17 April 2013

The 90 Percent Solution

Economic growth slows when public debt passes a threshold of 90% of GDP.

This factoid (or as economist prefer "stylised fact") had become part of the armoury of those defending austerity. It is now officially nonsense.

The idea came from a paper by Reinhart and Rogoff, the authors of an acclaimed book on financial crises, This Time Is Different: Eight Centuries of Financial FollyThe 90% myth however is from a different paper. That paper has recently been found to contain some errors of arithmetic which when corrected makes the 90 threshold disappear.

The paper has been criticised before, for example by Krugman , but now it is discredited. However I have always argued that the methodology, or the logic, was flawed. The two economists examined a vast dataset of countries with various levels of debt to GDP ratios. Here is how I explained the error of logic in an earlier post:
The paper simply slices the data into four sets where the debt ratio is below 30%, 30%-60%, 60%-90% and above 90% and then compares median and mean growth rates. So the 90% "threshold" is manufactured by the methodology. It does not emerge from the data.
In other words they chose 90% and so cannot conclude that 90% is a threshold. As an error of logic it is known as petitio principii or begging the question or a circular argument. What if they had cut the date into 20 % chunks instead. Would we have had an 80% threshold or a 100% threshold?

Indeed looking at the footnotes of the original paper we find that the authors were aware of this problem, (although it didn't prevent them boldly stating their conclusion):
The four “buckets” encompassing low, medium-low, medium-high, and high debt levels are based on our interpretation of much of the literature and policy discussion on what is considered low, high etc debt levels. ... Sensitivity analysis involving a different set of debt cutoffs merits exploration ...
At last, the notion of a threshold can be junked because of a mistake in a speadsheet. But don't let that put you off the book. It is in a different class altogether.

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