The limitations of the Absolute Palma Index, in two graphs

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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.

palma_avg

 

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!

palma_b10

 

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.

3 thoughts on “The limitations of the Absolute Palma Index, in two graphs

  1. Chris Hoy

    March 12, 2016 at 4:35am

    Hey Matt,

    Thanks for your commentary on the Absolute Inequality Paper. I agree with a number of things you raise, however I want to highlight two issues:

    1) The Absolute Palma was designed to measure changes in absolute inequality within countries over time. Whereas the charts you have made are looking across countries at one point in time.

    2) The most comprehensive study on perceptions of inequality, Cowell and Amiel (1999), highlights that people tend to perceive inequality in absolute terms as much as they do in relative terms. Ravallion has also shown this in recent work he was been doing at Georgetown. As such I think that it is unfortunate that inequality is typically only measured in relative terms.

    Anyway thanks again for your blog. It would be good to speak further about this if you are interested.

    Cheers,
    Chris

  2. Matt

    March 12, 2016 at 1:36pm

    Hey Chris,

    Thanks for the very fair comments!

    1) Very good point – something I incoherently tried to get at in my second to last paragraph. With more time, I wanted to see how the Absolute Palma changed over the available years in the Lakner/Milanovic data set (a combination of the PovCal data you used and the Branco’s World Income Database). Conceptually, there should be no major difference, but we all know that the current trajectories of growth differ a lot from cross-country snapshots.

    2) That’s cool – I think this is a important area of work. If absolute values do make a difference, I’d be curious to know

    The source of my push back here is mainly driven by a desire to see that kind of work pushed a bit further before we crown the AP the king of the inequality indices.

    Thanks again for engaging and the interesting paper – also happy to chat at some point!

    Matt

  3. Maya Forstater

    March 13, 2016 at 11:38am

    Interesting discussion and great graphs!

    Its worth noting that the Amiel and Cowell research which highlights that people perceive inequality in absolute as well as relative terms was based on a survey with university students in the UK, US, Germany, Israel etc which asked them to label various pairs of mathematical distributions and hypothetical situations as more or less unequal . The findings seem to reflect the limitation of language as much as anything – its like asking people to look at swatches of pale blue and dark blue colour and pick which corresponds most closely to their idea of ‘blue’ – it gives interesting results about concepts and categorisation but doesn’t necessarily tell you what shade to paint your bathroom.

    It seems like a big jump to go from this study to Chris Hoy’s framing that “In other words, a widening gap between the rich and the poor in society potentially concerns people more than how the ratio of incomes changes over time”. (I guess ‘potentially’ is doing a lot of work in this sentence!)

    On the other hand patterns of migration from rural to urban areas, and from the bottom left to the top right of Matt’s graph seem to suggest that people’s choices show that comparative levels of absolute inequality are low down on their list of priorities, compared to gains in absolute level of income. As Matt said – if we are worried that the incomes of the poor aren’t growing fast enough, then why isn’t it enough to measure that?

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