Instability of sunspot equilibria in real business cycles under adaptive learning

We examine the stability of equilibrium in sunspot-driven real business cycle (RBC) models under adaptive learning. We show that the general reduced form of this class of models can admit rational expectations equilibria that are both indeterminate and stable under adaptive learning. Indeterminacy of equilibrium allows for the possibility that non-fundamental “sunspot” variable realizations can serve as the main driving force of the model, and several researchers have put forward calibrated structural models where sunspot shocks play such a role. We show analytically how the structural restrictions that researchers have imposed on this type of model lead to reduced form systems where equilibrium is indeterminate but always unstable under adaptive learning. We thereby resolve a “stability puzzle” identified by Evans and McGough (2002).