The article of Reinhart and Rogoff (2010) as well as their descriptive analysis method have been criticised by a large number of authors. In particular, in their critical study Herdon et al. (2014) replicate the analysis of Reinhart and Rogoff in “Growth in a Time of Debt” and find out a series of coding errors as well as an inappropriate researching method. Starting from the dataset, Herdon et al. (2014) discover selective exclusion of data. Reinhart and Rogoff left out data of three countries experiencing high levels of public debt for a restricted period of time, whose exclusion according to Herdon et al. (2014) substantially influenced the final re-sults. Canada is the first country whose data has been omitted even if the public debt-to-GDP ratio was above the 90% threshold between 1946 and 1950. The Canadian mean GDP growth was 3% and the median GDP growth was 2.2% during these years. The data in the years be-tween 1946 and 1950 were omitted for Australia too, where the country had reached high debt levels but there was no decline of its growth rate. In the case of New Zealand, the years between 1946 and 1949 were excluded from the dataset. During these years New Zealand experienced debt levels above 90% of GDP but its real GDP growth rates were the following: +7,7%, +11,9%, -9.9% and +10.8%. Besides the exclusion of data, Herdon et al. (2014) dis-cover also a coding error where five countries in alphabetical order (Australia, Austria, Bel-gium, Canada and Denmark) were excluded unintentionally from the analysis. The third critic of Herdon et al. (2014) is turned to the weighting method used by the two authors to compute the mean and the median GDP growth of their dataset. Reinhart and Rogoff (2010) calculate the mean real GDP growth of each of the four debt categories computing the mean of the country-means in the respectively category. The mean of each country is calculated using the average of the real GDP growth for all observations of the country within the category. In this way the average growth of each country inside a category is as important as all others country averages in the group, without making any distinction between the years that a country has spent inside the category. Herdon et al. (2014) provide a good example to show why accord-ing to them the weighting methodology used by Reinhart and Rogoff results inappropriate, making each country count as a single observation. Herdon et al., (2014) find out that UK spent 19 years in the high debt-to-GDP category and its real GDP growth mean of all the years was 2.4%. This average counts as much as the value of New Zealand that spent only a year in the category and whose real growth was -7.6%. The medians of the sample were calcu-lated in the same way, i.e. the median of each category results as the median of each country´s median computed over all the years a country spent in a debt-to-GDP category. According to Herdon et al. (2014) the three errors discovered in Reinhart and Rogoff ‘s analysis have a great impact on the overall calculation and on the final results. Inserting the excluded and the missing data and calculating the mean GDP growth of the categories with a country-year weighting methodology, Herdon et al. (2014) find out different results for the category of public debt-to-GDP above 90%. In fact, instead of a mean GDP growth rate of -0.1% as re-sulted from Reinhart and Rogoff (2010) analysis, Herdon et al. (2014) find a 2.2% GDP growth rate for the high debt category. Finally, the critic of Herdon et al. (2014) deny the assumption that public debt has a negative influence on economic growth above the exoge-nously identified 90% threshold.
A second author develops a substantial critical analysis to Reinhart and Rogoff (2010), relying both on descriptive statistics and on formal econometric methodology. Égert (2015) employs for his article the dataset of Reinhart and Rogoff made public by Herdon et al., (2014). The descriptive analysis based first on average annual growth data for 1946 to 2009 points out similar results to the ones of Herdon et al. (2014), namely an average annual growth of 2.2% above the 90% threshold. In addition, Égert (2015) employs ten years non-overlapping aver-ages for real GDP growth in the sample. His second result shows that real GDP growth does not slow down after the 90% threshold, but between 30% and 60% of GDP when not using annual GDP data. Moreover, in order to overcome the issue of reverse causality, Égert com-pares lagged levels of central government debt with average annual growth rates. The outcome shows a decrease of the average annual growth rates of 1 percentage point when public debt increases from below the 30% threshold to between 30% and 60%. In line with his previous results, also in this case the level of public debt remains quite unchanged moving from be-tween 60% and 90% to above 90% of GDP. On the contrary, the analysis of historical data covering more than two centuries, from 1790 to 2010, delivers different results. The annual average growth rate decreases from 2.5 to 2.2 when central government debt increases from between 60% and 90% to above the 90% threshold. However, comparing average GDP growth with lagged central government debt reveals that growth rates above the 90% thresh-old are 0,1 points higher than between 60% and 90%. In order to give a better overview of the results by Reinhart and Rogoff (2010), Herdon et al. (2014) and Égert (2015), the following table displays a comparison and a summary of the main findings: