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Heterogeneous sunspots solutions under learning and replicator dynamics

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  • Michele Berardi

Abstract

In a linear stochastic forward-looking univariate model with predetermined variables, we consider the possibility of heterogeneous equilibria with sunspots emerging endogenously through adaptive learning and replicator dynamics. In particular, we investigate equilibria where only a fraction of agents in the economy condition their forecasts on a sunspot, and equilibria where di¤erent groups of agents use di¤erent sunspots. We comclude that, although such heterogeneous equilibria exist and can be stable under adaptive learning, they do no survive under endogenous replicator dynamics. Moreover, we show that even homogeneous sunspot equilibria require some degree of coordinations among agents for them to emerge in an economy. We conclude that heterogeneous equilibria with sunspots are fragile under endogenous selection of predictors by agents, and that even the relevance of homogeneous sunspot equilibria is questioned once agents are allowed to doubt about the importance of sunspots in their forecasts.

Suggested Citation

  • Michele Berardi, 2011. "Heterogeneous sunspots solutions under learning and replicator dynamics," Centre for Growth and Business Cycle Research Discussion Paper Series 160, Economics, The Univeristy of Manchester.
  • Handle: RePEc:man:cgbcrp:160
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    File URL: http://hummedia.manchester.ac.uk/schools/soss/cgbcr/discussionpapers/dpcgbcr160.pdf
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    1. 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.
    2. Berardi, Michele, 2009. "Heterogeneous expectations, sunspot equilibria and their fragility," Economics Letters, Elsevier, vol. 105(3), pages 276-279, December.
    3. Berardi, Michele, 2011. "Fundamentalists vs. chartists: Learning and predictor choice dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 776-792, May.
    4. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
    5. Roger E. A. Farmer, 1999. "Macroeconomics of Self-fulfilling Prophecies, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262062038, January.
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