This article presents global solutions to standard New Keynesian models to show how economic dynamics change when the nominal interest rate is constrained at its zero lower bound (ZLB). We focus on the canonical New Keynesian model without capital, but we also study the model with capital, with and without investment adjustment costs. Our solution method emphasizes accuracy to capture the expectational effects of hitting the ZLB and returning to a positive interest rate. We find that the response to a technology shock has perverse consequences when the ZLB binds, even when a discount factor shock drives the interest rate to zero. Although we do not model the large scale asset purchases used by the Fed since 2009, our results suggest that the economy may have trouble recovering if the interest rate remains at zero. Given the perverse dynamics at the ZLB, we evaluate how monetary policy affects the likelihood of encountering the ZLB. We find that the probability of hitting the ZLB depends importantly on the monetary policy rule. A policy rule based on a dual mandate, such as the one proposed by Taylor (1993), is more likely to cause ZLB events when the central bank places greater emphasis on the output gap.
