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Monday, April 22, 2013

Further insights on the Reinhart & Rogoff Research Controversy

James Hamilton at Econbrowser has written a nice summary of the major difference in opinion between the UMass students who challenged the Reinhart & Rogoff paper "Growth in a Time of Debt".   Simply put, if you have a handful of nations that persistently run debt > .9GDP, they will make up a large proportion of the sample.  How to weight them?  Do you weight the sample by incident or by nation?  The students argue by incident;  Reinhart - Rogoff did it by nation.   Is that clear?  Maybe using specific nations will help (quoting Hamilton):


"Now let's take a look at the details by which [the UMass students] 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%. ... the correct thing to do would be to act as if you have 19 observations ... 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 [the UMass students] 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."

Seems like a pretty obvious choice to me.