A Quadratic-Cubic Approximation of Optimal Policy

Abstract

We derive a 2nd-order approximation of optimal policy in a broad class of nonlinear DSGE models. Using a cubic expansion of welfare and a quadratic expansion of the economyís equilibrium conditions, the Quadratic-Cubic (QC) approximation relaxes symmetry in the objective function and certainty equivalence in the solution, as required by a Linear-Quadratic (LQ) approximation. Comparing QC with LQ in a New Keynesian economy with costly price and wage adjustment, the micro-founded objective is asymmetric and shock variances have important quantitative effects on optimal monetary policy. US households would be willing to pay almost one third (one eighteenth) of 1% of their annual consumption to avoid a Taylor rule under QC (LQ).