IDEAS home Printed from https://ideas.repec.org/a/oup/restud/v74y2007i4p1275-1303.html
   My bibliography  Save this article

Learning Under Ambiguity

Author

Listed:
  • Larry G. Epstein
  • Martin Schneider

Abstract

This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extreme—it models agents who are implausibly ambitious about what they can learn in complicated environments. The paper then provides a generalization of the Bayesian model that accommodates the intuitive choices in the thought experiments. In particular, the model allows decision-makers' confidence about the environment to change—along with beliefs—as they learn. A portfolio choice application compares the effect of changes in confidence under ambiguity vs. changes in estimation risk under Bayesian learning. The former is shown to induce a trend towards more stock market participation and investment even when the latter does not. Copyright 2007, Wiley-Blackwell.

Suggested Citation

  • Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1275-1303.
  • Handle: RePEc:oup:restud:v:74:y:2007:i:4:p:1275-1303
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/j.1467-937X.2007.00464.x
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Peter Bossaerts, 2000. "Learning-Induced Securities Price Volatility," Computing in Economics and Finance 2000 299, Society for Computational Economics.
    2. Kjetil Storesletten & Chris Telmer & Amir Yaron, 2007. "Asset Pricing with Idiosyncratic Risk and Overlapping Generations," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(4), pages 519-548, October.
    3. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    4. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    5. Marco Cagetti & Lars Peter Hansen & Thomas Sargent & Noah Williams, 2002. "Robustness and Pricing with Uncertain Growth," Review of Financial Studies, Society for Financial Studies, vol. 15(2), pages 363-404, March.
    6. Harrison Hong & Jeremy C. Stein, 2003. "Differences of Opinion, Short-Sales Constraints, and Market Crashes," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 487-525.
    7. Larry G. Epstein & Martin Schneider, 2008. "Ambiguity, Information Quality, and Asset Pricing," Journal of Finance, American Finance Association, vol. 63(1), pages 197-228, February.
    8. Mark Schneider & Jonathan W. Leland & Nathaniel T. Wilcox, 2018. "Ambiguity framed," Journal of Risk and Uncertainty, Springer, vol. 57(2), pages 133-151, October.
      • Mark Schneider & Jonathan Leland & Nathaniel T. Wilcox, 2016. "Ambiguity Framed," Working Papers 16-11, Chapman University, Economic Science Institute.
    9. Gennotte, Gerard, 1986. "Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    10. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819.
    11. Michael Haliassos & Alexander Michaelides, 2003. "Portfolio Choice and Liquidity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 143-177, February.
    12. Kandel, Shmuel & Stambaugh, Robert F, 1996. "On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
    13. repec:cup:macdyn:v:6:y:2002:i:1:p:40-84 is not listed on IDEAS
    14. Campbell, John Y., 1999. "Asset prices, consumption, and the business cycle," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 19, pages 1231-1303, Elsevier.
    15. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    16. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    17. Brennan, Michael J. & Xia, Yihong, 2001. "Stock price volatility and equity premium," Journal of Monetary Economics, Elsevier, vol. 47(2), pages 249-283, April.
    18. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    19. Epstein, Larry G. & Schneider, Martin, 2003. "IID: independently and indistinguishably distributed," Journal of Economic Theory, Elsevier, vol. 113(1), pages 32-50, November.
    20. Guiso, Luigi & Jappelli, Tullio, 2000. "Household Portfolios in Italy," CEPR Discussion Papers 2549, C.E.P.R. Discussion Papers.
    21. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    22. Bryan Routledge & Stanley Zin, 2009. "Model Uncertainty and Liquidity," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(4), pages 543-566, October.
    23. Feldman, M, 1991. "On the Generic Nonconvergence of Bayesian Actions and Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 301-321, October.
    24. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    25. Allan G. Timmermann, 1993. "How Learning in Financial Markets Generates Excess Volatility and Predictability in Stock Prices," The Quarterly Journal of Economics, Oxford University Press, vol. 108(4), pages 1135-1145.
    26. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    27. Truman F. Bewley, 1988. "Knightian Decision Theory and Econometric Inference," Cowles Foundation Discussion Papers 868, Cowles Foundation for Research in Economics, Yale University.
    28. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    29. Veronesi, Pietro, 1999. "Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 975-1007.
    30. Carsten Krabbe Nielsen, 1996. "Rational belief structures and rational belief equilibria (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 399-422.
    31. Brandt, M.W.Michael W. & Zeng, Qi & Zhang, Lu, 2004. "Equilibrium stock return dynamics under alternative rules of learning about hidden states," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 1925-1954, September.
    32. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
    33. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833.
    34. Abel, Andrew B., 2002. "An exploration of the effects of pessimism and doubt on asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1075-1092, July.
    35. Ang, Andrew & Bekaert, Geert & Liu, Jun, 2005. "Why stocks may disappoint," Journal of Financial Economics, Elsevier, vol. 76(3), pages 471-508, June.
    36. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
    37. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    38. Hansen, Lars Peter & Sargent, Thomas J. & Wang, Neng E., 2002. "Robust Permanent Income And Pricing With Filtering," Macroeconomic Dynamics, Cambridge University Press, vol. 6(1), pages 40-84, February.
    39. Sujoy Mukerji & Jean-Marc Tallon & CNRS-EUREQua & Universite Paris I, 2002. "Ellsberg`s 2-Color Experiment, Bid-Ask Behavior and Ambiguity," Economics Series Working Papers 114, University of Oxford, Department of Economics.
    40. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    41. Jonathan Lewellen & Jay Shanken, 2002. "Learning, Asset‐Pricing Tests, and Market Efficiency," Journal of Finance, American Finance Association, vol. 57(3), pages 1113-1145, June.
    42. Veldkamp, Laura L., 2005. "Slow boom, sudden crash," Journal of Economic Theory, Elsevier, vol. 124(2), pages 230-257, October.
    43. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
    44. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826.
    45. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    46. Detemple, Jerome B, 1986. "Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-391, June.
    47. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
    48. Alon Brav & J.B. Heaton, 2002. "Competing Theories of Financial Anomalies," Review of Financial Studies, Society for Financial Studies, vol. 15(2), pages 575-606, March.
    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. Larry G. Epstein & Martin Schneider, 2008. "Ambiguity, Information Quality, and Asset Pricing," Journal of Finance, American Finance Association, vol. 63(1), pages 197-228, February.
    2. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    3. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    4. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    5. Lorenzo Garlappi & Raman Uppal & Tan Wang, 2007. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 41-81, January.
    6. Agarwal, Vikas & Arisoy, Y. Eser & Naik, Narayan Y., 2017. "Volatility of aggregate volatility and hedge fund returns," Journal of Financial Economics, Elsevier, vol. 125(3), pages 491-510.
    7. Markus Leippold & Fabio Trojani & Paolo Vanini, 2008. "Learning and Asset Prices Under Ambiguous Information," Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2565-2597, November.
    8. Lubos Pastor & Pietro Veronesi, 2009. "Learning in Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 361-381, November.
    9. Trojani, Fabio & Wiehenkamp, Christian & Wrampelmeyer, Jan, 2014. "Ambiguity and Reality," Working Papers on Finance 1418, University of St. Gallen, School of Finance.
    10. Daniele Pennesi, 2013. "Asset Prices in an Ambiguous Economy," Carlo Alberto Notebooks 315, Collegio Carlo Alberto.
    11. Hening Liu, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Post-Print hal-00781344, HAL.
    12. Ludwig, Alexander & Zimper, Alexander, 2014. "Biased Bayesian learning with an application to the risk-free rate puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 79-97.
    13. Yiqun Mou & Lars A. Lochstoer & Michael Johannes, 2011. "Learning about Consumption Dynamics," 2011 Meeting Papers 306, Society for Economic Dynamics.
    14. Jianjun Miao, 2009. "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 257-279, November.
    15. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    16. Qi Nan Zhai, 2015. "Asset Pricing Under Ambiguity and Heterogeneity," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2015.
    17. Massa, Massimo & Simonov, Andrei, 2005. "Is learning a dimension of risk?," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2605-2632, October.
    18. Martin Schneider, 2010. "The Research Agenda: Martin Schneider on Multiple Priors Preferences and Financial Markets," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 11(2), April.
    19. So, Leh-chyan, 2013. "Are Real Options “Real”? Isolating Uncertainty from Risk in Real Options Analysis," MPRA Paper 52493, University Library of Munich, Germany.
    20. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Lists

    This item is featured on the following reading lists, Wikipedia, or ReplicationWiki pages:
    1. Learning Under Ambiguity (REStud 2007) in ReplicationWiki

    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:oup:restud:v:74:y:2007:i:4:p:1275-1303. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://academic.oup.com/restud .

    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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/restud .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.