Jim Hamilton (his text Time Series Analysis will be familiar to many who have suffered post-grad econometrics) has weighed in on the Reinhart and Rogoff v. Herndon, Ash, and Pollin debt debate (my effort is here)
His bottom line is the same as mine (whatever data set you look at, whatever way, more debt -> lower growth), but he has a great way of explaining the central tendency (mean v. average-average) debate.
Now let’s take a look at the details by which Herndon, Ash, and Pollin come to their numbers. First, they found a dumb error in Reinhart and Rogoff’s spreadsheet– Reinhart and Rogoff left the first 5 countries in the alphabet (Australia, Austria, Belgium, Canada, and Denmark) out of the set of cells selected for averaging. This is a numbskull error, but it turns out it would only have changed the estimate they reported by a few tenths of a percent.
The major differences come from a difference of opinion about how one should summarize the mean for these data. For example, the U.S. spent 4 years in this sample with debt levels above 90% of GDP, while Greece spent 19 years. How should we combine these two sets of observations?
One view one could take is that the expected growth rate when a country has a high debt level is a single number across all countries, that is, you expect the real growth rate for Greece when its debt is 90% to be exactly the same number as the real growth rate expected for the U.S. when its debt is 90%. If you further believed that the variance of Greek growth around this mean is the same as the variance of U.S. growth around this mean, then the correct thing to do would be to act as if you have 19 observations on the number of interest from Greece and 4 observations from the U.S., and take a simple average of those 23 numbers. In other words, you should base most of your inference on the data from Greece, because that is where you have the most observations. This is the approach that Herndon, Ash, and Pollin insist is the correct one to use.
Another view you could take is that the expected growth rates for the U.S. and Greece would be different even if the two countries had the same debt levels. From that perspective, there is a different expected growth rate for each particular country when it gets to the 90% debt level, and our goal is to estimate what that number is for a typical country. That view seems to underlie the method chosen by Reinhart and Rogoff, which was to estimate an average growth rate when debt is greater than 90% for the U.S., a separate average growth rate when debt is greater than 90% for Greece, and then take the average of those averages across different countries.
One could go a step further and spell out a complete statistical model of the view just espoused, for which the optimal way of combining different observations would weight the Greek average more heavily than the U.S. average (because the Greek average is estimated with greater precision), but not 19/4 times as heavily as Herndon and coauthors want (because the Greek average is estimating something different from the U.S. average). The optimal statistical estimate from that perspective would be somewhere in between the Reinhart-Rogoff number and the Herndon-Ash-Pollin number.
In any case, as seen in the table above, whichever number you used, you would still conclude that higher debt loads are associated with slower growth in the postwar advanced economy data set, just as they were in the postwar emerging economy data set, just as they were in the centuries-long individual country data sets, and as also was found to be the case in separate analyses of yet other data sets by Cecchetti, Mohanty and Zampolli (2011), Checherita and Rother (2010), and the IMF (2012), among others.