Ok this is a bit of pinball intro as I bounced first to the PEF to be greeted by a blog post by Erin Weir recommending we all read Nick Rowe poking at the President of the Minneapolis Federal Reserve with a sharp stick (more on that below).
Erin writes:
The President of the Minneapolis Federal Reserve had warned that unduly low interest rates would cause deflation. Of course, anyone with a handle on basic macroeconomics knows that the risk of leaving interest rates too low is inflation.
Ehhem, as everybody ought to know…ceteris paribus “anyone with a handle on basic macroeconomics knows that the risk of leaving interest rates too low is inflation.”
And what is often left out in inventory (introductory) macro is that ceteris paribus is crucial.
If you were to take Japan as your only data set and regress interest rates on the general price level you might be tempted to agree with the Pres. of the Min Fed. If you took Zimbabwe (interest rates and inflation rates only) as your case you would be tempted to argue the same: high interest rates cause high inflation! Neither of course is right. Back from the extremes; what is the relation between low interest rates in NA and the price level right now? There is a group of economists that have been promising, predicting, and now praying for an acceleration in the general price level since 2001. Ceteris paribus so is Erin if he believes that low interest rates ————> inflation. I do not think he does but it sure sounds like it.
Perhaps if intro to macro started with these real world examples they would be better courses. As everyone knows (don’t they?) both inflation and deflation are anywhere and everywhere decidedly more complex phenomena than simple causal arrows running from interest rates to general price levels. NB. Even the case where interest rates cause inflation or deflation they are going to be particular cases. The causal case (general law level) can only be sustained if and only if the economy being investigated conforms to the model. The theoretical model rarely will (and only loosely) so that too would be a particular case from which no general (———>) covering law can be given. Again the Fed Pres is wrong but not simply because he got the standard Macro 101 ass to front. As Nick Rowe notices and then notes.
I notice he has an undergraduate in maths, then went straight into a PhD in economics. My conjecture: I bet he never took Intro Economics, or anything vaguely similar. I bet he waded straight into the mathematical deep end. And so he never really learned economics. So he took the Fisher identity (nominal interest rates = real interest rates + expected inflation), added monetary super-neutrality (equilibrium real rates are independent of monetary policy in the long run), and ran with it. He never distinguished between the equilibrium thought-experiment and the stability thought-experiment. If you explain this in words, as you have to in Intro Economics, you have to get it right.
We should never, ever, let students do this. Yet we do it all the time.
And this is also why we should never frame monetary policy in terms of interest rates. If this guy can’t understand it, maybe some average people will get it wrong sometimes too, and have things going in the wrong direction
Sometimes I despair of my discipline. And for my economy.
None of which seems to have aught much to do with math save for in one sense; like alcohol, the math does a kind of confidence trick .
Relentlessly Progressive Political Economy 
I did not suggest that low interest rates always produce inflation. In fact, the sentence immediately following the two you quoted explicitly states that I do not see inflation as a serious threat in current circumstances.
My point was simply that low interest rates push in the direction of inflation as opposed to deflation. Of course, other factors can outweigh interest rates in determining the price level. (Indeed, low interest rates are particularly appropriate as a counterweight to deflationary factors.)
So, I think we are in agreement.
Yes and notice I said I did not think you thought that low interest rates caused inflation. To quote myself: “I do not think he does but it sure sounds like it.”
But the point of the post was that math did not have much to do with it rather how the simple inflation story is, in general, taught by the discipline. Krugman’s near month long rant and the comments to those rants show just how deeply ingrained the simple story of inflation is.
You say low interest rates lead in the direction of inflation. For what class of cases? The way you have it this is a covering law. I threw up two specific cases where this was not true and one large general case where this has not been true: NA. So for all these cases what is overdeterming the system such that low interest rates are not causing inflation? And the North American case is really interesting because prior to the GFC there was not much evidence that in a near full employment context low interest rates were causing anything other than an asset price inflation in housing. Instead of the general price level moving up to compensate for the housing bubble, housing deflated rather spectacularly in Britain the US, Spain and Ireland.
Look I am not an economist so you are going to have to walk me through this slowly because I have the simple story in my head somewhere, buried deeply as though it is an intuition, but, then, I have all these empirical cases running around that do not fit the intuition. I just want to know how a general law can be suspended across such a broad range of cases.
Back in Star Trek the Next Generation when the writers ran out of ideas they would bring in Q. Q was marvellous because he could do interesting things like suspend universal laws. So just who or what is this Deus ex machina that keeps the covering law right but explains its seeming suppression?
The extent to which low interest rates push toward inflation depends on the willingness of businesses and people to borrow to finance more investment and/or consumption. In any case, other factors can outweigh interest rates.
In Japan, deflationary pressure from a depressed economy was stronger than inflationary pressure from ultra-low interest rates. In Zimbabwe, inflationary pressure from printing money, etc. trumped interest rates.
These examples do not disprove the usual relationship between interest rates and inflation. They simply confirm that other factors can have even greater effects on the price level.
Cool so it is like the Marxist law of the tendency of the rate of profit to fall.
And what of NA?