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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?

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Technically you could do that, but it is well known that Gini is biased in a small samples (eg see Deltas 2003).

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) 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.

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  • $\begingroup$ 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. $\endgroup$
    – syre
    Nov 11, 2021 at 2:54
  • $\begingroup$ @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 $\endgroup$
    – 1muflon1
    Nov 11, 2021 at 6:56
  • $\begingroup$ 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). $\endgroup$
    – syre
    Nov 11, 2021 at 9:14
  • $\begingroup$ @syre oh that’s what you mean, well that does not matter for the Gini calculation $\endgroup$
    – 1muflon1
    Nov 11, 2021 at 10:07
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    $\begingroup$ @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 $\endgroup$
    – 1muflon1
    Nov 11, 2021 at 16:05

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