What’s happening on Global Inequality? Putting the ‘elephant graph’ to sleep with a ‘hockey stick’

muheedFor our second post on how to measure inequality (here’s the first), Muheed Jamaldeen, Senior Economist at Oxfam Australia, discusses absolute v relative

Back in December 2013, two economists at the World Bank – Christopher Lakner and Branko Milanovic; produced a paper on ‘Global Income Distribution’, which presented a newly compiled and improved database of national household surveys between 1988 and 2008. As part of the analysis in this paper, Lakner and Milanovic produced Growth Incidence Curves (GIC), which show percentage growth in income by global percentile.

One of these charts has come to be known as the ‘elephant graph’ – an inverted supine S shape gives rise to this name. The vertical (Y) axis shows the percentage increase in income between 1998 and 2008; the horizontal (X) axis shows  income percentiles – whereabouts you are in the global distribution of income.

This analysis shows that incomes for the poorest half of the world (up to the 50th percentile) have grown as fast as income increases experienced by the top 1% of the world.

muheed-fig-1This graph has proven to be extremely popular because it has simultaneously supported the arguments of the proponents of globalisation, and those who are concerned about its impacts on the middle class in rich countries. At Oxfam, we are concerned that the graph also gives the impression that inequality is not a problem in developing countries, as their incomes have grown.

Advocates of unrestrained free-market economics also use the growth rate of developing country incomes to argue that concerns about rising inequality are overblown (let’s call them the ‘naysayers’). This implies that any corrections to inequality might adversely impact on poverty reduction.

However, there are a number of reasons why using the ‘elephant graph’ (and income growth rates) in this way is, simply put – misleading.

Comparing income growth rates across vastly different income levels is meaningless

The first, and most important of these is that for the poorest people, income growth rates matter little. For instance, a 10% increase on an income of $100 translates to a $10 increase in income. By contrast, a 10% increase for a person on $10,000 income translates to an increase of $1000. You can buy a lot more with $1000 dollars than you can with $10. In the case of the ‘elephant graph’, those between the 40th and 50th percentiles experienced 70% increase in incomes – however, this is from a starting point of around $550 in 1998.

One way to correct for this misleading visual representation is to alter the point of reference for the calculation of the percentage increase. Instead of looking at the percentage income growth rate for each percentile, we used the common reference point of average incomes in 1998. This (purple line) represents the speed at which each percentile has grown compared to the average income level (around $3300) 20 years ago.


muheed-fig-2The ‘elephant graph’ immediately disappears, and is instead replaced with a ‘hockey stick’ graph (right axis). Since each percentile now uses the same reference point of 1988 average income (or common denominator for the numerically inclined!), we can now see that over the last 20 years the vast majority of income growth (in relative percentage terms) has accrued to the top 1%, and that the growth experienced by the poorest half of the world pales in comparison. Alternative common reference points produce similar ‘hockey stick’ shaped graphs.

Growth in income levels matter more than growth rates

In the graph below, we compare the income growth levels (right axis) with the original ‘elephant graph’ which shows percentage increases in income between 1998 and 2008 for each percentile (left axis). When both absolute level increases, and percentage increases are plotted on the same graph, it is clear that though those at the 40th and 50th percentile had a growth rate of 70%, the absolute increase in income is around $400.Though the top 1% experienced similar income growth in percentage terms, the absolute increase was over $25,000, rising from around $39,000 to over $64,000.

In other words, the top 1% experienced nearly 65 times the absolute income growth of the poorest half of the world – an astonishing fact concealed by the ‘elephant graph’. The plot of income growth levels (right axis), again, reveals a ‘hockey stick’ graph, showing that the vast majority of income growth (in levels) accrued to the richest. Early this year, Oxfam’s annual inequality report showed that nearly half (46%) of total global income growth went to the richest 10% whilst the poorest 10 saw less than 1% of total income growth.

muheed-fig-3To reduce inequality, much higher income growth rates are required for the poor

Since the ‘elephant graph’ shows that the poor have experienced ‘strong’ income growth rates, it is easy to think that inequality must be decreasing.

Let’s put that claim to the test.

In the graph below (orange line), we simulate the 20 year income growth rate (between 1988 and 2008) that would have been required for the bottom percentiles (up to the 70th) to achieve the average income levels in 2008 of around $4100. (The income growth rates for percentiles above P 60-70 were unchanged from the original data.) This shows (right axis) that the poorest percentile (<10%) needed to experience around 2000% (or around 17 percent compounding annually) between 1998 and 2008 just to get to the average income. Instead, this group experienced around 25% growth over two decades (or 1.1% compounding annually).

At the current rate (compounding every 20 years), it would take over 250 years for the poorest 10% to get to the 2008 average. For those between the 40th and 50th percentiles, it would take 55 years. Similarly for P 50-60, it would take 41 years, and for P 60-70 it would take 29 years at current income growth rates compounding every 20 years.

muheed-fig-4Again, these facts are simply not apparent from the ‘elephant graph’.

To be fair to Lakner and Milanovic, as shown below, they do note some of these limitations in their 2013 paper (see p.30).

While the global GIC showed relatively large gains for the portion of the distribution around the median, we need to recall that these gains were measured in relative (percentage) terms. But precisely because global income inequality is extremely high, and incomes at the top are several orders of magnitude greater than incomes at the median … the absolute gains are much greater for higher percentiles.

But of course, the naysayers use the ‘elephant graph’ with neither a rudimentary understanding of what it is trying to show, nor its limitations. Like all graphs and visuals it serves a political purpose for those with set ideological views, which, unfortunately compromises the intellectual integrity of the Lakner and Milanovic analysis.

The ‘elephant graph’ is also wrongly being used to argue that inequality is a developed country issue, and that global inequality is declining by virtue of high income growth rates for the bottom percentiles. We have shown three reasons why the ‘elephant graph’, though not intended, masks the true extent of global inequality.

It’s time to put the ‘elephant graph’ to rest, and replace it with the ‘hockey stick’ graph once and for all.

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2 Responses to “What’s happening on Global Inequality? Putting the ‘elephant graph’ to sleep with a ‘hockey stick’”
  1. For most outcomes that we care about in development, such as health, nutrition, and happiness, there is an extremely high return to income at very low levels and a much lower return at high levels. That is, there are *diminishing returns* to income in most of the dimensions of welfare that we care about. Most of the gains are realized precisely in the part of the income distribution that makes up the “head” of the elephant. The argument that “You can buy a lot more with $1000 dollars than you can with $10” depends entirely where you are in the distribution. An extra $10 to a poor person might save a child’s life, where for a rich person they might be able to pick up an extra laptop. It turns out that income growth rates really DO matter a lot for poor people.

    There is a very good reason why we don’t rely solely on absolute measures of inequality when thinking about income differences within and across countries: we get a lot of weird, counter-intuitive results. If you rank countries based on the absolute income version of the Palma Index, you find that Denmark is as unequal as South Africa. Most of us would think that is pretty silly because the median person in Denmark is doing a lot better than the median person in South Africa. http://aidthoughts.org/?p=4250

    Of course, if changes in absolute levels of income are massive enough that might imply an increase in inequality in these dimensions, but that extra year of life expectancy or rung of the happiness ladder remains pretty elusive at the upper levels of the income distribution. We should definitely be worried absolute inequality in dimensions where there are not diminishing returns to income (political power, for instance) as well as the fact that global incomes are converging too slowly.

    But the idea that the elephant graph is somehow wrong or misleading – or that the intellectual integrity of Lakner and Milanovic’s analysis has somehow been compromised – is plain daft. It’s perfectly ok to celebrate the massive gains the poorer-half of the global distribution has realized during those two decades AND be concerned about future convergence.

    Here is a challenge: why focus on income at all? Why not focus on changes in the global distribution of different proxies of human welfare? I suspect it would run up against the unrelenting narrative that the world is getting worse all the time.

  2. Muheed

    Thanks for your comment, and apologies for the delayed response.

    It is certainly the case that income (and consumption) exhibits diminishing marginal utility. That is, a relatively small increase in income to a person living in poverty is very important to a poor person and family – no disagreement there. In fact, a small increase for a poor person lot produces more ‘happiness’ (or utility in ‘econ-speak’) than the same dollar increase for a rich person.

    There is also no doubt that there has been significant progress in poverty eradication globally. As noted in Oxfam’s Inequality Report ‘Economy for the 1%’ – “Over the past 30 years, average annual GDP growth has been higher in low and middle-income countries than in richer ones. Average incomes in poorer countries are catching up with those in richer ones, and inequality between nations is falling. Emerging economy powerhouses are leading this catch-up process: China and India, for example, have driven much of the dramatic increase in the combined GDP of Asian countries. Between 1990 and 2011 economic growth in the region helped nearly a billion people to escape extreme poverty; 700 million in these two countries alone.”

    However, the analysis in this post should be read in the context of understanding income inequality.

    These ‘Growth Incidence Curves’ can be misleading because the percentage increases in income are measured against vastly different bases (denominators). I know it is a rather ‘technical’ point – but comparing percentage increases for variables with vastly different starting points can be misleading, as it gives the impression that the bottom decile, and top percentile have experienced similar income gains – when in fact the real income increase are vastly different. And, as I have noted in the post, Lakner and Milanovic rightly note this limitation, too.

    It is for this reason that I argue that using a common denominator (such as average income in the starting year) would produce a more accurate comparison of percentile income growth rates. The other option is to focus on absolute (level) increases in income by percentile. Such measures will paint a more accurate picture regarding the extent to which income growth has contributed to the reduction in income inequality.

    Hope that makes sense.

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