You can try with some negative income figures in the attached spread sheet. First arrange the data in ascending order and then estimate the Gini index as per the embedded formula.

I am not convinced that you are measuring income correctly. If someone has negative income, they must be dead. Debt does not correspond to income. Maybe debt service or debt payments but not debt.

I have come across a few articles that consider negative income values (eg: http://link.springer.com/article/10.1007/s10260-014-0293-4).

What did these people eat?

You can measure the Gini index with negative values (e.g. net wealth) but it could be not bounded between 0 and 1. In Stata try the command ineqdec0  

World Bank studies the problem of negative income too..... Obviously there is a lot of people who eat worse or better than P.F. Colwell.....

Specifically, this is an issue when you deal with some specific sources of income.

I studied it for some years, in the paper suggested by Garvita Bajaj (http://link.springer.com/article/10.1007/s10260-014-0293-4) where I am an author, you can find an easy way to normalize the Gini index with negative income.

In case you compute the Gini's index in the traditional way,  this will no longer be between 0 and 1, then you will have difficulty  interpreting or to comparing it.

Here a more recent contribution

http://link.springer.com/article/10.1007/s11205-016-1354-x

Income inequality is basically associated with distribution of income in a given year. Whatever produced is distributed among the households (whatever they earn). If some households do not receive income that means their income for that particular year is equal to zero. But if they do receive income and also borrow to fulfill their needs. In that case net income can be negative(if borrowing greater than they earn). To calculate inequality index, if households do not receive income they should be categorized households with zero income. If they do earn income and borrow too, we should ignore debt(borrowing) to avoid double counting.    Because inclusion of debt as income blur the picture.

For example, household (H1) borrow M1 amount of money from other households (H2). So M1 is income of second household. In Measuring inequality we have to include M1 in income of second household. 

Income is gross of consumption. So if someone earned nothing and yet consumed, then that person's income is equal to consumption. This is regardless of the source of the commodities that are consumed.

Yes I agree and i have used consumption expenditure to measure inequality that overcome the problem of negative income too. But i still believe that to measure inequality in real term we have to use income (not only earnings) but from all sources (earning (wage and profit), remittance income, dividends, government transfers). I believe that in measuring inequality we should not include debt or borrowing. 

Rizwana,

I was not trying to disagree with you. Instead, I was trying to keep the proponents of negative income from wasting their energies on trying to resolve negative income with Gini coefficients.

Peter

OK

Mihaela is right. Just add the minimum of your distribution to all incomes.

Hi, 

G(x) is not equal G(x+k)

@Stefano Could you please provide an example to show that G(x) is not equal to G(x+k)

Variance of G(x)= variance of G(x+c)

var G(x)=var(x)+var(c)

var of c(constant )=o

var of G(x)=Var G(x+c)

The Gini is surely not "location invariant". Just think of the following example :

10 people earning 1,2,3,4,5,6,7,8,9 and 10 respectively. The last person holds 10/55=18.2% of wealth, and the first person holds 1/55=1.8% of wealth.

Now give everyone 90 units each.

The richest person now has 100/955= 10.5% of wealth, and the poorest person holds 91/955=9.1% of wealth. A completely different income distribution resulting in a completely different Gini.

A colleague recently called my attention on the following very interesting paper on the issue Garvita raised in this post:

Article On the Gini coefficient normalization when attributes with n...