John Cochrane's blog post, Whither Inflation, is excellent reading. Basically, John takes a mainstream New Keynesian model and shows how it has Neo-Fisherian characteristics - if the central bank raises the nominal interest rate, inflation increases. Noah Smith seems to find this interesting, but he's got some problems with it. I'm going to attempt to answer his questions.

First, Noah says:

What about the Volcker disinflation, when Fed interest rate hikes were followed by disinflation?

Volcker was Fed Chair from August 1979 to August 1987. During that period the time series for the fed funds rate and the pce (year-over-year) headline inflation rate looks like this:The broad story in that picture is that Volcker began his 8-year term with high nominal interest rates and high inflation, and ended it with much lower nominal interest rates and much lower inflation. The scatter plot, with points joined in temporal sequence, looks like this:In that chart, inflation and the fed funds rate more often than not are moving in the same direction. Volcker didn't do Cochrane's experiment in reverse - the fed funds rate comes down gradually during the disinflationary period - but I don't see an inconsistency between what we see in the above 2 charts and what is coming out of Cochrane's experiments with the NK model.