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Beauty contests under private information and diverse beliefs: How different?

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  • Kurz, Mordecai
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    Abstract

    The paper contrasts theories that explain diverse belief by asymmetric private information (PI) with theories which postulate agents use subjective heterogenous beliefs (HB). We focus on problems where agents forecast aggregates such as profit rate of the S&P500 and our model is similar to the one used in the literature on asset pricing (e.g. Brown, D., Jennings, R., 1989. On technical analysis. Review of Financial Studies 2, 527-551; Grundy, B., McNichols, M., 1989. Trade and revelation of information through prices and direct disclosure. Review of Financial Studies 2, 495-526; Allen, F., Morris, S., Shin, H.S., 2006. Beauty contests and iterated expectations in asset markets. Review of Financial Studies 19, 719-752). We first argue there is no a-priori conceptual basis to assuming PI about economic aggregates. Since PI is not observed, models with PI offer no testable hypotheses, making it possible to prove anything with PI. In contrast, agents with HB reveal their forecasts hence data on market belief is used to test hypotheses of HB. We show the common knowledge assumptions of the PI theory are implausible. The theories differ on four main analytical issues. (1) The pricing theory under PI implies prices have infinite memory and at each t depend upon unobservable variables. In contrast, under HB prices have finite memory and depend only upon observable variables. (2) The "Beauty Contest" implications of the two are different. Under PI today's price depends upon today's market belief about tomorrow's mean belief as a function of the supply shock and inference from prices. Under HB it depends upon today's market belief about tomorrow's market beliefs. Tomorrow's beliefs are, in part, beliefs about future beliefs and are often mistaken. Market forecast mistakes are key to Beauty Contests, and are a central cause of market uncertainty called "endogenous uncertainty". (3) Contrary to PI, theories with HB have wide empirical implications which are testable with available data. (4) PI theories assume unobserved data and hence do not restrict behavior, while rationality conditions impose restrictions on any HB theory. We explain the tight restrictions on the model's parameters imposed by the theory of Rational Beliefs.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 44 (2008)
    Issue (Month): 7-8 (July)
    Pages: 762-784

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    Handle: RePEc:eee:mateco:v:44:y:2008:i:7-8:p:762-784

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    Web page: http://www.elsevier.com/locate/jmateco

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    Cited by:
    1. Guerrazzi Marco, 2012. "Expectations, Employment and Prices: A Suggested Interpretation of the New «Farmerian» Economics," Politica economica, Società editrice il Mulino, issue 3, pages 369.
    2. A. A. Brown & L. C. G. Rogers, 2009. "Heterogeneous Beliefs with Finite-Lived Agents," Papers 0907.4953, arXiv.org.
    3. Mordecai Kurz & Maurizio Motolese, 2007. "Diverse Beliefs and Time Variability of Risk Premia," Discussion Papers 06-044, Stanford Institute for Economic Policy Research.
    4. A. A. Brown, 2009. "Heterogeneous Beliefs with Partial Observations," Papers 0907.4950, arXiv.org.
    5. Thomas Chesney & Swee-Hoon Chuah & Robert Hoffmann, 2007. "Virtual world experimentation: An exploratory study," Discussion Papers 2007-14, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    6. Mordecai Kurz, 2011. "Symposium: on the role of market belief in economic dynamics, an introduction," Economic Theory, Springer, vol. 47(2), pages 189-204, June.
    7. Branch, William A. & McGough, Bruce, 2009. "A New Keynesian model with heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1036-1051, May.
    8. Craig S. Hakkio & William R. Keeton, 2009. "Financial stress: what is it, how can it be measured, and why does it matter?," Economic Review, Federal Reserve Bank of Kansas City, issue Q II, pages 5-50.
    9. Marco Guerrazzi, 2011. "Search And Stochastic Dynamics In The Old Keynesian Economics: A Rationale For The Shimer Puzzle," Metroeconomica, Wiley Blackwell, vol. 62(4), pages 561-586, November.
    10. Kurz, Mordecai & Piccillo, Giulia & Wu, Howei, 2013. "Modeling diverse expectations in an aggregated New Keynesian Model," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1403-1433.
    11. Gelain, Paolo & Guerrazzi, Marco, 2014. "A demand-driven search model with self-fulfilling expectations: The new `Farmerian' framework under scrutiny," MPRA Paper 55773, University Library of Munich, Germany.

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