Phillips curve and long-run inflation under commitment

PurposeThe 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/approachThis 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.FindingsCommitment 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/implicationsThis 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/valueThe results are the first to quantify the optimal long-run rate of inflation in a fully microfounded model that nests different Phillips curves.