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Updating toward the signal

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.

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This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Correspondence to Christopher P. Chambers.

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The authors thank Federico Echenique, Laurent Mathevet, Jim Peck, Larry Samuelson, and Leonard Stefanski for their valuable comments, and The Little River Band for their inspiration.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Chambers, C.P., Healy, P.J. Updating toward the signal. Econ Theory 50, 765–786 (2012). https://doi.org/10.1007/s00199-010-0588-0

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  • DOI: https://doi.org/10.1007/s00199-010-0588-0

Keywords

  • Signal extraction
  • Bayes’s rule
  • Reversion to the mean
  • Posterior beliefs
  • Bayesian robustness

JEL Classification

  • C11
  • D01
  • D81
  • D83
  • D84