Faculty of Science

Measuring inequality beyond Gini: Ricardas Zitikis explores the promise of the Zenga Index

By Mitchell Zimmer

Dr. Ricardas Zitikis

Dr. Ricardas Zitikis

When it comes to assessing economic inequality, arguably the most common tool that economists and sociologists use is the Gini index.  Roughly speaking, this index takes the average incomes of various bottom portions of population, compares them to the average income of the entire population, and then gathers all those comparisons into one measure of inequality.  This measure has helped policy makers in their decision making for almost a century.  However, in these times of economic turbulence, there is a widening gap between the rich and poor, so that some analysts have come to question whether the Gini index still adequately reflects the distributions seen in society.  Recently, Ricardas Zitikis has been looking at a new technique, called the Zenga index, to measure inequality.  This measure, just like Gini, also involves various bottom portions of the income distribution, but they are now compared to the average incomes of upper portions, instead of comparing to the average of the entire population.

Zitikis says that the different protocols for calculating the Gini and Zenga indices “are actually about two different philosophies of measuring inequality.”  When the Gini index is used, policy-makers can see how close various bottom subpopulations are to the average population income.  Looking from a broader perspective, this comparison may suggest that the society is encouraged to move towards mediocrity, and it is really difficult to imagine a policy-maker who would encourage this. The Zenga index, on the other hand, takes into account the fact that there is an inherent desire by most people for upward mobility: “we don’t wish to be just average, we want to be the best.” As Zitikis notes, “this philosophy is more natural and progressive than comparing yourself to the average, but I wouldn’t say that the Gini is outdated and that we should jump into using the Zenga index only – the two indices are just two different philosophies, and there can, and actually are, many more philosophies. It is just like going to work: sometimes we find it more prudent to use a bus and sometimes to just walk, or perhaps skateboard.”

Interestingly, regardless of political philosophies of policy-makers, which might be quite distinct, Zitikis notes that when it comes to incomes, “irrespectively of what measures you use, you don’t see `revolutions’ in developed countries when you go from one government to another, even though well-trained social scientists and economists may see some tiny shifts in the values of various indices.” But when it comes to populist movements, such as Occupy Wall Street, these indices are really of little value. “In some sense, those movements cannot use any scientific measures for their benefit because the movements are based on extremes, actually on extreme extremes,” says Zitikis, “and it is such extremes that catch headlines. What we are doing with Zenga and other indices is a very complex and serious science.” Then Zitikis adds with a smile, “what if instead of looking at just plain incomes, we would rank people according to the ratios of their incomes to the number of other people they employ? I guess this `ratio’ index would divert those young, brilliant and energetic minds from `occupying’ Victoria Park into setting up a multitude of start-up companies – what a vibrant and joyous atmosphere would settle into London, with little if any unemployment.”

The desire to see what is happening in various segments of population have long attracted Zitikis’s curiosity, but the idea of exploring the Zenga index came by chance just a few years ago. Giovanni Giorgi, the President of the Italian Society of Economics, Demography and Statistics, and under whom Zitikis has served on the editorial board of Metron, a journal founded by Gini in 1920, suggested to Zitikis to look at a presentation by Francesca Greselin and Leo Pasquazzi to be delivered at one of the Italian statistical meetings. Zitikis said, “when I looked at their paper and saw the Zenga index, I got immediately fascinated by it, as it matched my philosophy so nicely. I contacted Francesca, and she was such an open-minded and wonderful person, and our research on the topic started moving at the speed of light.” Since then Greselin, Zitikis, and their colleagues have coauthored a number of research papers exploring incomes in a number of countries.

“Our next step is to further fine-tune our techniques and explore them specifically on Canadian data,” says Zitikis. “Smaller geographic areas than the entire country or even provinces have to be looked at. These can be as small as, say, North, South, Downtown London, and so on. There are challenges with such geographies, and Statistics Canada has developed an elaborate system of statistical areas to address them.”  Taking statistical subtleties into account leads to a next step in testing how the Zenga index works. This is an ongoing project by Zitikis, his Western colleagues Bradley Corbett and Rebecca Williams, as well as by Francesca Greselin and Leo Pasquazzi from the University of Milano-Bicocca. “What we are trying to accomplish now is to fine-tune a number of methodological aspects so that we could use them on various Canadian geographic levels,” says Zitikis. “Smaller geographic areas might be more homogeneous and thus more attractive from the statistical point of view, but then you easily lose a broader picture of the entire country, and even of the provinces.” As to comparing the Gini and Zenga indices, “we can somehow relate and interpret the differences between the two indices, and see how they rank populations, sometimes differently; yet, we need to gain a deeper understanding of how the indices relate to the events that we see in real life.”