Statistic cited to defend austerity partially based on Excel error

How bad did Reinhart and Rogoff get it?

 

Reinhart and Rogoff

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.'"

Herndon, Ash and Pollin

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.

Reinhart and Rogoff Respond

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:

Does it even matter?

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.

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Will Euroscepticism prove an unbeatable advantage in the Conservative leadership race?

Conservative members who are eager for Brexit are still searching for a heavyweight champion - and they could yet inherit the earth.

Put your money on Liam Fox? The former Defence Secretary has been given a boost by the news that ConservativeHome’s rolling survey of party members preferences for the next Conservative leader. Jeremy Wilson at BusinessInsider and James Millar at the Sunday Post have both tipped Fox for the top job.

Are they right? The expectation among Conservative MPs is that there will be several candidates from the Tory right: Dominic Raab, Priti Patel and potentially Owen Paterson could all be candidates, while Boris Johnson, in the words of one: “rides both horses – is he the candidate of the left, of the right, or both?”

MPs will whittle down the field of candidates to a top two, who will then be voted on by the membership.  (As Graham Brady, chair of the 1922 Committee, notes in his interview with my colleague George Eaton, Conservative MPs could choose to offer a wider field if they so desired, but would be unlikely to surrender more power to party activists.)

The extreme likelihood is that that contest will be between two candidates: George Osborne and not-George Osborne.  “We know that the Chancellor has a bye to the final,” one minister observes, “But once you’re in the final – well, then it’s anyone’s game.”

Could “not-George Osborne” be Liam Fox? Well, the difficulty, as one MP observes, is we don’t really know what the Conservative leadership election is about:

“We don’t even know what the questions are to which the candidates will attempt to present themselves as the answer. Usually, that question would be: who can win us the election? But now that Labour have Corbyn, that question is taken care of.”

So what’s the question that MPs will be asking? We simply don’t know – and it may be that they come to a very different conclusion to their members, just as in 2001, when Ken Clarke won among MPs – before being defeated in a landslide by Conservative activists.

Much depends not only on the outcome of the European referendum, but also on its conduct. If the contest is particularly bruising, it may be that MPs are looking for a candidate who will “heal and settle”, in the words of one. That would disadvantage Fox, who will likely be a combative presence in the European referendum, and could benefit Boris Johnson, who, as one MP put it, “rides both horses” and will be less intimately linked with the referendum and its outcome than Osborne.

But equally, it could be that Euroscepticism proves to be a less powerful card than we currently expect. Ignoring the not inconsiderable organisational hurdles that have to be cleared to beat Theresa May, Boris Johnson, and potentially any or all of the “next generation” of Sajid Javid, Nicky Morgan or Stephen Crabb, we simply don’t know what the reaction of Conservative members to the In-Out referendum will be.

Firstly, there’s a non-trivial possibility that Leave could still win, despite its difficulties at centre-forward. The incentive to “reward” an Outer will be smaller. But if Britain votes to Remain – and if that vote is seen by Conservative members as the result of “dirty tricks” by the Conservative leadership – it could be that many members, far from sticking around for another three to four years to vote in the election, simply decide to leave. The last time that Cameron went against the dearest instincts of many of his party grassroots, the result was victory for the Prime Minister – and an activist base that, as the result of defections to Ukip and cancelled membership fees, is more socially liberal and more sympathetic to Cameron than it was before. Don’t forget that, for all the worry about “entryism” in the Labour leadership, it was “exitism” – of Labour members who supported David Miliband and liked the New Labour years  - that shifted that party towards Jeremy Corbyn.

It could be that if – as Brady predicts in this week’s New Statesman – the final two is an Inner and an Outer, the Eurosceptic candidate finds that the members who might have backed them are simply no longer around.

It comes back to the biggest known unknown in the race to succeed Cameron: Conservative members. For the first time in British political history, a Prime Minister will be chosen, not by MPs with an electoral mandate of their own or by voters at a general election but by an entirelyself-selecting group: party members. And we simply don't know enough about what they feel - yet. 

Stephen Bush is editor of the Staggers, the New Statesman’s political blog. He usually writes about politics.