My data is from the World Economic Outlook Database 2012 (WEO 2012) produced by the International Monetary Fund, which provides as assortment of variables including GDP and net debt for 186 countries over the period 1980 to 2011. As well, the WEO 2012 database also had a conversion rate to put valuations into US Purchasing Power Parity dollars. I worked out per capita GDP in US PPP dollars and compared the average annual growth rates in per capita GDP to the net debt to GDP ratios for just the OECD countries. Here are the results of a LOWESS smooth between the growth rate of per capita GDP and the net debt to GDP ratio. Note that this first smooth is only for net debt to GDP ratios that are 0 or higher. For example, Chile, Finland and Norway are countries that have experienced negative net debt to GDP ratios.
There is a negative relationship between the ratio of net debt to GDP and per capita income growth when the net debt to GDP ratio is positive with a steeper drop-off after reaching a debt to GDP ratio of about 110 percent. However, the vast bulk of the observations are for debt to GDP ratios below 100 percent. Moreover, in the range below a net debt to GDP ratio of 100 percent, the relationship is negative but is fairly gently sloped. As well, no other variables are being controlled for. So is there a negative correlation between net debt to GDP and economic growth? Yes. Do high debt to GDP ratios slow economic growth? Well, that does not have an answer based on what I can see. There seems to be an association between high debt and lower growth but you cannot really conclude from just a simple correlation between economic growth and net debt to GDP ratios that one causes the other. It is disturbing that the negative correlation between these two variables without any attempt to control for other factors has carried so much weight in the "policy debate" world.
By the way, if you are interested in the LOWESS smooth that includes the negative net debt to GDP ratios, here it is.
What is interesting here is that when the net debt to GDP ratio is positive, there is a negative correlation between higher net debt and per capita GDP growth. However, having really large negative net debt to GDP ratios (as in the case of Norway) does not seem correlated with large increases in the growth rate. I had alot of fun with these plots.