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Is Inequality All About the Tails? The Palma, the Gini and Post-2015

September 24, 2013
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Alex CobhamAlex Cobham and Andy Sumner bring us up to date on the techie-but-important debate over how to measure inequalityAndy Sumner mug

It’s about six months since we triggered a good wonk-tastic discussion here on Duncan’s blog on how to measure inequality. We proposed a new indicator and called it ‘the Palma’ after Chilean economist Gabriel Palma, on whose work it was based. We suggested the Palma would complement, or perhaps even replace the (in our view) less useful Gini index. Here we bring things up to date with a look at inequality in the post-2015 debate, and present some further findings on the relative merits of Gini and Palma, based on our new paper.

First, post-2015 and all that.

Last week the Center for Global Development held an event in Washington DC to discuss the best income inequality measures for post-2015, with both a technical panel (video) comparing alternative measures, including the median, the Palma, the Commitment to Equity indicator and a multidimensional approach.

There was also a ‘user’ panel (video) with wonks from the IADB, IMF, Oxfam, UNICEF and the World Bank, discussing the policy need and the scope for implementation. While panelists and other participants did not agree on the idea of a post-2015 inequality goal or target (surprise, surprise), there was near unanimity on the importance of measuring income inequality, and doing so better than we do now.

That consensus, however, seems to be lacking in the intergovernmental discussion on post-2015. There appears to be broad support for a focus on economic inequality from Latin American representatives, but more patchy support elsewhere. At the CGD event, Nancy Birdsall highlighted that, to the extent that governments reflect elite interests, there may not (yet) be a political consensus; but that there is instead a “people’s consensus”, with inequality riding high on the agenda of popular concern in countries at all income levels.

Whether this can be translated into more effective political support is unclear, though Oxfam and Save the Children are working on building that political consensus.

But back to feeding the wonks (and remember skimming the next section will save you from having to read the actual paper).

Our new paper, released to coincide with the event, makes three main points (we’re told always make three points – never more, lest people’s heads explode …).

First, inequality measures for policy frameworks such as post-2015 must be considered on the basis of policy criteria, not only the common technical criteria – in other words, we need to think about whether measures are useful for policy processes, not only whether they exhibit certain mathematical properties. A technically perfect measure which is unintelligible to most people (or which requires significant explanation) is highly unlikely to form the basis for policy-maker accountability. So we propose five policy axioms (bear with us):

  • That the value judgments of using this indicator are sufficiently explicit.
  • That it is clear what signal is being given to policymakers on the preferred direction of change of inequality (improving or worsening).
  • That it is clear to a public (ie non-technical) audience what has changed and what it means.
  • That the policy response is sufficiently clear to policy-makers (meaning how policies do or do not influence the indicator).
  • That it is possible to capture horizontal (e.g. gender and ethno-linguistic group) as well as vertical inequality in the indicator.

So, what? We think the Palma, which is the income share of the top 10% divided by the income share of the poorest 40% , is much more meaningful to policy makers and otherwise normal people, than the Gini and Theil measures, which are both relatively obscure statistical constructs.

Second, income inequality is in ‘the tails’ (the rich and the poor). That is, most of the difference when you compare countries, or the same country over time, is in what happens at the top and bottom of society rather than in the middle. For example, the middle 50% of the population have about half of national income in both Honduras and Morocco; but the poorest 40% in Morocco have more than twice the share of national income as in Honduras, and the top 10% correspondingly less (see figure below).

palma v giniIn the new paper we provide substantial new evidence for Gabriel Palma’s finding that the ‘middle’ 50% of the population, defined as households in the 5th to the 9th deciles, has a strikingly stable share of national income (around 50% in fact) – not only in countries at different income levels, but in any given country over time, and in addition through the fiscal stages of taxation and transfers. This demonstrates very clearly that inequality is about how much the rich (the top 10%) and poorest (the bottom 40%) get, or what are known as ‘the tails’.

But the Gini is overly sensitive to the middle of the distribution, so it is not well equipped to address this type of inequality – while the Palma is designed to do just that.

Third – and this is a bit technical – a criticism of the Palma: that it relies only on two points of the distribution, and so ignores too much information about inequality. We show that in regression analysis (bear with us), the same two points of the distribution (i.e. the income shares of the top 10% and bottom 40%) can perfectly explain the Gini – so that in practice it contains no more information than does the Palma.

The difference is that while the Palma is the simple ratio of the two, the Gini has the following form:

Gini = (0.581 * income share of top 10%) – (1.195 * income share of bottom 40%) + 0.419

Hardly intuitive to the person in the street, eh?

Corrado Gini

Palma's the one with the beard

Palma's the one with the beard

In practice, the Ginis that are used in much analysis contain no more information than the Palma, but the Palma is transparent about this, and we think intuitively clear – take what the rich get and divide it by what the poor get.

As we said when presenting the Palma last week, we’re not trying to completely replace the Gini, just saying that the Palma has something to add that is understandable to more people.

Our view is that multiple measures should be used to monitor income inequality for policy purposes – including not only the Palma but also, for example, the median income; and if you must, the Gini.

But if one measure alone is to be used: please don’t let it be the Gini.

Alex Cobham is a Research Fellow at the Center for Global Development.
Andy Sumner is Co-Director, King’s International Development Institute, King’s College London


  1. Thanks for the interesting post. The Palma is a good measure, but I’m afraid you may find it has little more intuitive explanatory value than the gini to the stats-phobic ‘person’ (newspaper editor) in the street.

    I think we’ve seen which inequality measure really resonates- the 1% vs the 99%, which has the added potency of firmly aligning the interests of the middle with the poor – cutting out the middle seems politically ill advised.

    On the measure itself, while ‘the middle’ may contain a constant share of the income, of course it doesn’t necessarily contain the same people over time. Opportunity and precarity would ideally be captured somehow for a policy-relevant indicator.

    If the bottom 40% were all the people under 30 years old, and the top 10% all over 70, would that be an equal or unequal society?

    Best –

  2. Love the PALMA, and your presentation at CGD Alex!

    Fascinating how uncomfortable academics get about measuring inequality “winners”. The Bank and UN think they have hardwired inequality into their work by measuring “poverty” in new ways. The UN wants to “leave no one behind” and the Bank wants “shared prosperity for the bottom 40%.

    Neither shows any interest in measuring the  other side of the inequality scale–those who profit unfairly from inequality, which to my thinking, is the real value added of an inequality measure.

    Would also like a super PALMA that looks at the top 1% (HT–Gawain K).

  3. Thanks for kind comments all.

    TB, agreed on need for mobility measures also; but complementary rather than alternative to better static measures like the Palma.

    TB and Paul; The super-Palma (or Palmax?) of 1% to 40% does have a certain appeal… Although getting both components from same data source is not as easy as you might think. Watch this space.

    Meanwhile, I should draw attention to the write-up, podcast and video from CGD’s event last Monday on inequality measures and post-2015:

  4. Problem not just that our most commonly used inequality statistic, the Gini, is not intuitively obvious, nor that it overweights changes in the middle and underweights changes at the ends. Problem is also that it shares with all the other ratio measures the defect of ignoring changes in absolute income gaps that do not amount to changes in relative gaps. So the Gini, like other ratios, is “conservative” (or to be polemical, right-wing), for only recognizing an increase in relative income gaps as an increase in inequality; anything less than this must be “inclusive”. For example, at one point in time A has income of 100 and B has 200; at a later time A has 200 and B has 400. The Gini and other ratio measures say that income inequality has NOT increased, though the absolute gap has increased from 100 to 200. Shouldn’t our measures of inequality also include what happens to absolute gaps? Don’t changes in absolute gaps matter to people’s experience of inequality? See my chapter in John Ravenhill (ed), Global Political Economy, OUP, 4th edition, January 2014.

  5. Nice post, and very nice article in its longer version (i.e., the one appeared in Significance). Thank you.
    I like the measure you propose. I prefer to use income shares myself, both for research and policy purposes. However, I have a couple of comments.
    First, the Gini index does have a practical Interpretation: it represents the expected income difference between two randomly selected individuals (or households). Example: suppose that in Manchester real average per capita consumption in 2013 amounted to £1000; and that the Gini index is 0.50. Thus in 2013 the per capita consumption of any two randomly selected Mancunians differed on average by £500 = 0.50*£1000. This is also quite intuitive, isn’t it? And it gives an appreciation of how “distant” we may be from the chap or lady sitting next to us on the metro…
    Second, the Gini index uses all the information about the income distribution, i.e., is a complete measure. The Palma measure does not have this property. The article argues that in practice this does not matter when comparing it to the Palma measure. This may well be true in normal times. But I am not so sure this is true when major political or economic events occur, like a global crisis. These are times when it is quite interesting to observe what is happening to the income of the middle class. Thus the Palma measure would not do a good job in such cases.
    That said, I am sure the Palma measure will become increasingly popular. Let’s also keep emphasising that inequality measures incorporate value judgements, which we should debate and make explicit to the policy maker and the public.

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