Internal work conducted at the Federal Reserve using 15-year rolling-window regressions suggests that the reversion of headline PCE inflation to core PCE inflation has been much stronger in samples that start after the early 1980s and also that the reversion of core inflation to headline inflation has been much weaker in that period. Results for other countries are more ambiguous.
In recent years, Canada appears to have had a similar reversion of headline inflation to their version of core inflation, along with little reversion of core inflation to headline inflation (Laflèche and Armour, 2006; also, Armour, 2006; Hogan, Johnson, and Laflèche, 2001).