A RECENT Free Exchange column ("Middle-income claptrap") expressed some scepticism about the notion of a middle-income trap. That notion has attracted a lot of attention recently thanks in part to a pair of papers (here and here) by Barry Eichengreen, Donghyun Park and Kwanho Shin. In the column we reported briefly on our attempt to replicate their work and play around with it. In case anyone is interested, I'd like to share a bit more of that number-crunching in this post.

Messrs Eichengreen, Park and Shin are interested in fast-growing economies that suffered sharp slowdowns. They define fast growth as 3.5% or quicker. (They look at countries that have enjoyed per-capita GDP growth of at least 3.5% a year on average, sustained for seven years.) They set the threshold for a sharp slowdown at 2 percentage points. (Average growth had to be at least 2 percentage points slower in the subsequent seven years than in the previous seven.)

The authors combed the international evidence in the Penn World Tables (PWT)* looking for examples of such slowdowns over the past six decades or so. They found scores of them. What is more, these slowdowns seemed to bunch at particular levels of income. Their original 2011 paper caused a bit of a splash with one chart in particular. It showed a sharp concentration of slowdowns at a handful of middle-income levels. The distribution of slowdowns appeared "uni-modal" as the authors later put it.

The original paper was, however, based on the August 2009 version of the Penn World Tables (version 6.3). That dataset was soon superseded by newer versions incorporating better information on price differences around the world. In a paper published last month, Messrs Eichengreen, Park and Shin repeated their analysis using the latest version (7.1) of the PWT. The second chart shows their main result. The result looks similar, but to my eye a little less satisfying. It is no longer obvious that slowdowns build to a peak at a certain middle-income level. Instead we seem to be looking at a slope, falling from top left to bottom right. The figure made me wonder what would happen if we extended the scale further to the left, bringing poorer countries into the picture.

Why aren't poorer countries already in the picture? The authors ignore any country with a per-capita income less than $10,000. They argue that slowdowns in poor countries are less interesting, because they are more likely to reflect either "conjunctural" forces or an inability to develop in the first place. I'm not sure about either of these objections. It seems to me that the authors' fast-growth threshold (3.5%-plus per capita growth for seven years) should allay their first concern, excluding countries that simply can't sustain growth. The first concern--that some slowdowns are conjunctural--is no doubt true. But it seems equally true of poor and non-poor countries alike. Even high- and middle-income countries can slow down sharply then rebound quickly when a bad conjuncture reconjoins. The $10,000 income floor also has the unfortunate effect of excluding slowdowns in countries like Argentina, Brazil and Malaysia, which are normally considered paradigmatic examples of the middle-income trap.** When the idea of a trap was first introduced, its proponents suggested that middle-income countries had grown less rapidly than either rich or poor countries. It was a comparative concept. For better or worse, the Eichengreen, Park and Shin papers drop one side of the comparison. They cast some worthwhile light on why and precisely when middle-income countries fail. But they beg the question of whether middle-income countries are particularly likely to falter. What happens if you put poor countries back in? I went looking for slowdowns across the full sample of 189 countries from 1950 to 2010 in PWT 7.1***, applying the authors' two thresholds (a 3.5% compound annual per-capita growth rate for seven years, followed by a 2-point slowdown in average growth for the next seven years). I found 829 years that met the two thresholds.

Why so many? In lots of instances, as the authors point out, a single country suffered more than one slowdown. Often, indeed, a country suffered a slowdown for several years in a row. This was sometimes because annual growth fell repeatedly. Other times, however, it simply reflected the way the slowdown threshold is defined. It is a seven-year average. Thus one very bad year will colour this average for seven years in a row.

To pinpoint the slowdowns more precisely, the authors rely on a Chow test. This procedure tests whether a statistical series (such as the growth rate from 1950 to 2010) is significantly better explained when split into two subsamples (1950-1972 and 1973-2010, for example). It is therefore useful for identifying watershed moments. As I understand it, they use the Chow test to pick out a single key year whenever a string of consecutive years qualify as slowdowns.

I did my best to mimic their Chow tests. I regressed annual per capita growth for each country on a constant. I then calculated a Chow statistic for every year of growth for each country. Whenever several years in a row qualified as slowdowns, I singled out the year with the most significant Chow statistic as the "key" year. So I was left with a combination of single-year slowdowns and "key" years picked out from multi-year slowdowns. This number-crunching reduced my 829 cases to 283. However, my key years don't quite match those in the Eichengreen, Park and Shin paper, which suggests that I baked my Chow a bit differently.

The next two charts show my results, both including and excluding energy exporters****. The first chart shows all 829 years that qualify as slowdown years. The second shows only the 283 "key" years. (In the Free Exchange column, we reported the results for all years.) Interested readers can download a file listing all the caseshere. The charts strongly suggest that slowdowns do not, in fact, cluster at the middle-income levels. They are far more prevalent among poorer countries.

I wondered if this was simply because the Penn World Table contains more observations of poor countries. (It includes 6,496 annual observations of countries with per capita incomes less than $10,000; only 2,385 of countries with incomes greater than that.) I needed some way to normalise the number of slowdowns. I tried to do this by dividing the number of slowdowns in each income bracket by the number of years that met the fast-growth threshold. Think of this as the number of slowdown cases divided by the number of potential cases. In the charts below (and in the Free Exchange column), we call this the "probability of a slowdown", expressed in percentage terms.

The "probability" of a slowdown, calculated in this fashion, bounces around an awful lot at higher income levels. (Note the spike at $27,000 in chart 3 and the spike at $23,000 in chart 4). This is mostly because the pool of potential cases is so shallow: few high-income countries can meet the fast-growth threshold. In chart 3, showing all 829 slowdown years, the probability also edges upwards a bit among countries in the $15,000-16,000 range. In chart 4 showing only the 283 "key" years, the probability is instead a little elevated in the $17,000-18,000 and $19,000-21,000 range. Are these bumps suggestive of a middle-income trap after all?

I don't think so. Note first that incomes of $19,000-$21,000 (even at PPP) qualify as high incomes by most definitions. Even the slowdowns at incomes of $17,000-18,000 include cases like New Zealand (1966), Denmark (1970) and Sweden (1965)--not countries we normally think of as casualties of the middle-income trap. The same could be said for the countries that slowed down at incomes of $15,000-$16,000 per capita. They include South Korea (1995), Singapore (1980-1981), Japan (1972 and 1974) and even Macau (1982), four economies that converged rapidly with high-income countries. The list also includes a variety of European nations (Greece and Spain in the 1970s, as well as Portugal in the 1990s) that have become well-off societies by world standards, whatever their recent travails. These slowdowns are all interesting examples of economic lulls and lapses. They are all cases worth identifying and investigating. But such slowdowns are no more likely to strike at middle-income levels. And even when they do, they are often not enough to trap an economy for long. *The PWT report per-capita incomes for 189 countries over six decades, holding prices constant over time and space. It's a remarkable database, which can now be downloaded from FRED (the Federal Reserve Economic Data) as well as the PWT site itself.

**I suspect the $10,000 floor suited PWT 6.3 better than PWT 7.1. The newer price data resulted in downward revisions of the real incomes of a number of developing countries.

***The PWT report two different income series for China. We used the second, higher series.

**** We excluded all of the oil exporters identified by Eichengreen, Park and Shin. In addition, we dropped a number of low-income energy exporters and Norway. The full list is: Algeria, Angola, Azerbaijan, Bahrain, Bolivia, Brunei, Chad, Republic of Congo, Ecuador, Equatorial Guinea, Gabon, Iran, Iraq, Kazakhstan, Kuwait, Lebanon (because it is excluded from the Eichengreen, Park and Shin papers), Libya, Nigeria, Norway, Oman, Qatar, Saudi Arabia, Sudan, Syria, Trinidad & Tobago, Turkmenistan, UAE, Venezuela, Yemen.