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On the fragility of sunspot equilibria under learning and evolutionary dynamics

  • Michele Berardi

In this paper we investigate the possibility of sunspot equilibria to emerge from a process of learning and adaptation on agents' beliefs. To such end, we consider both …finite state Markov sunspots and sunspots in autoregressive form and derive conditions for the existence of an heterogeneous equilibrium where only a fraction of agents condition their forecasts on the sunspot: such conditions impose restrictions across primitive parameters, which are the equivalent, in a heterogeneous setting, of the resonant conditions found in the literature for homogeneous equilibria. We then show that evolutionary dynamics on predictor selection imply that such restrictions need to evolve endogenously with population shares, and argue that such requirement questions the possibility of sunspot equilibria to emerge through a process of evolution and adaptation on agents' beliefs. It follows that, in order for a sunspot equilibrium to obtain, all agents must simultaneously coordinate on using the same sunspot variable at the same time.

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File URL: http://hummedia.manchester.ac.uk/schools/soss/cgbcr/discussionpapers/dpcgbcr186.pdf
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Paper provided by Economics, The Univeristy of Manchester in its series Centre for Growth and Business Cycle Research Discussion Paper Series with number 186.

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Length: 24 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:man:cgbcrp:186
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Web page: http://www.socialsciences.manchester.ac.uk/subjects/economics/our-research/centre-for-growth-and-business-cycle-research/

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  1. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  2. Hommes, C.H., 2007. "Bounded Rationality and Learning in Complex Markets," CeNDEF Working Papers 07-01, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  3. McGough, Bruce & Meng, Qinglai & Xue, Jianpo, 2013. "Expectational stability of sunspot equilibria in non-convex economies," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1126-1141.
  4. Berardi, Michele, 2009. "Heterogeneous expectations, sunspot equilibria and their fragility," Economics Letters, Elsevier, vol. 105(3), pages 276-279, December.
  5. George Evans & William Branch, 2003. "Intrinsic Heterogeneity in Expectation Formation," Computing in Economics and Finance 2003 312, Society for Computational Economics.
  6. George W. Evans & Seppo Honkapohja, 2001. "Existence of Adaptively Stable Sunspot Equilibria Near an Indeterminate Steady State," CESifo Working Paper Series 478, CESifo Group Munich.
  7. Kenneth Kasa, 2007. "Learning and Model Validation," 2007 Meeting Papers 548, Society for Economic Dynamics.
  8. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  9. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
  10. Evans, George W. & Honkapohja, Seppo & Honkapohja, Seppo, 1994. "Learning, convergence, and stability with multiple rational expectations equilibria," European Economic Review, Elsevier, vol. 38(5), pages 1071-1098, May.
  11. Michele Berardi, 2008. "Fundamentalists vs. chartists: learning and predictor choice dynamics," Centre for Growth and Business Cycle Research Discussion Paper Series 104, Economics, The Univeristy of Manchester.
  12. Branch, William A. & McGough, Bruce, 2008. "Replicator dynamics in a Cobweb model with rationally heterogeneous expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 65(2), pages 224-244, February.
  13. Eran A. Guse, 2008. "Heterogeneous Expectations, Adaptive Learning, and Evolutionary Dynamics," Working Papers 09-01, Department of Economics, West Virginia University.
  14. Bennett T. McCallum, 1981. "On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective," NBER Working Papers 0684, National Bureau of Economic Research, Inc.
  15. George W. Evans & Bruce McGough, 2007. "Representations and Sunspot Stability," University of Oregon Economics Department Working Papers 2007-1, University of Oregon Economics Department, revised 28 Aug 2008.
  16. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  17. George W. Evans & Bruce McGough, 2003. "Monetary Policy, Indeterminacy and Learning," University of Oregon Economics Department Working Papers 2003-34, University of Oregon Economics Department, revised 01 Apr 2004.
  18. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  19. Sethi, Rajiv & Franke, Reiner, 1995. "Behavioural Heterogeneity under Evolutionary Pressure: Macroeconomic Implications of Costly Optimisation," Economic Journal, Royal Economic Society, vol. 105(430), pages 583-600, May.
  20. 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.
  21. 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.
  22. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
  23. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  24. Guesnerie, Roger, 1986. "Stationary sunspot equilibria in an N commodity world," Journal of Economic Theory, Elsevier, vol. 40(1), pages 103-127, October.
  25. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
  26. George W. Evans & Bruce McGough, 2002. "Stable Sunspot Solutions in Models with Predetermined Variables," University of Oregon Economics Department Working Papers 2002-16, University of Oregon Economics Department, revised 29 May 2003.
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