Nonlinearities in the Phillips Curve for the United States: Evidence Using Metropolitan Data

Abstract

With the unemployment rate in the United States currently below estimates of its natural rate we examine if the relationship between inflation and unemployment is nonlinear. Using aggregate data we are unable to reject a linear relationship. However, using metropolitan-level data we find the slope of the Phillips curve is roughly twice as large when unemployment is low compared to when it is high. Nevertheless the simple nonlinear Phillips curves used here suggest a core CPI inflation rate that is only slightly different than the linear version over the next couple of years.

The Phillips Curve at the ECB

“…Overall, the finding that the evidence of non-linearities is stronger for the wage Phillips Curve than for the price Phillips Curve for the euro area is in line with the analogous finding by Babb and Detmeister (2017) for the United States.…”

“…This finding is in line with evidence from the Unites States, where Leduc and Wilson (2018) identify non-linearities based on the cross-geographical wage Phillips Curve. Babb and Detmeister (2017) also find in the US metropolitan area data that the impact of unemployment on inflation is twice as large when it is low than when it is large.…”

Insights from OECD Phillips curve equations on recent inflation outcomes

“…Given that linear Phillips curves imply very weak unemployment gap effects, the policy implications of having two to three times larger effects in boom phases are not necessarily alarming. Such a conclusion is supported by the findings of an entirely different type of study by Babb and Detmeister (2017), who find strong statistical support for a non-linear Phillips curve for the United States using metropolitan-wide data, but also calculate that the inflation implications are "only slightly different to the linear version over the next couple of years".…”

“…adding the square of the output or unemployment gap or the use of a dummy variable separating positive from negative gaps) to account for structural changes in the inflation process (Laxton et al, 1995;Fisher and Koenig, 2014). Alternative approaches have considered splitting short-run and long-run unemployment or using a spline to allow for a kink in the unemployment gap with the purpose of demonstrating varying steepness in the slope of the Phillips curve depending on the level of unemployment (Guichard and Rusticelli, 2011;Babb and Detmeister, 2017).…”

Finding a Stable Phillips Curve Relationship: A Persistence-Dependent Regression Model

“…Essentially, we use one-sided filtering to partition the real-time unemployment rate into 9 Asymmetry has been a hypothesized feature of the Phillips curve from its inception (Phillips 1958), and many previous studies have located evidence for asymmetry or convexity (for example, Debelle and Laxton 1997, Detmeister and Babb, 2017, or Murphy, 2017. Asymmetry is built into the Stock and Watson (2010) recession gap.…”