How bad did Reinhart and Rogoff get it?
How bad did Reinhart and Rogoff get it?
It's always hard to work out how much policy is based on actual evidence, rather than the preconceptions of politicians and policymakers, but if any research has had an effect, it's surely Carmen Reinhart and Ken Rogoff's 2009 book This Time it's Different. It's the source of a claim which has outgrown its roots, and come to be cited in policy debates worldwide: that growth drops precipitously if the ratio of debt to GDP rises above 90 per cent. But now, a new paper  shows that that claim is partially the result of some astonishing oversight – including an error in the authors' Excel spreadsheet which excluded five countries from the analysis.
The book itself examines the link between the ratio of debt to GDP and growth rates in a raft of countries from World War II onwards. It finds that the higher the debt to GDP ratio, the lower real growth in those countries – and that there is a massive drop of debt to GDP ratios rise above 90 per cent, when the average growth rate becomes slightly negative.
To be fair to Reinhart and Rogoff (or R&R, as the cool kids do not say), the claim they make has been spun out of proportion by supporters keen to use it for political ends. The authors don't explicitly present the 90 per cent level as a cliff, just highlight what the data says; and they don't draw a causal inference, speaking, as they point out today , "of 'association' and not 'causality.'"
Even so, however, no other researcher has been able to replicate their "association", and no satisfactory explanation has been given as to why that is. Until now. The new critique, "Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff " by Thomas Herndon, Michael Ash and Robert Pollin (HAP, in economistspeak), is damning. It highlights three inaccuracies in R&R: "coding errors, selective exclusion of available data, and unconventional weighting of summary statistics".
Of those, the first is the most painful, albeit the least important. Reinhart and Rogoff simply added up their spreadsheet wrong. Mike Konczal's report on the paper illustrates the error : the blue box encloses the cells which R&R used to estimate the average; notice how it doesn't go all the way to the bottom? It should:
Missing out the last five rows – particularly Belgium, which had an average growth rate of 2.6 per cent during the years it had a debt to GDP ratio above 90 per cent – changes the average from -0.1 per cent to 0.2 per cent.
That error explains why no-one else could replicate R&R's findings – but the other two problems cast further doubt on whether even the 0.2 per cent figure is acceptable.
The HAP paper finds that R&R exclude certain years in certain countries for no documented reason. These include five years in which New Zealand has a debt to GDP ratio of over 90 per cent. With those years included, the average growth during New Zealand's six years above the threshold is 2.58 per cent; with them excluded it plummets to -7.6 per cent. Similar, albeit smaller, results are found for Australia and Canada, which are also excluded for short periods immediately after the war.
Finally, the HAP paper addresses the way in which R&R weight the results. Each country's data is averaged out, and then the average of those averages is found. That has the effect of valuing the 19 data points that the UK offers above 90 per cent debt/GDP – which average 2.4 per cent growth – with the same weight as the single year that New Zealand offers, when growth was -7.6 per cent.
With all the criticisms applied, the HAP paper reports that the average growth rate for years with a debt/GDP ratio is not -0.1 per cent, but 2.2 per cent. The steep drop-off at 90 per cent disappears; and the credibility of those who cited it  should take a hit.
But Reinhart and Rogoff aren't taking it sitting down. With an astonishing turnaround, they have issued a response  – published at 3am Boston time – which addresses the critique.
They concede the Excel error – "full stop" – but give a defence for the other two points. The full data for the years excluded was not available when they did their research, they argue, and so while it may make sense to include now, they cannot be held responsible for its absence:
This charge, which permeates through their paper, is one we object to in the strongest terms. The “gaps” are explained by the fact there were still gaps in our public data debt set at the time of this paper.
They also defend the odd choice of weightings, saying that:
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.
That is, they argue that just because there is more data for Britain than New Zealand, that does not mean Britain should be weighed more strongly, since that runs the risk that its "peculiarities" might alter the result.
The problem is that neither approach is obviously preferable. While R&R have a point, so to do HAP – which leaves us in the position of questioning the viability of such analysis in the first place.
But R&R make one final defence:
[Herndon et al], too, find lower growth associated with periods when debt is over 90 per cent. Put differently, growth at high debt levels is a little more than half of the growth rate at the lowest levels of debt.
They published this table, via Business Insider , to make the claim clearer:
But here's the thing: Reinhart and Rogoff's claim that the HAP paper agrees with them is more evidence of the supreme obviousness of their associative claim. "A high ratio of debt to GDP is correlated with low growth in GDP" is not an interesting finding, it's as close to a mathematical truism as economic statements come. Reinhart and Rogoff's paper is only important insofar as people have read two things into it which aren't true: firstly, that high debt to GDP ratios cause low growth; and secondly, that there is a discontinuity at 90 per cent, where things get much, much worse.
Reinhart and Rogoff themselves disavow the first claim , writing that:
We are very careful in all our papers to speak of "association" and not "causality".
And the second claim has been put to bed by the Herndon et al paper. There is no major drop at 90 per cent, because that was an artefact of incomplete data, errors in coding, and an odd weighting system.
(Incedentally, the 90 per cent discontinuity was a red herring anyway, because it only exists due to the fact that R&R broke up their data into bands 30 percentage points wide. Anyone focusing too heavily on it as a "magic number" simply failed to read the methods section)
And so we are left in much the same place we were beforehand. There remains no evidence that high debt causes GDP growth to slow, rather than slow GDP growth causing high debt. And that lack of evidence will have precisely no effect on public debate, because it's basically all data-free anyway.
There is one change, though. The thesis that Excel is the most dangerous piece software in the world  just got a massive boost.