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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The strange death of boozy Britain: why are young people drinking less?

Ditching alcohol for work.

Whenever horrific tales of the drunken escapades of the youth are reported, one photo reliably gets wheeled out: "bench girl", a young woman lying passed out on a public bench above bottles of booze in Bristol. The image is in urgent need of updating: it is now a decade old. Britain has spent that time moving away from booze.

Individual alcohol consumption in Britain has declined sharply. In 2013, the average person over 15 consumed 9.4 litres of alcohol, 19 per cent less than 2004. As with drugs, the decline in use among the young is particularly notable: the proportion of young adults who are teetotal increased by 40 per cent between 2005 and 2013. But decreased drinking is not only apparent among the young fogeys: 80 per cent of adults are making some effort to drink less, according to a new study by consumer trends agency Future Foundation. No wonder that half of all nightclubs have closed in the last decade. Pubs are also closing down: there are 13 per cent fewer pubs in the UK than in 2002. 

People are too busy vying to get ahead at work to indulge in drinking. A combination of the recession, globalisation and technology has combined to make the work of work more competitive than ever: bad news for alcohol companies. “The cost-benefit analysis for people of going out and getting hammered starts to go out of favour,” says Will Seymour of Future Foundation.

Vincent Dignan is the founder of Magnific, a company that helps tech start-ups. He identifies ditching regular boozing as a turning point in his career. “I noticed a trend of other entrepreneurs drinking three, four or five times a week at different events, while their companies went nowhere,” he says. “I realised I couldn't be just another British guy getting pissed and being mildly hungover while trying to scale a website to a million visitors a month. I feel I have a very slight edge on everyone else. While they're sleeping in, I'm working.” Dignan now only drinks occasionally; he went three months without having a drop of alcohol earlier in the year.

But the decline in booze consumption isn’t only about people becoming more work-driven. There have never been more alternate ways to be entertained than resorting to the bottle. The rise of digital TV, BBC iPlayer and Netflix means most people means that most people have almost limitless choice about what to watch.

Some social lives have also partly migrated online. In many ways this is an unfortunate development, but one upshot has been to reduce alcohol intake. “You don’t need to drink to hang out online,” says Dr James Nicholls, the author of The Politics of Alcohol who now works for Alcohol Concern. 

The sheer cost of boozing also puts people off. Although minimum pricing on booze has not been introduced, a series of taxes have made alcohol more expensive, while a ban on below-cost selling was introduced last year. Across the 28 countries of the EU, only Ireland has higher alcohol and tobacco prices than the UK today; in 1998 prices in the UK were only the fourth most expensive in the EU.

Immigration has also contributed to weaning Britain off booze. The decrease in alcohol consumption “is linked partly to demographic trends: the fall is largest in areas with greater ethnic diversity,” Nicholls says. A third of adults in London, where 37 per cent of the population is foreign born, do not drink alcohol at all, easily the highest of any region in Britain.

The alcohol industry is nothing if not resilient. “By lobbying for lower duty rates, ramping up their marketing and developing new products the big producers are doing their best to make sure the last ten years turn out to be a blip rather than a long term change in culture,” Nicholls says.

But whatever alcohol companies do to fight back against the declining popularity of booze, deep changes in British culture have made booze less attractive. Forget the horrific tales of drunken escapades from Magaluf to the Bullingdon Club. The real story is of the strange death of boozy Britain. 

Tim Wigmore is a contributing writer to the New Statesman and the author of Second XI: Cricket In Its Outposts.