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Dropping Rational Expectations

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  • Lionel de Boisde¤re

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

We consider a pure-exchange sequential economy, where uncertainty prevails and agents, possibly asymmetrically informed, exchange commodities, on spot markets, and securities of all kinds, on typically incomplete financial markets. Consumers have private characteristics, anticipations and beliefs, and no model to forecast prices. We show that they face an incompressible uncertainty, represented by a so-calles 'minimum uncertainty set', which adds to the exogenous uncertainty, on the state of nature, an uncertainty over the price to prevail, on every spot market. Equilibrium is reached when agents expect the 'true' price as a possible outcome on every spot market, and elect optimal strategies, which clear on all markets. We show this sequential equilibrium exists in standard conditions, when agents' anticipations embed the minimum uncertainty set. This outcome is stronger than Radner's (1979), Duffie-Shaffer's (1985) or De Boisdeffre's (2021), which prove the generic existence of equilibrium when agents make perfect forecasts. From an asymptotic argument, our main theorem is derived from De Boisdeffre's (2007), which characterizes the exitence of equilibria on purely financial markets by a no-arbitrage condition.

Suggested Citation

  • Lionel de Boisde¤re, 2021. "Dropping Rational Expectations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03196897, HAL.
  • Handle: RePEc:hal:cesptp:halshs-03196897
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03196897
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    References listed on IDEAS

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    1. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    2. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    3. Ho-Mou Wu & Mordecai Kurz, 1996. "Endogenous uncertainty in a general equilibrium model with price contingent contracts (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 461-488.
    4. 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.
    5. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    6. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    7. Kurz, Mordecai, 1994. "On Rational Belief Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 859-876, October.
    8. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    9. Cornet, Bernard & De Boisdeffre, Lionel, 2002. "Arbitrage and price revelation with asymmetric information and incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 393-410, December.
    10. Lionel de Boisde¤re, 2021. "Equilibrium in incomplete markets with differential information: A basic model of generic existence," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03196857, HAL.
    11. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    12. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
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    Cited by:

    1. Lionel de Boisdeffre, 2021. "Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information and Restricted Participation," Post-Print halshs-03196923, HAL.
    2. Lionel de Boisdeffre, 2021. "Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information and Restricted Participation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03196923, HAL.

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