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Stable Finite-State Markov Sunspots

Author

Listed:
  • George W. Evans

    () (University of Oregon Economics Department)

  • Bruce McGough

    () (Oregon State University Economics Department)

Abstract

We consider a linear univariate rational expectations model, with a predetermined variable, and study existence and stability of solutions driven by an extraneous finite-state Markov process. We show that when the model is indeterminate there exists a new class of k-state dependent sunspot equilibria in addition to the k-state sunspot equilibria (k-SSEs) already known to exist in part of the indeterminacy region. The new type of equilibria, which we call ergodic k-SSEs, are driven by a finite-state sunspot but can have an infinite range of values even in the nonstochastic model. Stability under econometric learning is analyzed using representations that nest both types of equilibria. 2-SSEs and ergodic 2-SSEs are learnable for parameters in proper subsets of the regions of their existence. Our results extend to models with intrinsic random shocks.

Suggested Citation

  • George W. Evans & Bruce McGough, 2006. "Stable Finite-State Markov Sunspots," University of Oregon Economics Department Working Papers 2006-13, University of Oregon Economics Department.
  • Handle: RePEc:ore:uoecwp:2006-13
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    File URL: http://economics.uoregon.edu/papers/UO-2006-13_Evans_Sunspots.pdf
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    Keywords

    Markov sunspots; Learning; Indeterminacy; Expectational stability;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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