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Existence of adaptively stable sunspot equilibria near an indeterminate steady state

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  • Evans, George W.
  • Honkapohja, Seppo

Abstract

We examine the nonlinear model x_t = E_t F(x_(t+1)). Markov SSEs exist near an indeterminate steady state, hat(x)=F(hat(x)), provided |F'(hat(x)| > 1. Despite the importance of indeterminancy in macroeconomics, earlier results have not provided conditions for the existance of adaptively stable SSEs near an indeterminate steady state. We show that there exists Markov SSEs near hat(x) that are E-stable, and therefore locally stable under adaptive learning, if F'(hat(x))
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  • 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.
    • Handle: RePEc:eee:jetheo:v:111:y:2003:i:1:p:125-134
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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.
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    6. Evans George W & Honkapohja Seppo M.S. & Marimon Ramon, 2007. "Stable Sunspot Equilibria in a Cash-in-Advance Economy," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-38, January.
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    8. 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.
    9. 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.
    10. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    11. 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.
    12. J. B. Taylor & M. Woodford (ed.), 1999. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 1, number 1.
    13. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448, Elsevier.
    14. Howitt, Peter & McAfee, R Preston, 1992. "Animal Spirits," American Economic Review, American Economic Association, vol. 82(3), pages 493-507, June.
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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. Jess Benhabib & Stephanie Schmitt-Grohé & Martín Uribe, 2002. "Chaotic Interest-Rate Rules," American Economic Review, American Economic Association, vol. 92(2), pages 72-78, May.
    3. Stefano Eusepi, 2005. "Comparing forecast-based and backward-looking Taylor rules: a "global" analysis," Staff Reports 198, Federal Reserve Bank of New York.
    4. Evans George W & Honkapohja Seppo M.S. & Marimon Ramon, 2007. "Stable Sunspot Equilibria in a Cash-in-Advance Economy," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-38, January.
    5. Eusepi, Stefano, 2007. "Learnability and monetary policy: A global perspective," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1115-1131, May.
    6. GEORGE W. EVANS & BRUCE McGOUGH, 2007. "Optimal Constrained Interest-Rate Rules," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(6), pages 1335-1356, September.
    7. 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.
    8. 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.
    9. George W. Evans & Seppo Honkapohja, 2007. "The E‐Correspondence Principle," Economica, London School of Economics and Political Science, vol. 74(293), pages 33-50, February.
    10. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 2004. "Chaotic Interest Rate Rules: Expanded Version," NBER Working Papers 10272, National Bureau of Economic Research, Inc.
    11. Evans, George W. & McGough, Bruce, 2005. "Monetary policy and stable indeterminacy with inertia," Economics Letters, Elsevier, vol. 87(1), pages 1-7, April.
    12. Michele Berardi, 2011. "Heterogeneous sunspots solutions under learning and replicator dynamics," Centre for Growth and Business Cycle Research Discussion Paper Series 160, Economics, The University of Manchester.
    13. 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.
    14. Evans, George W. & McGough, Bruce, 2020. "Stable near-rational sunspot equilibria," Journal of Economic Theory, Elsevier, vol. 186(C).
    15. McClung, Nigel, 2020. "E-stability vis-à-vis determinacy in regime-switching models," Journal of Economic Dynamics and Control, Elsevier, vol. 121(C).

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    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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