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Sunspot Fluctuations Around a Steady State: The Case of Multidimensional One-Step Forward Looking Economic Models
Pierre-Andre Chiappori
Pierre-Yves Geoffard
Roger Guesnerie
Abstract
The paper investigates the existence of stationary sunspot equilibria (SSE) in the vicinity of a steady state in a general, one-step forward looking economic model of dimension $n$. It is shown that, whenever the steady state is indeterminate, for the associated deterministic dynamics--i.e., there exists a continuum of perfect foresight paths converging to the steady state--then there exists a continuum of SSE of finite order in any neighborhood of the steady state. The proof relies upon bifurcation theory; it provides a characterization of the random processes for which SSE may appear and a description of the location of the support of the SSE close to the bifurcation. The results apply in particular to linear models.
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