## Phillips Curves, Phillips Lines and the Unemplyment Costs of Overheating

WP/97/17-EAWP/97/17

Phillips Curves, Phillips Lines and the
Unemployment Costs of Overheating
by Peter B. Clark and Douglas Laxton

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 overheating and rapid deflation in
linear and nonlinear models of the Phillips relationship.