Updating toward the signal
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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.
KeywordsSignal extraction Bayes’s rule Reversion to the mean Posterior beliefs Bayesian robustness
JEL ClassificationC11 D01 D81 D83 D84
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- Andersen T.G., Bollerslev T., Diebold F.X., Labys P.: Great realizations. Risk 13(3), 105–108 (2000)Google Scholar
- Arrow K.J.: Essays in the Theory of Risk Bearing. Markham, Chicago (1971)Google Scholar
- Chambers, C.P., Healy, P.J.: On the robustness of good news and bad news, Ohio State University Working Paper (2009)Google Scholar
- DeGroot M.H.: Some problems of optimal stopping. J R Stat Soc Ser B 30(1), 108–122 (1968)Google Scholar
- Grossman S., Stiglitz J.E.: Information and competitive price systems. Am Econ Rev 66, 246–253 (1976)Google Scholar
- Grossman S., Stiglitz J.E.: On the impossibility of informationally efficient markets. Am Econ Rev 70, 393–408 (1980)Google Scholar
- Kahn P.M.: Credibility: Theory and Application. Academic Press, New York (1975)Google Scholar
- Markowitz H.M.: Portfolio selection. J Financ 7, 77–91 (1952)Google Scholar
- Markowitz H.M.: Portfolio Selection: Efficient Diversification of Investments. Wiley, New York (1958)Google Scholar
- Zhou B.: High-frequency data and volatility in foreign-exchange rates. J Bus Econ Stat 14(1), 45–52 (1996)Google Scholar