Kenneth Rogoff and Carmen Reinhart, the economists accused of getting their sums wrong in an influential study of the impact of high government debt, have hit back at their critics and defended their central claim.
The Harvard economists claimed that accusations of sloppy statistical analysis were misplaced and their central finding still stood that when government debt is above 90% growth is sent into reverse. Their argument has been quoted by politicians in defence of austerity measures.
The pair admit that researchers from the University of Massachusetts, Amherst, were right to point out a coding error that omitted several countries from an Excel spreadsheet of historical data used to make the calculations.
"It is sobering that such an error slipped into one of our papers despite our best efforts to be consistently careful," Rogoff and Reinhart said.
But after burning the midnight oil to check their calculations, Rogoff and Reinhart said they still found countries with debts that amount to more than 90% of GDP experienced much slower growth – the same conclusion reached in their original study.
Economist Dean Baker, at odds with academic economists who argue that high debt ratios harm growth, has labelled the R&R analysis bankrupt.
Baker and other Keynesians leapt on the Massachusetts study because the R&R hypothesis has been used repeatedly by right-wing politicians to justify their austerity policies.
Massachusetts professors Thomas Herndon, Michael Ash and Robert Pollin said in their critical report that when they repeated the R&R analysis over a longer timescale, which they argued made it more robust, they got a growth figure of 2.2%. Strikingly, they used data going back before the second world war, which they argued gave a longer perspective.
Pollin said R&R also distorted the results with weightings on countries that made little sense. He pointed to the inclusion of New Zealand's 1951 figures. In that year New Zealand's debts breached the 90% of GDP barrier and growth was minus 7.6%, weighing heavily on the overall result. Other years that distorted the data were included, he said.
"People make errors but when you combine the errors with the weighting that's where you get this result," said Pollin.
The scope of the study and the weighting applied to some countries in the study is key to the dispute.
R&R "objected in the strongest terms" to the criticism that they missed several years of data and supported their previous decision to apply controversial weightings.
"The 'gaps' are explained by the fact there were still gaps in our public debt data set at the time of this paper," they said. "Our approach has been followed in many other settings where one does not want to overly weight a small number of countries that may have their own peculiarities."
They also deflect criticism by arguing that they produced averages based on mean and median calculations. Rightwingers emphasised the mean figure, which showed growth of minus 0.1% in countries with more than 90% debt to GDP ratios, whereas they always preferred the median.
Is that the end of the matter? No. Paul Krugman, the Nobel prize winning Princeton economist, is incensed at the median/mean debate, saying R&R never disputed politicians who used the mean figure, especially Republican Paul Ryan, who cited it as the main reason to impose steep public spending cuts.
Like Dean, Krugman has never bought the line that high debts cause low growth. Instead he sees a negative causation: that low growth causes high debts. In his latest blog, he makes this point again.
And R&R, who were criticised for not releasing the coding and data sets for their study when it was first released, have similarly failed to provide a transparent view of their workings this time around. And until they do critics will continue to argue that their findings are based on selective data and unjustified weightings and poor analysis.