<p><strong>tl;dr</strong> No, it is not possible to have a negative Gini coefficient.</p>

<p><a href="http://en.wikipedia.org/wiki/Gini_coefficient">The Gini coefficient is the area between the line of equality and the Lorentz curve</a>, and this area cannot be negative. Let the area of equality as in the link be denoted by $A$, and the area under the Lorentz curve be denoted by $B$, then the Gini coefficient is given by</p>

<p>$$ G = \frac{A-B}{B}$$</p>

<p>If negative income (or whatever you are measuring) is not permitted, the maximum inequality is $1$. If negative income is permitted, it can potentially be larger than $1$. In any case, the minimum for the Gini coefficient is $0$, which corresponds to total equality.</p>

CC BY-SA 3.0
2015-04-07T22:07:45.243Z
I don't know why, but I've seen some pictures where the lorentz curve is above the line of equality...
An old man in the sea.
CC BY-SA 3.0
2015-04-07T19:30:35.363Z
2015-04-07T19:30:35.363Z
FooBar
<p>Is it possible to have a negative gini coefficient?
In which situations is it possible?</p>

<p>Any help would be appreciated.</p>

<microeconomics><econometrics>
Negative Gini Coefficiente?
An old man in the sea.
# Negative Gini Coefficiente?

(Asked by: username_0 on 2015-04-07)

Is it possible to have a negative gini coefficient?
In which situations is it possible?

Any help would be appreciated.

**Tags:** microeconomics, econometrics


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## 1 answers

### Answer by username_1 on 2015-04-07. Score: 8 | Accepted answer

**tl;dr** No, it is not possible to have a negative Gini coefficient.

[The Gini coefficient is the area between the line of equality and the Lorentz curve](http://en.wikipedia.org/wiki/Gini_coefficient), and this area cannot be negative. Let the area of equality as in the link be denoted by $A$, and the area under the Lorentz curve be denoted by $B$, then the Gini coefficient is given by

$$ G = \frac{A-B}{B}$$

If negative income (or whatever you are measuring) is not permitted, the maximum inequality is $1$. If negative income is permitted, it can potentially be larger than $1$. In any case, the minimum for the Gini coefficient is $0$, which corresponds to total equality.

> **Comments:**
> **username_0**: I don't know why, but I've seen some pictures where the lorentz curve is above the line of equality...  

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