Last year, the ODI’s Chris Hoy released a really useful and thoughtful paper¬†pointing¬†out that the basic maths of inequality are often not on the side of the poor. Even if economic growth is evenly spread, the absolute difference between the incomes of the poor and the richest must increase. That is, if you are 10 times as rich as I am and our incomes both grow by 10%, you’ll be taking home more money than I will at the end of the day. If we wanted to see a decrease in¬†absolute differences of income around the world, it would require that the income of the poorest grow a great, great deal faster than that of the richest, something we are unlikely to see any time soon.
The unanswered question, and one that Hoy even posits himself¬†end of the paper, is whether or not focusing on absolute differences in income makes more sense than doubling down on the relative differences in income that are captured by traditional inequality measures such as the Gini, Thiel or Palma indices. We know that income is correlated with lots of good outcomes for the beholder – better health, education, happiness and political power. However, if we are being truly honest with ourselves, we would have to admit that we don’t quite fully understand whether relationships¬†are absolute or relative in nature¬†(although we suspect both matter for happiness).¬†Do the richest 1% of Americans have more political power in the US¬†than the richest 1% of Nigerians have in Nigeria? These are the questions we must ask ourselves if we are to make a strong case for caring about absolute income differences.
In the meantime, I woke up this morning to find that Nick Galasso from Oxfam has made a pitch for using the¬†“Absolute Palma Index” as the next big measure of inequality. The Absolute Palma is a variation of the Palma Index of inequality, which itself is the ratio of the share of income earned by the top 10% of the distribution and that of the bottom 40% of the distribution. The Absolute Palma, by contrast, is the absolute difference between the average income of the top 10% and the average income of the bottom 40%.
As the title suggests, I think there are limitations to the Absolute Palma Index, so consider the post a word of caution.¬†I can think of one strong case against absolute measures: while they might be reasonable at describing immediate gains across a country’s income distribution after a year of growth, they aren’t very useful at describing differences between¬†countries across the globe.
I happened to be playing around with data from Christoph Lakner and Branco Milanovic’s paper on the global income distribution, so I decided to see how the Absolute Palma Index varied across countries. Check out the graph below, which looks at how the Absolute Palma Index varies with mean income across countries. I’ve also highlighted countries which are either very unequal, very equal or somewhere in the middle as measured by the traditional Palma Index.
The first thing to note is that there is almost a one-to-one relationship between the log of GDP and the log of the absolute Palma. This is hardly surprising – take any income distribution and raise all incomes by a set percentage and by definition you will see an increase in the Absolute Palma. What this means is that on this index, poor countries do really, really well and rich countries do terribly.¬†And that is most of the story.¬†Log per capita income explains about 93% of the variance in the log of the Absolute Palma. The relative Palma explains most of the remaining unexplained variance, but on the whole has very, very little explanatory power.
The result is that we get some pretty counter-intuitive results.¬†Even though Denmark, Sweden and Norway ¬†are considered by pretty much every person I’ve ever ever spoken to be the most equal places on the planet, they¬†come out as being more unequal than countries that are at the top of the relative Palma Rankings, places like South Africa, Honduras and Brazil.
Which of these countries would you rather be poor in? Presumably the one with the highest average income for the poorest 10%. If we graph the same relationship, instead using the average income of the bottom decile, we find the relationship is less strong, especially so for the poorest countries of the world. But if¬†I had to choose whether I wanted to be born poor in a country with a high or low Absolute Palma index,¬†sign me up for more inequality!
Now for the caveats: the data here is as good as 2008, so the basic cross-sectional relationship may have changed (although it hasn’t appeared to have done so ipapen the years leading up to 2008). There is also a difference between moving between countries of different average/median/poorest decile levels and observing individual countries as they grow richer or poorer. This means that there might be use in keeping track in how growth is `allocated’ across the income distribution, something which is already done (and was done carefully in Chris Hoy’s paper).
Absolute measures might tell us something interesting in the world, and I welcome more work on them. But there is a world of difference between adding a tool to the (now overflowing) box of inequality measures and pushing for headline¬†measure that automatically penalizes rich, developed countries for being rich and developed. In addition, before we begin agonizing about absolute differences within countries, someone needs to make a pretty compelling case that they matter more than both absolute levels or relative differences, because these are things we already go through great pains to measure.¬†If we are worried that the incomes of the poor aren’t growing fast enough, then¬†why isn’t it enough to measure that?
Stata code¬†and¬†underlying data available here.
Update:¬†good comments from Chris Hoy below.