The nonlinear Phillips curve and inflation forecast targeting: Symmetric versus asymmetric monetary policy rules

We study a simple, small dynamic economy that a policymaker is attempting to control via use of a monetary policy rule. The model features a convex Phillips curve, in that positive deviations of aggregate demand from potential are more inflationary than negative deviations are disinflationary. Using dynamic optimization techniques, we find that the form of the optimal monetary policy reaction function is asymmetric. We show that in the optimal rule the interest rate is a nonlinear function of the deviation of inflation from its target and of output from potential. With asymmetry, optimal monetary policy becomes more active as uncertainty about the impact of policy increases. We thus provide an important and novel theoretical reason why increased uncertainty can lead to more aggressive rather than toward more cautious optimal policies.