This does not have the fun dramatic flair of an Excel spreadsheet error, but this empirical analysis from Miles Kimball and Yichuan Wang is much more devastating to Reinhardt and Rogoff than anything we've seen yet. What Kimball and Wang did was actually set about to try to answer the causal question of whether high debt levels cause slow growth. And what they found is that there is no such evidence.
This is important, because as Kimball writes on his blog it really does seem like there ought to be at least a little evidence of this. The same Keynesian theory that predicts that increasing your deficit during a recession can spur growth also seems to say that high debt levels will create "crowding out" when you're not in a recession. But they ran the numbers and they don't find it. The statistical association between a high debt to GDP level and slow GDP growth appears in their data to come entirely from the fact that slow GDP growth leads to a high ratio. You rarely get a definitive empirical study, but this is pretty striking evidence.
And to step back a little bit, while Reinhardt & Rogoff out recently engaged in some pushback on Paul Krugman for alleged incivility and misrepresentation, I have to say that Kimball & Wang really sheds light on the core irresponsibility of their conduct. They had an empirical result that did not shed any evidence whatsoever on the direction of causation. They knew that it shed no evidence whatsoever on the direction of causation, because the paper is carefully worded and says that. But instead of following the paper up with subsequent research that was designed to shed light on the direction of causation, Rogoff in particular started writing op-eds and testifying before congress and doing high-profile speaking gigs that relied on a causal interpretation of his research that he knew perfectly well was not supported by the research. Academics face a lot of dilemmas when they want to cross the line into the world of policy advice and public intellectualism, but these two were not naifs. They were well-known economists involved in policy circles and public debates before "Growth in a Time of Debt" and they simply chose to skip from the correlation finding to the policy advice without investigating causation in any kind of rigorous way first.
Kimball & Wang tried to do the work and—oops!—there's no causal there there. Perhaps some other folks will take a pass at the data and find conflicting results, but that's the research program we should be talking about. In terms of theoretical underpinnings for the Kimball & Wang finding, I think Andy Harless offered one back in April: "In the 'long run' debt (1) should lead to austerity, which (2) should raise private investment, which (3) should increase growth." So the Reagan debt runup of the 1980s laid the groundwork for fiscal consolidation in 1990 and 1993 and a subsequent private investment boom. Maybe.