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Expectational stability of stationary sunspot equilibria in a forward-looking linear model

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  • Evans, George W.
  • Honkapohja, Seppo

Abstract

We consider the stability under adaptive learning of the complete set of solutions to the model x_i=beta(Ei*)(x_i+1) when |beat| >1. In addition to the fundamentals solution, the literature describes both finite-state Markov sunspot solutions and autoregressive solutions depending on an arbitrary martingale difference sequence. We clarify the relationships between these solutions and show that the stability properties of equilibria may depend crucially on the representations used by agents in the learning process. Autoregressive forms of solutions are not learnable, but finite-state Markov sunspot solutions are stable under learning if beta
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Suggested Citation

  • Evans, George W. & Honkapohja, Seppo, 2003. "Expectational stability of stationary sunspot equilibria in a forward-looking linear model," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 171-181, October.
  • Handle: RePEc:eee:dyncon:v:28:y:2003:i:1:p:171-181
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    References listed on IDEAS

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    1. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
    2. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
    3. 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 1097-1126, September.
    4. Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 297-317, March.
    5. George Evans & Seppo Honkapohja, 1986. "A Complete Characterization of ARMA Solutions to Linear Rational Expectations Models," Review of Economic Studies, Oxford University Press, vol. 53(2), pages 227-239.
    6. Desgranges, Gabriel & Negroni, Giorgio, 2003. "Expectations Coordination On A Sunspot Equilibrium: An Eductive Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 7-41, February.
    7. Gourieroux, C & Laffont, J J & Monfort, Alain, 1982. "Rational Expectations in Dynamic Linear Models: Analysis of the Solutions," Econometrica, Econometric Society, vol. 50(2), pages 409-425, March.
    8. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
    9. Evans George W. & Honkapohja Seppo, 1994. "On the Local Stability of Sunspot Equilibria under Adaptive Learning Rules," Journal of Economic Theory, Elsevier, vol. 64(1), pages 142-161, October.
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    Cited by:

    1. Evans, George W. & McGough, Bruce, 2005. "Monetary policy, indeterminacy and learning," Journal of Economic Dynamics and Control, Elsevier, pages 1809-1840.
    2. Michele Berardi, 2011. "Strategic interactions, incomplete information and learning," Centre for Growth and Business Cycle Research Discussion Paper Series 157, Economics, The Univeristy of Manchester.
    3. Evans, George W. & Honkapohja, Seppo, 2003. "Existence of adaptively stable sunspot equilibria near an indeterminate steady state," Journal of Economic Theory, Elsevier, vol. 111(1), pages 125-134, July.
    4. George W. Evans & Seppo Honkapohja, 2009. "Expectations, Learning and Monetary Policy: An Overview of Recent Research," Central Banking, Analysis, and Economic Policies Book Series,in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.), Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 2, pages 027-076 Central Bank of Chile.
    5. 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.
    6. Honkapohja, Seppo & Mitra, Kaushik, 2004. "Are non-fundamental equilibria learnable in models of monetary policy?," Journal of Monetary Economics, Elsevier, pages 1743-1770.
    7. Bennett T. McCallum, 2009. "Indeterminancy from inflation forecast targeting : problem or pseudo-problem?," Economic Quarterly, Federal Reserve Bank of Richmond, issue Win, pages 25-51.
    8. Seonghoon Cho & Antonio Moreno, 2008. "Expectational Stability in Multivariate Models," Faculty Working Papers 06/08, School of Economics and Business Administration, University of Navarra.
    9. Berardi, Michele, 2009. "Heterogeneous expectations, sunspot equilibria and their fragility," Economics Letters, Elsevier, vol. 105(3), pages 276-279, December.
    10. Ariane Szafarz, 2009. "How Did Financial-Crisis-Based Criticisms of Market Efficiency Get It So Wrong?," Working Papers CEB 09-048.RS, ULB -- Universite Libre de Bruxelles.
    11. Piero Ferri & Anna Maria Variato, 2007. "Macro Dynamics in a Model with Uncertainty," Working Papers (-2012) 0704, University of Bergamo, Department of Economics.
    12. Berardi, Michele, 2015. "On the fragility of sunspot equilibria under learning and evolutionary dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 251-265.
    13. Piero Ferri & Anna Maria Variato, 2007. "Endogenous Cycles, Debt and Monetary Policy," Working Papers (-2012) 0703, University of Bergamo, Department of Economics.

    More about this item

    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
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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