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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Today's immigration figures show why the net migration target should be scrapped

We should measure different types of migration separately and set targets that reflect their true impact.

Today’s net migration figures show, once again, that the government has raised expectations of tackling migration and failed to deliver. This is a recipe for disaster. Today’s numbers run far in excess of 300,000 – three times over what was pledged. These figures don’t yet reflect the fallout from Brexit. But they do show the government needs to change from business as usual.

It has been the current strategy, after all, that led the British public to reject the European Union regardless of the economic risks. And in the process, it is leading the government to do things which err on the side of madness. Like kicking out international students with degrees in IT, engineering or as soon as they finish their degrees. Or doubling the threshold for investor visas, and in the process bringing down the number of people willing to come to Britain to set up business and create jobs by 82 per cent. Moreover, it has hampered the UK’s ability to step up during last year’s refugee crisis - last year Britain received 60 asylum applications per 1,000 people in contrast to Sweden’s 1,667, Germany’s 587 and an EU average of 260.

The EU referendum should mark the end for business as usual. The aim should be to transition to a system whose success is gauged not on the crude basis of whether overall migration comes down, irrespective of the repercussions, but on the basis of whether those who are coming are helping Britain achieve its strategic objectives. So if there is evidence that certain forms of migration are impacting on the wages of the low paid then it is perfectly legitimate for government to put in place controls. Conversely, where flows help build prosperity, then seeing greater numbers should surely be an option.

Approaching immigration policy in this way would go with the grain of public opinion. The evidence clearly tells us that the public holds diverse views on different types of migration. Very few people are concerned about investors coming from abroad to set up companies, create jobs and growth. Few are worried about students paying to study at British universities. On the other hand, low-skilled migration causes concerns of under-cutting among the low paid and pressure on public services in parts of the country that are already struggling.

The first step in a new approach to managing migration has to be to abolish the net migration target. Rather than looking at migration in the aggregate, the aim should be to measure different types of migration separately and set targets that reflect their true impact. In the first instance, this could be as simple as separating low and high skilled migration but in the long term it could involve looking at all different forms of migration. A more ambitious strategy would be to separate the different types of migration - not just those coming to work but also those arriving as refugees, to study or be reunited with their families.

Dividing different flows would not only create space for an immigration policy which was strategic. It would also enable a better national conversation, one which could take full account of the complex trade-offs involved in immigration policy: How do we attract talent to the UK without also letting conditions for British workers suffer? Should the right to a family life override concerns about poor integration? How do we avoiding choking off employers who struggle to recruit nationally? Ultimately, are we prepared to pay those costs?

Immigration is a tough issue for politicians. It involves huge trade-offs. But the net migration target obscures this fact. Separating out different types of immigration allows the government to sell the benefits of welcoming students, the highly skilled and those who wish to invest without having to tell those concerned about low skilled immigration that they are wrong.

Getting rid of the net migration target is politically possible but only if it is done alongside new and better targets for different areas of inward migration – particularly the low-skilled. If it is, then not only does it allow for better targeted policy that will help appease those most vocally against immigration, it also allows for a better national conversation. Now is the time for a new, honest and better approach to how we reduce immigration.

Phoebe Griffith is Associate Director for Migration, Integration and Communities at IPPR