IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v50y2012i3p765-786.html

Updating toward the signal

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-010-0588-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-010-0588-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Rothschild, Michael, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 689-711, July/Aug..
    2. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    3. Steven Tadelis, 2003. "Firm reputation with hidden information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 635-651, March.
    4. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    5. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
    6. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    7. Feldman, M, 1991. "On the Generic Nonconvergence of Bayesian Actions and Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 301-321, October.
    8. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    9. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    10. Robert Wilson, 1977. "A Bidding Model of Perfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(3), pages 511-518.
    11. Yaron Azrieli & Ehud Lehrer, 2007. "Market Games in Large Economies with a Finite Number of Types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 327-342, May.
    12. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    13. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    14. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    15. Alvaro Sandroni, 2005. "Efficient markets and Bayes’ rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 741-764, November.
    16. Michael Rothschild, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown: A Summary," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 1, pages 293-294, National Bureau of Economic Research, Inc.
    17. William Novshek & Hugo Sonnenschein, 1982. "Fulfilled Expectations Cournot Duopoly with Information Acquisition and Release," Bell Journal of Economics, The RAND Corporation, vol. 13(1), pages 214-218, Spring.
    18. Daniel Quint, 2010. "Looking smart versus playing dumb in common-value auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(3), pages 469-490, September.
    19. Nidhiya Menon & Narayanan Subramanian, 2008. "Learning, diversification and the nature of risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 117-145, April.
    20. James Peck & Matthew O. Jackson, 1999. "Asymmetric information in a competitive market game: Reexamining the implications of rational expectations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 603-628.
    21. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
    22. Carl Shapiro, 1986. "Exchange of Cost Information in Oligopoly," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 433-446.
    23. Franklin Allen & Stephen Morris & Hyun Song Shin, 2006. "Beauty Contests and Iterated Expectations in Asset Markets," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 719-752.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Joseph McMurray, 2017. "Ideology as Opinion: A Spatial Model of Common-Value Elections," American Economic Journal: Microeconomics, American Economic Association, vol. 9(4), pages 108-140, November.
    2. Sarah Janzen & Nicholas Magnan & Conner Mullally & Soye Shin & I. Bailey Palmer & Judith Oduol & Karl Hughes, 2021. "Can Experiential Games and Improved Risk Coverage Raise Demand for Index Insurance? Evidence from Kenya," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(1), pages 338-361, January.
    3. Nunnari, Salvatore & Frydman, Cary, 2021. "Coordination with Cognitive Noise," CEPR Discussion Papers 16644, C.E.P.R. Discussion Papers.
    4. ,, 2014. "On the relationship between individual and group decisions," Theoretical Economics, Econometric Society, vol. 9(1), January.
    5. Gabriel Martinez & Nicholas H. Tenev, 2020. "Optimal Echo Chambers," Papers 2010.01249, arXiv.org, revised Jun 2025.
    6. Te Bao & John Duffy, 2021. "Signal extraction: experimental evidence," Theory and Decision, Springer, vol. 90(2), pages 219-232, March.
    7. Cappelen, Alexander W. & de Haan, Thomas & Tungodden, Bertil, 2024. "Fairness and limited information: Are people Bayesian meritocrats?," Journal of Public Economics, Elsevier, vol. 233(C).
    8. Yongheng Hu, 2025. "How Big Data Dilutes Cognitive Resources, Interferes with Rational Decision-making and Affects Wealth Distribution ?," Papers 2508.20435, arXiv.org, revised Aug 2025.
    9. Haeussler, Carolin & Harhoff, Dietmar & Mueller, Elisabeth, 2014. "How patenting informs VC investors – The case of biotechnology," Research Policy, Elsevier, vol. 43(8), pages 1286-1298.
    10. Georganas, Sotiris & Healy, Paul J. & Li, Nan, 2014. "Frequency bias in consumers׳ perceptions of inflation: An experimental study," European Economic Review, Elsevier, vol. 67(C), pages 144-158.
    11. Gagnon-Bartsch, Tristan & Bushong, Benjamin, 2022. "Learning with misattribution of reference dependence," Journal of Economic Theory, Elsevier, vol. 203(C).
    12. Joel Sobel, 2014. "On the relationship between individual and group decisions," Levine's Working Paper Archive 786969000000000950, David K. Levine.
    13. Park, Hyoeun & Tayawa, Jason Paulo, 2024. "Anchored belief updating from recommendations," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    14. Jerker Denrell & Christina Fang & Chengwei Liu, 2015. "Perspective—Chance Explanations in the Management Sciences," Organization Science, INFORMS, vol. 26(3), pages 923-940, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tunca, Tunay I., 2008. "Information precision and asymptotic efficiency of industrial markets," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 964-996, September.
    2. Christensen, K. & Podolskij, M. & Thamrongrat, N. & Veliyev, B., 2017. "Inference from high-frequency data: A subsampling approach," Journal of Econometrics, Elsevier, vol. 197(2), pages 245-272.
    3. Henning Fischer & Ángela Blanco‐FERNÁndez & Peter Winker, 2016. "Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(2), pages 113-146, March.
    4. Peter Yegon & W. Brent Lindquist & Svetlozar T. Rachev, 2025. "Asset Pricing in the Presence of Market Microstructure Noise," Papers 2511.00308, arXiv.org.
    5. Babalos, Vassilios & Caporale, Guglielmo Maria & Philippas, Nikolaos, 2012. "Efficiency evaluation of Greek equity funds," Research in International Business and Finance, Elsevier, vol. 26(2), pages 317-333.
    6. Neil Shephard & Dacheng Xiu, 2012. "Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices," Economics Series Working Papers 604, University of Oxford, Department of Economics.
    7. Christensen, Kim & Kinnebrock, Silja & Podolskij, Mark, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Journal of Econometrics, Elsevier, vol. 159(1), pages 116-133, November.
    8. Julien Chevallier & Benoît Sévi, 2011. "On the realized volatility of the ECX CO 2 emissions 2008 futures contract: distribution, dynamics and forecasting," Annals of Finance, Springer, vol. 7(1), pages 1-29, February.
    9. Vladimir Asriyan, 2014. "Balance sheet recessions with informational and trading frictions," Economics Working Papers 1463, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2018.
    10. Selma Chaker, 2013. "Volatility and Liquidity Costs," Staff Working Papers 13-29, Bank of Canada.
    11. James Peck & Matthew O. Jackson, 1999. "Asymmetric information in a competitive market game: Reexamining the implications of rational expectations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 603-628.
    12. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    13. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    14. Kalnina, Ilze & Linton, Oliver, 2006. "Estimating quadratic variation consistently in the presence of correlated measurement error," LSE Research Online Documents on Economics 4413, London School of Economics and Political Science, LSE Library.
    15. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," OFRC Working Papers Series 2004fe20, Oxford Financial Research Centre.
    16. Bretó, Carles & Veiga, Helena, 2011. "Forecasting volatility: does continuous time do better than discrete time?," DES - Working Papers. Statistics and Econometrics. WS ws112518, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    18. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
    19. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, vol. 161(2), pages 262-283, April.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:50:y:2012:i:3:p:765-786. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.