'On the fragility of sunspot equilibria under learning and evolutionary dynamics'

In this paper we investigate the possibility of sunspot equilibria to emerge from a process of learning and adaptation on agents' beliefs. To such end, we consider both …finite state Markov sunspots and sunspots in autoregressive form and derive conditions for the existence of an heterogeneous equilibrium where only a fraction of agents condition their forecasts on the sunspot: such conditions impose restrictions across primitive parameters, which are the equivalent, in a heterogeneous setting, of the resonant conditions found in the literature for homogeneous equilibria. We then show that evolutionary dynamics on predictor selection imply that such restrictions need to evolve endogenously with population shares, and argue that such requirement questions the possibility of sunspot equilibria to emerge through a process of evolution and adaptation on agents' beliefs. It follows that, in order for a sunspot equilibrium to obtain, all agents must simultaneously coordinate on using the same sunspot variable at the same time.