For those who don’t know, the Gini coefficient is used to measure equality of income. With a coefficient of zero everyone has exactly the same income. With a coefficient of one only one person has all the income and all the others have none. The left love this measure and seek to get it as low as possible by punishing success. They cannot see the difference between equality of opportunity and equality of outcome. So in socialist Britain we have a Gini coefficient of just over 0.5 before tax, but when our massively redistributive taxes are taken into account this comes down to about 0.34, which is pretty much where it has been since 1990. It was lower (approx 0.31) under Margaret Thatcher!
One problem is that Gini only measures relative wealth. So in a country where most of the people were millionaires and some were trillionaires the coefficient would be high and the socialists would hate it. We saw this effect in Britain during Gordon Brown’s immense recession, the rich were hit very hard indeed, so the Gini coefficient became a bit smaller. This should make the lefties very happy. But the reality was that the poor were also getting poorer, just on a far smaller scale. So the Gini coefficient can  fall when the poor are getting poorer and it can rise when everyone getting richer. Giving the opposite reality to what the lefties would be trying to tell us.
There is another way that it doesn’t reflect reality. If the world’s richest men: Vladimir Putin, Bill Gates, Carlos Slim, Warren Buffett, Amancio Ortega and Larry Ellison, all moved to live in sunny Tower Hamlets then the Gini coefficient for that borough would take a sharp jump upwards. But would there be any more real inequality? Of course not. Instead the presence of their wealth and spending, plus the economic multiplier effect would make everyone in Tower Hamlets better off. In other word adding extra rich people to an economy , whist annoying for the lefties, is in fact very good the the greater population.
The Gini coefficient follows a Lorenz curve and it is a fact that completely different distributions can give you the same number. So comparing the coefficient of one population with that of another population is fundamentally fallacious As is comparing the coefficient for the same population at different times. This completely removes any credibility Gini may have as a tool.
It is very difficult to analyse what Gini is saying, for instance a low number might signify a non diverse economy or a lack of opportunity just as much as it might signify something about the social justice of that society. So a low coefficient can be a bad thing.
Gini coefficient can be for the whole income or for disposable income. It can also be calculated for wealth. Add in the confusions above to these different measurements and you can see non professional economists very easily being led astray.
In the real world it does not matter if the rich are getting massively richer with the rest of society also getting richer but at a lesser rate, even though this will make the Gini coefficient go up. Wealth is not a zero sum game, it can be created by making profits. This takes enterprise, hard work, investment, skills and a bit of luck. Maximising productivity is very important. Obviously the state taking taxes out of society has the opposite effect, which is why low tax economies like Singapore and Hong Kong inevitable perform much better, despite having nearly nothing in the way of natural assets.
The reality that kills off Gini completely is that it doesn’t matter. Uneven wealth and income distribution does more harm than good. It is only in countries where envy has sadly been embedded into the social fabric that there is claimed to be a problem. Thomas Piketty can take a hike.