There is a considerable debate raging right now on the future level of inflation, exacerbated by the consensus busting April CPI print (here, here and here).
This piece, written by economists, is worth reading.
It proposes looking at median CPI to construct the Phillips curve, as it better reflects macroeconomic conditions.
The resulting relationship is stable pre- and post-pandemic and suggests, under bullish unemployment scenarios, that implied core PCE could hit 1.8-2.3% by 2023, “broadly consistent with the Fed’s average inflation targeting strategy with inflation modestly overshooting its long-term level following a number of years of undershooting it.“
They also don’t see, unlike others, temporary government spending causing an unanchored inflationary spiral given a better communication framework from the Fed and positive supply side effects of infrastructure spending.