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Synchronization in Sunspot Models

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  • Patir, Assaf

Abstract

This note illustrates how agents' beliefs about economic outcomes can dynamically synchronize and de-synchronize to produce business-cycle-like fluctuations in a simple macroeconomic model. I consider a simple macroeconomic model with multiple equilibria, which are different ways that sunspots can forecast future output in a self-fulfilling manner. Agents are assumed to learn to use the sunspot variable through econometric learning. I show that if different agents have different interpretations of the sunspot, this leads to a complex nonlinear dynamic of synchronization of beliefs about the equilibrium being played. Depending on the extent of disagreement on the interpretation of the sunspot, the economy will be more or less volatile. The dispersion of the agents' beliefs is inversely related to volatility, since low dispersion implies that output is very sensitive to extrinsic noise (the sunspot). When disagreement crosses a critical threshold, the sunspot is practically ignored and the output is stable. The equation describing the evolution of the economy can be interpreted as a nonlinear-stochastic version of the Kuramoto model, a prototypical model of synchronization phenomena, and simulations confirm that the qualitative features of the model are in agreement with results from the Kuramoto literature.

Suggested Citation

  • Patir, Assaf, 2019. "Synchronization in Sunspot Models," MPRA Paper 95720, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:95720
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    References listed on IDEAS

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    1. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    2. 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.
    3. Jess Benhabib & Pengfei Wang & Yi Wen, 2015. "Sentiments and Aggregate Demand Fluctuations," Econometrica, Econometric Society, vol. 83, pages 549-585, March.
    4. 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.
    5. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
    6. Honkapohja, Seppo & Mitra, Kaushik, 2004. "Are non-fundamental equilibria learnable in models of monetary policy?," Journal of Monetary Economics, Elsevier, vol. 51(8), pages 1743-1770, November.
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    More about this item

    Keywords

    sunspots; learning; synchronization;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • E0 - Macroeconomics and Monetary Economics - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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