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Bayesian Economist ... Bayesian Agents I: An Alternative Approach to Optimal Learning

El-gamal, Mahmoud A. and Sudaram, Rangarajan K. (1989) Bayesian Economist ... Bayesian Agents I: An Alternative Approach to Optimal Learning. Social Science Working Paper, 705. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170901-161946053

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Abstract

We study the framework of optimal decision making under uncertainty where the agents do not know the full structure of the model and try to learn it optimally. We generalize the results on Bayesian learning based on the martingale convergence theorem to the sequential framework instead of the repeated framework for which results are currently available. We also show that the variability introduced by the sequential framework is sufficient under very mild identifiability conditions to circumvent the incomplete learning results that characterize the literature. We then question the type of convergence so achieved, and give an alternative Bayesian approach whereby we let the economist himself be a Bayesian with a prior on the priors that his agents may have. We prove that such an economist cannot justify endowing all his agents with the same (much less the true) prior on the basis that the model has been running long enough that we can almost surely approximate any agent's beliefs by any other's. We then examine a possibly weaker justification based on the convergence of the economist's measure on beliefs, and fully characterize it by the Harris ergodicity of the relevant Markov kernel. By means of very simple examples, we then show that learning, partial learning, and non-learning may all occur under the weak conditions that we impose. For complicated models where the Harris ergodicity of the Markov kernel in question can neither be proved nor disproved, the mathematical/statistical test of Domowitz and El-Gamal (1989) can be utilized.


Item Type:Report or Paper (Working Paper)
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http://resolver.caltech.edu/CaltechAUTHORS:20171109-135228581Related ItemPublished Version
Additional Information:We wish to thank Larry Blume, David Easley, and Nick Kiefer and participants in the theory workshops of the University of Rochester and Penn State for valuable suggestions and comments. All remaining errors are of course our own. Published as El-Gamal, Mahmoud A., and Rangarajan K. Sundaram. "Bayesian economists… Bayesian agents: An alternative approach to optimal learning." Journal of Economic Dynamics and Control 17, no. 3 (1993): 355-383.
Group:Social Science Working Papers
Subject Keywords:Rational Expectations, bayesian learning, controlled Markov processes, sequential statistical decision framework.
Series Name:Social Science Working Paper
Issue or Number:705
Record Number:CaltechAUTHORS:20170901-161946053
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170901-161946053
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81111
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:05 Sep 2017 23:10
Last Modified:03 Oct 2019 18:39

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