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Updating toward the signal

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  • Christopher Chambers
  • Paul Healy

Abstract

Modelers frequently assume (either implicitly or explicitly) that an agent’s posterior expectation of some variable lies between their prior mean and the realization of an unbiased signal of that variable. We call this property updating toward the signal (UTS). We show that if the prior and signal error densities are both symmetric and quasiconcave then UTS will occur. If, for a given prior, UTS occurs for all symmetric and quasiconcave error densities, then in fact the prior must be symmetric and quasiconcave. Similar characterizations are derived for two additional updating requirements that are strictly weaker than UTS. Copyright The Author(s) 2012

Suggested Citation

  • Christopher Chambers & Paul Healy, 2012. "Updating toward the signal," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 765-786, August.
    • Handle: RePEc:spr:joecth:v:50:y:2012:i:3:p:765-786
    DOI: 10.1007/s00199-010-0588-0
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    More about this item

    Keywords

    Signal extraction; Bayes’s rule; Reversion to the mean; Posterior beliefs; Bayesian robustness; C11; D01; D81; D83; D84;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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