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The existence of rational expectations equilibrium: a retrospective

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  • Beth Allen
  • James S. Jordan
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    Abstract

    This paper provides a selective review of theoretical research on the consistency of rational expectations equilibrium and its properties in microeconomic models. The general equilibrium framework is emphasized throughout the paper. After defining rational expectations equilibrium for a pure exchange economy, the paper presents a simple counterexample to illustrate that rational expectations equilibria need not exist. Results are summarized for the generic existence of fully revealing rational expectations equilibria in smooth economies satisfying additional dimensionality assumptions. Then the rational expectations equilibrium existence problem is related to earlier analysis of informationally decentralized allocation mechanisms. Next the efficiency properties of rational expectations equilibrium allocations are examined. Finally, the possibilities for partially revealing rational expectations equilibria are discussed.

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    Bibliographic Info

    Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 252.

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    Date of creation: 1998
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    Handle: RePEc:fip:fedmsr:252

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    Keywords: Equilibrium (Economics) - Mathematical models ; Rational expectations (Economic theory);

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    References

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    1. Jordan, J. S., 1982. "A dynamic model of expectations equilibrium," Journal of Economic Theory, Elsevier, vol. 28(2), pages 235-254, December.
    2. Avraham Beja., 1976. "The Limited Information Efficiency of Market Processes," Research Program in Finance Working Papers 43, University of California at Berkeley.
    3. Anderson, Robert M. & Sonnenschein, Hugo, 1982. "On the existence of rational expectations equilibrium," Journal of Economic Theory, Elsevier, vol. 26(2), pages 261-278, April.
    4. Pradeep Dubey & John Geanakoplos & Martin Shubik, 1982. "Revelation of Information in Strategic Market Games: A Critique of Rational Expectations," Cowles Foundation Discussion Papers 634R, Cowles Foundation for Research in Economics, Yale University, revised Nov 1985.
    5. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    6. DEBREU, Gérard, . "Smooth preferences," CORE Discussion Papers RP -132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Debreu,Gerard Introduction by-Name:Hildenbrand,Werner, 1986. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521335614.
    8. Kenneth Mount & Stanley Reiter, 1973. "The Informational Size of Message Spaces," Discussion Papers 3, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Green, Jerry, 1977. "The Non-existence of Informational Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 451-63, October.
    10. Emile Grunberg & Franco Modigliani, 1954. "The Predictability of Social Events," Journal of Political Economy, University of Chicago Press, vol. 62, pages 465.
    11. Jordan, J. S., 1977. "Expectations equilibrium and informational efficiency for stochastic environments," Journal of Economic Theory, Elsevier, vol. 16(2), pages 354-372, December.
    12. Grossman, Sanford J, 1981. "An Introduction to the Theory of Rational Expectations under Asymmetric Information," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 541-59, October.
    13. Allen, Beth, 1985. "The existence of fully rational expectations approximate equilibria with noisy price observations," Journal of Economic Theory, Elsevier, vol. 37(2), pages 213-253, December.
    14. Jordan, J. S., 1982. "Admissible market data structures: A complete characterization," Journal of Economic Theory, Elsevier, vol. 28(1), pages 19-31, October.
    15. Laffont, Jean-Jacques M, 1985. "On the Welfare Analysis of Rational Expectations Equilibria with Asymmetric Information," Econometrica, Econometric Society, vol. 53(1), pages 1-29, January.
    16. Grossman, Sanford J & Stiglitz, Joseph E, 1976. "Information and Competitive Price Systems," American Economic Review, American Economic Association, vol. 66(2), pages 246-53, May.
    17. Green, Jerry R, 1981. "Value of Information with Sequential Futures Markets," Econometrica, Econometric Society, vol. 49(2), pages 335-58, March.
    18. 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.
    19. Futia, Carl A, 1981. "Rational Expectations in Stationary Linear Models," Econometrica, Econometric Society, vol. 49(1), pages 171-92, January.
    20. Allen, Beth, 1985. "The existence of rational expectations equilibria in a large economy with noisy price observations," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 67-103, February.
    21. Allen, Beth, 1982. "Strict rational expectations equilibria with diffuseness," Journal of Economic Theory, Elsevier, vol. 27(1), pages 20-46, June.
    22. Jordan, J. S., 1982. "The generic existence of rational expectations equilibrium in the higher dimensional case," Journal of Economic Theory, Elsevier, vol. 26(2), pages 224-243, April.
    23. Ausubel, Lawrence M., 1990. "Partially-revealing rational expectations equilibrium in a competitive economy," Journal of Economic Theory, Elsevier, vol. 50(1), pages 93-126, February.
    24. Allen, Beth E, 1981. "Generic Existence of Completely Revealing Equilibria for Economies with Uncertainty when Prices Convey Information," Econometrica, Econometric Society, vol. 49(5), pages 1173-99, September.
    25. Sanford Grossman, 1978. "Further results on the informational efficiency of competitive stock markets," Special Studies Papers 114, Board of Governors of the Federal Reserve System (U.S.).
    26. Jordan, J S, 1983. "On the Efficient Markets Hypothesis," Econometrica, Econometric Society, vol. 51(5), pages 1325-43, September.
    27. Hellwig, Martin F., 1980. "On the aggregation of information in competitive markets," Journal of Economic Theory, Elsevier, vol. 22(3), pages 477-498, June.
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    Cited by:
    1. Berliant, Marcus & Yu, Chia-Ming, 2009. "Rational expectations in urban economics," MPRA Paper 12709, University Library of Munich, Germany.
    2. Casella, Alessandra & Turban, Sébastien, 2012. "Democracy Undone. Systematic Minority Advantage in Competitive Vote Markets," CEPR Discussion Papers 9242, C.E.P.R. Discussion Papers.
    3. Philip Bond & Hulya Eraslan, 2007. "Information-based trade," Levine's Bibliography 122247000000001689, UCLA Department of Economics.
    4. Edison G. Yu, 2013. "Dynamic market participation and endogenous information aggregation," Working Papers 13-42, Federal Reserve Bank of Philadelphia.
    5. James Dow & Gary Gorton, 2006. "Noise Traders," NBER Working Papers 12256, National Bureau of Economic Research, Inc.

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