Austerity is justified by an error

Cory Doctorow at Boing Boing writes:

A new paper called Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff by Thomas Herndon, Michael Ash, and Robert Pollin from UMass Amherst tries and fails to replicate the classic work on austerity, Carmen Reinhart and Kenneth Rogoff's 2010 Growth in a Time of Debt.Reinhart-Rogoff is the main research cited in favor of cutting public services and spending in bad economic times. It's a big part of why the local library is shutting down, why they're kicking people out of public housing, shutting down arts programs, slashing education and public transit, and laying off public employees. It purports to show that countries with high debt-to-GDP ratios of 90 percent or more are a "threat to sustainable economic growth."
In the new Amherst paper, the authors reexamine Reinhart-Rogoff's original data and conclude that the numbers don't add up. They show that Reinhart-Rogoff cherry-picked which years of high-debt GDP they measure, that they put their thumbs on the scales with "unconventional weighting" and made a "coding error" that "entirely excludes five countries, Australia, Austria, Belgium, Canada, and Denmark." This last error -- literally the wrong formula in a spreadsheet cell -- badly skews the outcome.
Here's the tl;dr: "the average real GDP growth rate for countries carrying a public debt-to-GDP ratio of over 90 percent is actually 2.2 percent, not -0.1 percent as [Reinhart-Rogoff claim]."
Diagram above is from the original paper; open diamonds are the incorrect figures from Reinhart-Rogoff, filled circles are the correct figures.  Here's the analysis from the original paper on the spreadsheet error:

A coding error in the RR working spreadsheet entirely excludes five countries, Australia, Austria, Belgium, Canada, and Denmark, from the analysis.  (RR averaged cells in lines 30 to 44 instead of lines 30 to 49.)   The omitted countries are selected alphabetically and, hence, likely randomly with respect to economic relationships. This spreadsheet error, compounded with other errors, is responsible for a -0.3 percentage-point error in RR's published average real GDP growth in the highest public debt/GDP category. It also overstates growth in the lowest public debt/GDP category (0 to 30 percent) by +0.1 percentage point and understates growth in the second public debt/GDP category (30 to 60 percent) by -0.2 percentage point.

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