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Expectational Stability of Stationary Sunspot Equilibria in a Forward-looking Linear Model

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  • George W. Evans

    (University of Oregon Economics Department)

  • Seppo Honkapohja

    (University of Helsinki)

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

Suggested Citation

  • George W. Evans & Seppo Honkapohja, 2002. "Expectational Stability of Stationary Sunspot Equilibria in a Forward-looking Linear Model," University of Oregon Economics Department Working Papers 2001-9, University of Oregon Economics Department, revised 14 Jan 2002.
    • Handle: RePEc:ore:uoecwp:2001-9
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    References listed on IDEAS

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    1. 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.
    2. Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 297-317, March.
    3. George Evans & Seppo Honkapohja, 1986. "A Complete Characterization of ARMA Solutions to Linear Rational Expectations Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 227-239.
    4. Desgranges, Gabriel & Negroni, Giorgio, 2003. "Expectations Coordination On A Sunspot Equilibrium: An Eductive Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 7(1), pages 7-41, February.
    5. J. B. Taylor & M. Woodford (ed.), 1999. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 1, number 1.
    6. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
    7. Guesnerie, Roger, 1986. "Stationary sunspot equilibria in an N commodity world," Journal of Economic Theory, Elsevier, vol. 40(1), pages 103-127, October.
    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. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 725-737.
    10. Barnett,William A. & Geweke,John & Shell,Karl (ed.), 1989. "Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity," Cambridge Books, Cambridge University Press, number 9780521355636, October.
    11. 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.
    12. 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, vol. 29(11), pages 1809-1840, November.
    2. Michele Berardi, 2011. "Strategic interactions, incomplete information and learning," Centre for Growth and Business Cycle Research Discussion Paper Series 157, Economics, The University 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. repec:zbw:bofrdp:2007_032 is not listed on IDEAS
    5. 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.
    6. Honkapohja, Seppo & Mitra, Kaushik, 2004. "Are non-fundamental equilibria learnable in models of monetary policy?," Journal of Monetary Economics, Elsevier, vol. 51(8), pages 1743-1770, November.
    7. Jolana Stejskalova, 2016. "Impact of the information on tax burden on the stock market," MENDELU Working Papers in Business and Economics 2016-62, Mendel University in Brno, Faculty of Business and Economics.
    8. Saint-Paul, Gilles, 2012. "Some Properties of Autocoherent Models," CEPR Discussion Papers 8959, C.E.P.R. Discussion Papers.
    9. Seonghoon Cho & Antonio Moreno, 2008. "Expectational Stability in Multivariate Models," Faculty Working Papers 06/08, School of Economics and Business Administration, University of Navarra.
    10. Piero Ferri & Anna Maria Variato, 2007. "Macro Dynamics in a Model with Uncertainty," Working Papers (-2012) 0704, University of Bergamo, Department of Economics.
    11. 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.
    12. 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.
    13. 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.
    14. McClung, Nigel, 2020. "E-stability vis-à-vis determinacy in regime-switching models," Journal of Economic Dynamics and Control, Elsevier, vol. 121(C).
    15. Bennett T. McCallum, 2009. "Indeterminancy from inflation forecast targeting : problem or pseudo-problem?," Economic Quarterly, Federal Reserve Bank of Richmond, vol. 95(Win), pages 25-51.
    16. 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.
    17. Berardi, Michele, 2009. "Heterogeneous expectations, sunspot equilibria and their fragility," Economics Letters, Elsevier, vol. 105(3), pages 276-279, December.
    18. 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.
    19. Piero Ferri & Anna Maria Variato, 2007. "Endogenous Cycles, Debt and Monetary Policy," Working Papers (-2012) 0703, University of Bergamo, Department of Economics.
    20. Jolana Stejskalová, 2017. "The Impact of Attention to News about Tax Changes on the Stock Market," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 65(6), pages 2113-2121.

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    More about this item

    Keywords

    Indeterminacy; representations of solutions; learnability; expectational stability; endogenous fluctuations;
    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
    • 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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