We teach students that monetary policymakers have two objectives: to hit an inflation target and to minimise the output gap. Thanks to Michael Woodford, we can now claim that this objective function can be derived from the maximisation of representative agent utility, or we can simply appeal to a more informal discussion of the costs of involuntary unemployment and inflation. The question then arises why some countries, like the UK, have an explicit inflation target but no comparable output target.
In teaching terms, this becomes an opportunity to emphasise the key implication of the Phillips curve, which is that the two objectives are consistent with each other, so that if we succeed in keeping to the inflation target we must also be eliminating the output gap. We will, of course, talk about cost-push shocks to this relationship, adding an error term to the Phillips curve, but we will probably conclude by saying that therefore ‘flexible’ inflation targeting is quite compatible with the ‘dual mandate’ implied by the objective function. That I believe is the conventional wisdom.
Now to reality. The latest Bank of England Inflation Report sees CPI inflation above the target (2%) for the” next year or so”, and it now expects only 0.8% growth in 2012. Over the last four years CPI inflation has averaged about 3.5%, and unemployment has risen to above 8% following the recession. It may be possible to explain, within the Phillips curve framework, this conjunction of above target inflation and a large negative output gap by looking at a series of cost-push shocks (VAT, commodity prices, depreciation), perhaps coupled with some upward movement in inflation expectations . But even if it is, I think this combination has blown a large hole in the story that inflation targeting is compatible with our standard objective function.
We can see this in the decision by the Bank’s Monetary Policy Committee (MPC) not to undertake any further Quantitative Easing. Given the outlook for inflation and the output gap, a concern for both would normally imply the need for further monetary stimulus, rather than doing nothing. (I've disagreed with Chris Giles on fiscal policy, but I agree with him on this.) However, if the Bank’s inflation forecast is correct, additional monetary stimulus would probably involve inflation staying for a time nearer 3% rather than falling towards 2%, which clearly conflicts with the Bank’s own interpretation of inflation targeting. This is probably why it has chosen to sit on its collective hands.
Now you might argue that the MPC is nevertheless still being too timid, and that the inflation target is not that much of a constraint. Or that the forecast for inflation is wrong. However look at the US, where there is formally a dual mandate, and inflation has been more benign. Here again monetary policy makers appear content with an outcome involving roughly on target inflation and a large negative output gap. In other words, they seem happy not to maximise social welfare.
It is of course interesting to speculate why this is. Perhaps it is, as John Kay suggests, an obsession with credibility, involving a misreading of the theoretical literature. Perhaps they suspect, like Chris Dillow, further QE will be ineffective, so there is nothing they can do. (But if it is that, they should say so.) Perhaps it is because policymakers are really serving particular economic interests, as Steve Waldman suggests. Perhaps Rogoff was right, and central bankers really are ‘conservative’, in the sense of caring much less about unemployment than the rest of society. But whatever it is, it is not producing good policy for society as a whole. So we should think about moving to a monetary policy target that better reflects social costs. Maybe, as Britmouse in the UK and many others elsewhere suggest, that is a nominal GDP target, or maybe it is something else, but the status quo is not looking too good right now.
 Strictly this is not true in the New Keynesian Phillips curve, where there is a very small long run inflation/output gap trade-off.
 Suppose you had to choose between doing nothing, leading to inflation on target in two years time but an output gap of 3%, say, and monetary stimulus that might cut the gap to 2% but raise inflation temporarily 1% above target. If the social welfare function is quadratic in inflation and the output gap, you would only do nothing if excess inflation was five or more times more important than the output gap.