Comparison of Global Solution Methods to a Zero Lower Bound Model

During the Great Recession, the U.S. Federal Reserve lowered policy rates to zero, introducing a kink in its policy rule and calling into question traditional solution methods. Recent papers have solved fully nonlinear models that treats the zero lower bound (ZLB) as an occasionally binding constraint, but there is little work analyzing the relative performance of these nonlinear solution methods. Two proposed solution methods are policy function iteration with linear interpolation and regime-indexed policy function iteration with Chebyshev polynomial approximation. We examine the impact of making the policy functions conditional on whether the ZLB binds. Our solution algorithm uses evenly-spaced grid points, linear interpolation, and Rouwenhorst integration. This paper shows that the regime-indexed policy functions are quite nonlinear in a New Keynesian model with capital and are costly to approximate in terms of solution time.