IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/12648.html
   My bibliography  Save this paper

Learning and Disagreement in an Uncertain World

Author

Listed:
  • Daron Acemoglu
  • Victor Chernozhukov
  • Muhamet Yildiz

Abstract

Most economic analyses presume that there are limited differences in the prior beliefs of individuals, as assumption most often justified by the argument that sufficient common experiences and observations will eliminate disagreements. We investigate this claim using a simple model of Bayesian learning. Two individuals with different priors observe the same infinite sequence of signals about some underlying parameter. Existing results in the literature establish that when individuals are certain about the interpretation of signals, under very mild conditions there will be asymptotic agreement---their assessments will eventually agree. In contrast, we look at an environment in which individuals are uncertain about the interpretation of signals, meaning that they have non-degenerate probability distributions over the conditional distribution of signals given the underlying parameter. When priors on the parameter and the conditional distribution of signals have full support, we prove the following results: (1) Individuals will never agree, even after observing the same infinite sequence of signals. (2) Before observing the signals, they believe with probability 1 that their posteriors about the underlying parameter will fail to converge. (3) Observing the same sequence of signals may lead to a divergence of opinion rather than the typically presumed convergence. We then characterize the conditions for asymptotic agreement under "approximate certainty"---i.e., as we look at the limit where uncertainty about the interpretation of the signals disappears. When the family of probability distributions of signals given the parameter has "rapidly-varying tails" (such as the normal or exponential distributions), approximate certainty restores asymptotic agreement. However, when the family of probability distributions has "regularly-varying tails" (such as the Pareto, the log-normal, and the t-distributions), asymptotic agreement does not obtain even in the limit as the amount of uncertainty disappears. Lack of common priors has important implications for economic behavior in a range of circumstances. We illustrate how the type of learning outlined in this paper interacts with economic behavior in various different situations, including games of common interest, coordination, asset trading and bargaining.

Suggested Citation

  • Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:12648
    Note: EFG AP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w12648.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ottaviani, Marco & Sorensen, Peter Norman, 2006. "The strategy of professional forecasting," Journal of Financial Economics, Elsevier, vol. 81(2), pages 441-466, August.
    2. Muhamet Yildiz, 2003. "Bargaining without a Common Prior-An Immediate Agreement Theorem," Econometrica, Econometric Society, vol. 71(3), pages 793-811, May.
    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. Stephen Morris, 1996. "Speculative Investor Behavior and Learning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(4), pages 1111-1133.
    5. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    6. Baron, David P., 2004. "Persistent Media Bias," Research Papers 1845r, Stanford University, Graduate School of Business.
    7. Kurz, Mordecai, 1996. "Rational Beliefs and Endogenous Uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 383-397, October.
    8. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    9. Matthew Gentzkow & Jesse M. Shapiro, 2006. "Media Bias and Reputation," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 280-316, April.
    10. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    11. Ottaviani, Marco & Sorensen, Peter Norman, 2006. "Professional advice," Journal of Economic Theory, Elsevier, vol. 126(1), pages 120-142, January.
    12. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    13. Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2008. "Common Learning," Econometrica, Econometric Society, vol. 76(4), pages 909-933, July.
    14. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
    15. Miller, Ronald I. & Sanchirico, Chris William, 1999. "The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 170-190, October.
    16. Kurz, Mordecai, 1994. "On the Structure and Diversity of Rational Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 877-900, October.
    17. Drew Fudenberg & David K Levine, 2005. "Learning and Belief-Based Trade," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 42(126), pages 199-208.
    18. Muhamet Yildiz, 2004. "Waiting to Persuade," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 223-248.
    19. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    20. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    21. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(2), pages 323-336.
    Full references (including those not matched with items on IDEAS)

    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. Ian Ayres & Colin Rowat & Nasser Zakariya, 2004. "Optimal two stage committee voting rules," Game Theory and Information 0412006, University Library of Munich, Germany.
    2. , & , & ,, 2016. "Fragility of asymptotic agreement under Bayesian learning," Theoretical Economics, Econometric Society, vol. 11(1), January.
    3. Ian Ayres & Colin Rowat & Nasser Zakariya, 2004. "Optimal Two Stage Committee Voting Rules," Discussion Papers 04-23, Department of Economics, University of Birmingham, revised Mar 2007.
    4. Eric Van den Steen, 2010. "Culture Clash: The Costs and Benefits of Homogeneity," Management Science, INFORMS, vol. 56(10), pages 1718-1738, October.
    5. Rajiv Sethi & Muhamet Yildiz, 2012. "Public Disagreement," American Economic Journal: Microeconomics, American Economic Association, vol. 4(3), pages 57-95, August.
    6. Wei Xiong, 2013. "Bubbles, Crises, and Heterogeneous Beliefs," NBER Working Papers 18905, National Bureau of Economic Research, Inc.
    7. Felipe Zurita, 2004. "Essays on Speculation," Levine's Working Paper Archive 618897000000000849, David K. Levine.
    8. Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    9. Sergei Izmalkov & Muhamet Yildiz, 2010. "Investor Sentiments," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 21-38, February.
    10. Werner Güth & Loreto Erviti & Anthony Ziegelmeyer, 2011. "Asymmetric information without common priors: an indirect evolutionary analysis of quantity competition," Journal of Evolutionary Economics, Springer, vol. 21(5), pages 843-852, December.
    11. Sandroni, Alvaro, 1998. "Learning, Rare Events, and Recurrent Market Crashes in Frictionless Economies without Intrinsic Uncertainty," Journal of Economic Theory, Elsevier, vol. 82(1), pages 1-18, September.
    12. Markus K. Brunnermeier & Alp Simsek & Wei Xiong, 2014. "A Welfare Criterion For Models With Distorted Beliefs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1753-1797.
    13. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.
    14. Patrick Leoni, "undated". "When Are Market Crashes Driven by Speculation?," IEW - Working Papers 197, Institute for Empirical Research in Economics - University of Zurich.
    15. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    16. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    17. Klaus Nehring, 2003. "Common Priors For Like-Minded Agents," Economics Working Papers 0035, Institute for Advanced Study, School of Social Science.
    18. Elena Panova, 2009. "Confirmatory News," Cahiers de recherche 0912, CIRPEE.
    19. Lehrer, Ehud & Samet, Dov, 2014. "Belief consistency and trade consistency," Games and Economic Behavior, Elsevier, vol. 83(C), pages 165-177.
    20. Guarino, Pierfrancesco & Tsakas, Elias, 2021. "Common priors under endogenous uncertainty," Journal of Economic Theory, Elsevier, vol. 194(C).

    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:nbr:nberwo:12648. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    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.