Updated at 11:12 p.m.

In the years following the financial crisis, America has been obsessed with debt. Hurting from the crisis, consumers and businesses have been busy paying off debt, while the federal government has ramped up its borrowing through a combination of stimulus spending and lower tax revenue. And of course all this new government debt — which has reached 73% of GDP and is expected to remain roughly at that level for the next decade — has many policymakers and citizens deeply concerned, to say the least.

But exactly how concerned we ought to be over that debt level — and how radically we need to act to reduce it — remains hotly debated. Governments obviously need to be able to borrow, and nearly every government does so. But experts have reached no clear consensus over how much (relative to the size of its economy) a nation can safely borrow.

That is, no consensus had begun to emerge until the appearance in 2010 of a paper, by economists Carmen Reinhart and Kenneth Rogoff, called “Growth in the Time of Debt,” which found that countries with higher debt levels tend to grow more slowly than those with little debt. For those who tend to see the rising debt load of the U.S. as a serious problem, these findings were just the evidence needed to prove that America had to cut back on spending, and fast.

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Tim Fernholz at Quartz does a nice job summarizing just how influential this work has been in Washington and Europe. He points to a scene, from a recent book on the federal debt by Republican Senator Tom Coburn, in which a bipartisan group of senators meet with Reinhart and Rogoff, and are obviously in agreement with their conclusion that allowing total debt/GDP to grow beyond 90% would be very dangerous indeed. As Fernholz writes:

It’s hard to get bipartisan agreement on anything in the Senate, but you can see influential legislators from both parties were listening closely to the two economists as they engaged in key debates over the economy. Even the notoriously obstreperous Coburn noted that ‘there was remarkable agreement about the severity of the problem.’

Reinhart and Rogoff have always been careful to note that just because high-debt countries have tended to grow more slowly than low-debt countries, it doesn’t mean that high debt definitively caused slow growth. Critics have pointed out, quite justifiably, that the causation could be the other way around — that slow growth causes debt. But even though Reinhart and Rogoff’s research doesn’t prove causality, it didn’t stop them from writing as if it did. And proponents of austerity took their research as solid proof that high debt levels impede growth. For instance, Paul Ryan has used Reinhart and Rogoff’s research to argue for his deficit-slashing budgets, writing, “Economists who have studied sovereign debt tell us that letting total debt rise above 90% of GDP creates a drag on economic growth and intensifies the risk of a debt-fueled economic crisis.”

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But new evidence emerged yesterday throwing Reinhart and Rogoff’s research into question. In particular, economists following in the footsteps of Reinhart and Rogoff say their conclusion is based on faulty data. Here’s the Roosevelt Institute’s Mike Konzcal on the findings:

From the beginning there have been complaints that Reinhart and Rogoff weren’t releasing the data for their results (e.g. Dean Baker). I knew of several people trying to replicate the results who were bumping into walls left and right — it couldn’t be done. In a new paper, ‘Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff,’ Thomas Herndon, Michael Ash and Robert Pollin of the University of Massachusetts, Amherst, successfully replicate the results. After trying to replicate the Reinhart-Rogoff results and failing, they reached out to Reinhart and Rogoff, and they were willing to share their data spreadsheet. This allowed Herndon et al. to see how Reinhart and Rogoff’s data was constructed. They find that three main issues stand out. First, Reinhart and Rogoff selectively exclude years of high debt and average growth. Second, they use a debatable method to weight the countries. Third, there also appears to be a coding error that excludes high-debt and average-growth countries.

What Herndon, Ash and Pollin find is that countries with debt loads higher than 90% of GDP actually grow an average of 2.2% per year, rather than the –0.1% found by Reinhart and Rogoff. The details of the errors are technical, but pretty embarrassing for such respected and influential research.

Reinhart and Rogoff responded to the critique yesterday afternoon — noting that despite the growth-rate discrepancy, both papers find that countries with higher debt loads grow more slowly on average — but fail to address the supposed data errors. (In fairness, the new paper just came out yesterday, and Reinhart and Rogoff deserve more time to respond thoroughly.) Nor did they address the most powerful critique of their research, namely the issue of causation. As Paul Krugman points out, we know that Japan’s high debt levels are the result of slow growth caused by a financial crisis, not the other way around. In addition, the research can’t explain why the U.K. grew so quickly after World War II, despite high debt levels.

Unfortunately, calling Reinhart and Rogoff into question doesn’t answer the fundamental question — How much debt is too much? — one way or another. We still don’t know for sure that our current debt levels aren’t an imminent threat. But if you’re looking for evidence that there will be serious consequences if we don’t cut spending immediately, Reinhart and Rogoff isn’t it.

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UPDATE: Reinhart and Rogoff have issued a second, more in-depth response, here