The Gini coefficient

In a previous post, I wrote about the wealth gap in the UK and I should acknowledge that I started with the preconceived view that there was indeed a wealth gap. What I mean by a wealth gap (and I presume this is roughly consistent with what is generally meant) is that wealth/income is distributed in such a way that a small portion of the population get most of the income. By the end of the post, I found myself slightly confused and although the numbers I had looked up didn’t indicate that there wasn’t a wealth gap, they also didn’t seem to indicate that there was. One of the problems is probably that simply considering numbers like median and mean income and looking at graphs showing how income is distributed doesn’t necessarily allow one to determine if there is indeed a income gap.

There is, however, a way of quantifying the income distribution. This is known as the Gini coefficient which is determined from the Lorentz curve. The Lorentz curve (shown in the figure on the right) shows what percentage of the total income the bottom x % of households have. If income is completely evenly distributed, the Lorentz curve is a diagonal line known as the line of equality (bottom 10% have 10% of the income, bottom 50 % have 50 % of the income etc.). Lorentz_curve The other extreme is the case where one person has all the income and everyone else has nothing. The Lorentz curve would then be a straight horizontal line along the x-axis that suddenly turns up at the end. In reality the Lorentz curve is somewhere between these two extremes. The Gini coefficient is then the ratio of the area between the line of equality and the Lorentz curve itself (A) and the total area below the line of equality (A+B). In the figure shown the Gini coefficient is A/(A+B). If we assume that the x and y axes run from 0 to 1 (rather than from 0 – 100 %), A+B = 0.5 and the Gini coeffiicient is 2A. The Gini coefficient would then be a number between 0 and 1, although it is sometimes multiplied by 100.

The Gini coefficient can vary wildly throughout the world, with poorer countries tending to have larger Gini coefficients. Namibia has one of the largest Gini coefficients (0.71) while Sweden has one of the lowest (0.23). The UK has a Gini coefficient of about 0.34 while the USA has a Gini coefficient of about 0.45.

So, what does this all mean? The UK has a Gini coefficient that appears to be quite similar to many other developed nations, although there are a number of countries that do have considerably lower Gini indexes (Norway, Sweden, Germany, Belgium, to name a few). What is possibly more interesting is that the UK’s Gini coefficient has changed quite considerably in the last 30 years, increasing from about 0.24 in the late 1970s to about 0.34 (maybe even 0.38) today. There appears, in the UK at least, to be a general view that it is worth giving most of the income to a small proportion of the population (in theory the most motivated, creative and skilled members of our society) because this will lead to economic growth and wealth will anyway then trickle down to the rest of society. If this were true you might expect there to be a significant change in Gross Domestic Product (GDP) growth rates in the last 30 years or so because the highest earners are taking a bigger fraction of the total income today than they were in the late 1970s. This doesn’t however, seem to be the case. According to the IMF data the growth rate of UK GDP has been highly variable from 1980 till today. It does not seem to be the case that as a smaller proportion of the population has taken a larger portion of the income, there has been a corresponding rise in the growth rate of the UK economy.

All in all, it seems that the UK has a Gini coefficient that is similar to other developed nations and doesn’t seem to indicate some kind of massive wealth gap. The wealth/income distribution has however changed quite substantially over the last 30 years or so with a bigger fraction of the income going to a smaller fraction of the population. If this has lead to a corresponding rise in GDP, ultimately benefiting everyone, this may seem perfectly reasonably. This, however, doesn’t seem to be the case. It’s my view, therefore, that we should be aiming to optimise GDP together with the Gini coefficient. There is no point in having a small Gini coefficient if the GDP is so low that no one has any wealth. By the same token, there is no point (at least not for the majority) in having a large Gini coefficient if again the GDP is such that the majority of the population is living in poverty. If anything, being moderately socialist, I feel that we should be aiming to reduce the Gini coefficient (i.e., distributing wealth more evenly) until it appears to be having a negative impact on GDP at which point we could assume that we have reached the optimum wealth distribution. A smaller Gini coefficient and we would start having a negative impact on the economy. A larger Gini coefficient and we would be giving more income to a smaller proportion of society for no real obvious reason.

Data is from various sources including wikipedia, the CIA world handbook, and the IMF

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6 thoughts on “The Gini coefficient

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