Phillips Curves, Phillips Lines and the Unemplyment Costs of Overheating

The objective of the paper is to reconsider the issue of nonlinearity of the Phillips curve and to underscore its importance for policymaking. A true Phillips curve implies that the relationship between inflation (adjusted for inflation expectations) and excess demand is asymmetric: a given amount of unemployment below the nonaccelerating inflation rate of unemployment (NAIRU) generates more inflation than the same amount of unemployment above the NAIRU lowers it. This asymmetry implies an important role for stabilization policy that is absent from linear models of the unemployment-inflation process. In particular, there can be significant gains from preventing an overheating of the economy, since the gains when unemployment is below the NAIRU are more than offset by the increase in unemployment needed to stabilize inflation. Moreover, convexity in the Phillips curve by itself (abstracting from inflation adjustment arising from forward-looking expectations and credibility effects) will result in higher cumulative unemployment costs, the faster is the pace of disinflation. The paper briefly reviews the history of the Phillips curve and the theoretical basis for nonlinearity. It argues that the importance of nonlinearity in the original work of Phillips and Lipsey was lost in subsequent analyses that focused on explaining shifts in the curve. The paper then provides a derivation of the Phillips relationship, showing that the curvature reflects a structural parameter that links in a nonlinear manner the level of the real wage to the unemployment rate. The paper also shows that convexity in the Phillips curve implies that there is an important distinction between the NAIRU and the natural rate of unemployment that must be taken into account in estimation. Finally, estimated equations for the U.S. Phillips curve are used to calculate the unemployment costs of overheatingand rapid deflation in linear and nonlinear models of the Phillips relationship.