Global sunspots in OLG models

This paper discusses sunspots equilibria in a context that is general in the sense that: (i) the evolution of the system takes place in a general state space (i.e., a space which is not necessarily finite or even countable); and (ii) the orbits of the unperturbed, deterministic component of the system converge to subsets of the state space which can be more complicated than a stationary state or a periodic orbit, i.e., they can be aperiodic or chaotic. This problem is represented mathematically as a system of stochastic difference equations the invariant probability distributions of which correspond to stationary sunspots equilibria. The conditions for stochastic stability are recalled and the theoretical results are applied to a model of overlapping generations with individuals living three periods. A computational analysis of this model is provided, covering the basic different cases suggested by the theory.