One of the more influential studies that's often used to argue for austerity has come in for an extensive new critique. (Update: The authors respond down below.)

The paper in question is Carmen Reinhart and Kenneth Rogoff's famous 2010 study "Growth in a Time of Debt," which found that economic growth severely suffers when a country's public debt level reaches 90 percent of GDP. That 90 percent figure has often been cited in the past few years as one big reason why countries must trim their deficits — even if their economies are still weak.


Now, those are two methodological objections. But there's also a third problem, as Mike Konczal details here. Reinhart and Rogoff appear to have made an error with one of their Excel spreadsheet formulas. By typing AVERAGE(L30:L44) at one point instead of AVERAGE(L30:L49), they left out Belgium, a key counterexample:

This discrepancy wasn't caught earlier because Reinhart and Rogoff hadn't made their full underlying data public. They only shared their spreadsheet with the Herndon, Ash and Pollin after the latter three tried to replicate the initial results and failed.

Taken together, those three changes lead to a different analysis. Herndon, Ash, and Pollin conclude that "the average real GDP growth rate for countries carrying a public debt-to-GDP ratio of over 90 percent is actually 2.2 percent, not -0.1 percent as as published in Reinhart and Rogoff."

It's worth emphasizing, however, that the Excel coding error itself is only responsible for a small portion of this difference in results — about 0.3 percentage points. So the spreadsheet mistake, by itself, does not appear to be fatal. Here's the difference between the two studies in chart form:

Chart: Jared Bernstein

A few extra points:

--This is not the first critique of Reinhart-Rogoff. As Dylan Matthews explained here, other economists have argued that the initial paper got the causality backward. Countries have high debt-to-GDP ratios because they have slow growth, rather than the other way around. This is a far more substantive criticism than the debate over the precise numbers above.

--Reinhart has responded to the critique of causality this way: "We’re quite aware that you have causality going in both directions,” she told Dylan. “But please point out to me what episodes from 1800 to the present have we had advanced economies who carried high levels of debt growing as rapidly or more rapidly than the norm..”

--At the same time, Reinhart-Rogoff isn't the only study finding that high debt levels are associated with low growth. A 2010 paper (pdf) from the IMF, for instance, found that "a 10 percentage point increase in the initial debt-to-GDP ratio is associated with a slowdown in annual real per capita GDP growth of around 0.2 percentage points per year, with the impact being somewhat smaller in advanced economies." Still, similar questions about causality apply to these papers too.

--Tyler Cowen has some additional thoughts here. He tentatively agrees with the critiques of the paper, but suggests that Reinhart and Rogoff's influence on the austerity debate has been overstated: "The 'case for austerity' didn’t rest much on R&R in the first place, rather on the notion that the bills have to be paid, dawdling on adjustment is not always so easy, and the feasible sum of international redistribution is quite low."

Update: Reinhart and Rogoff have now responded. I've bolded the key parts:




