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

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.