# Poverty reduction, growth, and movements in income distribution

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Last week the President of the World Bank Group launched at the Spring Meetings the report "Prosperity for All." One of the interesting areas the note reported on was the interrelationship between growth, movements in the income distribution and poverty reduction.

There are various ways of showing the impact of growth on people’s income and its interrelationship with a country’s income distribution. In comparing distributions over time, one of the more useful graphs is a Pen’s Parade (figure 1a), named after another Dutch economist as so many inequality or poverty measures are (other examples are the Theil index and Thorbecke for the Foster-Greer-Thorbecke Poverty Measure).

The Pen’s parade lines up every person from poorest to richest on the horizontal axis, while the vertical axis shows the level of expenditure (or income) per capita. The $1.25 a day line intersects with Pen’s parade for 1990 and 2010 at 43.1 and 20.6 percent respectively, providing the percentage of the population living below the extreme poverty line in the developing world in those years. One can see that growth in developing countries has accrued to a large extent to the middle quintiles, as the difference between the income earned in 1990 and 2010 is the largest at those percentiles.

Another way of depicting an income distribution is to show income on the horizontal axis, count how many people earn that particular level of income, then stack them on top of one another such that the number on the vertical axis represents them (figure 1.b). One can see that in 1990 the largest number of people making the same income (the peak of the distribution graph), made less than $1.25 a day, while in 2010 the peak had come close to $1.65 a day. Note that the full population of the developing world in 1990 and 2010 is captured below each income distributional line respectively.

As such, one can get an informed idea about the implication of shifts in the income distribution often caused by growth. In turn a picture also emerges of the effect of those shifts on the extreme poor.**Figure 1a: Pen’s parade****Figure 1b: Income distribution for developing countries**

Another interesting observation from figure 1b is that far fewer people lived on or close to US$1.25 a day in 2010 than in 1990. Hence, shifting the income distribution to the right using the same growth rates as experienced in the recent past will lift fewer people out of poverty than was the case in 1990. This happens not just because there are fewer extremely poor, as we can see from figure 1a, but also because the 2010 income distribution lies well below the 1990 income distribution. Consequently, it will likely become harder and harder to lift people out of poverty through growth alone. While growth remains vital, we need to complement efforts to enhance growth with policies that allocate more resources to the extreme poor. This can be accomplished to some extent by focusing on inclusiveness, particularly with respect to job creation, and/or through government programs, such as public works, and cash transfer programs.

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I agree these two charts are really useful for understanding changes in global poverty over the last 20 years, and the relationship between growth, distribution and poverty.

However, I have some misgivings with both.

According to the first chart, the richest 1% of the developing world has a daily per capita income of less than $10. So much for the emergence of a global middle class! Based on data from Povcalnet, the richest 6 centiles (6%) should appear above the $10 mark in 1990, and by 2010 the richest 11 centiles (11%) should be above this threshold. So there must be an error somewhere in the calculations behind this chart, or at least in the labeling of the y-axis.

On the second chart, my concern is not strictly with the chart but the way it has been interpreted. You note that the largest number of people making the same income (illustrated by the peak of the distribution graph) is around $1.65 in 2010. But this is not strictly correct. Again, using data from Povcalnet, it can be shown that around 15 million people are estimated to live on $1.65 to the nearest cent. However, a much larger 18 million people live on $1.22, the true statistical mode. You'll notice that this is, curiously enough, almost exactly equal to the international poverty line of $1.25. My colleagues and I made this point in our 2013 paper, The Final Countdown: http://www.brookings.edu/~/media/research/files/reports/2013/04/ending%…

The explanation here is that the x-axis uses a logarithmic scale. It is accurate to say that the peak of the density function occurs at around the natural log of $1.65. But this is not the same as saying that the largest number of people making the same income falls at $1.65, which wrongly interprets the log scale as a linear scale.

Despite these misgivings, I agree wholeheartedly with the conclusions you draw from the two charts and look forward to more analysis on the Bank's twin goals.

Thanks for your comment. It is quite interesting and to some extent worrying that you get different results from the same dataset i.e. povcal.net. Log linear or normal linear, the peak remains at 1.64-65 a day in our distribution function for 2010. I will send you by email the excel file with our numbers so you can compare them with yours. Figure 1a might not completely show the tails well at the upper end (and lower end) of Pen’s parade and hence you should not jump to conclusions. Anyway, have a look at the excel file I am sending you and let’s get together and exchange notes, ideas and future work?

Thanks Jos. As discussed over email, after seeing your data I now suspect that the reason we arrive at different estimates of the statistical mode (the peak of the distribution graph) is that we use different methods for approximating the shape of the income distribution.

The estimates I provided in my earlier comment are drawn directly from Povcalnet, where the shape of the distribution is based on the best fit between a General Quadratic and Beta lorenz curve. I would favor my $1.22 estimate of the mode since it is faithful to (and therefore consistent with) the Bank's method for compiling global poverty estimates. But no approximation of the shape of the distribution can be definitively correct as all approximations are…approximations.

Thanks again for an interesting post.