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Do Bayesians learn their way out of ambiguity?

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  • Alexander Zimper

Abstract

In standard models of Bayesian learning agents reduce their uncertainty about an eventÂ’s true probability because their consistent estimator concentrates almost surely around this probabilityÂ’s true value as the number of observations becomes large. This paper takes the empirically observed violations of SavageÂ’s (1954) sure thing principle seriously and asks whether Bayesian learners with ambiguity […]

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  • Alexander Zimper, 2011. "Do Bayesians learn their way out of ambiguity?," Working Papers 240, Economic Research Southern Africa.
    • Handle: RePEc:rza:wpaper:240
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    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    4. 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.
    5. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    6. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    7. Klaus Adam & Albert Marcet & Juan Pablo Nicolini, 2016. "Stock Market Volatility and Learning," Journal of Finance, American Finance Association, vol. 71(1), pages 33-82, February.
    8. Tonks, Ian, 1983. "Bayesian Learning and the Optimal Investment Decision of the Firm," Economic Journal, Royal Economic Society, vol. 93(369a), pages 87-98, Supplemen.
    9. , & ,, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
    10. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
    11. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    12. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    13. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-250, July-Aug..
    14. Barberis, Nicholas & Thaler, Richard, 2003. "A survey of behavioral finance," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 18, pages 1053-1128, Elsevier.
    15. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    16. R. M. Cyert & M. H. DeGroot & C. A. Holt, 1978. "Sequential Investment Decisions with Bayesian Learning," Management Science, INFORMS, vol. 24(7), pages 712-718, March.
    17. Cogley, Timothy & Sargent, Thomas J., 2008. "The market price of risk and the equity premium: A legacy of the Great Depression?," Journal of Monetary Economics, Elsevier, vol. 55(3), pages 454-476, April.
    18. Quiggin, John & Horowitz, John, 1995. "Time and Risk," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 37-55, January.
    19. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    20. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    21. 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..
    22. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-1272, November.
    23. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    24. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    25. Pok-sang Lam & Stephen G. Cecchetti & Nelson C. Mark, 2000. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good to Be True?," American Economic Review, American Economic Association, vol. 90(4), pages 787-805, September.
    26. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    27. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
    28. Allan G. Timmermann, 1993. "How Learning in Financial Markets Generates Excess Volatility and Predictability in Stock Prices," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 1135-1145.
    29. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    30. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 1.
    31. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    32. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    33. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    34. 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.
    35. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    36. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
    37. Hammond, P.J. & , ., 1987. "Consequentialist foundations for expected utility," LIDAM Discussion Papers CORE 1987016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    38. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    39. Cohen, M. & Gilboa, I. & Jaffray, J.Y. & Schmeidler, D., 2000. "An experimental study of updating ambiguous beliefs," Risk, Decision and Policy, Cambridge University Press, vol. 5(2), pages 123-133, June.
    40. 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.
    41. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, January.
    42. Alexander Ludwig & Alexander Zimper, 2008. "A Parsimonious Choquet Model of Subjective Life Expectancy," Working Papers, Center for Retirement Research at Boston College wp2008-20, Center for Retirement Research, revised Dec 2008.
    43. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    44. Viscusi, W Kip, 1990. "Do Smokers Underestimate Risks?," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1253-1269, December.
    45. Viscusi, W. Kip, 1985. "A Bayesian perspective on biases in risk perception," Economics Letters, Elsevier, vol. 17(1-2), pages 59-62.
    46. Hanany Eran & Klibanoff Peter, 2009. "Updating Ambiguity Averse Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-53, November.
    47. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    48. Viscusi, W Kip & O'Connor, Charles J, 1984. "Adaptive Responses to Chemical Labeling: Are Workers Bayesian Decision Makers?," American Economic Review, American Economic Association, vol. 74(5), pages 942-956, December.
    49. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    50. Viscusi, W Kip, 1991. "Age Variations in Risk Perceptions and Smoking Decisions," The Review of Economics and Statistics, MIT Press, vol. 73(4), pages 577-588, November.
    51. Robert B. Barsky & J. Bradford De Long, 1993. "Why Does the Stock Market Fluctuate?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(2), pages 291-311.
    52. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
    53. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 2.
    54. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    55. 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.
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    Cited by:

    1. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    2. Nicky Nicholls & Aylit Romm & Alexander Zimper, 2015. "The impact of statistical learning on violations of the sure-thing principle," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 97-115, April.
    3. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    4. Alexander Ludwig & Alexander Zimper, 2013. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Annals of Finance, Springer, vol. 9(4), pages 625-665, November.
    5. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Philippe Delquié & Kenneth C. Lichtendahl & Jason R. W. Merrick & Ahti Salo & George Wu, 2011. "From the Editors ---Probability Scoring Rules, Ambiguity, Multiattribute Terrorist Utility, and Sensitivity Analysis," Decision Analysis, INFORMS, vol. 8(4), pages 251-255, December.
    6. Alexander Zimper & Wei Ma, 2017. "Bayesian learning with multiple priors and nonvanishing ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 409-447, October.
    7. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors ---Group Decisions, Preference Elicitation, Experienced Utility, Survival Probabilities, and Portfolio Value of Information," Decision Analysis, INFORMS, vol. 10(2), pages 99-102, June.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • 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

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