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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"We repealed, then forgot": the long shadow of Section 28 homophobia

Why are deeply conservative views about the "promotion" of homosexuality still being reiterated to Scottish school pupils? 

Grim stories of LGBTI children being bullied in school are all too common. But one which emerged over the weekend garnered particular attention - because of the echoes of the infamous Section 28, nearly two decades after it was scrapped.

A 16-year-old pupil of a West Lothian school, who does not wish to be named, told Pink News that staff asked him to remove his small rainbow pride badge because, though they had "no problem" with his sexuality, it was not appropriate to "promote it" in school. It's a blast from the past - the rules against "promoting" homosexuality were repealed in 2000 in Scotland, but the long legacy of Section 28 seems hard to shake off. 

The local authority responsible said in a statement that non-school related badges are not permitted on uniforms, and says it is "committed to equal rights for LGBT people". 

The small badge depicted a rainbow-striped heart, which the pupil said he had brought back from the Edinburgh Pride march the previous weekend. He reportedly "no longer feels comfortable going to school", and said homophobia from staff members felt "much more scar[y] than when I encountered the same from other pupils". 

At a time when four Scottish party leaders are gay, and the new Westminster parliament included a record number of LGBTQ MPs, the political world is making progress in promoting equality. But education, it seems, has not kept up. According to research from LGBT rights campaigners Stonewall, 40 per cent of LGBT pupils across the UK reported being taught nothing about LGBT issues at school. Among trans students, 44 per cent said school staff didn’t know what "trans" even means.

The need for teacher training and curriculum reform is at the top of campaigners' agendas. "We're disappointed but not surprised by this example," says Jordan Daly, the co-founder of Time for Inclusive Education [TIE]. His grassroots campaign focuses on making politicians and wider society aware of the reality LGBTI school students in Scotland face. "We're in schools on a monthly basis, so we know this is by no means an isolated incident." 

Studies have repeatedly shown a startling level of self-harm and mental illness reported by LGBTI school students. Trans students are particularly at risk. In 2015, Daly and colleagues began a tour of schools. Shocking stories included one in which a teacher singled out a trans pupils for ridicule in front of the class. More commonly, though, staff told them the same story: we just don't know what we're allowed to say about gay relationships. 

This is the point, according to Daly - retraining, or rather the lack of it. For some of those teachers trained during the 1980s and 1990s, when Section 28 prevented local authorities from "promoting homosexuality", confusion still reigns about what they can and cannot teach - or even mention in front of their pupils. 

The infamous clause was specific in its homophobia: the "acceptability of homosexuality as a pretended family relationship" could not be mentioned in schools. But it's been 17 years since the clause was repealed in Scotland - indeed, it was one of the very first acts of the new Scottish Parliament (the rest of the UK followed suit three years later). Why are we still hearing this archaic language? 

"We repealed, we clapped and cheered, and then we just forgot," Daly says. After the bitter campaign in Scotland, in which an alliance of churches led by millionaire businessman Brian Souter poured money into "Keeping the Clause", the government was pleased with its victory, which seemed to establish Holyrood as a progressive political space early on in the life of the parliament. But without updating the curriculum or retraining teaching staff, Daly argues, it left a "massive vacuum" of uncertainty. 

The Stonewall research suggests a similar confusion is likely across the UK. Daly doesn't believe the situation in Scotland is notably worse than in England, and disputes the oft-cited allegation that the issue is somehow worse in Scotland's denominational schools. Homophobia may be "wrapped up in the language of religious belief" in certain schools, he says, but it's "just as much of a problem elsewhere. The TIE campaign doesn't have different strategies for different schools." 

After initial disappointments - their thousands-strong petition to change the curriculum was thrown out by parliament in 2016 - the campaign has won the support of leaders such as Nicola Sturgeon and Kezia Dugdale, and recently, the backing of a majority of MSPs. The Scottish government has set up a working group, and promised a national strategy. 

But for Daly, who himself struggled at a young age with his sexuality and society's failure to accept it, the matter remains an urgent one.  At just 21, he can reel off countless painful stories of young LGBTI students - some of which end in tragedy. One of the saddest elements of the story from St Kentigern's is that the pupil claimed his school was the safest place he had to express his identity, because he was not out at home. Perhaps for a gay pupil in ten years time, that will be a guarantee. 

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