.
    16. Wei Xiong & Jialin Yu, 2011. "The Chinese Warrants Bubble," American Economic Review, American Economic Association, vol. 101(6), pages 2723-2753, October.
    17. Carlos J. Perez & Manuel Santos, 2017. "On the Dynamics of Speculation in a Model of Bubbles and Manias," Working Papers 2017-02, University of Miami, Department of Economics.
    18. Barlevy, Gadi, 2014. "A leverage-based model of speculative bubbles," Journal of Economic Theory, Elsevier, vol. 153(C), pages 459-505.
    19. Jianping Mei & Jose Scheinkman & Wei Xiong, 2005. "Speculative Trading and Stock Prices: An Analysis of Chinese A-B Share Premia," Levine's Bibliography 122247000000000867, UCLA Department of Economics.
    20. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    21. Ernst Fehr & Jean-Robert Tyran, 2005. "Individual Irrationality and Aggregate Outcomes," Journal of Economic Perspectives, American Economic Association, vol. 19(4), pages 43-66, Fall.

    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:hal:wpaper:halshs-00586045. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.