Inflation is a monetary phenomenon. Since the Central Bank controls the money supply, then by definition the Central Bank controls inflation.

I meant they control the interest rates, which do not control inflation. Inflation comes about from the creation of money, which the central bank does to fund the government deficits.

The central bank can limit money creation but can't force consumers, businesses or the treasury to borrow or spend money.

Yes, that is true, but it is still part of their mandate. Supply and demand of money gets reflected in inflation and the Fed responds by changing interest rates. Isn't this a free market mechanism?

> Isn't this a free market mechanism?

No. In Friedman's "Monetary History of the United States" he shows how the Fed setting interest rates was rather erratic and much more unstable than the earlier free market mechanism. The Fed would guess at what the S+D point was, since the Fed was not subject to market forces. This meant they were always late and always wrong.