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Stable near-rational sunspot equilibria

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  • Evans, George W.
  • McGough, Bruce

Abstract

We introduce a new class of solutions to nonlinear forward-looking models called near-rational sunspot equilibria (NRSE). NRSE are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. Generic results for existence and stability under learning are established. NRSE in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model's minimal state variable solution is E-stable. NRSE are readily computable, and our results make it possible to use the standard linear tools to search for stable NRSE. We illustrate our results using a canonical nonlinear New Keynesian model.

Suggested Citation

  • Evans, George W. & McGough, Bruce, 2020. "Stable near-rational sunspot equilibria," Journal of Economic Theory, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jetheo:v:186:y:2020:i:c:s0022053119301334
    DOI: 10.1016/j.jet.2019.104987
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    2. Ascari, Guido & Mavroeidis, Sophocles & McClung, Nigel, 2023. "Coherence without rationality at the zero lower bound," Journal of Economic Theory, Elsevier, vol. 214(C).
    3. Evans, George W. & McGough, Bruce, 2020. "Equilibrium stability in a nonlinear cobweb model," Economics Letters, Elsevier, vol. 193(C).
    4. Evans, David & Evans, George W. & McGough, Bruce, 2022. "The RPEs of RBCs and other DSGEs," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).

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    More about this item

    Keywords

    E-stability; Sunspot equilibria; Nonlinear dynamics; Indeterminacy; MSV principle;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E71 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on the Macro Economy

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