Econometrica: Sep 1992, Volume 60, Issue 5

Sunspot Fluctuations Around a Steady State: The Case of Multidimensional One-Step Forward Looking Economic Models

https://doi.org/0012-9682(199209)60:5<1097:SFAASS>2.0.CO;2-I
p. 1097-1126

Pierre-Andre Chiappori, Pierre-Yves Geoffard, Roger Guesnerie

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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