#### The Phillips curve is nonlinear when inflation is low

Some researchers argue that the slope of the curve in the United States fell substantially around 20 years ago so that unemployment now has little or no effect on inflation. This paper shows that another hypothesis is equally consistent with the data: The Phillips curve may be nonlinear when inflation is low, with the economy having operated in the flat region of the curve for most of the past 20 years. The next few years may be decisive in the debate between these hypotheses, as unemployment has returned to a range in which a nonlinear curve ought to display significant steepness. A flat Phillips curve implies little change in inflation going forward, but a nonlinear curve implies moderate increases in inflation over the next few years.

Low Inflation Bends the Phillips Curve

*Authors: Joseph E. Gagnon, Christopher G. Collins
From: Peterson Institute for International Economics*

#### Improving the Phillips curve with alternative gap variables

Kevin Lansing proposes the inclusion of an interaction variable, defined as the multiplicative combination of lagged inflation and the lagged output gap, in a typical Phillips curve predictive regression. He argues that including this interaction variable helps improve the accuracy of Phillips curve inflation forecasts over various sample periods.

What explains the more stable slope coefficient in **Figure 3** versus **Figure 1**? One explanation is that multiplying the output gap by inflation rescales the gap, producing a new variable that appears better able to capture the true underlying inflationary pressure associated with the gap itself.

Improving the Phillips Curve with an Interaction Variable

*By: Kevin J. Lansing – Federal Reserve Bank of San Francisco*