As is often the case after several rounds of arguments, I feel that with the latest iteration of Reinhart & Rogoff responding to their critics what's happened is that we've lost the plot over what we're arguing about. TL;DR—when challenged, R&R retreat from a theoretical claim that bolsters the policy argument for austerity to a much weaker empirical claim that's irrelevant to the policy debate.
The longer version is that to the best of my knowledge nobody has ever proposed that a country deliberately attempt to run a budget that implies an endlessly rising debt to GDP ratio. Nor is there a dispute about the fact that given an inflation-targeting central bank, large deficits can stifle growth via the mechanism of high interest rates. Nor is there a dispute about the fact that a high debt:GDP ratio plus high interest rates can stifle growth via high debt service costs. The question at hand has always been whether a country that isn't suffering from high interest rates, crowding out, or large debt service costs ought to worry about its debt:GDP ratio.
For context, US government borrowing costs:
And US government debt service costs:
A statistical study that merely establishes the existence of a broad correlation between high debt and slow growth is uninteresting in this context because the correlation is easily explained by reverse causation (slow growth causes high debt:GDP ratio) and the interest rate channel. The question is whether there's some other reason—macroeconomic dark matter—to worry about debt accumulation even when the interest rate channel is irrelevant.
The allegedly interesting Reinhart and Rogoff empirical finding in this regard was the discovery of a debt tipping point that occurs at a debt:GDP ratio of 90 percent. Such a tipping point is difficult to explain in terms of interest rate dynamics, and thus is either a random statistical artifact or else evidence for the existence of dark matter. Since the original publication of their study, R&R have been engaged in a loud and noisy political activist campaign in favor of the dark matter interpretation of their research. What we see not only from their critics but also from their response is that there is no evidence of dark matter.
When pressed R&R disavow having evidence for any strong causal claims. It's also clear that their research method is inappropriate for judging the tipping point question. What they did was put countries into different buckets and discovered that growth was slower in the >90% bucket than in the <90% buckets. That's perfectly consistent with the existence of a theoretically uninteresting linear relationship. Owen Zidar is a PhD candidate at Berkeley so he needs to be polite about this, but he has a post that shows quite clearly that there is no discontinuity of the sort R&R claim to have discovered. R&R are out there arguing that the existence of a linear relationship constitutes come kind of confirmation or backing for their activist campaign, but that's not the case. It's backwards. Absent the tipping point you have no evidence for dark matter and no justification for the campaign of political activism. All you have is a rehashing of the well-known point that high debt levels often lead to high interest rates which often lead to low growth. That's an important and well-understood fact but it has zero implications for a country that doesn't have low interest rates.
Throught this whole process, R&R—and especially Kenneth Rogoff—keep equivocating about what causal links they're trying to establish and for what purpose. Attack their strong claims and they retreat to weaker ones. But to establish the political argument that Rogoff has advanced in sworn testimony before the United States Congress requires strong evidence that there's some reason other than interest rates and debt service costs that high debt burdens lead to slow growth. A broad correlation does not constitute evidence for that proposition. Only a tipping point does. And it's clear that the evidence for a tipping point is extremely weak and depends on a series of contestable methodological claims that smack of specification-searing.