Existence and Uniqueness of Solutions to Dynamic Models with Occasionally Binding Constraints

Abstract

We present the first necessary and sufficient conditions for there to be a unique perfect-foresight solution to an otherwise linear dynamic model with occasionally binding constraints, given a fixed terminal condition. We derive further results on the existence of a solution in the presence of such terminal conditions. These results give determinacy conditions for models with occasionally binding constraints, much as Blanchard and Kahn (1980) did for linear models. In an application, we show that widely used New Keynesian models with endogenous states possess multiple perfect foresight equilibrium paths when there is a zero lower bound on nominal interest rates, even when agents believe that the central bank will eventually attain its long-run, positive inflation target. This illustrates that a credible long-run inflation target does not render the Taylor principle sufficient for determinacy in the presence of the zero lower bound. However, we show that price level targeting does restore determinacy providing agents believe that inflation will eventually be positive.