Inflation Expectations and Nonlinearities in the Phillips Curve 
The Phillips curve, which shows the connection between inflation and unemployment, typically reflects an inverse relationship: as inflation increases, unemployment decreases, and vice versa. During the 1970s and ‘80s, much research focused on understanding the causes and costs of high inflation using this model. Since then, researchers have challenged the validity of the Phillips curve—particularly during the 2010s, when the unemployment rate skyrocketed but inflation did not decline as much as the curve predicted it would. The authors of this paper set out to explore the apparent lack of validity of the Phillips curve during the missing disinflation of the 2010s.
Key Findings
- The missing disinflation of the 2010s can be explained by nonlinearities in the Phillips curve, in which case high unemployment in the aftermath of the 2008 Great Recession would not lead to a decrease in inflation as sharp as in a linear relationship.
- Intuitively, if the Phillips curve is a convex curve and not linear, a further increase in unemployment when unemployment is already high leads to a smaller disinflation than during periods of historically average unemployment.
- Consumer expectations of inflation turned out to remain quite significant in these nonlinear specifications.
- The significance of nonlinearities relative to consumer expectations depends on the inflation measure used.
Implications
This paper builds on recent literature concluding the legitimacy of the Phillips curve, confirming and extending that conclusion by looking at the curve through a different lens: nonlinearities. The authors find that it is important to consider both consumer expectations and nonlinearities for a range of inflation measures and historical episodes. This finding suggests that the cost of inflation and the inflation-unemployment tradeoff may differ from their historical averages during the times of low unemployment.
Abstract
This paper shows that a simple form of nonlinearity in the Phillips curve can explain why, following the Great Recession, inflation did not decrease as much as predicted by linear Phillips curves, a phenomenon known as the missing disinflation. We estimate a piecewise-linear specification and document that the data favor a model with two regions, with the response of inflation to an increase in unemployment slower in the region where unemployment is already high. Nonlinearities remain important, even when we account for other factors proposed in the literature, such as consumer expectations of inflation or financial frictions. However, studying a range of specifications with different measures of inflation and economic activity, we conclude that, in most cases, consumer expectations are more robust than nonlinearities. We find that the role of consumer expectations was especially important in the 1970s and ’80s, during a turbulent rise in inflation followed by the Volcker disinflation; the nonlinearities make disinflation more problematic and require the inflation expectations process to be more forward-looking during this period, thereby putting a larger weight on survey expectations. We conclude that a nonlinear Phillips curve with forward-looking survey expectations can be a useful tool to understand inflation dynamics during episodes of rapid disinflation and persistent inflation.