Monetary policy with a nonlinear Phillips curve and asymmetric loss

Recent theoretical and empirical work has cast doubt on the hypotheses of a linear Phillips curve and a symmetric quadratic loss function underlying traditional thinking on monetary policy. This paper studies the one-period optimal monetary policy problem under an asymmetric loss function corresponding to the "opportunistic approach" to disinflation and a convex Phillips curve. The policy-inaction range and its properties are derived analytically. Numerical simulations are then used to assess the implications of asymmetric loss for the distributional properties of the equilibrium levels of inflation and unemployment. For parameter values relevant to the U.S., it is found that the asymmetric loss function yields an average inflation rate in excess of the target, and that bias is larger than the standard symmetric loss function. For moderate policy-maker preferences, the asymmetric loss function also yields a smaller gap between average unemployment and the natural rate, and higher (lower) variance of inflation (unemployment) compared to the symmetric benchmark. Calibrating the model to match the observed average unemployment rate requires a high degree of inflation aversion and small asymmetry.