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Synchronization in Sunspot Models

Patir, Assaf (2019): Synchronization in Sunspot Models.

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Abstract

This paper illustrates how agents’ beliefs about economic outcomes can dynamically synchronize and de-synchronize to produce business cycle-like fluctuations in a simple macroeconomic model. We consider a simple macroeconomic model with multiple equilibria, which represent different ways in which sunspots can forecast future output in a self-fulfilling manner. Agents are assumed to learn to use the sunspot variable through econometric learning. We show that if different agents have varied interpretations of the sunspot, this leads to a complex nonlinear dynamic of synchronization of beliefs concerning the equilibrium played. Depending on the extent of disagreement on the interpretation of the sunspot, the economy will be more or less volatile. The dispersion of 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 output is stable. The model naturally generates stochastic volatility (although there is no aggregate uncertainty), and explains features found in surveys of professional forecasters.

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