They look at a wide array of household-level evidence on the distribution of income in more than 100 countries, and then use various assumptions (essentially assuming that within-country inequality of incomes doesn't continue to change over time) to project what the distribution of global income will look like in the future. The green line in the figure shows the distribution of global income per person in 2003, with a mean of $3451 and a median of $1090; the blue line shows the global distribution of income in 2013,m with a mean of $5375 and a median of $2010; and the red line shows their forecase for 2035, with a mean of $9,112 and a median of $4,000. The distribution of global income is clearly becoming flatter and more equal over time. Hellebrandt and Mauro write: "Global income inequality started declining significantly at the turn of the century, and we project that this trend will continue for the next two decades, under what we consider the profession’s “consensus” projections for the growth rates of output and population."
However, it's important not to exaggerate how quickly this reduction in global inequality of incomes will occur. For example, the median income projected for 2035 (with half the world population below that level) is well below the average or mean income for 2013. The authors offer a useful illustration measuring inequality by the 90:10 ratio--that is, the ratio of the 90th percentile of the income distribution to the 10th percentile of the income distribution. (Calculations using the Gini coefficient look much the same.) The global 90:10 ratio shows greater inequality than almost any individual country in the world, with the exception of South Africa. By 2035, although the global 90:10 ratio falls, it will still be substantially higher than any even moderately large economy other than South Africa is currently experiencing.
The figure also offers some comparisons of the current level of income inequality across countries using the 90:10 ratio. The US economy clearly has one of the most unequal distributions of income among the high-income countries, but it is more equal than a number of emerging economies around the world.
The exercise in this paper reminds of an article by Robert E. Lucas Jr. that appeared in the Winter 2000 issue of the Journal of Economic Perspectives, called "Some Macroeconomics for the 21st Century." (Full disclosure: I have been Managing Editor of JEP since 1987. All JEP articles from the most recent issue back to the first issue are freely available on-line compliments of the American Economic Association.) Lucas offers a hypothetical model of growth patterns in the global economy that works like this:
"We begin, then, with an image of the world economy of 1800 as consisting of a number of very poor, stagnant economies, equal in population and in income. Now imagine all of these economies lined up in a row, each behind the kind of mechanical starting gate used at the race track. In the race to industrialize that I am about to describe, though, the gates do not open all at once, the way they do at the track. Instead, at any date t a few of the gates that have not yet opened are selected by some random device. When the bell rings, these gates open and some of the economies that had been stagnant are released and begin to grow. The rest must wait their chances at the next date, t + 1. In any year after 1800, then, the world economy consists of those countries that have not begun to grow, stagnating at the $600 income level, and those countries that began to grow at some date in the past and have been growing every since. ...
"[A]n economy that begins to grow at any date after 1800 grows at a rate equal to a α = .02, the growth rate of the leader, plus a term that is proportional to the percentage income gap between itself and the leader. The later a country starts to grow, the larger is this initial income gap, so a later start implies faster initial growth. But a country growing faster than the leader closes the income gap, which by my assumption reduces its growth rate toward .02. Thus, a late entrant to the industrial revolution will eventually have essentially the same income level as the leader, but will never surpass the leader’s level."Lucas acknowledges repeatedly that this model is a very simple one. But he points out that it offers some interesting predictions. It predicts that global inequality of income will at first expand dramatically, as it indeed did from the 19th century well into the 20th century. It predicts that countries which start growing later will experience faster "catch-up" growth, which has held true in a number of countries including Japan, Korea, China, and others. Under the assumptions that Lucas uses, his model predicts that the global rate of economic growth will peak around 1970, at a time when a large share of the world is catching up at a rapid pace. It predicts that during the time period in the last few decades of the 20th century, global inequality won't change by much. And it predicts that in the 21st century, as the remaining nations that had not previously entered a period of rapid economic growth start to do so, global inequality of incomes will diminish. If Lucas's model captures the underlying dynamics of the global growth process, and predictions like those of Hellebrandt and Mauro hold up, the 21st century would be a time of rising equality across the global income distribution.