I wanted to make an observation on what Noah Smith calls the "Neo-Fisherite" idea that raising interest rates raises inflation. I don't intend to go over all aspects of it; suffice it to say, I think the idea is flawed. I just wanted to look at one particular point which I think is interesting in that it says quite a lot about how economists of different schools frame questions differently.
The Fisher equation says that the expected real rate of interest is (approximately) equal to the nominal rate of interest less expected inflation. The Neo-Fisherite idea is that if the central bank increases its nominal rate and holds it there, then the rate of inflation will adjust to restore the natural real rate of interest. One way this might be achieved in theory would be through a sudden sharp fall in the price level as the immediate response to the change in interest. From this point, the price level could then drift upwards at the increased inflation rate. Needless to say, the sharp fall in prices is somewhat implausible. What is rather more realistic in this scenario is that prices would edge down very slowly with depressed output in the mean time.
If this were the analysis, it would be fairly unremarkable. What we would really be saying is that high interest rates lead to a prolonged period of deflation, which may eventually reach the point at which it can turn around. For the Neo-Fisherite case to be interesting, it must involve no significant deflationary period.
There are all sorts of things to be said here, but one thing that intrigues me is what happens to government debt in this scenario. If the central bank were to permanently raise its rate, then the price of long-dated bonds must fall. So, without a sharp drop in the general price level, the immediate result of this policy would be a fall in the real value of government debt held by the private sector. So we can't claim monetary neutrality - we have to accept there will be real effects.
You could deal with this by simply assuming all debt is short term or assuming that the revaluation has no effect on private sector behaviour. However, to me this seems rather pointless, because you're then just assuming away most of the most important reasons why the Neo-Fisherite position shouldn't apply.
In Stephen Williamson's QE paper (which provides a detailed model in which the Neo-Fisherite case holds), this problem is avoided a different way. With regards to fiscal policy, Wlliamson makes the assumption that taxes and transfers respond passively to central bank policy, so as to maintain a constant real value of government debt (unnumbered equation appearing between (25) and (26)). So, because an increase in the central bank rate reduces the real value of debt, as described above, we are saying here that the government responds with expansionary fiscal policy.
So the argument appears to be that if the central bank raises rates and the government reacts by cutting taxes, then we will get inflation.
Which is not really a very surprising result. You could put that into an IS-LM / AS-AD model and get the result that raising interest rates would raise inflation. You just need to assume that the fiscal policy is sufficiently expansionary to validate the central bank's inflation target, which is what Williamson's assumption achieves.
It may well be that this assumption is not essential for Williamson's result. As I said, there are other ways of avoiding the problem, although to me all they do is make it more questionable whether that the result wouldn't apply in the real world. It just seems really odd to me to make an assumption like this about fiscal policy and pay such little regard to it, when the same assumption would have massive consequences in a differently framed model.