From the always excellent Money Illusion blog:
The key point is that if the Fed pays attention to inflation at all, it should be increases in the price of stuff built with American labor. They shouldn’t care about the inflation rate that matches some mythical “cost of living,” as the Fed can’t do anything about adverse supply shocks.
In a small open economy like New Zealand we are constantly peppered by supply shocks. In such an environment what the RBNZ “should” and “can” be doing is very different to targeting the “cost of living” – which is truly set by real economy factors.
A lot of people in NZ get confused, and think that the RBNZ sets the cost of living – this is a myth that comes from, IMO, poor explanations by economists regarding what inflation is and why we should target it. This myth needs to be dispelled.