How can something so wrong seem so right?

In a generally righteous post, CGD’s Charles Kenny repeatedly claims that not only are the World Bank’s country groupings arbitrary and not useful, there actual is no “natural grouping” of countries by income.

Of course, I don’t know what Kenny means by “natural”, but there are very strong and detectable country income groupings in the data.

In my research with Norman Maynard (we use Maddison’s income data) where we fit a finite mixture of log-normals model with an endogenous number of components (using reversible jump MCMC), we find that a two component model fits the data best from 1950 – 1970 and a three component model from 1980 – 2008.

Here is a picture of the situation in 1970:


And here is how much things changed in the next 30 years:



These models fit the data pretty well:

“It is also worth noting that our sampler does a good job of assigning countries to a particular component density. In 1970 (the last cross section with a posterior mode at k = 2), 113 of our 135 countries can be assigned to one of the components with probability of .66 or above. In 2008, using k = 3, 124 of our 135 countries can be assigned to one of the three components with probability of .66 or above. That is 84% in 1970 and 92% in 2008”

From the perspective of our work, there was no such thing as a middle income trap before 1980 because there was no middle income group!

As of 2008, the mean of the low component (in 1990 ppp adjusted dollars)  is $1,113, the mid-group mean is $6217 and the high group mean is $22,670. The weights are 31% on the low group, 48% on the middle group, and 21% on the high group.

As far as “conjured” poverty traps go, we find 29 countries that are assigned to the lowest income component with a probability of over 0.66 every decade from 1950 to 2008.

And, regarding the “middle income trap” we find extremely limited mobility out of the middle group and into the top group from 1980 – 2008. More countries fall out of the top group than rise into it.