Deconstructing the Phillips curve
Jordà and al. find that while changes in economic slack have had next to no effect on the dynamics of inflation before and after the Great Recession, the contribution of future expectations has increased proportionately, almost doubling since the Great Recession. This increase implies that expectations now have a large effect on where inflation is headed. In addition, they argue that inflation persistence has also declined considerably, reducing the feedback loop somewhat. They estimate that an unanticipated percentage point increase in inflation will raise inflation in the next quarter by about 0.45 percentage point. In contrast, prior to 2007, the effect on inflation would be about 0.71 percentage point.

Inflation: Stress-Testing the Phillips Curve
By: Òscar Jordà, Chitra Marti, Fernanda Nechio, and Eric Tallman – Federal Reserve Bank of San Francisco
Is inflation around the corner?
Coibion and al. use an expectations-augmented Phillips curve and a novel data set of inflation expectations for the period from 2000 to 2018, to estimate the global inflation gap: the common component of the deviation of inflation from inflation expectations across advanced economies. They find that this gap has gradually risen since its low in the mid-2010s, but it is still negative which suggests that there remains economic slack across most advanced economies.
In short, while output gaps are likely closing given that the gap between inflation and inflation expectations is shrinking, we find no evidence that inflation is on the brink of surging ahead.

Is Inflation Just Around the Corner? The Phillips Curve and Global Inflationary Pressures
Authors: Olivier Coibion, Yuriy Gorodnichenko, and Mauricio Ulate
From: University of Texas, University of California, Berkeley