How an Excel error fueled panic over the federal debt

One of the most fearsome statistics in the war against the federal deficit has always been the country’s ratio of debt to gross domestic product. When this ratio reaches 90%, the argument goes, watch out -- lower economic growth is on the horizon. And that’s scary, because that’s where the U.S. has been heading.

This idea comes from Harvard economists Ken Rogoff and Carmen Reinhart, who featured it in a 2010 paper and popularized it in a book entitled “This Time is Different: Eight Centuries of Financial Folly.�

Since then, the stat has been cited countless times, including by Rep. Paul D. Ryan in rationalizing the draconian spending cuts in his proposed budgets. Now it turns out the authors may have counted wrong.

A new study by three researchers at the University of Massachusetts finds that Rogoff and Reinhart made several mistakes that invalidate their thesis.

In their analysis of growth rates of 20 industrialized countries, including the U.S., from the postwar period through 2009, Rogoff and Reinhart excluded data for three countries that had both high debt-to-GDP and high economic growth, which contradicted their finding. They tweaked other figures in a way that minimized overall growth rates for some high debt/GDP countries.

Most important, they made a spreadsheet error that resulted in their leaving five countries out of an all-important average of countries with higher than 90% debt-to-GDP ratios. By restoring the full average, the UMass authors say, the growth rate for countries in that range becomes 2.2%, not the -0.1% cited by Rogoff and Reinhart. That makes the average growth rate at that ratio “not dramatically different than when debt/GDP ratios are lower.�

Rogoff and Reinhart haven’t yet responded to the UMass paper. But if the new analysis holds up, it knocks a key leg out from under the argument that our economic growth depends on cutting the deficit and reducing the national debt without delay.

One irony of the finding stems from the fact that the debt-to-GDP ratio always was something of a heffalump. As economist Robert Shiller pointed out in 2011, yoking the two statistics together doesn’t necessarily tell you anything useful. Debt is measured in currency, he observed; GDP is measured in currency units per year. But there’s “nothing special about using a year.... A year is the time that it takes for the Earth to orbit the sun, which, except for seasonal industries like agriculture, has no particular economic significance.�

If GDP were conventionally measured not over a single year but over five years, or 10, the ratio would look much lower -- indeed, that ratio might make more sense, because debt typically comes due over the long term, not in a year.

The one-year juxtaposition, however, did make for a convenient rhetorical yardstick because it generated big numbers, and as we all know, extreme numbers are the devil’s debating tools.

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