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A note on learning chaotic sunspot equilibrium

  • Araújo, Aloísio Pessoa de
  • Maldonado, Wilfredo Fernando Leiva

In this paper we prove convergence to chaotic sunspot equilibrium through two learning rules used in the bounded rationality literature. The rst one shows the convergence of the actual dynamics generated by simple adaptive learning rules to a probability distribution that is close to the stationary measure of the sunspot equilibrium; since this stationary measure is absolutely continuous it results in a robust convergence to the stochastic equilibrium. The second one is based on the E-stability criterion for testing stability of rational expectations equilibrium, we show that the conditional probability distribution de ned by the sunspot equilibrium is expectational stable under a reasonable updating rule of this parameter. We also report some numerical simulations of the processes proposed.

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Paper provided by FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil) in its series Economics Working Papers (Ensaios Economicos da EPGE) with number 423.

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Date of creation: 01 May 2001
Date of revision:
Handle: RePEc:fgv:epgewp:423
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  1. Grandmont Jean-michel, 1985. "Stabilizing competitive business cycles," CEPREMAP Working Papers (Couverture Orange) 8518, CEPREMAP.
  2. Jean-Michel Grandmont, 1997. "Expectations Formation and Stability of Large Socioeconomic Systems," Working Papers 97-27, Centre de Recherche en Economie et Statistique.
  3. 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.
  4. Chatterji Shurojit, 1995. "Temporary Equilibrium Dynamics with Bayesian Learning," Journal of Economic Theory, Elsevier, vol. 67(2), pages 590-598, December.
  5. Woodford, Michael, 1986. "Learning to Believe in Sunspots," Working Papers 86-16, C.V. Starr Center for Applied Economics, New York University.
  6. Lawrence J. Christiano & Sharon G. Harrison, 1996. "Chaos, sunspots, and automatic stabilizers," Staff Report 214, Federal Reserve Bank of Minneapolis.
  7. Chiappori, P.A. & Guesnerie, R., 1990. "Sunspot Equilibria in Sequential Markets Models," DELTA Working Papers 90-05, DELTA (Ecole normale supérieure).
  8. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
  9. Majumdar, Mukul & Mitra, Tapan, 1994. "Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 649-76, August.
  10. Evans, George W & Honkapohja, Seppo, 1995. "Local Convergence of Recursive Learning to Steady States and Cycles in Stochastic Nonlinear Models," Econometrica, Econometric Society, vol. 63(1), pages 195-206, January.
  11. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
  12. 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.
  13. Wilfredo L. Maldonado & Aloisio P. Araujo, 2000. "Ergodic chaos, learning and sunspot equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(1), pages 163-184.
  14. Guesnerie, Roger, 1993. "Theoretical tests of the rational expectations hypothesis in economic dynamical models," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 847-864.
  15. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
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