Sunday, February 15, 2009

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.

38 Comments:

Anonymous Anonymous said...

Technological progress-induced deflation?

Mon Feb 16, 12:02:00 AM EST  
Anonymous Anonymous said...

Try a Baxter-King filter ?

Mon Feb 16, 03:30:00 PM EST  
Blogger Karl Smith said...

KNZN

Suppose that agents expected inflation to be falling over the period. Would it then not be possible for inflation to fall at a zero output gap?

This doesn't seem unreasonable in this case since we are looking at 1980 to 2007.

If you constrained the intercept wouldn't you be biasing the co-effecient.

That is the .5% intercept represents expected disinflation. But it does not effect the relationship between output an unexpected disinflation.

Mon Feb 16, 04:04:00 PM EST  
Blogger knzn said...

But if you're applying the result to 2010, we can't assume a priori that the expected change in the inflation rate will be the same as it was in the earlier period. The way I was thinking of it is that the lagged inflation rate is a proxy for the expected inflation rate, and it's a good proxy in that it should be unbiased in the long run. Once you bring actual expectations into the picture, it becomes clear that the relationship depicted is not a structural one, and we've got Lucas Critique coming out of our ears. Tne way to finesse ones way around the Lucas Critique is to make a "neutral" assumption about expectations.

Of course, if you do consider expectations, the picture may look even bleaker. Presumably a gap below potential output will lead people to expect disinflation/deflation, and the actual gap would be associated with an inflation rate below the expected rate. I haven't thought this through, but it seems that you could have a deflationary meltdown occur spontaneously and immediately, because everyone is trying to bid below everyone else's expectations, and therefore the expectations shift downward, and therefore everyone tries to bid below the new expectations, so they shift downward again, and so on. Is there any RE equilibrium above P=0?

Mon Feb 16, 04:27:00 PM EST  
Anonymous Anonymous said...

Since Paul Krugman didn't post the standard errors for the estimates, we don't know whether the constant is significantly different from zero or not. Given that the constant is pretty low, it looks like it will be statistically indistinguishable from zero.

Julian Silk

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