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

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Abstract

When information is of lower dimension than the model generating the data, Bayesian learning need not converge to the truth. Because the information is of lower dimension than the model, agents face an identification problem, affecting the role of data in inference. We provide conditions under which Bayesian learning is asymptotically inconsistent with positive probability, and sometimes almost surely. Robustly, two agents with differing priors who observe identical, unambiguous data may disagree forever, with stronger disagreement the more data is observed. Agents rationally use common observations to differentially update beliefs about different parameters.

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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 Apr 2017.
  • Handle: RePEc:wil:wileco:2016-18
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    File URL: http://web.williams.edu/Economics/wp/LohPhelanDimensionalityDisagreement.pdf
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    References listed on IDEAS

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    1. Péter Kondor, 2012. "The More We Know about the Fundamental, the Less We Agree on the Price," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 1175-1207.
    2. James Andreoni & Tymofiy Mylovanov, 2012. "Diverging Opinions," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 209-232, February.
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    Cited by:

    1. Ceren Baysan, 2017. "Can More Information Lead to More Voter Polarization? Experimental Evidence from Turkey," 2017 Papers pba1551, Job Market Papers.
    2. Benoît, Jean-Pierre & Dubra, Juan, 2018. "When do populations polarize? An explanation," MPRA Paper 86173, University Library of Munich, Germany.

    More about this item

    Keywords

    beliefs; polarization; learning; Bayesian updating; bounded rationality;

    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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