Sunday, June 14, 2015

Horses for Courses

The other day, Branko Milanovic wrote a blog post detailing his reservations of the Palma index. For those unfamiliar, Palma is a proposed substitute for the Gini index. Whereas Gini measures the longest perpendicular distance between the Lorenz Curve -- which shows the percentage of overall income going to given percentages of the population -- and a line representing complete equality, Palma is a simple ratio between the incomes of the top 10% and the bottom 40%.

Palma came about as the result of an observed regularity in inequality data showing that the 50% of the population between these two quantiles doesn't change that much in the short run. Unlike Gini, Palma is not on a particular scale (Gini can range from zero to one), and thus may be difficult to use in cross-country and intertemporal comparisons.

Milanovic's beef with Palma seems to be in its construction. His basic problem revolves around this immobile middle. In particular, what do you do if the middle does change? I think this is a valid concern, but Milanovic gives little indication as to why Gini is substantially better.

Gini itself has its own problems. Given that it presumes a relatively smooth exponential income distribution, any irregularities can throw off the index.

My major point of contention with Milanovic here is not so much on the superiority of one index over the other, but rather the implication that we should invest ourselves in finding a superior index for inequality. Indices, merely by virtue of distilling the data from an entire economy down to one number, are inherently going to be problematic in terms of universal application. The choice of index (or indices if you're into that whole "robustness" thing) should be guided by the data you have and the questions you intend to answer.

Gini is a pretty good measure of whether incomes are skewed towards the rich, but it doesn't give a very clear picture of the degree of stratification. Palma fills in this gap by focusing exclusively on the rich and poor rather than where the middle is. There are of course many other indices to choose from when investigating inequality, each with its own ideal application and limitations. It is our duty as data scientists to approach each problem with the appropriate tools rather than attempting to force a particular approach as the one-size-fits-all tool.

Different horses for different courses.