Another round on the “elephant curve”

A report from the Resolution Foundation has touched off another round of analysis of Branko Milanovic‘s work on global income growth. Much of what they discuss can be found elsewhere. Including here. But I want to focus for a moment on their claim that

we find that the weak figures for the mature economies as a whole are driven by Japan (reflecting in part its two ‘lost decades’ of growth post-bubble, but primarily due to likely flawed data) and by Eastern European states (with large falls in incomes following the collapse of the Soviet Union after 1988).

Not to suggest that these things did not occur; rather, I find weak the argument that they drive the results. In the figure below, I have estimated the “quasi-nonanonymous” GIC. We see there the growth in real per-capita income among country-deciles sorted by their 1988 income percentiles— with and without China. I have not “reshuffled” incomes when including China, so it is as if Chinese growth had been comparable to its 1988 income peers.

In other words, excess growth in China accounts for nearly all of the fast growth in the 20-70th percentiles. The growth which remains to that half of the world distribution is quite modest— about 1.7 percent per capita annually. True, the more developed 70-99th percentiles seem to have grown somewhat more slowly (1.3 percent per capita annually); even including Japan and Eastern Europe as done here, the severe stagnation which the “elephant” misleadingly suggested does not really exist.

Of course, this latter point was already made clear in Milanovic’s work, as he reminds us.

When we do quasi non-anonymous chart with 1988 country/deciles fixed, we keep 1988 decile populations fixed. Fixed! pic.twitter.com/pdPHcxg6JQ

— Branko Milanovic (@BrankoMilan) September 14, 2016

Ultimately, there are two points:

1. The years 1988-2008 had seen considerable change in what it means to be part of the global middle class.
2. Outside China, the global 10-99th enjoyed only modest growth. To the extent those years saw stagnation among more developed economies, it extended to most of the world. Except China.

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.

The Incredible Story of Developing Country Income Growth: Was it Just China?

To what extent has the age of globalization benefitted developing countries—and what of the poor in those countries? To what extent has such progress been driven by local policy decisions rather than a more global phenomenon? Has such development come alongside stagnation of poor and middle incomes within more developed countries and large benefited the extremely rich?

One way—however incomplete—to begin an investigation would be to look at the global “growth incidence curve” (GIC) of Lakner and Milanovic. They estimate the worldwide distributions of income in both 1988 and 2008, which allows them to answer questions such as “How does median (the 50th percentile) income change between the two years.” The GIC is sometimes referred to as the “elephant curve” for its resemblance to the beast.

Figure 1 shows the worldwide GIC as produced directly by Lakner and Milanovic’s public data and code.

Figure 1: Lakner and Milanovic Growth Incidence Curve

Source: Lakner and Milanovic

As seen in the figure, the average income representing the world’s 50-55th percentiles rose more rapidly than any other group. Entrance into the upper half of the world distribution required in 2008 some 76 percent more income—adjusted for inflation—than it did in 1988. Likewise, the average income defining the top 1% rose only 65 percent over the same period. Between, however, the distribution become much more compressed. The average income of the world’s 75th-80th percentiles in 2008 was \$3831—up only 1.3 percent from \$3782 in 1988.

Milanovic looks at this “global reshuffle of income” and finds “it would be hard to dismiss the period 1988-2008... as being one of failure.” While two decades of 2.9 percent annual growth would be reasonable enough, this appears to be much less global and much more local—driven by China’s very rapid progress. Doubtless, China’s poor represented a large fraction of the world’s poor, and growth there greatly increased their incomes. Still, it is critical to investigate how much of the reshuffle is specific to China. With a simple edit of line 12 of their code¹ we may re-run with China excluded from the data.