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Optimal policy design in nonlinear DSGE models: An n-order accurate approximation

Isaac Gross and James Hansen

European Economic Review, 2021, vol. 140, issue C

Abstract: We derive an n-order accurate approximation of optimal policy for a wide class of nonlinear DSGE models analytically. Using Taylor polynomials to approximate welfare and the equilibrium, the n,n+1 approximation relaxes symmetry in the objective and certainty equivalence in the solution, as implied by a Linear–Quadratic (LQ) approximation with n=1. When n>1, we illustrate how curvature in preferences and the constraints can affect optimal policy, deriving a solution that is n-order accurate as opposed to first-order accurate only. Comparing solutions when n=2 (a Quadratic–Cubic approximation) and n=1 (LQ), in a New Keynesian economy with nominal frictions, we find significant differences in the optimal response to shocks; the joint distributions of wage inflation, the output gap and nominal interest rates; welfare and accuracy.

Keywords: Linear–Quadratic approximation; (n, n+1) approximation; Optimal monetary policy; Optimal Ramsey policy; Nonlinear dynamics (search for similar items in EconPapers)
JEL-codes: C54 C61 E61 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.euroecorev.2021.103918

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