*This post was originally published in The Broker. *

Last month, we published a draft paper setting out a potential new measure of inequality: the Palma, which is the ratio of the income share of the top 10% to that of the bottom 40%. We also posted a blog which summarised the paper and noted the interesting mix of reactions that the paper provoked from the early reviewers – like Marmite, people either loved it or hated it. A couple of comments gave us reason to look at the data again, and we present some additional findings here.

First, why the Palma? The reason to isolate this particular ratio ahead of others (eg the top 20% to the bottom 20%) is that the ‘middle’ 50% - those household between the fifth and the ninth decile – have a relatively stable share of national income both across countries and over time. Gabriel Palma made the original discovery of this phenomenon, hence our suggested title. It is important because it means that much of the politics of distribution can be summarised by this ratio, and that relatively little information is lost in this way.

We stop short of arguing that the Palma therefore captures the entire distribution; clearly that would require the stylised fact of a stable middle 50% share to be rigidly observed, which will not always hold. We appreciate the greater clarity on this point that arises from the suggestion of Ricardo Fuentes-Nieva in this debate – namely that we should present the Palma as a measure of income concentration, so as to avoid the (in our view, misplaced) critique that it does not measure inequality in the entire distribution.

Ricardo also highlighted comments made by Branko Milanovic, who provided us with very helpful feedback on an earlier draft: “Suppose that you have (for simplicity) no overall growth, but you have an increase in the bottom share, and an even greater increase in the top share. Palma goes up. The middle class share declines. So inequality increased although the poor are now better off. ”

We make three points in response to this: first, it is an infrequent occurrence; second, when it has occurred it doesn't actually look very bad; and third, a related failing of the Gini provides stark examples of why policymakers should not rely on it.

If we leave aside the ‘no growth’ assumption, then from our 76 countries with data for c.1990 and c.2010, precisely one country meets the criteria of a rising bottom 40% share, rising top 10% share and a falling middle 50% share: Burundi. The graph summarises the following data: the income share of the bottom 40% increased from 20.0% to 20.8%, the top 10% share increased from 26.6% to 28.0%, and the middle 50% share fell from 53.4% to 51.1%. As a result the Palma rose from 1.33 to 1.35 (by 1.4% if you like), and the Gini fell from 33.33 to 33.27 (0.2%).

We see how it would be possible to make an argument that the Gini is closer to capturing the two-decade change in Burundian inequality; but at best this seems uncertain. The Palma probably does capture a genuine, though small, increase in inequality – but again, the actual changes are sufficiently small that the best summary is probably ‘little change’. We don’t see anything here to suggest a serious problem with the Palma.

It’s interesting, however, to look at the other two cases in our sample where the middle 50% share and the Gini both fall, but the Palma rises. One is Moldova, where the middle 50% share fell from 55.6% to 54.0% and the Gini recorded a 4% fall in inequality; but the top and bottom moved in opposite directions and the Palma ratio rose by 60% from 0.81 to 1.30. It is difficult to see how the Gini view can be defended here.

If anything, the other case is more striking. In Mexico, the middle 50% share fell from 61.9% (a real outlier) to 49.5%, and the Gini fell by 5%. Again, however, as the graph shows the top and bottom moved in opposite directions and the Palma rose sharply from 251%, from 0.80 to 2.81.

Looking at the graph, it’s extremely difficult to see how the perception given by the Gini’s 5% fall can be defended as any kind of measure of what happened to inequality.

The remaining criticism of the Palma revolves around its failure to meet a set of axioms that have become broadly accepted for measures of the inequality of the entire distribution. Given that the Palma is not one of these, this is perhaps unsurprising. Nonetheless, we do intend to explore the Palma’s characteristics further – even if the Gini’s ability to meet most of the axioms does not prevent it producing counter-intuitive findings such as those we have highlighted.

Given the over-sensitivity of the Gini to the middle of the distribution, and the (deliberate) insensitivity of the Palma, policymakers could consider a choice between the two: which aspect of the distribution are you more concerned with? Given the relative stability of the middle, and the relative intuitive clarity of the Palma, the arguments for the Gini do not seem strong.

There is, however, no reason for an absolute choice to be made. As emerged unambiguously from the UN consultation, the eventual post-2015 framework – and indeed any domestic policy framework – can and should contain multiple inequality indicators. This means targets and indicators for group inequalities across the whole framework – including gender, disability, age, ethnolinguistic, urban-rural and regional, and the important intersections. The Palma would be an obvious addition, allowing targets and indicators in relation to income group inequalities also.

We would also support a stand-alone goal on inequality, for the norm-setting power as much as anything. Further thought is still needed on whether this should include both gender and economic inequalities, and – more generally – on whether the Gini still has a useful role to play.