To Gini Or Not To Gini

Funny how the subject keeps popping up. First the IMF, then this lovely history lesson from Prof Frances Wooley (excerpt):

Why the Gini?

Stephen Gordon recently posted an excellent analysis of trends in income inequality in Canada and elsewhere. Stephen, like almost all of the other authors cited in his post and the subsequent discussion, measured inequality using the Gini coefficient.

The very next day, I saw a paper by Francesca Greselin arguing that the Gini is inferior to the new Zenga inequality index and should be replaced.

Talk about deja vu all over again. Various limitations of the Gini inequality index have been known for years. Tony Atkinson described some and proposed an alternative to back in 1970; other indices for measuring inequality are the Theil index, and the Hoover index. Greselin and co-authors set out new arguments, and make a convincing case for replacing the Gini. But I don't expect to see the Zenga index in wide use any time soon.

We keep on using the Gini because that's the way people have always done it. But why did people even start using the Gini in the first place?...

...Simple. Intuitive. Because people were used to visualizing inequality with Lorenz curves, and not with frequency distributions. But the Gini coefficient is seriously defective as a measure of inequality, for two reasons.

Reason 1. Suppose society is composed of two groups, reds and greens. One group is more privileged than the other. A reasonable question to ask is: how much of the inequality in society is attributable to differences between these two groups, and how much inequality is attributable to differences within these groups.

The Gini coefficient cannot answer this question, because it is not easily decomposed into between group and within group inequality. Other measures can be, and that's one reason to use the Theil or another index in preference to the Gini.

Reason 2. Suppose that there is diminishing marginal utility of income - that is, people get more satisfaction from their 100th dollar than their 100,000th. In this case, the best way to get the maximum possible amount of happiness from a given amount of resources is to distribute them as equally as possible. Just like serving a blueberry pie to a group of friends and family. Sure, some might end up with a bit less because they're dieting or a bit more because they're growing. But basically happiness is maximized by sharing the pie, not letting one or two people to hog it all.

In othe[r] words, the reason we care about inequality is that it reduces the happiness achievable from a given amount of income. How much depends upon the happiness/income relationship.

In my post the other day, the Gini numbers for Malaysia don’t appear to have moved much since the late 1980s. Yet there’s an increasing perception that inequality has increased – count me in as one – even as the empirical evidence says otherwise.

Perhaps the change in people’s perceptions of inequality is not that inequality itself has increased, but that we as a society care more about it. That fits in with some of the research I’ve read – for starters higher income economies tend to have lower levels of inequality, largely due to redistributional efforts such as use of tax and transfer policies.

The question remains whether high income results in lower inequality or the other way around, or both. The link for the first is fairly well established – as incomes grow, concerns over inequality starts rising. The latter two are less well established, though the IMF articles lend support to the idea that lower inequality helps increase economic growth (thus yielding higher incomes).

So whether or not inequality in Malaysia is increasing, social pressure to address it is likely to continue rising. And this is a social and political issue as much as an economic one.