Update: Brad DeLong makes my point with graphs.

Their letter is here.

This could go on forever, and both they and I have other things to do. So let me just state — clearly, I hope — where their analytical sin lies.

To some extent it lies in the downplaying of causality issues — of whether high debt causes slow growth, slow growth causes high debt, or both high debt and slow growth are the result of third factors (as was the case in demobilizing postwar America, which they highlighted in their original paper).

But the more important sin involves the misuse of the “90 percent” criterion.

There is, as everyone in this debate has acknowledged, a negative correlation in the data between debt and growth. As a result, draw a line at any point — 80 percent, 90 percent, whatever — and countries with debt above that level will tend to have slower growth than countries with debt below that level.

There is, however, an enormous difference between the statement “countries with debt over 90 percent of GDP tend to have slower growth than countries with debt below 90 percent of GDP” and the statement “growth drops off sharply when debt exceeds 90 percent of GDP”. The former statement is true; the latter isn’t. Yet R&R have repeatedly blurred that distinction, and have continued to do so in recent writings.

And for a country with debt in the vicinity of the 90 percent level — as, for example, in both the US and the UK — the distinction is crucial. It’s the difference between arguing that failure to impose an austerity program amounting to a few percent of GDP might reduce GDP a decade from now by a fraction of a percent at most — which is what the actual correlation suggests — to suggesting that it will reduce future GDP by 10 percent, which is what the threshold claim suggests.

Austerity-minded policy makers, of course, seized on the latter claim, citing R&R — and if the authors ever made an effort to correct this misconception, or indeed if they have ever even acknowledged that it’s a misconception, it was done very quietly.

I’m sorry, but the failure to clear up this misconception has done a great deal of harm — and this harm is not significantly mitigated by various remarks in passing to the effect that austerity might be overdone.