Comparing recursive equilibrium in economies with dynamic complementarities and indeterminacy

We develop a new multistep monotone map approach to characterize minimal state-space recursive equilibrium for a broad class of infinite horizon dynamic general equilibrium models with positive externalities, dynamic complementarities, public policy, equilibrium indeterminacy, and sunspots. This new approach is global, defined in the equilibrium version of the household’s Euler equation, applies to economies for which there are no known existence results, and existing methods are inapplicable. Our methods are able to distinguish different structural properties of recursive equilibria. In stark contrast to the extensive body of existing work on these models, our methods make no appeal to the theory of smooth dynamical systems that are commonly applied in the literature. Actually, sufficient smoothness to apply such methods cannot be established relative to the set of recursive equilibria. Our partial ordering methods also provide a qualitative theory of equilibrium comparative statics in the presence of multiple equilibrium. These robust equilibrium comparison results are shown to be computable via successive approximations from subsolutions and supersolutions in sets of candidate equilibrium function spaces. We provide applications to an extensive literature on local indeterminacy of dynamic equilibrium.