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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 attitudes will reduce their ambiguity when sample information becomes large. To address this question, I develop closed-form models of Bayesian learning in which beliefs are described as Choquet estimators with respect to neo-additive capacities (Chateauneuf, Eichberger, and Grant 2007). Under the optimistic, the pessimistic, and the full Bayesian update rule, a Bayesian learnerÂ’s ambiguity will increase rather than decrease to the effect that these agents will express ambiguity attitudes regardless of whether they have access to large sample information or not. While consistent Bayesian learning occurs under the Sarin-Wakker update rule, this result comes with the descriptive drawback that it does not apply to agents who still express ambiguity attitudes after one round of updating.

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Bibliographic Info

Paper provided by Economic Research Southern Africa in its series Working Papers with number 240.

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Length: 34 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:rza:wpaper:240

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Keywords: Non-additive Probability Measures; Bayesian Learning; Choquet Expected Utility Theory;

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References

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  1. Eichberger, J. & Kelsey, D., 1996. "E-Capacities and the Ellsberg Paradox," Discussion Papers 96-13, Department of Economics, University of Birmingham.
  2. Alexander Ludwig and Alexander Zimper, 2013. "Biased Bayesian Learning with an Application to the Risk-Free Rate Puzzle," Working Papers 390, Economic Research Southern Africa.
  3. Sarin, R. & Wakker, P.P., 1996. "Revealed likelihood and knightian uncertainty," Discussion Paper 1996-59, Tilburg University, Center for Economic Research.
  4. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  5. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-80, November.
  6. 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 1039-59, July.
  7. 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.
  8. 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(02), pages 123-133, June.
  9. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1275-1303.
  10. Adam, Klaus & Marcet, Albert & Nicolini, Juan Pablo, 2012. "Stock Market Volatility and Learning," Working Papers 12-06, University of Mannheim, Department of Economics.
  11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  12. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
  13. Lars Peter Hansen & Thomas J. Sargent & Thomas D. Tallarini Jr., 1997. "Robust Permanent Income and Pricing," Levine's Working Paper Archive 596, David K. Levine.
  14. 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.
  15. 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.
  16. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  17. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
  18. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  19. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.
  20. Viscusi, W. Kip, 1985. "A Bayesian perspective on biases in risk perception," Economics Letters, Elsevier, vol. 17(1-2), pages 59-62.
  21. Klibanoff, Peter & Hanany, Eran, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
  22. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
  23. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November.
  24. Stephen G. Cecchetti & Pok-sang Lam & Nelson C. Mark, 1998. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good To Be True?," NBER Working Papers 6354, National Bureau of Economic Research, Inc.
  25. 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.
  26. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  27. Viscusi, W Kip, 1990. "Do Smokers Underestimate Risks?," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1253-69, December.
  28. Tonks, Ian, 1981. "Bayesian Learning and the Optimal Investment Decision of the Firm," The Warwick Economics Research Paper Series (TWERPS) 192, University of Warwick, Department of Economics.
  29. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  30. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  31. Quiggin, John & Horowitz, John, 1995. "Time and Risk," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 37-55, January.
  32. Hammond, P.J. & , ., 1987. "Consequentialist foundations for expected utility," CORE Discussion Papers 1987016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  33. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  34. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
  35. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  36. Siniscalchi, Marciano, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
  37. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  38. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  39. 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 942-56, December.
  40. 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.
  41. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
  42. 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.
  43. Viscusi, W Kip, 1991. "Age Variations in Risk Perceptions and Smoking Decisions," The Review of Economics and Statistics, MIT Press, vol. 73(4), pages 577-88, November.
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Cited by:
  1. Alexander Ludwig & Alexander Zimper, 2012. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Working Papers 296, Economic Research Southern Africa.
  2. 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.

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