Nope, the Fed cares about PCE because that’s the inflation measure it targets over time. Consequently, core PCE and core PCE services ex-housing.
CPI and PPI matter for policy setting to the extent that their components feed into PCE. But Core CPI Services-XH and Core PCE Serviced-XH have little overlap in their components. The Fed is concerned about the latter falling because real rates, in the model that the Fed uses, get tighter the longer rates remain on hold. Just look at the last quarterly SEP—it forecasts PCE not CPI.
CPI and PPI matter for policy setting to the extent that their components feed into PCE. But Core CPI Services-XH and Core PCE Serviced-XH have little overlap in their components. The Fed is concerned about the latter falling because real rates, in the model that the Fed uses, get tighter the longer rates remain on hold. Just look at the last quarterly SEP—it forecasts PCE not CPI.