A Working Paper released earlier this week by Herndon, Ash and Pollin (HAP) of the University of Massachusetts identified some data processing errors in the widely cited 2010 paper “Growth in a Time of Debt”, by Reinhart and Rogoff (RR). These errors cast doubt on some of RR’s conclusions. Unfortunately, in the Working Paper and an April 17th opinion piece in the Financial Times by Robert Pollin and Michael Ash, claims about the empirical relationship between public debt and growth are exaggerated. HAP’s conclusion that countries with public debt ratios in excess of 90% grow no more slowly than countries with public debt ratios of 30% to 90% is incorrect and based on an inappropriate statistical test.
RR’s thesis is that there is a threshold for the debttoGDP ratio beyond which a country’s growth rate drops markedly. Although their previous work suggested that debt thresholds are “importantly countryspecific”, their 2010 paper suggested that for many countries the debt threshold was about 90% of GDP. A conclusion from the simple empirics in their 2010 paper is that a country’s growth rate is likely to drop once its public debt exceeded 90% of its GDP, but debt ratios below 90% had no significant impact on growth.
The following Table is based on the corrected RR data used by HAP in their Table 4. It shows an inverse relationship between public debt to GDP ratios and GDP growth. Growth rates are significantly slower for countries with debt ratios between 30% and 90% relative to countries with debt ratios less than 30%. There is no significant difference, however, in the growth rates of countries with debt ratios in the 30% to 60% and 60% to 90% ranges.
Debt /GDP 
Avg. Growth 
Avg. Growth Relative to <30% Debt/GDP (tstatistic) 
Observations 
< 30% 
4.17% 

426 
30%90% 
3.12% 
1.05% (5.74) 
639 
30%60% 
3.09% 
1.08% (5.43) 
439 
60%90% 
3.19% 
0.99% (3.93) 
200 
>90% 
2.17% 
2.01% (6.41) 
110 
90%120% 
2.41% 
1.77% (4.93) 
79 
>120% 
1.56% 
2.61% (4.80) 
31 
In the Financial Times Pollin and Ash state: “Using the Reinhart/Rogoff data, we found that the average GDP growth rate for countries carrying public debt levels greater than 90 percent of GDP was either comparable to or higher than those for countries whose debt ratios ranged between 30 percent and 90 percent.”
This assertion is based, in part, on the statistical test described in the notes to their Table 4. HAP tested the joint hypothesis that the 3.19% growth rate in countries with a debt ratio of 60% to 90% and the 2.41% growth rate in countries with debt ratios of 90% to 120% are both equal to the 3.09% growth rate for countries with debt ratios of 30% to 60%. HAP fail to reject this joint hypothesis, with a pvalue of .11.
HAP conducted a statistical test that is inappropriate for evaluating the RR claim of a debt ratio threshold at 90%. RR do not claim that debt ratios of 60% to 90% are associated with lower growth rates than debt ratios of 30% to 60%. It is unclear why HAP conducted a joint test and compared growth rates among countries with moderate debt. HAP failed to find significant differences in growth rates among countries with public debt ratios from 30% to 120% because they conducted a joint statistical test that included a hypothesis unrelated to the 90% threshold.
Using the same data, I conducted alternative statistical tests of the ReinhartRogoff claim that debt ratios in excess of 90% reduce growth compared to debt ratios in the 30% to 90% range:
 The 2.41% growth rate in countries with debt ratios of 90% to 120% is significantly lower (pvalue=.041) than the 3.12% growth rate in countries with debt ratios of 30% to 90%.
 The 2.17% growth rate in countries with debt ratios of 90% or more is significantly lower (pvalue=.002) than the 3.12% growth rate in countries with debt ratios of 30% to 90%.
In the countries and time periods used in the HAP study, average growth rates were significantly lower when debt ratios were above 90%. This empirical finding merely reflects an association between growth rates and debt/GDP. The threshold effect for debt ratios that RR describe is weakened by the adjustments and corrections noted by HAP. However, it is inaccurate to say that average growth rates in countries with debt ratios in excess of 90% are comparable or higher than growth rates in countries with 30% to 90% debt ratios.
The data used by RR, as corrected by HAP, show that growth is significantly slower in countries with debt ratios in excess of 90% compared to countries with debt ratios of 30% to 90%. Growth rate differences around a 90% debt threshold are less dramatic after making the corrections suggested by HAP. Although simple comparisons of average debt ratios and growth rates across countries and over time are illustrative, at best, the HAP critique has not changed the evidence; high public debt is associated with slower growth.
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