THE debate over government debt and its relationship to economic growth is at the forefront of policy debates across the industrialized world. The role of the economics profession in shaping the debate has always come under scrutiny.

In particular, attention has focused on the findings of the Harvard economists Carmen M. Reinhart and Kenneth S. Rogoff, whose 2009 book, “This Time Is Different: Eight Centuries of Financial Folly,” received acclaim for its use of hard-to-find historical data to draw conclusions about the origins and nature of financial crises and how long it takes to recover from them.

Ms. Reinhart and Mr. Rogoff have published several other papers, including a 2010 academic article, “Growth in a Time of Debt.” It found that economic growth was notably lower when a country’s gross public debt equaled or exceeded 90 percent of its gross domestic product.

Earlier this month, we posted a working paper, co-written with Thomas Herndon, finding fault with this conclusion. We identified a spreadsheet coding error — which Ms. Reinhart and Mr. Rogoff promptly acknowledged — that affected their calculations of growth rates for big economies since World War II. We also asserted that the two of them erred by omitting some data and improperly weighting other statistics. In an Op-Ed essay and appendix last week, Ms. Reinhart and Mr. Rogoff denied those accusations.

They referred to this debate as an “academic kerfuffle,” but we believe the debate has been constructive, because it has brought greater clarity over the ideas shaping austerity policies in both the United States and Europe.

The most important insight for anyone following this debate, and one that Ms. Reinhart and Mr. Rogoff acknowledge, is that there is no evidence supporting the claim that countries will consistently experience a sharp decline in economic growth once public debt levels exceed 90 percent of G.D.P. Although the two of them partly backed away from that claim in a 2012 paper in The Journal of Economic Perspectives, they have now done so more definitively, saying the 90 percent figure is not “a magic threshold that transforms outcomes, as conservative politicians have suggested.”

However, Ms. Reinhart and Mr. Rogoff stubbornly maintain that “growth is about 1 percentage point lower when debt is 90 percent or more of gross domestic product,” a core finding of their 2010 paper.

There are serious problems with this claim. The most obvious is that the median growth figures they reported in the 2010 paper are distorted by the same coding error and partial exclusion of data from Australia, Canada and New Zealand that tainted their average growth figures. When we corrected for these errors, the difference in median economic growth rates was only 0.4 percentage points between countries whose public-debt-to-G.D.P. ratio was between 60 percent and 90 percent, and those where the ratio was over 90 percent (2.9 percent median growth, versus 2.5 percent). The difference between 0.4 percent and 1 percent is quite substantial when we’re talking about national economic growth.

(Ms. Reinhart and Mr. Rogoff have substantial disagreements with us about the proper selection and weighting of data. They elaborated on these points in their Op-Ed appendix. We have presented all our data, calculations and methodological arguments on the Web site of the Political Economy Research Institute at the University of Massachusetts, Amherst, where we teach.)

Our critique of Ms. Reinhart and Mr. Rogoff — one they have not adequately rebutted — emphasizes the fact that the relationship between public debt levels and G.D.P. growth varies substantially by country and over time.

Especially significant here is the pattern for the most recent decade in their postwar data set: 2000 to 2009. There is no evidence in these most recent years for any drop-off at all in economic growth when public debt exceeds 90 percent of G.D.P. While Ms. Reinhart and Mr. Rogoff have been commended for tracking down historic economic records going back centuries, we believe that the correlation between debt and growth over the last decade is more informative and useful for assessing present-day policy concerns than data from the post-World War II era or, say, the Industrial Revolution.

We agree with Ms. Reinhart and Mr. Rogoff that the United States and Europe face extremely difficult challenges in trying to recover from the 2007-8 financial crisis and the Great Recession that followed. Sadly, in our view, they abetted, or at least failed to stop, the use of their scholarship by politicians who latched on to their findings — in particular the now discredited 90 percent figure — to call for severe cuts in government budgets and services, layoffs of public-sector employees and tax increases.

What this debate has demonstrated is that policy makers cannot defend these austerity measures on the grounds that public debt exceeding 90 percent of G.D.P. will consistently produce sharp declines in economic growth.

History suggests that there is some threshold beyond which piling on public debt definitively yields lower economic growth, but there is no consensus on what that threshold is, and the evidence suggests, in any event, that the United States and Europe are not anywhere close to it.

Responsible policy makers must balance the relative costs and benefits of austerity at a time when high unemployment is exacerbating rising inequality, and threatening the social fabric of advanced industrial democracies around the world.

Robert Pollin and Michael Ash are professors of economics at the University of Massachusetts, Amherst.

Creative Commons License

Republish our articles for free, online or in print, under a Creative Commons license.

Robert Pollin is Professor of Economics at the University of Massachusetts in Amherst. He is the founding co-Director of the Political Economy Research Institute (PERI). His research centers on macroeconomics, conditions for low-wage workers in the US and globally, the analysis of financial markets, and the economics of building a clean-energy economy in the US. His latest book is Back to Full Employment. Other books include: A Measure of Fairness: the Economics of Living Wages and Minimum Wages in the United States, and Contours of Descent: US Economic Fractures and the Landscape of Global Austerity.