Phillips curve and long-run inflation under commitment

Purpose - The purpose of this paper is to study the optimal long-run rate of inflation in the presence of a hybrid Phillips curve, which nests a purely backward-looking Phillips curve and the purely forward-looking New Keynesian Phillips curve (NKPC) as special limiting cases. Design/methodology/approach - This paper derives the long-run rate of inflation in a basic New Keynesian (NK) model, characterized by sticky prices and rule-of-thumb behavior by price setters. The monetary authority possesses commitment and its objective function stems from an approximation to the utility of the representative household. Findings - Commitment solution for the monetary authority leads to steady-state outcomes in which inflation, albeit small, is positive. Rising from zero under the purely forward-looking NKPC, the optimal long-run rate of inflation reaches its maximum under the purely backward-looking Phillips curve. In this case, inflation bias arises, while, under the hybrid Phillips curve, positive long-run inflation is associated with an output gain. Research limitations/implications - This paper serves as a clarification against the misperception that log-linearized models take as given the steady-state inflation rate rather than being capable of determining it. Analysis is sensitive to the basic NK setting, with the assumed rule-of-thumb behavior by price setters and price staggering. Originality/value - The results are the first to quantify the optimal long-run rate of inflation in a fully microfounded model that nests different Phillips curves.