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CPI ain't PCE my guy. Other than suggesting a firm January print, this print has not really changed forecasts for core PCE--the Fed's preferred target---to hit 2% yoy by May.
Core services inflation is up and the Fed doesn't just care about only one number, and I'm not your guy.
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.

A hike seems unlikely, but it seems likely that rates are going to stay where they are for a while. I wouldn't be surprised if cuts come much later than the expected June timeframe.
Higher rates require indebt government to borrow more money issuing more bonds. Higher bond issuance required FED to monetize them and increase money supply. Increased money supply increases inflation. Higher inflation forces FED to increase the rates.

Get your popcorn ready (while you can still afford it).

> Shelter prices and wage gains in a tight U.S. labor market are putting upward pressure on prices.

Ah yes, the classic "wage gains are eating into our profits" inflation.