The economic literature is full of excellent articles that are not read outside small academic circles. There are, however, important exceptions. “Growth in a Time of Debt”, by Carmen R. Reinhart and Kenneth S. Rogoff, published in the American Economic Review (Papers and Proceedings), May 2010, is one of these exceptions.

Technically speaking, the paper is not particularly sophisticated. But it conveys a strong message: high public debt levels reduce economic growth. To prove this point, Reinhart and Rogoff looked at historical data for 20 advanced economies. They found that “median growth rates for countries with public debt over roughly 90% of GDP are about one percent lower than otherwise”.

Policymakers, especially in Europe, have often quoted the work of Reinhart and Rogoff to provide an intellectual foundation to the fiscal austerity policies that they have used to try to address the ongoing Eurozone crisis.

But just a few days ago, this powerful intellectual structure cracked.

## Formulagate

Last week, Thomas Herndon, Michael Ash, and Robert Pollin published a working paper that casts serious doubts on the validity of Reinhart’s and Rogoff’s analysis.

Herdon, Ash, and Pollin argue that the results of Reinhart and Rogoff heavily depend on some unorthodox methodological choices. Even more importantly, they uncovered an error in one of the Excel formulas used by Reinhart and Rogoff to compute averages of public debt and growth across countries.

Once more orthodox methodological choices are applied and the coding errors removed, Herdon, Ash and Pollin obtain results that look quite different from those reported by Reinhart and Rogoff.

The critique of Herdon, Ash and Pollin has quickly become very popular on economics blogs, with economists of the calibre of Nobel Prize laureate Paul Krugman being particularly vocal about the Reinhart and Rogoff fiasco.

So, now that Reinhart and Rogoff have been proved wrong, should we expect a change in policy in Europe?

The answer to this question involves two considerations. First, Reinhart and Rogoff have made mistakes, but are probably not completely wrong.

Second, independently from the mistakes, their paper does not justify fiscal austerity in times of recession and the policymakers who use it for this purpose either never read it or, if they read it, did not understand it.

## Correct formula, similar story

In their paper, Herdon, Ash and Pollin report that average annual GDP growth is 2.2% in countries carrying a debt to GDP ratio above 90%, 3.2% in countries with debt to GDP ratio between 30% and 90%, and 4.2% in countries with debt to GDP ratio below 30%.

Reinhart and Rogoff report both average and median growth rates. Their average growth rates are similar to those of Herdon, Ash and Pollin for countries with debt to GDP ratio below 90%.

But for countries above the 90% threshold, they indicate that average growth is -0.1%.; that is, much lower than the 2.2% reported by Herdon, Ash and Pollin. It is indeed in the computation of this -0.1% that Reinhart and Rogoff have apparently used the wrong Excel formula.

Median growth rates of Reinhart and Rogoff are instead comparable to the average growth rates of Herdon, Ash and Pollin.

One can certainly blame Reinhart and Rogoff for the inappropriate methodological choices and sloppy calculations. But the “correct” results of Herdon, Ash, and Pollin do confirm that high levels of debt are associated with lower growth. The adverse effect of debt is not as strong as it would appear from Reinhart’s and Rogoff’s data, but it is still large.

A simple numerical example based on Herdon, Ash and Pollin’s findings can help understand the point. Consider two countries that initially have the same level of per-capita income: one grows at 2.2% a year (the growth rate of countries with debt above 90% of GDP) and the other grows at 3.2% a year (the growth rate of countries with debt between 30% and 90% of GDP).

After 45 years, per-capita income in the second country would be 1.5 times the per-capita income in the first country. After 60 years (the time horizon of Herdon, Ash and Pollin’s analysis), per-capita income in the first country would be more than 1.75 times per-capita income in the first country.

So, Reinhart and Rogoff got the numbers wrong, but Herdon, Ash, and Pollin are not telling a substantially different story.

## Wrong formula, wrong interpretation

Saying that countries grow faster if they carry lower debt does not provide any intellectual support to the fiscal austerity approach currently undertaken in Europe.

In this sense, Reinhart’s and Rogoff’s article, independently from the mistakes that have now been uncovered, has been misinterpreted (or misused) by European policymakers. There is nothing in that paper that supports the adoption of draconian fiscal policies to balance the budget in times of recession.

The policy implication of Reinhart and Rogoff, which also arises from Herdon, Ash and Pollin’s analysis, is that countries should avoid excessively high debt to GDP ratios in the long term. This does not require fiscal austerity, especially during cyclical recessions.

In fact, the most effective way to maintain the debt to GDP ratio under control is to adopt a countercyclical fiscal policy. This means that in times of recession, fiscal policy should be expansionary (lower taxation, higher expenditure); conversely, in times of expansion, fiscal policy should be contractionary (higher taxation, lower expenditure).

The countercyclical use of fiscal policy guarantees that the deficits realised during recessions are compensated by the surpluses realised in expansions, so that there is no long-term accumulation of debt.

Moreover, such a countercyclical fiscal policy would help stabilise the cyclical fluctuations of the economy, with positive effects on the long term growth potential of the economy.

Economists will long discuss the mistake in the formula used by Reinhart and Rogoff. But those policymakers who are insisting on fiscal austerity as a way out of the European crisis are making a much bigger mistake — a mistake that cannot be blamed on Reinhart and Rogoff.