Anchored expectations contribute to the flattening of the Phillips curve in the U.S.
In this paper, Bobeica et al. analyze to what extent the declining pass-through of labor costs to price inflation could be attributed to three important trends that have recently shaped the US economy. In particular, they look at the role played by: (i) the improved anchoring of inflation expectations; (ii) the changing constellation of shocks that hit the economy; (iii) the increased trade openness and (iv) the rise in firm market power. Their empirical analyses are designed to capture the role of each individual factor by adapting their baseline parsimonious SVAR model and also construct a novel industry-level database which allows to map the link between the labor cost-price inflation pass-through on the one hand and trade openness and market power, respectively, on the other hand. They conclude:
We find that all factors contributed to the weakening of the link between labor cost and price inflation in the United States. However, the increased anchoring of inflation expectations appears to have played a particularly relevant role.

The changing link between labor cost and price inflation in the United States
Authors: Elena Bobeica, Matteo Ciccarelli, Isabel Vansteenkiste
From: ECB
Anchored expectations contribute to the steepening of the Phillips curve in the U.S.
In this paper, Jorgensen and Lansing use a simple three-equation New Keynesian model to demonstrate how expected inflation can become more firmly anchored via an endogenous mechanism. According to their model agents have an imperfect understanding of the inflation process but nevertheless behave as econometricians in a boundedly-rational manner. They conclude:
The improved anchoring of expected inflation induced by a stronger policy response to inflation reduces the correlation between changes in inflation and the output gap. But at the same time, improved anchoring increases the correlation between the level of inflation and the output gap. Intuitively, improved anchoring reduces the sensitivity of actual inflation to both lagged inflation rates and cost-push shocks. To the extent that these sensitivities impart negative comovement between the level of inflation and the output gap, improved anchoring serves to “steepen” the original Phillips curve.

Anchored Inflation Expectations and the Slope of the Phillips Curve
Authors: Peter Lihn Jorgensen, Kevin J. Lansing
From: Federal Reserve Board of San Francisco