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 pru-dent discretion, and their loss function is symmetric. Optimal mon-etary policy also induces positive co-movement between average in-flation, 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.