You mean they are buying assets and thus the money is simply providing liquidity and has tangential value. They aren't just printing it and giving it away, this subtle but significant difference is one of the reasons that money supply and inflation have very little if anything to do with one another.

Yes, buying assets, but basically buying risk-free treasuries that come in inexhaustible quantities. When they make the purchase that money goes directly to the federal government to be spent.

And that money is in competition with others who are buying treasuries, driving down the interest rate (since it’s an auction) and presumably pushing that money to other uses.

So you are right, it’s not “given away”, but it’s a pretty frictionless way for “new money” to enter the financial system. It’s not like the money is put in a bank account and just sits there.

But your point is well taken. There is no “2 + 2 = 4” rule when it comes to money supply and inflation.