Monday, July 22, 2013

More on Growth and Convergence Within Countries

In my last post on China, I touched on the issue of Chinese growth by showing a graph with the distribution of Chinese per capita incomes by province, and arguing that there is a strong convergence story pushing China towards more growth. In the comments, Tamar makes a note that many countries do not converge. For example, per capita incomes in Mississippi and Connecticut differ by a factor of about 2, even though the United States is a relatively developed Country. He also suggested that I take a look at Brazil. And so I did. I took a look at the distribution of  province per capita income divided by country per capita income for three emerging market economies: Brazil, Mexico, and China, and found that indeed, they were quite close!

I wondered if it was because I didn't weight for populations, so I downloaded some Mexican population data from their government's website. I didn't have time to do Brazil, but even comparing China and Mexico I found that the distributions were quite similar.

On first pass, this bodes poorly for a convergence hypothesis.

But let's think back to the Solow model. We should only observe convergence in income levels if technologies and savings rates are all identical. But it's entirely plausible that these can differ across provinces, and that they differ for extended periods of time. Therefore a better metric to evaluate convergence is not whether they converge in levels, but rather if they converge in growth rates. In the Solow model, at the steady state, all countries grow at a rate equal to the rate of population growth plus the rate of technological change. If they're all bound together (eg if they're all large counties in one country), then g should be similar across them, and demographic trends typically do not differ hugely among provinces in the long run.

So if we look at growth rates, now we see convergence at work. As a technical note, I only had data for Mexico from 2003 to 2010. So I got the ratio by exponentiating the 7 year ratio by 10/7. 

So even though Mexico and China have similar distributions in terms of their with country income levels, they have widely different distributions for growth. Therefore I stand by my original belief that China still has a lot of long run growth potential to go as the poor provinces catch up to the rich.


  1. How does this work with the China urbanization thesis which has rural migration as a big factor. Would not population growth be therefore larger in the more prosperous provinces, and with demographic trends slowing for China as a whole, be actually negative in some of the poorer provinces therefore preventing even a convergence in growth rates between the provinces. The rich get richer. A Us example would be Detroit experiencing pop exodus exacerbating low growth trends leading to negative loop.

  2. Tamer,

    Each provinces has its cities, so urbanization within provinces can still cause convergence for the same reason convergence happens on a cross-country basis. However, you do bring up a good point to see if there is conditional convergence between rural and urban areas.

  3. I enjoyed this post, and am working on something similar in other SE Asian countries. Quick bleg: which software package did you use to draw these graphs?

    1. I do almost all my drawing through R. I recently wrote a more formal Quartz article on these convergence issues, and you can check those out (with code samples!) here: