# Unobserved Country Heterogeneity: GDP Levels or Growth Rates

Have you ever noticed that, when considering the economic performance of different countries, people often just report the GDP growth rate without any corrections for e.g. initial GDP ? It’s as if they thought that countries generally have about the same growth rate and any deviation from the world average is interesting.

This is very odd as most growth models imply that growth rates should be very different for different countries so such a simple measure is not a reasonable assessment of performance.

It’s as if people think that there is a lot of heterogeneity in GDP levels but not so much in GDP growth rates. Marco Alfò, Giovanni Trovato and I, decided to ask a computer if that’s what it saw in the Heston and Summers data set. The computer (on Gianni’s desk top) said “absolutely”. The paper is here (subscription required for download. If you are using a work IP address or mirror you can hope to get it without paying (please try if you are interested)).

update: Greg in comments has kindly translated the post into English. I pull his comment up here.

[snip]

Perhaps an English summary:

a) Standard Economic Theory, the shibboleth we will be destroying today, says that GDP levels will converge, that is, poor countries will get richer, and rich countries will get richer … slower than the poor countries. (Apocalyptic Econ allows for us all converging at some substantially lower level, of course). This will result in all countries being smarter than average.b) We’ve run some Fancy Number Analysis that shows this is not true. The Usual Analysis says this because two things confuse the numbers: i) within groups of similarly poor (rich) countries, there is some convergence, and ii) this within-group convergence tends to look like overall convergence.

c) This is Real Important because lots of analysis doesn’t correct for this, and hence draws conclusions that are, um, stupid.

d) Using a short-form analysis (asking your neighbour) may have been more accurate by being less clever (“it’s a fine line between clever and stupid”).

Of course, one might best avoid using Shibboleth in the simplified version.

Grateful comments/clarification if I’ve gotten anything fundamentally wrong.

Greg | 07.24.08 – 5:15 pm |

Thank you Greg.

All of my F-fort to right plane English is now below the jump (jump at your own risk).

The idea is to take a minimal model for GDP levels or Growth (basically the Mankiw Romer and Weil equation for levels applied to growth too by Bernanke (yes that Bernanke) and Gürkaynak and to allow the computer to look for remaining heterogeneity in levels and/or growth rates with minimal parametric restrictions. We used a semi parametric finite mixture random effects model in which the distribution of the unobserved disturbance to the growth and/or level of per capita GDP is drawn from a finite number of points. As the number of such points goes to the number of countries in the sample, all heterogeneity can be explained, so the approach is, in some sense stressed by Heckman, non-parametric. Like everyone we used information criteria (including Akaike they all agreed) to choose the number of points (results are not too sensitive to the number).

The result is that the computer decides that there is huge unobserved heterogeneity in levels and virtually no heterogeneity in growth rates (the unobserved points in level growth rate space have extremely different levels and the similar growth rates). There is no hint of convergence in GDP per capita levels of the different groups of countries which are, therefore, convergence clubs.

So why has every variable and it’s cousin (except for tax rates) proven to be significant in at least one cross country growth regression ? The initial GDP per capita level is always included in these regressions. It has a negative coefficient because of convergence within convergence clubs. Thus the silly computer is convinced that countries in different convergence clubs should converge (that is the one in the poorer club should have higher growth). The other variables help to explain growth by undoing this error. Regressions of just the growth rate on variables *not* including initial per capita GDP are much less likely to be significant.

The bottom line is that a computer with no hints as to the conventional wisdom very firmly told us that there is a huge amount of heterogeniety in per capital GDP levels and very little heterogeneity in growth rates of per capita GDP, just as everyone who doesn’t run regressions tends to assume.

Now the whole experience reminds me of something Zvi Griliches said long long ago (in a presidential address to the AEA I think). To understand economies better we need more information as in data not new and fancy analysis of the same old data. This was a very popular line in the Harvard ec department back when I was there. In particular, he said there was not point in the zillions analysis of the Heston and Summers data set no matter how econometrically rigorous and original. Back at the time I nodded my head and wispered the un-religious analogue of “amen”. Irony of ironies I find my most recent publication to be … the ten zillionth analysis of the Heston and Summers data set and I honestly think it adds something new. I maintain my almost perfect 0% record as a prognosticator.