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Dimensionality and Disagreement: Asymptotic Belief Divergence in Response to Common Information

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Abstract

We provide a model of boundedly-rational, multidimensional learning and characterize when beliefs will converge to the truth. Agents maintain beliefs as marginal probabilities rather than joint probabilities, and agents' information is of lower dimension than the model. As a result, for some observations agents may face an identification problem affecting the role of data in inference. Beliefs converge to the truth when these observations are rare, but beliefs diverge when observations presenting an identification problem are frequent. Robustly, two agents with differing priors who observe identical, unambiguous information may disagree forever, with stronger disagreement the more information received.

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  • Isaac Loh & Gregory Phelan, 2016. "Dimensionality and Disagreement: Asymptotic Belief Divergence in Response to Common Information," Department of Economics Working Papers 2016-18, Department of Economics, Williams College, revised Jan 2019.
    • Handle: RePEc:wil:wileco:2016-18
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    Keywords

    Heterogeneous beliefs; divergence; learning; Bayesian updating; bounded rationality; sparsity;
    All these keywords.

    JEL classification:

    • D10 - Microeconomics - - Household Behavior - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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