<p>Technically you could do that, but it is well known that Gini is biased in a small samples (eg see <a href="https://www.jstor.org/stable/3211637" rel="nofollow noreferrer">Deltas 2003</a>).</p>
<p>When you apply Gini to whole country you don’t need to worry about having small sample, even small countries have typically several thousands or even millions of individuals. However, typically it is hard to get  GDP per capita data on small segments of a country, and if you just look at a large segments such as for example 12 provinces of the Netherlands, calculating Gini would not be appropriate.</p>
<p>Nonetheless, there is some research that applies Gini-based measures to regional inequalities. Such as the work of  <a href="https://link.springer.com/article/10.1007/s11205-019-02208-7" rel="nofollow noreferrer">Panzera &amp; Postiglione (2020)</a> that applies Gini correlation to measure regional inequality in Italy. However, it is worth noting that the authors were able to get data on GDP for over 100 small Italian regions.</p>

CC BY-SA 4.0
2021-11-11T02:54:09.710Z
My metric is not GDP and I hope my samples are large enough for Gini (33 cities and 360 districts respectively). However, you haven't answered my main point, which is the appropriateness of applying Gini to a ratio. Unless I'm mistaken, Panzera & Postiglione (2020) only appear to apply Gini to a ratio since their metric is regional GDP per capita weighted by population shares, which simplifies to regional GDP over national population. Dividing by a constant does not affect the Gini coefficient.
syre
CC BY-SA 4.0
2021-11-11T06:56:43.473Z
@syre oh you said output so I presumed you will use GDP which is the standard measure of output. Also what exactly you mean by applying Gini as a ratio? Gini itself is a ratio, I am not sure if I understand what you want to do there
1muflon1
CC BY-SA 4.0
2021-11-11T09:14:12.350Z
I mean calculating the Gini coefficient of a ratio metric such as GDP per capita (e.g. across regions) rather than the Gini coefficient of a non-ratio metric such as income (e.g. within a country/region).
syre
CC BY-SA 4.0
2021-11-11T10:07:00.677Z
@syre oh that’s what you mean, well that does not matter for the Gini calculation
1muflon1
CC BY-SA 4.0
2021-11-11T10:13:25.757Z
I know it can be calculated but I'm asking about _interpreting_ the Gini coefficient of a ratio.
syre
CC BY-SA 4.0
2021-11-11T16:05:53.470Z
@syre oh that’s what you had in mind. You can still interpret it, for example Gini of 0 would mean every single region has exactly the same GDP per capita, Gini of 1 would mean only one region has non-zero GDP per capita
1muflon1
CC BY-SA 4.0
2021-11-10T12:25:58.543Z
2021-11-10T12:25:58.543Z
1muflon1
<p>The Gini coefficient is widely used to measure the concentration of income in a population. Similarly, the Gini coefficient can be used to measure the concentration of economic output or population across regions.</p>
<p>Can we use the Gini coefficient to assess the &quot;concentration&quot; of the <em>ratio</em> of output per capita across regions or is the Gini coefficient of a ratio too convoluted to interpret reliably?</p>

<mathematical-economics><gini>
Gini coefficient of output per capita across regions
syre
# Gini coefficient of output per capita across regions

(Asked by: username_0 on 2021-11-10)

The Gini coefficient is widely used to measure the concentration of income in a population. Similarly, the Gini coefficient can be used to measure the concentration of economic output or population across regions.

Can we use the Gini coefficient to assess the "concentration" of the *ratio* of output per capita across regions or is the Gini coefficient of a ratio too convoluted to interpret reliably?

**Tags:** mathematical-economics, gini

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## 1 answers

### Answer by username_1 on 2021-11-10. Score: 1

Technically you could do that, but it is well known that Gini is biased in a small samples (eg see [Deltas 2003](https://www.jstor.org/stable/3211637)).

When you apply Gini to whole country you don’t need to worry about having small sample, even small countries have typically several thousands or even millions of individuals. However, typically it is hard to get GDP per capita data on small segments of a country, and if you just look at a large segments such as for example 12 provinces of the Netherlands, calculating Gini would not be appropriate.

Nonetheless, there is some research that applies Gini-based measures to regional inequalities. Such as the work of [Panzera & Postiglione (2020)](https://link.springer.com/article/10.1007/s11205-019-02208-7) that applies Gini correlation to measure regional inequality in Italy. However, it is worth noting that the authors were able to get data on GDP for over 100 small Italian regions.

> **Comments:**
> **username_0**: My metric is not GDP and I hope my samples are large enough for Gini (33 cities and 360 districts respectively). However, you haven't answered my main point, which is the appropriateness of applying Gini to a ratio. Unless I'm mistaken, Panzera & Postiglione (2020) only appear to apply Gini to a ratio since their metric is regional GDP per capita weighted by population shares, which simplifies to regional GDP over national population. Dividing by a constant does not affect the Gini coefficient.  
> **username_1**: @syre oh you said output so I presumed you will use GDP which is the standard measure of output. Also what exactly you mean by applying Gini as a ratio? Gini itself is a ratio, I am not sure if I understand what you want to do there  
> **username_0**: I mean calculating the Gini coefficient of a ratio metric such as GDP per capita (e.g. across regions) rather than the Gini coefficient of a non-ratio metric such as income (e.g. within a country/region).  
> **username_1**: @syre oh that’s what you mean, well that does not matter for the Gini calculation  
> **username_0**: I know it can be calculated but I'm asking about _interpreting_ the Gini coefficient of a ratio.  
> **username_1**: @syre oh that’s what you had in mind. You can still interpret it, for example Gini of 0 would mean every single region has exactly the same GDP per capita, Gini of 1 would mean only one region has non-zero GDP per capita  

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