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WASHINGTON — In recent years, policy makers in Europe and the United States have fastened on the notion that reaching a certain heavy burden of debt would threaten future economic health — often to justify austerity budgets that increased unemployment and sapped economic strength in the here and now.

But now some economists are challenging the very foundations of that idea, raising questions about whether such a debt threshold even exists and setting off a fierce debate that flared up on Tuesday across the Internet about whether potentially flawed research is at least partly responsible for the slow growth that has bedeviled most advanced industrial countries since the recovery from the financial crisis began in 2009.

The debate comes at a particularly perilous time, as economic officials from the United States and other countries gather for the annual spring meeting of the World Bank and International Monetary Fund in Washington, where many are expected to urge high-debt Europe to ease up on its commitment to austerity in the face of rising unemployment and new economic contractions.

The controversy stems from a provocative new paper by economists at the University of Massachusetts, Amherst that claims to have found some basic errors in one of the most pathbreaking and influential economic studies to come out in the last few years.

That was a 2010 research paper by Carmen M. Reinhart and Kenneth Rogoff of Harvard, also authors of a best seller, “This Time Is Different: Eight Centuries of Financial Folly.” The economists, analyzing 3,700 separate economic observations, found little relationship between growth and debt for countries with debt-to-gross-domestic-product ratios of 90 percent or less. But for countries with debt loads equivalent to or greater than 90 percent of annual economic output, “median growth rates fall by 1 percent, and average growth falls considerably more.”

Many politicians interpreted the research as showing a direct relationship between debt and growth. If a country reached a debt burden of more than 90 percent of its annual economic output, the logic went, it would quickly fall into a debt trap that would leave it struggling to grow in the coming years. Prominent politicians — including Olli Rehn of the European Commission and Representative Paul D. Ryan, the chairman of the House Budget Committee — cited it as a reason to try to impose major budget cuts.

The Harvard economists’ research was always more nuanced about the causal relationship between debt and growth than the popular view. Some economists expressed skepticism of the “threshold” theory to begin with. And many others noted how hard it could be to draw straight lines between debt and economic growth, given the panoply of factors at work.

But now, Thomas Herndon, Michael Ash and Robert Pollin of the University of Massachusetts, Amherst, in trying to replicate the Reinhart-Rogoff results, are challenging the conclusions for a different reason. They say they found some simple miscalculations or data exclusions that sharply altered the ultimate results. According to their rerunning of the figures, “the average real G.D.P. growth rate for countries carrying a public debt-to-G.D.P. ratio of over 90 percent is actually 2.2 percent, not –0.1 percent,” they write. In other words, heavy debts were not associated with the malaise that Professors Reinhart and Rogoff — and much of the world’s economic elite — thought that they were.

The new paper, released this week, has set off a storm within the economics profession, with some commentators even arguing that it undermines the austerity policies that have proved so prevalent in the last few years.

“How much unemployment was caused by Reinhart and Rogoff’s arithmetic mistake?” asked Dean Baker of the left-leaning Center for Economic and Policy Research, for instance.

But in interviews, several economic experts cautioned that it would take time to sort out the statistical implications of any problems in the highly technical research.

“I think it’s totally fair to say it’s embarrassing,” said Justin Wolfers, an economist at the University of Michigan, who added that he had not had the chance to study the results and noted that debates over supposed statistical problems were common in the profession. “But the mistakes that are most embarrassing are the least consequential” to Professor Reinhart and Rogoff’s conclusion, he added.

Other experts said that separate pieces of research had found similar results to the Harvard professors’ paper, using alternative data sets and significantly strengthening the argument that higher-debt economies suffered from slower growth. Those include studies by the I.M.F., the Organization for Economic Cooperation and Development and the Bank for International Settlements.

“There’s nothing about this that will change my view of the universe,” said Douglas Holtz-Eakin, a former director of the Congressional Budget Office and prominent Republican economist. “The sun still rises in the east. It sets in the west. And a lot of debt is still bad.”

In an e-mailed statement, Professors Reinhart and Rogoff did not directly address the assertions of mathematical errors, and noted that they had only just started to sift through the new paper. But they argued that the Amherst authors had also found lower growth rates when a country had debts equivalent to or greater than 90 percent of annual economic output. “It is hard to see how one can interpret these tables and individual country results as showing that public debt overhang over 90 percent is clearly benign,” they wrote.

The seemingly esoteric debate within the economics profession has collided this week with a broader challenge to excessive budget-cutting in countries around the world. The I.M.F. cautioned Washington against cutting its budget too fast, too soon, even as it saw the American economy strengthening. And on Tuesday, Olivier Blanchard, the fund’s chief economist, warned that Britain was “playing with fire” with its austerity policy.

Professors Reinhart and Rogoff “are right to say the basic structure of the result stands,” Professor Wolfers said. “The authors of the critique are right to say its force is lessened.”

The debate, he added, is far from over.