Did Reinhart and Rogoff Flub a Major Statistic?

A much-cited figure on debt and growth comes under fire.

Bit of a bombshell in the econoblogosphere yesterday. Several economists from the University of Massachusetts are contesting one of the key findings by the authors of This Time is Different, a landmark study of financial crises and debt dynamics from Carmen Reinhart and Ken Rogoff. At issue is their observation that once the debt-to-GDP ratio passes 90%, growth slows down dramatically.

We should be careful about what we're actually refuting. Since this critique broke, there's been a bit of strengthening up Rogoff and Reinhart's claims in order to beat them down--claiming, for example, that Rogoff and Reinhart asserted that high debt mechanically causes low growth. I've interviewed both of them about their work, and they've always been most modest in their claims, emphasizing that they've isolated an empirical regularity, not causality. While the paper under question does speculate about possible vehicles for causality, its claims are more modest than both its critics, and those who have bandied about the 90% statistic, would have you believe.

Why are there thresholds in debt, and why 90 percent? This is an important question that merits further research, but we would speculate that the phenomenon is closely linked to logic underlying our earlier analysis of “debt intolerance” in Reinhart, Rogoff, and Savastano (2003). As we argued in that paper, debt thresholds are importantly country-specific and as such the four broad debt groupings presented here merit further sensitivity analysis. A general result of our “debt intolerance” analysis, however, highlights that as debt levels rise towards historical limits, risk premia begin to rise sharply, facing highly indebted governments with difficult tradeoffs. Even countries that are committed to fully repaying their debts are forced to dramatically tighten fiscal policy in order to appear credible to investors and thereby reduce risk premia. The link between indebtedness and the level and volatility of sovereign risk premia is an obvious topic ripe for revisiting in light of the more comprehensive cross-country data on government debt.

Of course, there are other vulnerabilities associated with debt buildups that depend on the composition of the debt itself. As Reinhart and Rogoff (2009b, ch. 4) emphasize and numerous models suggest, countries that choose to rely excessively on short term borrowing to fund growing debt levels are particularly vulnerable to crises in confidence that can provoke very sudden and “unexpected” financial crises. Similar statements could be made about foreign versus domestic debt, as discussed. At the very minimum, this would suggest that traditional debt management issues should be at the forefront of public policy concerns.

I've seen more than one suggestion today that Rogoff and Reinhart must have deliberately or subconsciously biased their work because they're such mad advocates of fiscal austerity. But I interviewed Rogoff about the fiscal cliff last fall, and he was emphatic that we should not simply slam on the brakes and cut spending drastically, immediately. In fact, he was moderately dovish on stimulus. For example, he said "Back in 2008-9, there was a reasonable chance, maybe 20% that we’d end up in another Great Depression. Spending a trillion dollars is nothing to knock that off the table."

Rogoff is basically an austerity moderate: he thinks we should be spending a little more now, while making plans to cut back in the future. And note that the main vehicle by which they suggest high debt causes slow growth is . . . that it forces sudden fiscal contraction.

That said, many more radical austerity hawks have naturally been drawn to that 90% figure. Such a lovely, round, precise number is bonza for stump speeches and TV sound bytes, and unsurprisingly, it's been found in a lot of them. So it matters whether it's in error. And it does seem to be at least somewhat in error.

The UMass authors (heretofore to be known as Herndon et al) argue that there are three major problems with Rogoff and Reinhart's work, or at least with the claim that very high debt causes negative average growth rates:

1. They excluded the immediate postwar-growth years for Australia, Canada, and New Zealand.

2. There is a coding error in the spreadsheet which caused them to exclude the first five countries in their analysis: Austria, Australia, Canada, Belgium, and Denmark.

3. They weighted each country's growth rate during high-debt episodes equally, rather than by the number of years for which the debt persisted.

Number one is arguably the most troubling, but funnily enough, it is mostly taken care of by the coding error. We're actually arguing mostly about New Zealand.

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Herndon et al. argue that New Zealand, plus the decision to weight by country, instead of the number of years that each country was in debt, lowers the growth rate during high-debt episodes from a somewhat robust 2.2% average to a terrible -0.1% average. Basically, they're arguing that because New Zealand had one year of very high debt and very bad growth, when you weight all the countries equally, you multiply that one bad year into a spurious "tipping point" where high debt destroys your GDP growth rate.

Obviously this is a problem. I'm unable to tell exactly how much of a problem, because the country-year method is also arguably problematic. The years that a country spends in debt are serially correlated--which is to say that if you had a debt load above 90% of GDP last year, you're much more likely to have a similar debt load this year than a country which had a debt load in the 30% of GDP range. So weighting by country year is also likely to produce problems with your data. You could argue about how to calculate this for years--and I hope that these guys, and Rogoff/Reinhart, will do just that.

Frustratingly, though the authors of the paper break out the results in various ways, the labelling is not very clear, and as far as I can tell they do not show you what the data looks like if you put all the New Zealand & miscoded years back, but use the Rogoff/Reinhart weighting method. I'd really like to see this to get a sense of how much of their dispute hinges on omissions, and how much over disagreements about weighting methods.

Nonetheless, I think it's fair to say that a result should not hinge on a single bad year from New Zealand. And Herndon et al are arguing that the "strong" version of Reinhart-Rogoff, where debt levels of above 90 of GDP are actually correlated with negative growth rates, is almost entirely driven by that one bad year, plus the choice of weighting method.

This is not, to put it mildly, a very robust result. The question remains: how much does it matter?

As a policy matter, in my humble opinion is: not at all. As I say, critics of Rogoff-Reinhart--including Herndon et al--have been rather overstating two things:

1. The extent to which deficit hawkery among policy wonks rests on this single paper from 2010

2. The extent to which policy was made based on the much-bandied 90% figure.

To take the first point, the 2010 paper was not the only paper which has found that debt is associated with economic slowdowns, and Rogoff and Reinhart are not the only economists who have argued that too much debt is a drag on economic growth. They aren't even the only people who've argued for a tipping point.

In fact, if you are among the many left-of-center people who credit Bill Clinton's policies for the economic boom of the late 1990s, you believe that too much debt is a drag on economic growth. That's because the only even remotely plausible mechanism for Clinton's wondrous powers of economic restoration lies in the 1993 deficit reduction bill, which is supposed to have freed up capital to be invested in the real economy rather than getting absorbed by government borrowing. So if you've been excoriating George Bush's poor economic management, and comparing it unfavorably with Bill Clinton's responsible stewardship, surprise! You agree with Reinhart and Rogoff.

And you're not alone. I think it's fair to say that most economists and wonks think that at some level, government borrowing becomes a problem. And I'd guess the majority think that the problems kick in somewhere around the 100% of GDP mark.

To the second point, Reinhart and Rogoff had, to a first approximation, zero actual effect on policy.

I'll explain that in a minute. But first, a little aside for those who have not been following the Great Austerity Debate at home.

The Great Austerity Debate, which has been raging across blogs and think tanks panels for a couple of years now, is a very odd proxy battle in which mostly American pundits have fierce debates over European budget policy. This is the wonk version of those weird Cold War side conflicts, where you can't attack the Soviet Union directly, so instead you invade Paraguay.

To be sure, undoubtedly many American pundits would have vague opinions about British budget policy even if we weren't in the middle of a global financial crisis. But as it happens, I spent several years covering European budget policy, and currency rules, and other related policy topics, just before the financial crisis hit. And I can't recall Americans working for American universities or Ameircan think tanks or American news outlets ever got into furious, vengeful disputes with each other over the correct level of Irish domestic spending, or Greek pension reform.

I pause to note this because Reinhart and Rogoff were most influential in American policy rhetoric--but almost all of the austerity that Reinhart and Rogoff are supposed to have caused occurred in Europe. And for the life of me, I cannot understand why anyone thinks that this paper caused European governments to do anything.

There are basically three batches of austerity that the Great Austerity Debate has covered: Britain, the peripheral members of the eurozone (Portugal, Ireland, Italy, Greece, and Spain, or the PIIGS), and aspiring eurozone members like Estonia. Austerity in these places happens for different reasons, none of which have much to do with Reinhart and Rogoff.

Britain got austerity because that's what the Tories who formed their government campaigned on--in spring of 2010, just as the paper in question was making its way into the world. I've talked to British economics officials about this, and to the best of my memory, Reinhart-Rogoff never came up. Britain is a small, very open economy, and there are legitimate worries that stimulus will "leak" into other nations--or trigger a debt crisis. And you definitely don't need R&R to have those worries; there's quite a large volume of literature on that sort of thing.

Austerity in the PIIGS is driven by the fact that their borrowing costs were spiralling upward until the rest of the eurozone (read: Germany) bailed them out. Germany is not working on some elaborate theory of debt dynamics; they are simply trying to minimize their taxpayers' exposure to a possible default, and make the citizens of the PIIGS pay as much of the burden of restructuring as possible. And since the PIIGS cannot borrow money affordably without German assistants, they have had no choice but to embrace austerity. The result would have been the same no matter what Reinhart and Rogoff found--unless they'd found a money fairy who would airdrop billions of dollars into the eurozone periphery without worrying about getting paid back.

Estonia did austerity because it was trying to join the euro, and maintaining their eligibility to join the euro meant that they could neither inflate, nor run massively large budget deficits. Now, you can argue that this was a bad idea; I myself thought that this was rather like going on a crash diet so you'd be eligible for a suicide cult. But again, it had nothing to do with Reinhart and Rogoff; Estonia's europhilia is, as far as I know, mostly about a fervent desire to get themselves as far as possible from Russia's sphere of influence.

So what about the United States, the actual meta-subject of all these passionate disputes over European budget policy?

Paul Ryan cited the 90% figure in his budget, and I've heard other conservative budget wonks use it. But I'm unable to tell whether they're relying on "Strong" Rogoff and Reinhart (negative growth over 90% of debt), or the weaker claim that growth over 90% is associated with slower growth, which it is. And those same politicians and wonks were opposed to massive stimulus in 2009, before Reinhart and Rogoff (2010) came out.

(Just as many of those on the other side seem to find that 90% figure much more interesting and important now that it has apparently been at least partially refuted). I think there is a roughly 0% chance that US economic policy would be detectably different if Reinhart and Rogoff had never been published.

This is obviously going to be embarassing for Reinhart and Rogoff, because coding errors always are, and especially when your coding error produced a widely cited figure. To point out the obvious, conservative wonks and politicians should stop citing that result.

And to point out the somewhat-less-obvious, people on all sides should be cautious about lovely, round numbers. Even if there had been no coding error, no disagreements about the country weights, this still would have been one number from one study. People were relying on this figure because it gave the illusion of precision. For some stupid reason, things sound more like a fact if there's a number attached.

On the flipside, no one should be acting as if discrediting this single number somehow defeats the hawkish arguments over government borrowing. Even if this one number is wrong, there is still ample reason to worry about debt dynamics and crowding out--some of that evidence from Reinhart and Rogoff, but also from many other sources. Indeed, Herndon et al show a relationship. They say that this relationship is not statistically significant. But "not statistically significant" is not the same as "unlikely to be true". There is other empirical work, and some good theoretical reasons, to think that too much debt is dangerous.

The reasons for debt hawkery can certainly be argued with. But they neither stand nor fall on a single paper, much less a single number from it.