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Stochastic Consistent Expectations Equilibria

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  • Cars Hommes

    (CeNDEF, University of Amsterdam)

Abstract

Recently the notion of consistent expectations equilibria (CEE) was introduced in a non-linear deterministic framework with expectational feedback. Along a CEE the sample mean and sample autocorrelations of realizations of the non-linear system coincide with the mean and autocorrelations corresponding to the linear forecasting rules agents are using. Along a CEE expectations are thus self-fulfilling in a linear statistical sense. In this paper the CEE concept is generalized to a non-linear stochastic framework. A stochastic CEE occurs when the non-linear stochastic system has an invariant measure with mean and (auto)co-variances that coincide with the mean and (auto)co-variances of the linear stochastic process agents believe in. Steady state, 2-cycle as well as chaotic stochastic CEE will be discussed. Convergence of OLS and sample autocorrelation learning to these different CEE will also be discussed. Applications to the cobweb and the OLG model will be given.

Suggested Citation

  • Cars Hommes, 2001. "Stochastic Consistent Expectations Equilibria," CeNDEF Workshop Papers, January 2001 PO1, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    • Handle: RePEc:ams:cdws01:po1
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    Cited by:

    1. Potzelberger, Klaus & Sogner, Leopold, 2003. "Stochastic equilibrium: learning by exponential smoothing," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1743-1770, August.
    2. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    3. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    4. Böhm, Volker & Wenzelburger, Jan, 2002. "Perfect Predictions In Economic Dynamical Systems With Random Perturbations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 687-712, November.

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