On inequality, let’s do the Palma (because the Gini is so last century)

Alex CobhamWhat better place than South Africa to run an inequality week on the blog? Today’s guest post from Alex Cobham (left) and Andy Sumner (right) summarizes their Andy Sumner mugnew paper on inequality – got a feeling this one might be quite important. Tomorrow, Brazil v South Africa.

There’s one measure of inequality that gets all the attention – the Gini index. The Gini was developed in the early 1900s – in fact about 100 years ago – by Italian Statistician, Corrado Gini (see pic, looks like a real party animal). A century later our paper argues that it may be time for a rethink on measuring inequality. Why?

it's no fun being a guru
it's no fun being a guru

The Gini reflects the difference between the actual cumulative distribution of income, or anything else in a population, and perfect equality (the yellow area in the graphic). A Gini value of zero would mean that the distribution is completely equal and a Gini value of one would mean that one person had all the income and everyone else nothing (i.e. all of the green area would be yellow).

Simple, eh? So, what’s the difference between a country A with a Gini of 0.4 and country B with a Gini of 0.45? We can say country B (0.45) is a bit less equal than country A (0.4). What we can’t is where that inequality exists. Is it a squeezed middle? Or is it at the poor’s end of the distribution?

So if you’re a policy maker working for an incoming president elected on a mandate to address inequality and increase the share of income to the poor, the Gini won’t be a great deal of help.

It’s also long been known thanks to inequality guru Tony Atkinson that the Gini is over-sensitive to changes in the middle of the distribution – and, as a consequence, insensitive to changes at the top and bottom. That’s a problem because we care most about what happens at the top and bottom in developing countries.

So, we’ve just put out a new paper, predictably titled ‘Putting the Gini back in the Bottle?’, exploring an alternative measure for policy, which is sensitive to exactlygini area that. We’ve called it the ‘Palma’ as it is based on the research of Chilean economist, Gabriel Palma (below). When Palma started looking at the finer grain of inequality, rather than just the Gini, he made a startling observation (see Duncan’s take on it here).

He found that the ‘middle classes’ – more accurately the middle income groups between the ‘rich’ and the ‘poor’ (defined as the five ‘middle’ deciles, 5 to 9) – tend to capture around half of GNI – Gross National Income wherever you live and whenever you look. The other half of national income is shared between the richest 10% and the poorest 40% but the share of those two groups varies considerably across countries.

Palma suggested distributional politics is largely about the battle between the rich and poor for the other half of national income, and who the middle classes side with.

So, we’ve given this idea a name – ‘the Palma’ (brilliant eh?) or the Palma Ratio. It’s defined as the ratio of the richest 10% of the population’s share of gross national income (GNI), divided by the poorest 40% of the population’s share. We think this might be a more policy-relevant indicator than the Gini, especially when it comes to poverty reduction.

inequality cartoon 2

In the paper, we do a few things. First, we confirm the robustness of Palma’s main results over time: the remarkable stability of the middle class capture across countries, coupled with much greater variation in the 10/40 ratio.

Second, we suggest that the Palma might be a better measure for policy makers to track as it is intuitively easier to understand for policy makers and citizens alike. For a given, high Palma value, it is clear what needs to change: to narrow the gap, by raising the share of national income of the poorest 40% and/or reducing the share of the top 10%.

Third, we also present some tentative but striking evidence of a link between countries’ Palma and their rates of progress on the major Millennium Development Goal (MDG) poverty targets. More work is needed, and there are all sorts of caveats, but the results indicate that countries that reduced their Palma exhibit mean rates of progress which, compared to countries with rising Palmas, are three times higher in reducing extreme poverty and hunger, twice as high in reducing the proportion of people lacking access to improved water sources, and a third higher in reducing under-five mortality. If that isn’t worth a closer look we don’t know whatGabriel Palma is.

Of course not everyone is going to like our paper – we sent it around the great and the good of the inequality world and really got a ‘marmite effect’ –people love or hate it (Andy’s New Bottom Billion paper on poverty in middle income countries got much the same initial response). Who likes it? Without naming names, here are the main love/hate responses – stylized – for a few salient groupings (those who commented on the paper shouldn’t get too hung up on this table).

Love it Hate it
Inequality gurus and wonks Those who appreciate the point about communicability and policymaker accountability Those who feel the mathematical properties of an inequality measure are more important
Other wonks Those who feel tackling inequality (or at least, vertical inequality) is central to development Those who prioritise other aspects, e.g. the 0.7 target for aid
Economists More ‘political’ economists, philosophers More technical economists

We think there’s an important debate to be had on measuring inequality, especially if the post-2015 discussions take it into central account. So let’s start with a vote (see right), preferably after you’ve taken a look at our paper.

Andy Sumner is co-director of the newly established, International Development Institute at King’s College London, that is seeking to study development from a different angle. Alex Cobham is a research fellow at the Center for Global Development in Europe and a member of the advisory group of the UN consultation on inequalities in post-2015.

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14 Responses to “On inequality, let’s do the Palma (because the Gini is so last century)”
  1. Chris

    wow, those are some really striking statistics regarding “the Palma” and the MDGs, it would be definitely be interesting to see some more indepth research on this. If they follow this trend and the Palma gains traction it could provide a great motivator to put inequality high-up on the development agenda, both at the international and national level.

  2. This is great! In the water sector, in the post 2015 discussions on how to measure the reduction in inequalities in access to water and sanitation we did look at the Gini. A couple of experts got to the conclusion that it was not very helpful. The Palma does look promising – will look further into applying it.

  3. max

    really great blog. palma it is then.one question-how would palma also be used to measure wealth? as I understand it the focus on income has hugely under-represented inequality over the years. can we have a wealth palma?

    and also when can we start fighting inequality and not just measuring and talking about it?

  4. Alex Cobham

    Thanks for comments and votes – more please!

    Chris, we are certainly pursuing the result. Watch this space…

    Catarina, as we discuss a little in the paper, part of our thinking comes from exploring the set of group inequality measures that seem likely to be part of the post-2015 framework (e.g. on gender and ethnolinguistic group), and seeing some value in having a comparable measure for economic inequality. There’s a little discussion of that in the synthesis report of the post-2015 inequalities consultation report too – but I know your sector has done a good deal of thinking about measurement issues already, in fact I’ve drawn on a bit of it for a DHS-based paper that’s in the works.

    Max, no reason not to use this for wealth – am also trying that in the aforementioned DHS bit of work. Though of course we need much better data on wealth, it makes the income distribution data look quite good which is no mean feat.

    As to when we can start fighting inequality, not just measuring and talking about it: our hope is that the intuitive simplicity of the Palma can make this whole area resonate much more readily than the Gini with citizens and policymakers alike. Bring it on!

  5. On a more philosophical note, I’m a little bit concerned that inequality is becoming so in vogue.

    What about opportunity? It’s a bit more sketchy, but doesn’t it trump inequality, justice-wise?

    Take a busker and a banker – no reason they shouldn’t have lots of inequalities, right? If they both went to Eton, and had a similar enough menu of life choices – good; if the busker wants to be a banker (or vice-versa), not so good.

    The problem comes when you start to wish your past menu choices were different, but can’t retread (path dependence). For me, for example, dropping maths means I’m unlikely to get an Economics PhD. Some people are never given the opportunity to be musical (a much harsher deprivation, in my view).

  6. gawain kripke

    In general, i’m sold on la palma. wondering a couple things:

    1. did the World Bank in setting it’s strategic goal on the growth of the bottom 40% go for la palma and then lose their nerve before they got to the top 10%. what gives? how do you interpret that?

    2. I wonder if the top 10% is actually a good enough selection. After all, in the US, it’s hardly the growth of the top 10% that’s driving inequality. Even the top 1% is probably too expansive. the big driver of inequality is the extraordinary, outrageous growth in the top 0.01%. NOt sure how applicable that is in other countries/contexts. But politically, it’s important. If new taxes and other confiscations are necessary, we want to do good and effective targeting. And, not trivially, we don’t want to make unnecessary enemies. So, how about a “super Palma” = income share of 1%/40%? How different would that be? Would it have any analytical or other value?

  7. Alex Cobham

    Thanks Gawain.

    1. Ha! Not sure; Adam Wagstaff points out that the leaked documents are only drafts and can change, so I’m hoping that means the Palma might yet feature.

    2. I like it – although the data challenges are significant. It’s probably worth mentioning that some defenders of the Gini have criticised the Palma precisely because the data on the top end of the distribution is bad. (As if it somehow speaks in favour of the Gini that it is insensitive to a badly measured bit of the distribution.)

    There isn’t the same stability of the omitted bit of the distribution as the Palma seems to have, which makes it less attractive. But on the other had, we could call it ‘extreme Palma’, or Palmax…

  8. One thing that is really cool about ratios is that you can combine them and compare them. Perhaps we need not consider this a dichotomous choice.

    In particular, because they are both generated from the same data (income distributions), it would not be difficult to track them side by side. Then one could determine which one is more interesting to a given topic at hand using statistical analysis to form a theory about which type of inequality is most pertinent.

    Although the normative assumptions about the Gini coefficient are important to consider, we might also consider whether it is of practical importance if it gives us information about where the Palma is going. If the Gini coefficient is more sensitive to changes in the middle, then we might ask what these changes indicate, and what this can tell us about other issues, rather than dismissing this as less useful than a different type of predictive power.

    Although your results for the Palma and MDGs are really interesting, I think that your note that “Given the findings of section 3, it follows that similar results are likely for the Gini
    also.” is more critical than the parentheses imply. The question seems less either/or and more, which does a better job predicting what?

    It might be that different inequality distributions have different importance in different situations, just like we measure both blood pressure and heart rate, and these are different in men and women.

    Congratulations on this excellent paper and thanks for your work. I hope that the development community can take a balanced approach to putting another tool in the toolkit of poverty analysis and reduction.

  9. Mark

    Hi Duncan, some thoughts
    1. Income is presumably easier to collect data on than wealth. But in places like SA and Kenya, where the wealth (real estate etc) has historically been in the hands of a tiny minority (an elite, in fact – rather different characteristics in the two countries), and where there has been massive asset inflation, the share of a nation’s wealth that stays in the hands of this tiny minority merits attention (not least because it is not earned)
    2. I agree that, from a communications point of view, the Palma is much more compelling than the Gini. But I still think the focus on relative income shares (ie proportions), as opposed to share of income in absolute terms, misses an important part of the story.

    From the tables it looks as though the top 10%’s share of income in Kenya declined from about 50% to about 40% over the 20 years, where the bottom 40%’s share increased from about 10% to about 13% (sorry, can’t see the exact figures).

    Let’s assume Kenya’s national income was 100 in 1990 and grew at 3% compound for the next 20 years (recent growth has been faster, of course), it would now be 180. The top guys’ share would have gone up from 50 to 72 (+22), whereas the bottom guys’ share would have gone up from 10 to 23 (+13). Big deal, one might say, in the context. I guess this speaks to the issue that the paper raised about the difficulty of determining what an acceptable level of inequality is, or, for that matter, what we should consider to be an acceptable rate at which inequality declines.

  10. Michael Ossipoff

    The Palma is undeniably better than the Gini. The Gini is riddled with unnecessary faults.
    If the Palma is the current competitor to the Gini, then immediately switch to the Palma. Plenty of time later to consider further refinements and improvements.
    The Gini is a good measure of inequality.
    …until you compare it to any one of the other measures of inequality.
    Regarding the Gini, the good news is that there’s a way in which it could make some (but not much) sense as a sum of weighted departures from the mean. The bad news is that it doesn’t, because its response to above-mean incomes makes no sense. (So disregard the above-mean income, or do include them via a separate Gini calculation that responds to them in keeping with the stated purpose of inequality-measures.
    What’s wrong with the simple, natural and obvious CV?
    …or just the bottom 10%’s percentage of its equal-share?

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