## Wednesday, 17 October 2012

### On inequality and the Gini coefficient

This week's edition of The Economist (October 13th-19th 2012) deals excessively with the problems caused by inequality. Empirical evidence shows that higher inequality correlates with higher political instability and reduced investment rates, the mentioned study being just one of the many. And while inequality seems hardly measurable, it's actually quite easy, thanks to two scientists - economist Max O.Lorenz and statistician Corrado Gini. This post will firstly tell about the Gini coefficient, a common measure of inequality, and secondly list intriguing phenomena regarding it's use.

### History

To measure inequality - how disproportionate is the distribution of wealth in an economy is - one firstly has to find a way to quantitatively measure the distribution of wealth. The tool to do so, the so-called Lorenz Curve, was invented by the economist Max O. Lorenz in 1905. Lorenz at the time was 29, yet to write his doctorate - yet the curve he invented offers such an elegant visual presentation of wealth distribution that it's been named after him and used ever since. Using his graph, the Italian statistician Corrado Gini invented the so-called Gini coefficient in 1912 - the same year Lorenz's curve was first named after him.
 Source: Wikimedia.org

### Calculation

The image above represents a Lorenz curve, used to depict income distribution within an economy. The horizontal share represents the a given bottom share of a country's population, while the vertical their respective share of total income in the country. For example, at the point where the horizontal axis reads 20% and the vertical 10%, the bottom quintile of the population get's 10% of that nation's total income, making distribution unequal. The linear function shows when the distribution is totally equal, with the bottom 10% receiving 10%, the bottom quintile 20% and so on respectively.
The Gini Coefficient itself is calculated by dividing the two areas under the graphs - in this case, Gini = A/(A+B), if the letter A only signals the grey area. A coefficient near zero signals that the economy is largely equal - the territorial difference is small, while a coefficient nearing 1 shows that most of the income goes to a few people.

### Phenomena

Having said all this, it can easily be understood while the Gini coefficient is such a popular method for calculating inequality - it only requires semi-basic calculus (the usage of integral) and a division. Nonetheless, the coefficient has it's setbacks. Below, we list three phenomena when the usage of the coefficient is either unreliable, or produces unexpected results.

1)There is no single Gini coefficient
Since the term 'cumulative income distribution' is very, very vague, the different types of the Gini coefficient depends on what kind of income economists measure. Consumption differs less than income, because people borrow to make up for wage differences. Yet income is still more equal than total wealth, since the former changes more year to year.
India is often thought to be more equal than China, since India's Gini is 0.33 and China's is a substantially higher 0.48. But China measures this based on income, while India on consumption. If we calculate the income Gini for India - like economists Peter Lanjouw and Rinku Murgai of the World Bank did -, we'd find that India's Gini jumps to a whopping 0.54.

2) Gini is not the same as the top 1%

Movements like the Occupy Wall Street have generally attacked the huge amounts of wealth distributed to the top 1% of the American population - yet that share doesn't necessarily mean a high Gini as well. Even if the 1% gains a huge percentage of income (say 43%), the rest of the population can divide the remaining percentage relatively equally, which means that the USA's Gini is a relatively modest 0.39.

3) World Gini changes don't equal Domestic Gini changes

Despite what many would believe, a rise in inequality around the world - (By calculating a Gini coefficient for the whole world economy and population)  need not rise or fall overlapping the changes in individual countries' Gini coefficients. Until the 1970's, for example, the Gini coefficient in the USA has been steadily decreasing, mainly due to the disappearance of the Gilded Age fortunes after the two World Wars. Yet meanwhile, the World Gini coefficient has been rising - since emerging economies, with the notable exceptions of Japan and Taiwan, failed to enter the same age of economic prosperity that affected emerged economies. Then the trend reversed to the opposite - USA Gini has increased by a whopping 30% since 1980, while the  World Gini has dropped by a still remarkable 10%.