Global Dynamics at the Zero Lower Bound

This article presents global solutions to standard New Keynesian models with a zero lower bound (ZLB) constraint on the nominal interest rate. Rather than focus on specific sequences of shocks, we provide the solution for all combinations of technology and discount factor shocks and a thorough explanation of how dynamics change across the state space. Our solution method emphasizes accuracy to capture important expectational effects of going to and returning from the ZLB, which commonly used solution methods based on specific sequences of shocks cannot capture. We focus on the New Keynesian model without capital, but we also study the model with capital, with and without capital adjustment costs. Capital adds another mechanism for intertemporal substitution, which strengthens the expectational effects of the ZLB and impacts dynamics even before the ZLB is hit. We also evaluate how monetary policy affects the likelihood of hitting the ZLB. A policy rule based on a dual mandate is more likely to cause ZLB events when the central bank places greater emphasis on output stabilization.