Updating toward the signal
type: Item
instance of: scholarly article
title: Updating toward the signal
zbMATH Open document ID: 1255.91057
author: Christopher P. Chambers
author: Paul J. Healy
published in: Economic Theory
publication date: 2012-09-04T00:00:00Z
review text: In economic theory, it is frequently assumed that agents infer the value of some random variable based on imperfect observation. For example, bidders in auctions infer the unknown value of an object from private signals (cf. [\textit{R. Wilson}, Rev. Econ. Stud. 44, 511--518 (1977; Zbl 0373.90012)]). Modelers often assume that the posterior expectation lies between the prior expectation and the observed signal for every possible signal value. We will call this property updating toward the signal (UTS). This property was verified in some cases such as under normal prior with a normally distributed and independent signal error. However, UTS is not verified in general, although many authors take this property as necessary for the results they present (cf. [\textit{D. A. Moore} and \textit{P. J. Healy}, Psychol. Rev. 115, 502--517 (2008)]). The authors also study a weaker updating requirement, where the posterior mean must lie in the same direction as the signal, relative to the prior mean. They refer to this property as UDS. Finally, mean reinforcement (MR) is also considered. It requires that the posterior mean equal the prior mean when the signal equals the prior mean. They show that if the prior and signal error densities are both symmetric and quasiconcave then UTS will occur. Moreover, if for a given prior, UTS occurs for all symmetric and quasiconcave error densities, then the prior must be symmetric and quasiconcave. Similar characterizations are derived for UDS and MR. Examples are used to verify that the results are tight. In the economics literature, this paper is similar in spirit to [\textit{P. R. Milgrom}, Bell J. Econ. 12, 380--391 (1981)], though the current article seeks to order the posterior mean relative to the prior mean while Milgrom's goal is to order various posterior distributions according to their signal realizations. Demonstrations of some results make use of changes of variables and Bayes's rule. They finally show their main results by apply…
reviewed by: Balbina Casas-Méndez
Mathematics Subject Classification ID: 91A28
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 91G10
zbMATH DE Number: 6076612
zbMATH Keywords: signal extraction
zbMATH Keywords: Bayes's rule
zbMATH Keywords: reversion to the mean
zbMATH Keywords: posterior beliefs
zbMATH Keywords: Bayesian robustness signal extraction
zbMATH Keywords: Bayesian robustness
MaRDI profile type: Publication
full work available at URL: s00199-010-0588-0
OpenAlex ID: W1983584024
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DOI: 10.1007/S00199-010-0588-0
description: scientific article; zbMATH DE number 6076612