His critics blame Alan Greenspan for setting interest rates too low, which caused the house-price bubble, which then burst and caused the financial crisis. As I argued back in February, the critics are typically confused between interest rates that are low, and interest rates that are low relative to the natural rate.

The topic is making the rounds of the economics blogs again, with Brad DeLong cogently making the same point about the natural rate. I want to add a Canadian twist. Canada also had a big increase in house prices. But since average Canadian inflation over the same period was almost exactly equal to the Bank of Canada's 2% target, we know that the Bank of Canada did not on average set interest rates below the natural rate.

If you can't blame the Bank of Canada for the boom/bubble in Canadian house prices, how can you blame the Fed for the boom/bubble in US house prices?

If the central bank sets an interest rate below the natural rate, inflation will rise relative to expected inflation; and if it tries to keep it below the natural rate, actual and expected inflation will rise without limit. If the central bank sets an interest rate  above the natural rate, inflation will fall relative to expected inflation; and if it tries to keep it above the natural rate, actual and expected inflation will fall without limit. That's what the "natural rate" is best defined to mean.

It is economic nonsense to blame a central banker for keeping interest rates too low, unless you mean to blame him for keeping interest rates too low relative to the natural rate. Because using monetary policy to try to set interest rates above the natural rate would cause a deflationary spiral, and that is not what central bankers are supposed to do.

So, if we are to make any sense of Greenspan's critics, they must be saying that Greenspan set interest rates below the natural rate. What evidence is there for such a statement?

We do not observe the natural rate of interest. We cannot tell, in real time, if the actual rate is above or below the natural rate. But with hindsight, things may become clearer.

In Canada, things definitely become a lot clearer in hindsight. That's because Canada has a well-defined inflation target for monetary policy. If the Bank of Canada gets monetary policy right, expected inflation is supposed to stay anchored at the 2% inflation target. So if inflation rises above 2%, it is above what expected inflation is supposed to be, and we know, with hindsight, that the Bank of Canada had previously set interest rates too low, relative to the natural rate, and given the inflation target. (The only ambiguities concern when precisely the Bank of Canada had interest rates too low, and whether it could reasonably be expected to have known in real time what we all now know with hindsight).

We know, for example, that Canadian inflation (both total and core CPI) was above the 2% target from mid-2002 to mid-2003, so we can say with hindsight that the Bank of Canada had set interest rates too low about a year or two earlier. But at other times, inflation was below the 2% target, and we know with hindsight that the Bank of Canada had set interest rates too high.

The US does not have a well-defined target for monetary policy. And in particular, the Fed does not have an inflation target against which we can judge what actual and expected inflation are supposed to be. So we cannot say, even with hindsight, whether the Fed set interest rates "too low", without making some additional judgment about what inflation and expected inflation should have been.

The US had a big increase in house prices. So did Canada. The Teranet-National Bank composite index (Canada's version of Case-Shiller) shows an 85% nominal increase from July 2000 to the peak in July 2008. (The data begin in January 2000, but I have chosen July 2000 to get rid of seasonal effects.)

From July 2000 to July 2008, Canadian core inflation averaged just slightly less than 2%, and total CPI inflation averaged just slightly more than 2%. Since 2% is the target for both actual and expected inflation, we can say, with hindsight, that during the house price boom in Canada, the Bank of Canada, on average, had set interest rates almost exactly equal to the natural rate.

You can't blame the Bank of Canada's setting interest rates too low (relative to the natural rate) for Canada's house price boom/bubble, because we know that the Bank of Canada did not set interest rates too low, on average, relative to the natural rate, during the period when Canadian house prices were rising.

Greenspan's critics need to do two things to make their case: first they have to show that the Fed set interest rates too low, relative to the natural rate (and that is not easy without a clear inflation target); second they need to argue some kind of "American exceptionalism", because their argument that the house price bubble needed low interest rates, relative to the natural rate, doesn't seem to work elsewhere.