Mike Konczal at the Next New Deal provides a thorough review of the work by Thomas Herndon, Michael Ash, and Robert Pollen, "Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff."
For a thorough review of the arguments you can turn to Mark Thoma or Tyler Cowen. If the RR paper were the only paper that showed a substantial slowdown in growth resulting from excessive levels of government debt, then yes, this a very concerning result. We should never place a large emphasis on one result. Fortunately, we didn't. The RR paper motivated a large literature and their results were found to be largely true by a number of other authors. Here are two key papers:
"The Real Effects of Debt" by Cecchetti, Mohanty, and Zampolli:
"The Impact of High and Growing Government Debt on Economic Growth. An Empirical Investigation for the Euro Area" by Checherita and RotherAt moderate levels, debt improves welfare and enhances growth. But high levels can be damaging. When does debt go from good to bad? We address this question using a new dataset that includes the level of government, non-financial corporate and household debt in 18 OECD countries from 1980 to 2010. Our results support the view that, beyond a certain level, debt is a drag on growth. For government debt, the threshold is around 85% of GDP. The immediate implication is that countries with high debt must act quickly and decisively to address their fiscal problems. The longer-term lesson is that, to build the fiscal buffer required to address extraordinary events, governments should keep debt well below the estimated thresholds. Our examination of other types of debt yields similar conclusions. When corporate debt goes beyond 90% of GDP, it becomes a drag on growth. And for household debt, we report a threshold around 85% of GDP, although the impact is very imprecisely estimated.
(Here is a similar published version)
These are two papers that come to mind that show supporting evidence in favor of the RR results. There are also papers that don't necessary support the RR hypothesis. Here is one that comes to mind are:This paper investigates the average impact of government debt on per-capita GDP growth in twelve euro area countries over a period of about 40 years starting in 1970. It finds a non-linear impact of debt on growth with a turning point—beyond which the government debt-to-GDP ratio has a deleterious impact on long-term growth—at about 90-100% of GDP. Confidence intervals for the debt turning point suggest that the negative growth effect of high debt may start already from levels of around 70-80% of GDP, which calls for even more prudent indebtedness policies. At the same time, there is evidence that the annual change of the public debt ratio and the budget deficit-to-GDP ratio are negatively and linearly associated with per-capita GDP growth. The channels through which government debt (level or change) is found to have an impact on the economic growth rate are: (i) private saving; (ii) public investment; (iii) total factor productivity (TFP) and (iv) sovereign long-term nominal and real interest rates. From a policy perspective, the results provide additional arguments for debt reduction to support longer-term economic growth prospects.
"Public Debt and Economic Growth. Is There a Casual Effect." by Panizza and Presbitero
The mistakes made in the Reinhart-Rogoff paper are concerning, but that find does not dismiss the results found by many other authors.This paper uses an instrumental variable approach to study whether public debt has a causal effect on economic growth in a sample of OECD countries. The results are consistent with the existing literature that has found a negative correlation between debt and growth. However, the link between debt and growth disappears once we instrument debt with a variable that captures valuation effects brought about by the interaction between foreign currency debt and exchange rate volatility. We conduct a battery of robustness tests and show that our results are not affected by weak instrument problems and are robust to relaxing our exclusion restriction.