It was a mistake in a spreadsheet that could have been easily overlooked: a few rows left out of an equation to average the values in a column.

The spreadsheet was used to draw the conclusion of an influential 2010 economics paper: that public debt of more than 90% of GDP slows down growth. This conclusion was later cited by the International Monetary Fund and the UK Treasury to justify programmes of austerity that have arguably led to riots, poverty and lost jobs.

Now the mistake in the spreadsheet has been uncovered – and the researchers who wrote the paper, Carmen Reinhart and Kenneth Rogoff, have admitted it was wrong.

The correction is substantial: the paper said that countries with 90% debt ratios see their economies shrink by 0.1%. Instead, it should have found that they grow by 2.2% – less than those with lower debt ratios, but not a spiralling collapse. Yet cutting public spending to avoid that contraction has become a linchpin of both George Osborne's and the IMF's policies.

For Reinhart and Rogoff, who have a huge reputation in the field – both worked at the IMF, Reinhart is a former chief economist at Bear Stearns, and Rogoff worked at the Federal Reserve – the discovery has been hugely embarrassing. "It is sobering that such an error slipped into one of our papers," they said in a statement.

The focus now is on whether the economic theory that had seemed to bolster austerity programmes will follow them into full reverse – and whether politicians and bankers will stick with programmes that are having dubious effect.

"Cutting the debt was the be-all and end-all for Osborne," said Danny Blanchflower, a former member of the monetary policy committee at the Bank of England and now professor of economics at Dartmouth College in New Hampshire. "This is the foundations of that house being ripped away. Reinhart-Rogoff [as the paper was known] was the fundamental building block."

Jonathan Portes, former chief economist at the Department for Work and Pensions and now director of the National Institute of Economic and Social Research, said: "This was an exceptionally influential and widely cited paper, and George Osborne has repeatedly made clear that Ken Rogoff, who he has frequently met, has been very influential on his thinking."

Rogoff, a former chief economist at the IMF, is regularly canvassed by the chancellor as he seeks a robust defence for the UK's slow recovery. He and Reinhart are the only economists consistently quoted by the chancellor in his speeches. Portes points to Osborne's speech at the prestigious Mais lecture in February 2010, not long before he took office, at which the chancellor said: "Perhaps the most significant contribution to our understanding of the origins of the crisis has been made by professor Ken Rogoff, former chief economist at the IMF, and his co-author, Carmen Reinhart." The chancellor then quoted the finding from their paper: "The latest research suggests that once debt reaches more than about 90% of GDP, the risks of a large negative impact on long-term growth become highly significant."

This week Rogoff and Reinhart are fighting to salvage their reputations from the humiliating experience of having their paper torn to shreds. The paper, which they continue to defend despite admitting mistakes, came under scrutiny after the pair released the spreadsheet calculations underpinning their model to rival academics at Massachusetts University. The error was discovered by Thomas Herndon, a PhD economics student at Massachusetts.

The Massachusetts economists who led the attack on the 2010 paper questioned why their Harvard rivals used a generic Excel spreadsheet to carry out ground-breaking research. According to the European Spreadsheet Risk Group, spreadsheets were behind the collapse of the Jamaican banking system in the late 1990s, and their use was key in the development of collateralised debt obligations – the financial instruments that promised sub-prime mortgages could somehow become AAA-rated investments.

Labour said the chancellor's plans had lost credibility. "We warned that rapid fiscal tightening when the global economy is weak risked backfiring and that's what has happened. The idea of expansionary fiscal contraction has been exposed as total nonsense," said Ed Balls, the shadow chancellor.

In the US, Nobel prizewinning economist Paul Krugman said the unravelling of Rogoff and Reinhart's paper was a hammer blow to Republicans who had campaigned for spending cuts to reduce Washington's 100% debt-to-GDP level.

Rogoff defended his work, saying that the errors failed to undermine the general message. He said: "Carmen and I have consistently been strongly in favour of major restructuring as a centrepiece of the solution for eurozone periphery public debt and senior bank debt. We believe that the current plan of relying on a mix of austerity and optimistic growth forecasts is riskier than restructuring would be."

An aide to the chancellor said the result "remains robust". He added: "The suggestion that the case for dealing with fiscal deficits and debt rests on one paper is patently absurd. It remains the case that the majority of economists still back the government's strategy."