This is what I understand "standard" monetary theory to say about the relation between inflation and nominal interest rates.
I want to distinguish two cases.
In the first case the central bank pegs the time-path of the money supply. The money supply is exogenous. The nominal interest rate is endogenous. Standard monetary theory says that a permanent 1 percentage point increase in the growth rate of the money supply will (in the long run) cause both the nominal interest rate and the rate of inflation to rise by 1 percentage point. The Fisher relation holds as a long-run equilibrium relationship. The real interest rate is unaffected by monetary policy in the long run.
In the second case the central bank pegs the time-path of the nominal rate of interest. The nominal interest rate is exogenous. The money supply is endogenous. Start in equilibrium (never mind how we got there). Standard monetary theory says that if the central bank pegs the time-path of the nominal interest rate permanently 1 percentage point higher, this will cause the price level, and the rate of inflation, and the stock of money, to fall without limit. The Fisher relation will not hold, because there is no process that will bring us to a new long run equilibrium. The real interest rate will rise without limit.
These two cases are very different, because a different variable is assumed exogenous in each case.
I am assuming super-neutrality of money, in long-run equilibrium. The Fisher relation is a long run equilibrium relationship. We never get to the new long-run equilibrium in the second case, and so the Fisher relation does not hold.
Worthwhile Canadian Initiative 
One further note: I’m new to the blogosphere, and I’m not a full fledged macroeconomist, though I do play one in a public policy school. Some of my posts on this issue have bordered on snarky, but I think it’s because I was offended by the Econ 101 thing. In general, while the follow-up discussions to a lot of these blogs have been fascinating, and as a student of economics I’ve learned a lot, but the headline blogs have been unedifying.
But let’s stick with the Econ 101 theme, and the stuff we’d fail our students for. Turnabout is fair play: It is a big thing nowadays for students to evaluate their teachers. The scores so far: based on his Fed speech, I wouldn’t go with Kocherlakota because the paragraph we’ve been dwelling on really wasn’t clear and is open to multiple interpretations-indeterminacy, if you will. You can resolve the indeterminacy by applying your own prejudices, as Krugman does- but then you learn more about Krugman than the economy. So no. Nick Rowe? I’ve got apples and poles, but none of it is really on point. Start with an arbitrary equilibrium and then permanently peg the interest rate 1% higher? Oh Christ, Oh Christ, Oh Christ- how about starting out of equilibrium, and choose a point near the lower bound, which is actually the case we are discussing? Williamson? It is clear to him what NK. was talking about, but it isn’t clear to me. He’s found an equilibrium where NK is right. Great, but how do we get there? You need a model, as Delong points out. Problem with models is that they are like assholes: everybody’s got one. Delong’s model? Well, I got the most useful bibliography off of Delong’s site, so he is in the lead, but if you draw your graphs in an arbitrary fashion, you get arbitrary results.
Anybody else teaching Econ 101?
Jay, your characterization of the existing theory is utterly false. The theory says exactly what the Fed should do in the current situation, it’s just that Bernanke hasn’t yet decided to follow the advice of this theory.
As for Kocherlakota, he said much more than just: low rates and deflation go together. We’d all agree with that. And Williamson did not find and equilibrium where NK is right. Williamson simply found an equilibrium where low rates and deflation go togther. Kocherlakota said much more than that.
Here’s part of NK’s quote taken from Nick’s post:
“”To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation.”
That could be interpreted two ways: a wrong way, and maybe, just maybe, a right way.
“When real returns are normalized, inflationary expectations could well be negative, and there may still be a considerable amount of structural unemployment. If the FOMC hews too closely to conventional thinking, it might be inclined to keep its target rate low. That kind of reaction would simply re-enforce the deflationary expectations and lead to many years of deflation.”
Nope. He definitely meant it the wrong way. If the economy returns to normal, and the natural rate of interest rises, the Fed must raise its target rate of interest. (So far so good). If it doesn’t, the result would be….deflation. (“Inflation” would be the right answer).”
Nick is right, NK is wrong, the right answer would be inflation. It’s deflation that causes the low rates and not the other way around.
Adam, the issue isn’t low rates now, it is promises of low rates in the future, which have a different impact. And I don’t think anyone but you seriously believes that the monetary “silver bullet” out of this crisis is in every Econ department across the land, just waiting to be loaded. I’ve seen no overwhelmingly persuasive theories accounting for Japan.
Jay, you said: “I think a greater problem is that the Fed honestly doesn’t know what to do, and is feeling its way along. I blame the academics: standard theories don’t seem developed enough to help at this point.”
I said that’s wrong, the standard theory (at least a large body of it) does offer a prescription but the Fed has so far refused to implement it. I never once claimed it was a silver bullet guaranteed to work. But how can you blame the academics if their prescriptions have been ignored?
Would you also blame your doctor if he prescribed you a medicine but you refused to take it and got sicker?
Adam: so what should the Fed do?
Decalare a price level target for 2 years from now that is 10% higher than the current price level. Explicitly promise that if the price level falls short of the target the same thing will be repeated with another 10% added to the previous target (so if cumulative inflation over the next 2 years is 7% then the fed aims for 13% over the following 2 years).
Back it up by expanding he balance sheet to $5trillion beginning immediately.
Essentially Quantative Easing- do we really know if/how it works? (Papers, studies?)
No, the driver is the price level target. The balance sheet expansion to facilitate hitting the target works by reflating asset prices (important for Bernanke-Gertler reasons to facilitate an expansion in private credit).
For the papers see Woodford, Svensson and friends.
Unless you count devaluing against gold in depression, which did work, I don’t know of any examples where this has been tried. But if it works the theoretical papers tell us perfectly well how it works.