Given that there is a direct short-term trade-off between growth and inflation targeting inflation is the same as stabilising short-term growth – this of course presumes that the only stabilisation role for monetary policy is the face of “demand side” shocks.

The only growth story that matters is short-term growth (as the nominal shock associated with printing money doesn’t influence long-run activity), and this is implicitly targeted when sticking to an inflation target.

But inflation is endogenous to the behaviour of the central bank – it is still their focus. If inflation is not an issue (if it is not going to be too low or too high) then the central bank has acted sufficiently to stabilise economic activity – there is no need to focus on output independently.