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Stationary Bubble Equilibria in Rational Expectation Models

Author

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  • Christian Gouriéroux

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Joann Jasiak
  • Alain Monfort

    (Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique)

Abstract

A linear rational expectation model with current expectations admits a unique linear stationary dynamic equilibrium only under specific restrictions on the parameter values. This paper shows that, in general, there is a multiplicity of stationary dynamic equilibria due to the existence of nonlinear stationary equilibria. These nonlinear stationary equilibria are consistent with the self-fulfilling prophecies that characterize the rational expectation equilibria, and can display speculative bubbles, volatility induced mean reversion and/or stochastic autoregressive patterns. They are also compatible with the transversality conditions when the model involves intertemporal optimization. The stationary nonlinear dynamic equilibria are economically relevant. Their analysis requires revised methods of identification for the stationary equilibrium, impulse response analysis, and estimation techniques, which are presented in this paper. Standard econometric and economic methods, which ignore the nonlinear stationary solutions provide misleading outcomes, which may affect the validity of an economic policy or portfolio strategy.

Suggested Citation

  • Christian Gouriéroux & Joann Jasiak & Alain Monfort, 2020. "Stationary Bubble Equilibria in Rational Expectation Models," Post-Print hal-03330912, HAL.
    • Handle: RePEc:hal:journl:hal-03330912
    DOI: 10.1016/j.jeconom.2020.04.035
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    Cited by:

    1. Telg, Sean, 2024. "Time aggregation of mixed causal–noncausal models," Economics Letters, Elsevier, vol. 244(C).
    2. Hecq, Alain & Voisin, Elisa, 2021. "Forecasting bubbles with mixed causal-noncausal autoregressive models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 29-45.
    3. Chetan Dave & Marco M. Sorge, 2025. "Fat‐tailed DSGE models: A survey and new results," Journal of Economic Surveys, Wiley Blackwell, vol. 39(1), pages 146-171, February.
    4. Fries, Sébastien, 2018. "Conditional moments of noncausal alpha-stable processes and the prediction of bubble crash odds," MPRA Paper 97353, University Library of Munich, Germany, revised Nov 2019.
    5. Fries, Sébastien & Zakoian, Jean-Michel, 2019. "Mixed Causal-Noncausal Ar Processes And The Modelling Of Explosive Bubbles," Econometric Theory, Cambridge University Press, vol. 35(6), pages 1234-1270, December.
    6. Marina Friedrich & Sébastien Fries & Michael Pahle & Ottmar Edenhofer, 2020. "Rules vs. Discretion in Cap-and-Trade Programs: Evidence from the EU Emission Trading System," CESifo Working Paper Series 8637, CESifo.
    7. Alain Hecq & Sean Telg & Lenard Lieb, 2017. "Do Seasonal Adjustments Induce Noncausal Dynamics in Inflation Rates?," Econometrics, MDPI, vol. 5(4), pages 1-22, October.
    8. Christian Gouriéroux & Yang Lu, 2023. "Noncausal affine processes with applications to derivative pricing," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 766-796, July.

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