# Global income inequality

Via Overcoming Bias I spotted this paper on global income inequality, 1970-2009. Robin points out to be careful, as this doesn’t capture non-financial inequality, and it doesn’t look at the “lifecycle” of individuals – just snapshots of income dispersion at a point in time. Of course, these missing bits are due to data limitations, the authors would have known this full well.

It shows the global static income inequality has fallen, especially over the last decade. Lovely. However, we only get a small part of the story by looking at that graph – the paper also decomposed changes in the global Gini coefficient into ‘between’, ‘within’, and ‘overlapping’ components. In fact, this decomposition was really the main purpose of the paper!

So let us talk about these things, talk about what happened with them, and see where that leaves us

**Between, within, overlapping – what?**

When we have a set of outcomes, it is sometimes nice to look at broader “groups” – as there may be some reason why these groups will be different, or some reason why we may value these groups differently!

Looking at inequality within a nation, we will often group up households based on the “type” of household (eg couple with kids, single person with kids, couple without kids, single person with no kids). When we have different groups we know there will be income differences *between* the groups and *within* those groups. The idea of this decomposition is to figure out what proportion of measured inequality exists between groups, and what proportion exists within the given groups – given we may value that inequality differently.

In the Liberati study the groups are countries, we are interested in “between” and “within” country inequality.

To get a handle of what is going on with this type of breakdown we could head back to the initial papers that looked into doing this (Theil (1967) and Bhattacharya and Mahalanobis (1967)) – however, the literature has moved on since then, and I also can’t find online copies of them . Conveniently, a neat way of conceptualising the decomposition can be found in Peter Lambert’s ‘the distribution and redistribution of income‘ (2001).

Start off with complete equality. Then, given the groups of interest, introduce “between group inequality”. Doing this involves imagining that each individual is a ‘group’ earns the same income as each other individual in a group – but that the groups earn different incomes. Order these groups by income, and draw up your Lorenz curve! Ok, now we’ve done that, we need to accept that within group inequality does exist – so we get this figure by recognising the actual incomes of households/individuals in each group!

Now this second process creates what is called a “concentration curve” rather than a Lorenz curve – and the reason for that is that it is no longer ordered from poorest to richest! Our “income parade” is all out of order. For this reason the between and within inequality figures aren’t sufficient to decompose our Gini coefficient – and we are left with a “residual term”. This residual term (called overlapping, or a reranking term) is the reranking we would have to do to switch households/individuals around in that previous process to get to our Lorenz curve, and its scalar representation in the Gini coefficient!

So now we can tell that the inequality being reported is being broken down to tell us about the relative fortunes of the average person in different countries, the relative fortunes of people within countries, and the “overlap” in income between nations!

Given this, we know that the sharp drop in the between country inequality that has occurred has been partially cancelled out by greater inequality “within” countries. Furthermore, the author points out that if we exclude Asia overall global income inequality has been falling over the past decade – but only after a sizable increase in the prior two decades – but if we include Asia, income inequality is falling sharply, and is well down on its peaks in the 1970s!

All in all, this indicates that we are in a very different world than we were 40 years ago, and many people say. However, if we are willing to move away from a Western centric view to think about the global economy as a whole, the way the world is different may be surprising for some!

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