Comparing Recursive Equilibrium in Economies with Dynamic Complementarities and Indeterminacy

We prove the existence of a minimal state space recursive equilibrium (RE) for a broad class of infinite horizon dynamic general equilibrium models with positive externalities, dynamic complementarities, public policy, equilibrium indeterminacy and sunspots. These are new "multistep" monotone map methods, and apply to economies for which results on the existence of dynamic equilibria are unknown and existing methods do not apply. Our methods are global, based on monotone operators defined on Euler equations, and do not appeal to the theory of smooth dynamical systems that are commonly applied in the literature. Rather, using partial ordering methods, we provide a qualitative theory of equilibrium comparative statics in the presence of multiple equilibrium. These comparison results are computable via successive approximations from upper and lower bounds of particular sets of functions. We provide applications of our results to an extensive literature on local indeterminacy of dynamic equilibrium