I'll bet you Debt to Donuts ...

There's been much well-deserved razzing of Reinhardt and Rogoff for their Excel error and their ... interesting choices about which data to exclude.

Brad DeLong did a post last week building off the work of a Berkeley grad student, Owen Zidar. Zidar put observations about countries into 50 bins of equal size, grouping observations by debt as a percentage of GDP, and looking at average growth over the following 5 years. When he plotted it, he got this chart:

Today DeLong revisited  the subject and added in a line at 90%, and then the average growth rate to the left of the line (countries with debt below 90% of GDP) and the average growth rate to the right of the line (countries with debt higher than 90% of GDP).

The moral of the story: slightly slower growth; no cliff. (And as people have been pointing out since R&R's paper in 2010, the causality isn't clear in any case.)

Looking at DeLong's modification, I was struck by those two particularly low bins just to the right of the 90% line. So if we were instead to draw the line at something like 95%, we'd take the lowest and third-lowest observations out of the "high-debt" group and put them in the "low-debt" group. And since those two dots were lower than the average in either group, the group they left would see its average go up, and the group they joined would see its average go down.

My drawing above is just an eyeballing approximation since I haven't taken the time to ask Zidar for his binned-up data, but the lines do have to move in the direction I've shown. It seems unlikely that this little shift has such a big effect that the countries with debt below 95% actually do worse than countries above, but we can say for sure that by placing the cutoff at 95% instead of at 90%, the effect of high debt moves in the direction of being trivial.

But notice something peculiar. Countries with debt greater than 90% do in fact perform worse than countries with debt greater than 95%. It's those two horrible dots between 90% and 95%.

What if we have three groups? Less than 90%, greater than 95%, and the middle. We get something like this:

Obviously, the real problem is neither high debt nor low debt, but debt in the very narrow window of 90 to 95% of GDP. That stuff's just a catastrophe. Talk about threshold effects. It's reminiscent of the "donut hole" in patient reimbursement that was built into the Medicare prescription drug benefit under GW Bush, only narrower.

Put another way, we're looking at something like this:

http://blogs.wsj.com/photojournal/2010/05/27/pictures-of-the-day-407/

The solution is clear. When your debt is approaching 90% from below, putting on the brakes might accomplish nothing useful. You'll merely slow down enough to go tumbling off the edge of the debt cliff into the 90-95 chasm. What you need to do is load up on debt big time--accelerate hard, make sure you clear the gap.

(Thanks ClipArt!)

Once you're on the other side, it's clear sailing.

Gee, it sure is a snap cooking up important public-policy findings when you know what to do with the data. Maybe I, too, can work for the Peterson Institute ...

UPDATE: Here's a post-length comment on Crooked Timber that's worth a read about the state of economics. (And the original post is short and sweet: scroll up and enjoy it.)