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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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Citations

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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 201223, University of Pretoria, Department of Economics.
  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, Elsevier, vol. 36(4), pages 610-628.

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