What happens to the inflation when the output gap is zero?

In a blog post a couple of weeks ago, Paul Krugman presents a scatterplot of the change in the inflation rate (y) as a function of the output gap (x), with the following regression line:

y = 0.5228 x - 0.4739

I'm puzzled as to why he includes a constant term in this regression. (Maybe he was using graphics software that won't do a no-constant fit?) If you take the regression line at face value, it means that the inflation rate is predicted to fall by almost half a percentage point each year when the output gap is zero. It also means that the economy must run nearly a full percentage point above potential in order to prevent the inflation rate from falling. That doesn't make any sense.

The sensible way to do the fit is to constrain the constant term to zero (which makes the math a lot easier if you're doing the fit by hand, but some software insists on doing things the hard way even when it doesn't make sense).

It turns out it doesn't make much difference in the conclusion: the slope of the line is still approximately 0.5, and in the relevant region (with output gap above 6 percent) the intercept is not of much relative consequence. But I would have found the whole thing more convincing if the plot had displayed a reasonable regression line to begin with. When you show a line that implies that the inflation rate declines even under normal conditions, it's not that impressive when you conclude that it will decline too much under unusual conditions.


UPDATE: Paul Krugman responds. His main point is that the IMF's definition of potential output doesn't require that the inflation rate be constant when actual output equals potential (i.e. when the gap is zero). So now I understand that the IMF's construction doesn't have that property. But I'm having trouble understanding the theoretical meaning of that construction. Doesn't the IMF's filter amount to an empirical way of making a guess at a concept that still should have that property theoretically?

I suppose I can understand that you don't want to force a constraint on the guess after it has already been made. (See Prof. Kurgman's point about circular reasoning.) But the chart still doesn't look right to me. Since the CBO's potential output concept does imply stable inflation at the zero point, how can you plug the CBO's gap forecast into the IMF's gap equation and get a meaningful result? (Well, OK, the result is meaningful for our purposes, because the fitted line passes close enough to the origin to give approximately the right result, to at least the level of precision necessary for the original point about deflation risk, and because the two methods for estimating the output gap lead to reasonably similar results for the US historically -- again, given that we don't really need much precision.) Under the circumstances, since we're mixing two different concepts anyhow, it's an arbitrary decision whether to impose the zero constraint, and I think the chart would look prettier if the line went through the origin. (I suppose that's a matter of personal taste.)

I also don't like the idea of using a filter that needs to know the whole series before it can do the smoothing (which IIRC is the case with the Hodrick-Prescott filter used by the IMF). It seems to me there is still a bit of circular reasoning involved, or at least, that you're constructing a fake data series that can't necessarily be expected to have the same properties in real time as it does with benefit of hindsight. I suppose if I were doing this, and if I wanted to keep the T's crossed &c., I would avoid the CBO's gap forecasts entirely and just use raw GDP. Then I could determine historical potential output by putting the data through a one-directional filter which I could then apply to the CBO's forecasts. But it's still unclear whether the fitted line should be constrained to have a zero intercept. It seems to me, the only reason to interpret the fitted relationship as a structural one is that we have a theory wherein such a relationship exists. And in the theory, as I understand it, the line does have to pass through the origin.