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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. We provide the solution for all combinations of technology and discount factor shocks and a thorough explanation of dynamics. We initially focus on the New Keynesian model without capital (Model 1) but then study the model with capital (Model 2). Capital adds another mechanism for intertemporal substitution, which strengthens the expectational effects of the ZLB. We use these models to analyze why technology shocks at the ZLB may have unconventional effects, the likelihood of ZLB events, and the tradeoffs faced by the central bank under a dual mandate. Three main findings emerge: (1) In Model 1, the output gap specification in the Taylor rule may reverse the effects of technology shocks at the ZLB; (2) When the central bank targets the steady-state output gap in Model 2, a positive technology shock at the ZLB leads to more pronounced unconventional dynamics than in Model 1; (3) In Model 1, the constrained linear solution provides a decent approximation of the nonlinear solution, but meaningful differences exist between the solutions in Model 2.

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