There has been a lot of discussion today on Reinhart and Rogoff’s work on Debt to GDP & future economic growth (see Mike Konczal, Krugman, CEPR, Brad Plumer, and the original critique from Herden, Ash, Pollin), so I wanted to highlight some work on this issue that I put together when helping Brad Delong and Laura Tyson on an IMF presentation on fiscal policy after the crisis.

I pulled data from R&R’s AER paper on debt to GDP and economic growth to see if there is any evidence of a break at a 90. Here are three preliminary conclusions and supporting graphs:

- Persistently 90+ Public Debt to GDP countries tend to grow less quickly over next 5 years, but the distribution of historical outcomes suggests that disaster scenarios are much less common than modestly slower 5 year growth for these countries.

- Nonparametric graphs of Public Debt to GDP and subsequent GDP growth show that
**there’s no break at a debt to GDP ratio of 90.** - The slope of this nonparametric graph is negative, which indicates that higher public Debt to GDP is associated with modestly slower subsequent growth.

*It’s important to note that these are not causal relationships! You should read Dylan Matthews nice post on how to interpret this correlation and whether causality goes the other way. And note that it is not at all obvious how (and by how much) changing Debt to GDP would affect subsequent economic growth in practice for a given country. For instance, high Debt to GDP countries with high interest rates are quite different than high Debt to GDP countries with low interest rates. Also, growth across decades and across countries is systematically different, so compositional effects are important to consider when interpreting this graph. And it’s certainly not a natural experiment. Keep these issues in mind when interpreting the following two graphs:*

Graph for point 1:

* This graph shows a comparison of subsequent 5 year per capita GDP growth for (A) countries that have had a Debt to GDP ratio above 90 for each of the last 5 years vs (B) those that haven’t. *

Graph for point 2 & 3 (which is also in this Delong Tyson presentation):

* I took all countries with Public Debt to GDP ratios above 50 and evenly divided them into 50 equalized sized bins of Debt to GDP*. Then I plot the mean of the outcome of interest for each bin. I made this because it would show clean breaks at a Debt to GDP ratio of 90 if they actually exist. The mean outcome of interest in this graph is cumulative GDP growth over the next 5 years. Again, this is a correlation, not a causal relationship. *

** I also capped Debt to GDP at 200 if it was above 200 in order to show everything on the same graph. This procedure doesn’t affect any bins in the region of interest (*

*i.e. 50 to 150).*

Is there even such a thing as “Nonparametric graphs”? We can graph non-parametric functions but is that the same thing as a non-parametric graph?

I noticed that too. Also, does the second graph actually show a nonparametric function? It looks like a simple linear regression, which is parametric. Since linear regression is the standard approach for this type of analysis, I think some clarification is warranted here.

And if it is a linear regression, I’d really like to see a graph of residuals and some examination of outliers. Just a link would be fine. I suspect that the small number of high debt-to-GDP ratio have too much influence on the slope.

I show mean outcomes by bin which is nonparametric, and a linear best fit line to help see the general (parametric) relationship

Kickass post!!

FYI Mike Konczal’s last name contains an “a”…

Thanks

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Reblogged this on owenzidar and commented:

This was my most popular post in 2013.