The least common denominator of the various plausible inflation theories is that inflation rates will rise slowly during an expansion. Although this is somewhat useful to know, it is not giving us a lot of information. Instead, we need to take deep dives into the price index data, and try to understand what is happening at the sector level. My feeling is that a lot of the drivers for the inflation rate in the current environment have little to do with the output gap story that the Federal Reserve allegedly has power to control.
I recommend the article "Considerations on Cost Disease" by Scott Alexander. He discusses the some of the major drivers of inflation in recent decades, which are all in the services sector. These components of the price index have exploded relative to the rest of the index....Bond Economics
U.S. Inflation Trends -- Not Really A Macro Theory Story