# Gini with negative incomes

I have data on disposable income, where some households have negative income. Albeit I can immediately compute the Gini with these dataset (e.g. with ineqdec0, inequal7 or fastgini in Stata), it is well known that Gini with some negative values could be higher than 1. An example from such reference:

Is there an "optimal" method to deal with such observations?

I can think of some approaches like:

• truncating: eliminating all observations with negative income
• censoring: assign zero income to all negative income
• translation: add to every observation the largest negative income, so that the poorest observation has zero income
• some type of normalisation, like the one the reference above gives:

In all these cases, the Gini will now be between 0 and 1. Is there a "preferred" or an "usual" method? (perhaps by multilateral organisations like IMF, OECD, etc)

As a secondary question, is there an inequality index that is better poised to deal with negative income?

• How would somebody have a negative income? What is your interpretation of those observations in the data? Are they measurement error or do they reflect some real phenomenon? Are you sure you are computing a Gini for income? – Tobias Jul 5 '17 at 14:31
• @Tobias A net definition of income will include any payment in term of debt (mortgages, etc). These are (mostly) not errors. You can explore some examples here. – luchonacho Jul 5 '17 at 14:45
• I think this is a weird income definition. To me debt repayment is saving and I don't see why you would deduct that from incomes. Anyways I'd recommend to check papers on wealth inequality where negative values are common and see how they measure inequality. None of the solutions you propose here seem good to me, and I think if you have data with negative values then you should use a measure that is suited to this kind of data. I could think of p90-p10 differences and the like. – Tobias Jul 5 '17 at 19:06
• @Tobias Negative income is a common feature of almost every household income survey I know. Regarding p90/p10 ratio, that only works if the p10 is positive. – luchonacho Jul 5 '17 at 19:39
• Self-employed traders can make losses: if they had made a profit it would be counted as income, so their losses could count as negative income. Personally I would set their income to $0$ at the start of the calculation – Henry Jul 5 '17 at 20:51