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

  • Evans, George W.
  • Honkapohja, Seppo

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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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 28 (2003)
Issue (Month): 1 (October)
Pages: 171-181

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Handle: RePEc:eee:dyncon:v:28:y:2003:i:1:p:171-181
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  1. 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.
  2. 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.
  3. 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 409-25, March.
  4. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
  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. 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.
  7. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
  8. Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 297-317, March.
  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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