This is a good post on optimal monetary policy by Scott Sumner. He says the following:
I’ve often argued that the supposed “welfare costs of inflation” are better thought of as the welfare costs of volatile or excessive NGDP growth.
It is good to see this assumption shown transparently – if this is indeed the case having NGDP targeting as optimal policy makes sense.
I don’t believe output is trend stationary, I don’t believe optimal output grows at a stable rate. As a result, I support flexible inflation targeting. However, if I’m shown otherwise I’d be happy to switch camps – this is very much the old “level” vs “growth” debate.
Obviously if you think the CPI is a good proxy for the welfare costs of inflation, then inflation is likely to play a role in your optimal policy rule. And if you think (as George and I do) that NGDP is a better proxy for the welfare costs of inflation then NGDP may play a role in your policy rule. That’s just common sense.
We aren’t yet at the stage where mathematical models can show which policy is best. We simply don’t know enough about the welfare costs of inflation
This is true – we still can’t derive the true structure of the economy and work out optimal policy. This is something that is unlikely to happen, and part of the reason why economists use a lot of partial rules to try to understand what is going on.
Soctt goes on to criticise mathmatical modeling. This is the bit I disagree with. We do need to be more transparent about where the “costs of inflation” come from, but I would say this is the reason to make sure we build more, transparent, models so that we can clearly articulate different assumptions. Yes we should be able to describe these in words, but maths gives us a concise way to frame and compare these issues.