The Relationship between Debt Levels and Growth

Rather than rehashing all the details of the dispute between Reinhart and Rogoff and their critics, some of which I addressed in an earlier post, let’s focus on what both sides agree on. If you combine data covering dozens of countries collected since the Second World War, you find that higher debt-to-G.D.P. ratios are associated with lower levels of G.D.P. growth. According to the paper by the three Amherst economists—Thomas Herndon, Michael Ash, and Robert Pollin—countries with debt-to-G.D.P. ratios below thirty per cent grew at an annual rate of 4.2 per cent; countries with debt-to-G.D.P. ratios of between thirty and sixty per cent grew at an annual rate of 3.2 per cent.

That’s an interesting finding, and it’s hardly surprising that Reinhart and Rogoff have seized upon it to argue that there isn’t anything new in the Amherst paper. But, wait a minute. Annual growth of 3.2 per cent doesn’t sound too bad. Is there a level of indebtedness at which growth ceases or turns negative? Reinhart and Rogoff argued that there was, and that’s what gave their pro-fiscal-consolidation message its potency. In the 2010 paper at the center of the dispute, they identified the threshold as a debt-to-G.D.P. ratio of ninety per cent. Once debt rose above that level, they said, the average growth rate was negative 0.1 per cent.

Ninety per cent wasn’t just any old figure. With large budget deficits and debt-to-G.D.P. ratios in the range of sixty to eighty per cent, many advanced countries, including the United States and Britain, were fast approaching the threshold of doom, or so it seemed. If you took Reinhart and Rogoff’s findings at face value, as many people did, it was hard to argue with the Hooveresque logic of, say, Osborne.

It turns out, however, that the ninety per cent threshold is phooey: it doesn’t exist. When the Amherst economists reworked Reinhart and Rogoff’s calculations to take account of programming errors and data omissions, they came up with a figure of positive 2.2 per cent for average growth in countries with a debt-to-G.D.P. ratio of ninety per cent or more. That’s less than 3.2 per cent—the figure for countries with debt ratios of sixty to ninety per cent—but it’s not zero, or negative.

Some defenders of Reinhart and Rogoff point out that a shortfall in growth of one per cent a year eventually compounds into big differences in living standards. That’s true, but there’s another note of caution about the data. If you eliminate from Reinhart and Rogoff’s sample countries with very high indebtedness—those with debt-to-G.D.P. ratios of more than a hundred and twenty per cent—and very low indebtedness—those with debt-to-G.D.P. ratios less than thirty per cent—the negative relationship between growth and debt is hard to discern. The scatterplot is all over the place, with perhaps a slight negative lean. In fact, after carrying out some formal tests, Herndon, Ash, and Pollin report that “differences in average GDP growth in the categories 30-60 percent, 60-90 percent, and 90-120 percent cannot be statistically distinguished.”

To sum up, there may well be a threshold at which high levels of public debt tend to be associated with very bad growth outcomes and financial crises, but it isn’t ninety per cent of G.D.P., or even a hundred per cent. Maybe it’s a hundred and twenty per cent, although that figure isn’t a firm one, either.

So far, I haven’t mentioned the issue of causation. Do high debts cause low growth, or vice versa? Theoretically, it could go either way. High levels of public debt, through their impact on interest rates and business confidence, can crowd out private-sector spending and reduce growth. But low growth depresses tax revenues and forces the government to spend more on things like unemployment insurance and food stamps. That increases the budget deficit, which necessitates the issuance of more debt.

Reinhart and Rogoff acknowledge this ambiguity. “Our view has always been that causality runs in both directions,” they said in their Times Op-Ed, “and that there is no rule that applies across all times and places … Nowhere did we assert that 90 percent was a magic threshold that transforms outcomes, as conservative politicians have suggested.”

Set aside the last sentence, which is another example of Reinhart and Rogoff trying to distance themselves from their intellectual protégés. Whichever way the causation goes, the issue has always been whether there was room for further fiscal stimulus, or whether debt levels were getting so high that further borrowing and spending was likely to be counter-productive. Back in 2010 and 2011, the Keynesians said there was room; the austerians said there wasn’t. Purely on the basis of the corrected Reinhart and Rogoff figures, there was, and is, room. In the United States, the ratio of net debt-to-G.D.P. is seventy-three per cent. In the United Kingdom, it is about the same. In Germany, it is about eighty per cent. In France, it is about ninety per cent.

How Seriously Should We Take Economics?

Since this post is getting long, and I’ve already addressed this issue at book length, I’ll try and keep it brief. Economics is a science—it proceeds via hypothesis and empirical testing—but it’s a soft and squishy one, and any argument to the contrary should be treated with great suspicion. Especially in macroeconomics, hard-and-fast laws are hard to find. So are stable parameters and reliable empirical studies. Often, about the best we can do is isolate general tendencies, and then look carefully to see whether they apply in the case under consideration.

Reinhart and Rogoff identified what they said was one such tendency, but they and the policy makers who seized upon this work pushed the argument too far. In Britain and Europe, great damage has been done as a result. In the United States, we’ve been more fortunate, but even here there are dangers. By raising payroll taxes and letting the sequester go into effect, we’ve recently introduced a little mini-austerity experiment of our own, the early results of which, as evidenced by that disappointing G.D.P. report, are hardly encouraging.

Illustration by Marc Rosenthal