Euler Equation Branching

Some macroeconomic models exhibit a type of global indeterminacy known as Euler equation branching (e.g., the one-sector growth model with a production externality). The dynamics in such models are governed by a dierential inclusion _x 2 F (x), where F is a set-valued function. In this paper, we show that in models with Euler equa-tion branching there are multiple equilibria and that the dynamics are chaotic. In particular, we provide sucient conditions for a dynamical system on the plane with Euler equation branching to be chaotic and show analytically that in a neighborhood of a steady state, these sucient conditions will typically be satised. We also extend the results of Christiano and Harrison (1999) for the one-sector growth model with a production externality. In a more general setting, we provide necessary and sucient conditions for Euler equation branching in this model. We show that chaotic and cyclic equilibria are possible and that this behavior is not dependent on the steady state being \locally " a saddle, sink or source