## Chart of the day, reverse-causality edition

April 18, 2013

This chart comes from Arindrajit Dube, who has a fantastic post chez Rortybomb on whether high debt causes lower growth or whether it’s the other way around. What you’re looking at is the famous Reinhart-Rogoff dataset, as made available by their critics (and Dube’s colleagues), Herndon, Ash and Pollin. Reinhart and Rogoff are the poster children for the statement that high debt loads cause lower growth, especially once those debt loads exceed 90%. But do they?

There does seem to be an inverse correlation between debt and growth, but Dube shows that the correlation is strongest at low levels of debt, below 30% of GDP, rather than at high levels of debt. Countries with debt of 30% of GDP have a significantly lower growth rate, on average, than countries with debt of 10% of GDP, while the numbers at debt ratios above 90% have much wider error bars and are much less useful.

But let’s grand the correlation, for the sake of argument: the next question is whether the correlation implies causation, and if so, which way the causation flows. Here’s Dube:

Here is a simple question: does a high debt-to-GDP ratio better predict future growth rates, or past ones? If the former is true, it would be consistent with the argument that higher debt levels cause growth to fall. On the other hand, if higher debt “predicts” past growth, that is a signature of reverse causality.

That’s what you’re seeing in the charts. Both of them have the same axes: GDP growth on the y-axis, and debt/GDP on the x-axis. Both of them plot the correlations in the dataset, with the dark line being the signal and the dotted lines showing the 95% confidence interval. And just as in the main dataset, the correlations are much clearer at low levels of debt/GDP than they are at higher levels.

But the two charts are different, all the same, especially at levels of debt/GDP above that 90% level. If you look at the left-hand chart, it shows that it really doesn’t matter how much debt you have: you’re likely to average about 3% GDP growth a year over the next three years. On the other hand, if you look at the right-hand chart, it shows that the more debt you have, you’re significantly more likely to have experienced low growth in the past three years.

In other words, the causation here seems about as clear as causal analysis can ever be: low growth causes high debt, rather than high debt causing low growth. Indeed, once you get past 90% of GDP, your debt load doesn’t seem to have any significant effect on future growth at all!