Three quick notes on the debate over the Reinhart and Rogoff kerfuffle.

First, in their response, they move far from what has been interpreted (often with their encouragement) as the key claim of their paper—that there exists a clear, well-defined threshold for a nation’s public debt (90 percent of total gross domestic product) above which debt exerts a “secular drag on growth.” In commenting on the Herndon, Ash and Pollin (HAP) paper which demonstrates that a few improvements to the paper’s methodology (including correcting a coding error) makes this well-defined threshold disappear, Reinhart and Rogoff (R&R, hereafter) point to the HAP finding that as debt ratios rise in their sample, growth rates are slightly (and not statistically significant) lower. R&R try to cast this as somehow supportive of their own original finding. But it’s really not. Nobody has denied that there could be a statistical association between high levels of debt and slow growth—the key argument was that the causality could easily run from slow growth to higher debt ratios. What R&R claimed, and more importantly what became crucially important in fiscal policy debates, was that 90 percent was a bright line of debt that policymakers dare not flirt with. In some arenas they have been more judicious than that, but in others they wrote things like:

“…we find that very high debt levels of 90% of GDP are a long-term secular drag on economic growth.”

This 90 percent line has been hugely influential—fears of debt stabilizing at some higher ratio essentially drive the now-ubiquitous calls for aggressive 10-year deficit reduction targets.

Second, a key issue raised by HAP is the somewhat odd weighting R&R used in their study. Given that the study has been interpreted (again, often with the authors’ encouragement) as identifying an iron law of public debt—that when it exceeds 90 percent of GDP it exerts a powerful drag on growth—one might think that the proper weight for each year during which a  given country’s debt ratio exceeds 90 percent should be given the same weight. But this is not what they did—instead, they calculated the within-country average growth rate for each year that its debt ratio exceeded 90 percent and then took that single average as one observation. Concretely, this means that the 19 years during which the UK saw debt ratios exceeding 90 percent are collapsed into a single observation and given no more weight than the single year during which New Zealand saw a debt ratio exceeding this (Mike Konczal explains this point well). Some have argued that “serial correlation” in country/year high debt episodes—particularly when the years are consecutive—might mean that each country/year observation is actually not providing another fully independent data point in their sample and that weighting each as such might be inappropriate. Maybe, but it’s a long way from this insight to thinking that a proper fix is that the “year” part of the country/year observation should be completely ignored and each high debt year for a given country should just be collapsed into one single data point.

Further, R&R have never been hugely clear about the economic transmission mechanism that allows high debt ratios to slow growth (indeed, they note that the most logical prime suspect—rising interest rates, do not seem to be up to the job of explaining this association). What they have strongly implied is that it is the problem of debt exceeding 90 percent is greatest when it comes in long-lived episodes rather than in one or two-year bursts (their latest paper on “debt overhangs,” in fact, focuses exclusively on episodes of debt exceeding 90 percent of GDP for five years or more).

Given this, one might think that  serial correlation would make their results stronger when one switches to country/year observations. That is, long-lived episodes of high debt (the 19 years in the UK) should be much more damaging to growth than one-off years that see debt barely move over the 90 percent threshold and then retreat (the one year of New Zealand data in their sample). But as HAP show, weighting each country/year observation equally (which should allow serial correlation to influence the results) actually makes most the R&R findings on debt exceeding 90 percent melt away.

Lastly, I should flag one other thing I didn’t raise yesterday on the issue of causality. The issue here, again, is that a statistical association of high debt ratios with slow growth could well be (in fact is more likely to be) driven by causality that runs from slow growth to high debt ratios, and the not the reverse causality that R&R strongly argue. In an interview with Dylan Matthews, Reinhart dismissed this:

“Reinhart dismisses these criticisms as wishful thinking. ‘We’re quite aware that you have causality going in both directions,’ she says. ‘But please point out to me what episodes from 1800 to the present have we had advanced economies who carried high levels of debt growing as rapidly or more rapidly than the norm.’”

This seems to miss the point, no? If the criticism is that your statistical association between high debt and slow growth is real but that the causality is different than you ascribe, you can’t defang this criticism simply by pointing again at the statistical association.