## Monday, July 25, 2016

### More on the “elephant curve”

Based on feedback from my previous post, I have started a FAQ.

Moving on, I would like to make a couple points. First, the results are not terribly fragile. Previously, I used the data and code of Lakner and Milanovic to produce GICs with and without China. One interesting quirk of their approach is that quantile populations are not necessarily very even. In 1988, the 20th-25th percentile represents less than 150 million people, while the 40th-45th represents more than 275 million. While this might seem like a big problem, it is not. In Figure 1, I use a different method for binning the data. In particular, I allow country-decile groups to split across quantiles. This helps make much more uniform the population size represented by each percentile.

Figure 1: Growth Incidence With Decile Splitting
Source: Lakner and Milanovic and author’s calculations

Clearly, the story is very much the same. But these “anonymous” GICs are easy to misinterpret. With China included in the data, the incomes associated with the 75th-80th percentiles hardly budged; this does not mean that the incomes of people in the those percentiles failed to rise. Lakner and Milanovic also produce “quasi-nonanonymous” GICs which show the average income growth for the actual country-deciles represented in the 1988 quantiles. (pdf) They estimate that across the board, growth exceeded 20 percent and broke 90 percent in the middle of the income distribution.

That method is laid out in their paper, but I take a more direct approach. First, however, I estimate the 1988 and 2008 population and per-capita income for each country-decile based on the observed growth rates. Then, dividing the country-deciles into global quantiles ranked by 1988 per-capita income, I compute the aggregate per-capita growth from 1988 to 2008 treating the quantile as a single aggregate. $$G_\mathrm{quantile} = 100\times\frac{\sum_{\in\mathrm{quantile}}{\mathrm{Pop}_{2008}\times\mathrm{Inc}_{2008}}}{\sum_{\in\mathrm{quantile}}{\mathrm{Pop}_{1988}\times\mathrm{Inc}_{1988}}}\times\frac{\sum_{\in\mathrm{quantile}}{\mathrm{Pop}_{1988}}}{\sum_{\in\mathrm{quantile}}{\mathrm{Pop}_{2008}}}-100$$ Then, keeping the quantile definitions, I re-compute the growth without China. The resulting quasi-nonanonymous GICs are seen in Figure 2. We see that— except for the bottom decile— the results are similar to what Lakner and Milanovic.

Figure 2: Quasi-Nonanonymous Growth Incidence
Source: Lakner and Milanovic and author’s calculations

Without China, growth at the 10th-70th percentiles was quite modest— about 1.7 percent per-capita per year. This agrees with earlier analysis based on very different methods. Excluding the global top percentile, higher-income countries did not grow quite as fast— about 1.3 percent per year. Progress in more developed countries has been uneven, favoring the top incomes there. But we do not see the utter collapse of middle-class incomes a naïve reading of the anonymous GIC would suggest.