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A new International Monetary Fund Working Paper, Debt and Growth: Is There a Magic Threshold?, further discredits the claim, notoriously propounded by Carmen Reinhart and Kenneth Rogoff, and used by conservatives around the world to rationalize austerity policies, that a country's economic growth collapses once it crossed the 90% debt-to-GDP threshold. Earlier, graduate students at the University of Massachusetts had revealed errors in the professors' spreadsheet. When corrected, the supposed correlation disappeared. (For more on this, see John Cassidy's New Yorker article, The Reinhart and Rogoff Controversy: A Summing Up.)

Now, three IMF researchers "present[] new empirical evidence," analyzing "the relation between debt and growth over longer periods of time." Their

results do not identify any clear debt threshold above which medium-term growth prospects are dramatically compromised. On the contrary, the association between debt and medium-term growth becomes rather weak at high levels of debt, especially when controlling for the average growth performance of country peers
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As Danny Vinik explains in The New Republic:

Recessions reduce economic growth and often increase a country’s debt as automatic stabilizers kick in (as happened in the United States in recent years). Is slower growth the result of the higher debt or vice versa? Many took Reinhart and Rogoff’s analysis to mean it was always the former.

But IMF researchers Andrea Pescatori, Damiano Sandri, and John Simon try to correct for this by looking at growth not just in the following year, but over the next five, ten, and 15 year periods.

“If high debt (that is, debt above some threshold) operates as a drag on growth over anything but the short-run, however, we would expect to observe weak growth not only in the year after the debt ratio exceeds the threshold, but also during the subsequent years,” the authors write.

Over the ten and 15 year periods, higher debt is associated with just about the same economic growth. There’s no threshold at all.

The IMF researchers themselves conclude:
Our analysis of historical data has highlighted that there is no simple threshold for debt ratios above which medium-term growth prospects are severely undermined. On the contrary, the association between debt and growth at high levels of debt becomes rather weak when one focuses on any but the shortest-term relationship, especially when controlling for the average growth performance of country peers. Furthermore, we find evidence that the relation between the level of debt and growth is importantly influenced by the trajectory of debt: countries with high but declining levels of debt have historically grown just as fast as their peers. The fact that there is no clear debt threshold that severely impairs medium term growth should not, however, be interpreted as a conclusion that debt does not matter. For example, we have found some evidence that higher debt appears to be associated with more volatile growth. And volatile growth can still be damaging to economic welfare.

As in previous empirical studies, our analysis is still subject to potential endogeneity
concerns that should caution against drawing strong policy implications. However, by
mitigating the short-term and mechanical reverse causality problems whereby low growth leads to higher debt, we show that the prima facie case for debt thresholds is substantially weakened. We find no evidence of threshold effects over any but the shortest-term horizons. Furthermore, the remaining relationship between debt and growth is relatively muted and the magnitude is much smaller than the dramatic figures suggested in earlier studies. Notwithstanding this, because of residual issues that confound the interpretation of the medium-term relationship between debt and growth, we emphasize that this does not establish what the underlying structural relationship is. That must wait for more sophisticated work that can properly address the complex identification issues that characterized this area of research.

This is not to say that national debt never matters. But as Brad DeLong observes in Risks of Debt: not when interest rates remain low; inflation remains subdued; and stock prices are buoyant.
A country that spends and spends and spends and does not tax sufficiently will eventually run into debt-generated trouble. Its nominal interest rates will rise as bondholders fear inflation. Its business leaders will hunker down and try to move their wealth out of the corporations they run for fear of high future taxes on business. Real interest rates will rise because of policy uncertainty, and make many investments that are truly socially productive unprofitable. When inflation takes hold, the web of the division of labor will shrink from a global web he'd together by thin monetary ties to a very small web solidified by social bonds of trust and obligation--and a small division of labor means low productivity. All of this is bound to happen. Eventually. If a government spends and spends and spends but does not tax sufficiently.

But can this happen as long as interest rates remain low? As long as stock prices remain buoyant? As long as inflation remains subdued. My faction of economists--including Larry Summers, Laura Tyson, Paul Krugman, and many many others--believe that it will not. As long as stock prices are buoyant, business leaders are not scared of future taxes or of policy uncertainty. As long as interest rates remain low, there is no downward pressure on public investment. And as long as inflation remains low, the extra debt that governments are issuing is highly-prized as a store of value, helps savers sleep more easily at night, and provides a boost to the economy as it assists deleveraging and raises the velocity of spending.

Economists, you see, don't watch just quantities--the amount of debt a government has issued--but prices. And the prices of government debt are the rate of inflation, the nominal interest rate, and the level of the stock market as people trade bonds for commodities, bonds for cash, and bonds for stocks. And all three of these prices are flashing green: saying that markets would prefer and it would be better for the economy if government debt were growing at a faster pace than under current forecasts.

In short, under the economic circumstances that have prevailed since the beginning of the Great Recession (Lesser Depression?), our debt-to-GDP ratio is a red herring. The real issue is equitable economic growth.
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