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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://www.socialsciences.manchester.ac.uk/medialibrary/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. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
  2. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  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. Cars H. Hommes, 2009. "Bounded Rationality and Learning in Complex Markets," Chapters, in: Handbook of Research on Complexity, chapter 5 Edward Elgar Publishing.
  5. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
  6. 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.
  7. 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.
  8. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
  9. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  10. Branch, William A. & Evans, George W., 2006. "Intrinsic heterogeneity in expectation formation," Journal of Economic Theory, Elsevier, vol. 127(1), pages 264-295, March.
  11. Guse, Eran A., 2010. "Heterogeneous expectations, adaptive learning, and evolutionary dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 74(1-2), pages 42-57, May.
  12. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  13. In-Koo Cho & Kenneth Kasa, 2006. "Learning and Model Validation," 2006 Meeting Papers 178, Society for Economic Dynamics.
  14. Michele Berardi, 2011. "Fundamentalists vs. chartists: Learning and predictor choice dynamics," Post-Print hal-00796301, HAL.
  15. 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.
  16. 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.
  17. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
  18. 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.
  19. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  20. 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.
  21. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  22. 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.
  23. 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.
  24. Berardi, Michele, 2009. "Heterogeneous expectations, sunspot equilibria and their fragility," Economics Letters, Elsevier, vol. 105(3), pages 276-279, December.
  25. Guesnerie, Roger, 1986. "Stationary sunspot equilibria in an N commodity world," Journal of Economic Theory, Elsevier, vol. 40(1), pages 103-127, October.
  26. 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.
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