Optimal Monetary Policy with a Convex Phillips Curve

This paper shows that convexity of the short-run Phillips curve is a source of positive inflation bias even when policymakers target the natural unemployment rate, that is when they operate with prudent discretion, and their loss function is symmetric. Optimal monetary policy also induces positive co-movement between average inflation, average unemployment and inflation variability---suggesting a new motive for inflation stabilization policy---and positively skewed unemployment distributions. The reduced form model is applied to the post-disinflation period (1986-2006) in developed countries and its properties are illustrated numerically for the United States.