In an NBER working paper, James Stock and Mark Watson argue that the correlation between cyclically sensitive inflation (CSI) and bandpass filtered activity measures is high and has not declined over the last decades, contrary to standard measures of the slope of the Phillips curve.
… we construct a new price index designed to maximize the cyclical variation in the price index. This index, which we call Cyclically Sensitive Inflation (CSI), estimates the weights on the component prices to maximize the correlation of the CSI with our bandpass measure of aggregate cyclical variation. … this index places low weights on tradeable goods, such as energy, motor vehicles & parts, and durable household equipment. The index also places low weight on the least well-measured sectors, such as clothing & footwear and final consumption of nonprofit institutions serving households (NPISH). The sectors that receive the greatest weight – housing excluding gas & electric utilities, followed by food & beverages for off-premises consumption, and recreational services – tend to be both locally determined (nontradeable) and relatively well-measured.
On VoxEU, Stefan Gerlach reviews the case for tilting Phillips curves in Switzerland.
Previous research had suggested that the Swiss Phillips curve had steepened in the second half of the 20th century. Gerlach estimates a Phillips curve model that includes lagged inflation, an output gap measure, and a measure of import price inflation. His model suggests several structural breaks:
The first structural break occurs in 1936-37. The estimated Phillips curves indicate that inflation became much more inertial, as evidenced by the fact that the parameter on lagged inflation more than doubled.
The second break occurs in 1970-71 … While the sensitivity of inflation to the output gap essentially doubles, other parameters are broadly unchanged. This impies that the Phillips curve steepened sharply in the 1970s.
The third break occurs in 1993-94 … The parameter on the output gap falls to zero and becomes insignificant. The parameter on lagged inflation also falls sharply and loses significance. This implies that between 1994 and 2015 inflation in Switzerland was insensitive to the output gap and displayed little persistence, and seems to have fluctuated only in response to changes in import prices.
A graph from the Wall Street Journal as reported by John Cochrane.