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Stable Finite-State Markov Sunspots

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Author Info
George W. Evans () (University of Oregon Economics Department)
Bruce McGough () (Oregon State University Economics Department)

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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.

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Publisher Info
Paper provided by University of Oregon Economics Department in its series University of Oregon Economics Department Working Papers with number 2006-13.

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Length: 45
Date of creation: 09 Oct 2006
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Handle: RePEc:ore:uoecwp:2006-13

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Related research
Keywords: Markov sunspots Learning Indeterminacy Expectational stability

Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - 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, and Information
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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References listed on IDEAS
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  1. Evans, George W. & McGough, Bruce, 2005. "Stable sunspot solutions in models with predetermined variables," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 601-625, April. [Downloadable!] (restricted)
    Other versions:
  2. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-81, September. [Downloadable!] (restricted)
  3. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March. [Downloadable!] (restricted)
    Other versions:
  4. Chiappori, Pierre-Andre & Geoffard, Pierre-Yves & Guesnerie, Roger, 1992. "Sunspot Fluctuations around a Steady State: The Case of Multidimensional, One-Step Forward Looking Economic Models," Econometrica, Econometric Society, vol. 60(5), pages 1097-126, September. [Downloadable!] (restricted)
    Other versions:
  5. Azariadis, Costas & Guesnerie, Roger, 1986. "Sunspots and Cycles," Review of Economic Studies, Blackwell Publishing, vol. 53(5), pages 725-37, October. [Downloadable!] (restricted)
  6. Evans, George W. & Honkapohja, Seppo & Honkapohja, Seppo, 1994. "Learning, convergence, and stability with multiple rational expectations equilibria," European Economic Review, Elsevier, vol. 38(5), pages 1071-1098, May. [Downloadable!] (restricted)
  7. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April. [Downloadable!] (restricted)
  8. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December. [Downloadable!] (restricted)
  9. Howitt, Peter & McAfee, R Preston, 1992. "Animal Spirits," American Economic Review, American Economic Association, vol. 82(3), pages 493-507, June. [Downloadable!] (restricted)
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  10. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August. [Downloadable!] (restricted)
  11. Guesnerie, Roger, 1986. "Stationary sunspot equilibria in an N commodity world," Journal of Economic Theory, Elsevier, vol. 40(1), pages 103-127, October. [Downloadable!] (restricted)
  12. G. Desgranges & G. Negroni, 2001. "Expectations Coordination on a Sunspot Equilibrium: an Eductive Approach," THEMA Working Papers 2001-13, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise. [Downloadable!]
  13. Davila, J. & Guesnerie, R., 1999. "Sunspot Equilibria in Systems with Memory: an Introductory Presentation," DELTA Working Papers 1999-05, DELTA (Ecole normale supérieure).
  14. Evans, Geroge W & Honkapohja, Seppo & Romer, Paul, 1998. "Growth Cycles," American Economic Review, American Economic Association, vol. 88(3), pages 495-515, June. [Downloadable!] (restricted)
    Other versions:
    • Paul Romer & George Evans & Seppo Hokapohja, . "Growth Cycles," Home Pages _001, Stanford University. [Downloadable!]
    • George Evans & Seppo Honkapohja & Paul Romer, 1996. "Growth Cycles," NBER Working Papers 5659, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  15. Julio DÂvila, 1997. "Sunspot fluctuations in dynamics with predetermined variables," Economic Theory, Springer, vol. 10(3), pages 483-495. [Downloadable!] (restricted)
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