So as far back as 1982, here is a model in which lower interest rates correspond with lower inflation, both in the short run and the long run. John's model has money in it, so the mechanics are a pre-announced monetary contraction.
Sargent's famous "Ends of four big inflations" tells an even more radical story.
On solving the governments' fiscal problems, inflation ends instantly. Sargent and Wallace alas do not have interest rate data, but from the inflation data it's pretty plausible that interest rates fell like a stone when the fiscal reforms are implemented. They have money stock measures -- and the ends of these inflations did not have any monetary tightening at all. Money stock measures all expanded substantially as inflation ended.
I've been having an interesting back and forth with a correspondent about Milton Friedman's views. In "Do higher interest rates raise or lower inflation?" I quoted Friedman's 1968 address, and said he believed that an interest rate peg is unstable. Not so fast says my correspondent, and passed on a lovely memo written by Milton Friedman -- better still once owned by Anna Schwartz. (Yes I checked that it's ok to post this)
As I read this quote, Friedman emphasizes that lower interest rates come only with lower inflation in the long run, so there is some Fishery theory here. But in the short run, if the Fed lowers money growth, then interest rates will first rise but then decline as inflation declines. So the implied short run relationship goes the other way.
As I read it, then, Friedman says it is possible to target interest rates. But to do so requires particularly active money growth policy to offset the instability that would result from simply announcing a fixed interest rate.
That leads to a very interesting question, how the same interest rate path could be supported by different money growth paths.