Two Harvard economists whose work is the ideological basis of those advocating tough government austerity measures acknowledged Wednesday that their key study justifying lower government debt loads contained an important mathematical error.

In 2010, Harvard professors Carmen Reinhart and Kenneth Rogoff published a report, titled "Public Debt Overhangs: Advanced-Economy Episodes Since 1800," which attempted to compile hundreds of years worth of data from advanced economies, to see what relationship, if any, exists between government debt loads and economic output.

One of the report's key findings was that heavily indebted nations — which the paper defines as those whose debt loads sit at more than 90 per cent of the country's GDP — generally tend to have sluggish or even shrinking economies over the long term.

A key line in the report concluded that countries where the debt-to-GDP ratio exceeds 90 per cent see their economies shrink by 0.1 per cent per year, on average.

That contention was a powerful argument in favour of austerity, the global trend that's currently leading governments the world over to slash their spending, cut back services, and reduce public sector workers in the name of paying down debt.

It was even cited by U.S. vice-presidential nominee Paul Ryan in his shadow budget that formed the basis of the Republican Party's campaign to take back the White House last year.

"Economists who have studied sovereign debt tell us that letting total debt rise above 90 per cent of GDP creates a drag on economic growth and intensifies the risk of a debt-fueled economic crisis," Ryan said on the campaign trail. He repeated the 90 per cent figure on a Fox News interview as recently as last month.

Mathematical error

The two academics have since published further research on the topic, and the original report was a key part of their New York Times best-selling book, This Time Is Different: Eight Centuries of Financial Folly.

But a trio of unheralded economists from the University of Massachusetts named Thomas Herndon, Michael Ash and Robert Pollin made headlines this week by going through Rogoff and Reinhart's work and discovering that the widely repeated 90 per cent threshold is in fact based on a mathematical error.

In recalculating the data, the trio discovered that data from certain years and certain countries were excluded from the average. When the complete data set is included, it shows that the average growth rate of countries with 90 per cent debt loads is 2.2 per cent — a significant difference from the 0.1 per cent decline.

That mistake "led to serious errors that inaccurately represent the relationship between public debt and growth," the trio said in their research published this week.

The new report set off a firestorm of reaction from academics and policymakers questioning the wisdom of tough austerity measures in a time when the global economy is struggling to gain traction.

America's debt load is currently in excess of 100 per cent of its GDP. And Canada's national debt load remains under 40 per cent of GDP, but that figure does not include debt accrued by the provinces. In many European nations, the debt-to-GDP ratio is in excess of 150 per cent.

Mistakes were made

Rogoff and Reinhart's initial reaction to the report was to point out that the core finding of their research — that high debt constrains growth — remains true, even after the recalculated figures are considered. And in a statement to news outlets Tuesday, Rogoff noted that the paper never attempted to draw a causal relationship between debt and economic output — it merely studied whether some sort of correlation existed.

In an emailed response to a request for comment Wednesday, Reinhart acknowledged to CBC News that some mistakes were made.

"It is sobering that such an error slipped into one of our papers despite our best efforts to be consistently careful," she said. "We will redouble our efforts to avoid such errors in the future."

Reinhart reiterated, however, that even with the recalculated figures, the core finding of the research — that high debt is bad for the economy — remains true.

"We do not, however, believe this regrettable slip affects in any significant way the central message of the paper or that in our subsequent work," she said.

She notes that economic output during high debt periods is still less than half as much as what it is during low debt periods, even with updated figures.

"Herndon, Ash and Pollin have written a useful paper, finding a significant mistake in one of our figures, and helped reconcile why one result is out of line with all the other results in our original paper," she said.

"We have no issues with Herndon, Ash and Pollin for bringing attention to any data question regarding our work."