Reinhart and Rogoff's critics agree: more debt, slower growth
How should we aggregate the data into an informative bottom line? To Reinhart and Rogoff's critics, the natural approach is to take the average for each debt level across all years in all countries. This would, for example, give a country with 10 years of very high debt 10 times the weight of a country with only one year. Instead, Reinhart and Rogoff took an average growth rate for each country experiencing very high debt, then calculated the average across countries. In their approach, all countries with any experience of very high debt get the same weight.
Which approach makes more sense? That depends on the question you want to answer. Reinhart and Rogoff are trying to find the average country's growth rate during episodes of very high debt. Their critics are seeking the average growth rate of GDP when debt is very high. These are subtly different.
From a statistical perspective, your preference might depend on your judgment about what drives differences in economic growth at a given level of debt. If you think broad country characteristics such as geography or quality of governance are the most important, you might choose Reinhart and Rogoff's approach of averaging out the national idiosyncrasies to determine the experience of the "typical country." If you believe that country and time-specific factors such as domestic- policy decisions matter most, then you might want to weight all years equally to average out these one-time influences.
Betsey Stevenson and Justin Wolfers