Talk:Gini coefficient

Motivate the math for non-quants please

This topic is of interest to anyone who wishes to think precisely about equality, and most such people are not deeply versed in statistics. Yet the concepts in play are not terribly complex. In other words, non-quants should be able to follow the presentation, and could if the author explained as he went along how each number or equation related to the guiding project of quantifying equality. (Yes, I know this is partly subjective.) Personally, I became impatient with the math and decided not to invest time trying to understand it, since the author had not earned my trust. That is, I didn't sense that by the end of the article I would understand Gini coefficient and its the strengths and weaknesses as a quantitative measure of equality of income or whatever else it can be applied to. 24.125.43.171 (talk) 21:30, 3 August 2008 (UTC) Peter Henderson

There is no shortcut to understanding quantitative relationships. You must learn some mathematics. --Kjb (talk) 15:57, 10 May 2009 (UTC)

I think you're overstating the case, Kjb. We could add some text to the article that explains how the mathematical formulae represent inequality in a way that would be very accessible to someone who did not want to deal with the details of the integral. (Right now the article has some very nice and clear explanations of how the computation works that are accessible to non-math types, but no explanation of *why* those computations are the right ones.) If there are no objections, I'll take a shot at adding such text.

Japan not colored right in Picture

In the image titled "Gini coefficient, income distribution by country." Japan is colored yellow turkey, which would mean it has the lowest Gini coefficient of all nations (<0.25). However, Japan's Gini value is 0.38 which would make it light green. —Preceding unsigned comment added by 76.230.234.52 (talk) 07:15, 10 June 2008 (UTC)

I'm going to change Japan's Gini coefficient in the intro paragraph to what the Japan article says - .38. There's a citation in the japan article and no citation in here, so I'll default to that. Meviin (talk) 03:44, 24 August 2008 (UTC)

abused concept

The gini is a much abused concept that this article doesnt reflect.

Firstly socialists use it to imply that unequal income distribution is bad, whereas this is absolutely not the case. In itself the use of the word "perfect" distribution implies that a perfect straight line is some of form of goal. A straight-line distribution is neither desierable nor necessarily acheivable.

Inequality is the natural product of individual choices expressed as preferences for differentiated options. See Albert-László Barabási: Linked, the new science of networks. These preferential attachments, as Barabási calls them are mathematically shown to result in power law distributions. Which are distributions of vast inequality.

The underlying principle can simple be explained as small difference in a set options yield vast differences in outcome.

The implication is very clear that inequality in society can be the natural result of fair and free trade, so the factors that alter inequality in either positive or negative are not comparable with gini.

The gini coefficient tells you nothing about any particular society other then as a fairly meaningless comparative number.

Deus777

I think that the article does quite a good job in describing Gini coefficient limitations. Have in mind that this is just a measure (and it is important to understand a measure of what, exactly). Whether particular value is 'good or 'bad' is a matter of interpretation. Of course, those who moan about Gini coefficient (or other similar indices) abuse prefer to sweep data about startling inequalities in some highly developed countries under the rug. --bonzi (talk) 09:50, 10 February 2008 (UTC)

What about large gini coefficients, in comparison to other countries or the world average, says more than 0.5? does that tell us anything about the country? It sounds rather unhealthy. --Vsion 02:06, 26 August 2005 (UTC)

no because you can't tell what is the normal degree of inequality and what factors changed it. you also have to consider the dynamic nature of a society. what is the rate of change over time? You cant compare two societies with vastly different tax system because they create inequality at different speeds, but eventually the higher taxing system will arrive at the same place as the lower taxing system. I think you can only meaningfully compare one set of data against itself over time if you know what are the causes of the differences.

some distributions are extremely unequal, for example distributions of market share of search engines, but this is a good thing because it means more people are using the better search engines.

A single number doesnt really tell you where in its evolution a country is or why its inequality deviates from expectation or even what its expectation is.

the UK has a gini index of 36. Uzbekistan has a gini index of 26 and papua new guinea 51. yet the later are both very poor countries. You cant infer much from these numbers without looking at what is happening in each country. vietnam has an index of 36.1 which is nearly indentical to the UK. yet you would expect the UK to have a vastly different inequality to vietnam.

Deus777

If a country has a high gini index say more than .50, then i would say the country has an income distribution problem, leading to social instability and crimes. Unless it is caused by natural disaster, the problem probably indicates an unfair distribution of the country's resources (fertile land, mineral resources, govt. revenue, restriction on internal migration, ethnic discrimination, etc). Of course, we can't summarize a whole society into a single number, we alway need to examine further to better understand. --Vsion 03:35, 26 August 2005 (UTC)

Perhaps you can point to evidence of any study that shows a corelation between a gini number and crime or social instability. Denmark has more property crime then the US and as much as the UK but has one of the lowest gini coeficients in the world. gini doesn't measure opportunity and restriction on opportunity is a better indicator of a society with a problem. Uzbekistan has a very low gini yet has a lot of social instability same with most of the former yugoslav republic. Rwanda is another example of a very low gini with catastrophic social instability.

A counter example is Hong Kong, above .5 for a long time but the only social unrest is against china not inequality.

Inequality in itself is fairly benign if opportunity is present. In fact an excess of equality can be a sign of a society with serious problems. Deus777

Anyway today is generally accepted as better a low one. Think too about envy in a not equal society.

Granite26

I think the issue is that according to this, a 'perfect' distribution has a doctor (8+ years of schooling) making the same income as a janitor(High School, maybe), and somebody working 50 hours a week making the same as somebody working 30.

It could be argued that there is nothing wrong with a doctor and janitor making the same amount. Just because you perform more skilled work, which law, moral, or god's book says you deserve a bigger cut of the natural resources and energy spending of a country? "Wealth" tied to what you do is a concept that's at the core of capitalism, and not one that holds in general. For example, what if there was an economy where manufacturing of everything had been completely automated (no human intervention), but most services (medical, teaching, cleaning, even hair dressing) were still provided by people. Does it make sense that all of a sudden the doctor has more right to more of the machines' output, for example 10 BMWs and the hair dresser has right to only bicycles? Who makes that call? If you say the "market", then that means that you are only considering capitalism. We must think further ahead people! Post-capitalism may one day be a reality ... —The preceding unsigned comment was added by 129.162.1.31 (talk) 23:38, 9 January 2007 (UTC).

As a 'concept', the Gini coefficient (better use the Theil index) just is about measurement, not about socialists or communists or rightists or marsians or whatsoever. As for judgements and interpretation of data, the following excellent book could help: Yoram Amiel: Thinking about Inequality: Personal Judgment and Income Distributions, 2000. The book adds meaning to maths.
DL5MDA (talk) 23:49, 10 February 2008 (UTC)

I agree with the above two responses. I study political science, and if the Gini coefficient was just about edifying a socialist worldview, I would be against it on grounds of childish oversimplification. However, the Gini coefficient has and can be used for theories predicting social conflict. Such theories are commonly variants of relative deprivation theory, a theory that is attributed to Ted Gurr (who wrote "Why Men Rebel") or Davies (see "J-curve theory") but can be traced back as far as Aristotle's "The Politics":

"The universal and chief cause of...revolutionary feeling... [is] the desire of equality, when men think that they are equal to others who have more than themselves; or again the desire of inequality and superiority, when conceiving themselves to be superior they think that they have not more but the same or less than their inferiors....(1236-1237)

I think the Gini coefficient can be helpful, though it is unclear of how useful it is when predicting conflict in low-income societies where conflicts can be over land (the "minifundia" or by comparison the "landlessness" theories of social conflict), drugs (which may possibly be tied to land, such as in Columbia or Afghanistan), or other resources like oil or diamonds. —Preceding unsigned comment added by 68.197.126.201 (talk) 07:38, 24 April 2008 (UTC)

Granite 26: For more on this concept you might want to check out Johan Galtung's "intellectual proletariat" theory of social revolution, if you are not already familiar with it. By the way, I appreciate your enthusiasm, but you have to realize socialism is a very old concept. Again, it goes back to Aristotle (see Book Two: Part 5). The problem with socialism is not a lack of imagination on the part of "the masses," but that it is predicated on false assumptions of human nature - that is, that reward and punishment are not operative on human motivation, and that moral dilemmas can be eradicated through Draconian laws against inequality. I think socialists need to be more imaginative at this point, not capitalists. —Preceding unsigned comment added by 68.197.126.201 (talk) 07:55, 24 April 2008 (UTC)

Strange discussion. None of the inequality measures has any normative implication on what is right or wrong, on wether inequality is good or bad etc. Those measures just describe inequality. Forget about socialism and capitalism and just do honest science. That starts with unbiased observation and measurement. The abuse of inequality measures is labeling them socialist or capitalist or whatsoever. The difference between the inequality measures is the distribution model behind the inequality measures. Gini's coefficient basically has no model, but it is "intuitive" to people who like the Lorenz curve. And there is lots of empirical experience with that measure. Hoover's "Robin-Hood-Index" is proportional to the effort required to get from inequality to equality with maximum information and minimum effort. Theil's index assumes a model, in which stochastical changes eventually lead to equality in a closed system. Now pleaseplease hold your horses: This does NOT mean, that equality is a teleological goal of redistribution. Equality of everything just is the most probable final state of a closed system. In open living systems you always need a difference between maximum entropy of a category (perfectly equal distribution within that category) and the actual entropy of a category, which is given by inequal distribution within that category. In information theory such a security gap is called "redundancy" (ISO/IEC DIS 2382-16:1996). That is what also keeps societies alive. (They do that since the stoneage by defining system borders by means of "us" and "them" and exporting entropy to "them". "Them" is, where the litter is.) However, too much inequality results in turbulent adjustment processes, which may destroy structures required to stay alive. Different inequalities in different categories have different implications, which can be shown by the non-proportional relation between Hoover's and Theil's index. All those aggregating measures have in common, that socialists, communists, Austrian school disciples, anarcho capitalists etc. can abuse them in fighting against each other. But that isn't science anymore. The Gini-Coefficiont just is a statistical measure. What you make out of it should be discussed under distributive justice etc. And with the Theil index you even can do research on where inequality can have optima under certain conditions. If one can not deal with measuring before judging, one should stay away from economics as a science and turn to learn the rules belief systems and ideology, which deal with any analytic measurement as a threat to their stability. And reading Yoram Amiel's Thinking about Inequality: Personal Judgment and Income Distributions and Sen's & Foster's On Economic Inequality could save you lots of time which otherwise is wasted in normative and biased discussions. Regards from Munich -- DL5MDA (talk) 16:47, 26 April 2008 (UTC)

Yes, statistics, in themselves, are morally and politically neutral. The motivation behind why someone would collect them is not. Why does the Census ask for your race and not your eye color? DanBishop (talk) 05:29, 27 February 2009 (UTC)

The case of India and China

How come that the coefficient is so low in India and China? I mean disparities between rich and poor are tremendous down there and forms of child labour are commonplace. I'm also astonished by the case of Russia.Mitch1981 (talk) 19:26, 7 January 2008 (UTC)

Is it Income or savings or ...? If income, then what kind of income? How has the coefficient be computed? How reliable are statistics in India, China, Russia etc.? The sources of confusion are endless ;-)

Try: http://www.wider.unu.edu/research/Database/en_GB/database/

DL5MDA (talk) 01:24, 8 January 2008 (UTC)

There are 1.3 billion and 1 billion people in China and India respectively. There may be a huge gap between the rich and poor, but the vast, vast majority of their citizens make the same money and live the same poor life. As for Russia, according to the CIA factbook/wiki, their middle-class has grown from 5 million to 55 million over the past 7 years, with the average weekly salary increasing 10 fold. Your idea of income inequality in Russia may be outdated. —Preceding unsigned comment added by Sbw01f (talk • contribs) 06:20, 19 January 2008 (UTC)

Disadvantages of Gini coefficient as a measure of inequality

"As an extreme example, an economy where half the households have no income, and the other half share income equally has a Gini coefficient of ½; but an economy with complete income equality, except for one wealthy household that has half the total income, also has a Gini coefficient of ½"

According to these calculator, a society where 2 individual have an income of 0 and other two have an income of 15 has a gini index of 0.5.

A society where 3 individual earn 5 and one earn 15 has a gini index of 0.25.

How is right (wrong) - the article or the calculator?--83.132.102.216 (talk) 17:32, 10 April 2008 (UTC)

Someone {{fact}}tagged the assertion in this article that, "As an extreme example, an economy where half the households have no income, and the other half share income equally has a Gini coefficient of ½; but an economy with complete income equality, except for one wealthy household that has half the total income, also has a Gini coefficient of ½". I did a quick check with the Gini calculator here,with results that data of "1000, 1000, 1000, 1000, 1000, 0, 0, 0, 0, 0" produces a Gini coefficient of 0.5, but data of "2500, 500, 500, 500, 500, 500" produces a Gini coefficient of 0.333333. I tried again with data of "2500, 250, 250, 250, 250, 250", and that produces a Gini coefficient of 0.5, so I reworded the assertion to say "As an extreme example an economy where half the households have no income, and the other half share income equally has a Gini coefficient of 0.5; and an economy with one wealthy household that has half the total income and the rest of the households share the other half equally also has a Gini coefficient of 0.5". -- Boracay Bill (talk) 23:22, 10 April 2008 (UTC)

But the second situation is not "an economy with one wealthy household that has half the total income and the rest of the households share the other half equally" - it is "an economy with one wealthy household that has two thirds of the total income and the rest of the households share the remaining third equally" (the total income is 3750 = 2500 + 5*250; 2500 is 2/3 of 3750)--83.132.77.218 (talk) 23:35, 11 April 2008 (UTC)

I don't what I was thinking. I trashed the link above to the Gini calculator (now corrected) and garbled the info. The earlier example had problems and so did my ham-handed attempt to fix it. I've removed the "As an extreme example ..." bit -- Boracay Bill (talk) 01:39, 12 April 2008 (UTC)

Is there a measure of the gini coefficient excluding indigenous people? (ie, are not a part of the normal flow of economy.) Obviously such a measure also has it problems... do you want to discount the rural population of china since china is actively trying to incorporate them in the society, and soon they will be counted? but it also has advantages (how much of brasil's inequality is structural versus how much is really just their extreme preservation of hundreds of local indigenous cultures) — robbiemuffin ^{page talk} 22:49, 18 June 2008 (UTC)

Split proposal

In many places in the article, remarks pertaining only to the Gini index of wealth in a country or region interfere with general discussion of the Gini coefficient, which can be used in any context, but which even in economics has other applications. I propose we move treatment of the Gini index for wealth to a separate article (where we can also discuss use of the coefficient rather than the index for wealth). Classical geographer (talk) 09:15, 15 May 2008 (UTC)

What? Do you mean that splitting the article up so that there is a clear distinction between the economic use of the term, plus the other applications of gini coefficients such as in biology and the other things? I'm not so sure about that. Economics uses it quite alot, whereas other disciplines dont afaik. Still, it can be discussed. 58.7.206.131 (talk) 15:04, 25 May 2008 (UTC)

I agree!! As a measure of dispersion it can be used accross disciplines, there should be a regular statistics entry for it! —Preceding unsigned comment added by 138.253.73.55 (talk) 01:46, 17 June 2008 (UTC)

I agree that the article should be split. The present title could be kept for the maths stuff, with something more directly meaningful for the "measure of inequality" stuff.Melcombe (talk) 09:12, 20 June 2008 (UTC)

I don't think the article should be split. Yes, GINI can be used to talk about any inequalities, but its application to economics significantly outweighs other applications. Odds are that anyone who came here searching came for economics. The article is still short enough that any disambiguation can/should happen within the article itself. Cretog8 (talk) 15:19, 20 June 2008 (UTC)

Agree with Cretog8 against a split. Dbfirs 21:57, 20 June 2008 (UTC)

Also agree with Cretog8 against a split. You can still create a disambig if needed (leaving this article in place with a small tag at the top) or create a section in this article for alternative meanings. Morphh ^(talk) 19:01, 29 June 2008 (UTC)

Also against a split for the reasons stated by Cretog8. I'm not sure we have enough information for a separate mathematics article. The article focuses on the economic uses of the Gini coefficient. The first sentence says it well: "most prominently used as a measure of inequality of income distribution". That is, it is most notable as a measurement in economics. It should not come as a surprise that the article focuses on the economic uses of the coefficient. Besides, there's a link to Statistical dispersion#Measures of statistical dispersion in the first line, if users are actually looking for the mathematical application, even though that seems unlikely because there are so many other (less ambiguous) ways of expressing statistical dispersion. I think Morphh's idea of putting the little tag at the top is good, something like "This article is about the use of the Gini coefficient in economics. For its use in mathematics and statistics, see Statistical dispersion". Ultimately, the economics article should be kept here (without a disambiguation page) since economics is the most common application of the term Gini coefficient: look at "What links here". Nearly all of those links refer to the Gini coefficient as a measure in economics. Phlyght (talk) 17:44, 26 October 2008 (UTC)

Against any split as per Cretog8 Chico (talk) 19:24, 26 November 2008 (UTC)

Talk page archival

I've taken the liberty of archiving some of the older topics on this page. Let me know if there are issues with the archive. Thanks. -FrankTobia (talk) 01:49, 26 May 2008 (UTC)

Brazil´s 2008 GINI

Recent Brazilian steady growth has reduced its GINI to a 2008 value of 50.5 (http://en.wikipedia.org/wiki/Brazil). Brazil is after all being able to reflect its economic boom into social improvement results, it was recently announced that 20% of the total population has left de poverty zone. —Preceding unsigned comment added by 77.54.45.160 (talk) 13:22, 26 June 2008 (UTC)

I agree this page is way badly written, it should contain a listing of countries by GINI instead of the not updated chart. —Preceding unsigned comment added by 213.22.33.64 (talk) 10:53, 20 September 2008 (UTC)

"Disadvantages"

"However, Gini coefficient can also be calculated for any kind of distribution, e.g. for wealth." has been added to "It measures current income rather than lifetime income. A society in which everyone earned the same over a lifetime would appear unequal because of people at different stages in their life; a society in which students study rather than save can never have a coefficient of 0." The addition is right. The original sentence simply describes one out of many uses of inequality measures. That is not a "disadvantage". --DL5MDA (talk) 22:26, 8 August 2008 (UTC)

There is a lot of information that the coefficient does not give. I think this is not a series of "disadvantages" but "limitations". 77.20.185.243 (talk) 09:25, 11 May 2009 (UTC)

Yes, that is a limitation, but a desired one. The loss of information is a feature of all inequality coefficients. Such kind of measures you provide to quickly get an overview. Based on that you then may or may not want to look at more detailed data. --DL5MDA (talk) 19:10, 11 May 2009 (UTC)

A simple Gini model

While the cases G=0 and G=1 are intuitively clear, the meaning of intermediate values is not very obvious. A simple "two social classes" model can help in this direction.

If we assume the total income equal to 1 and consider two population groups, the poorer X earning total income A and the rest 1-X earning total income 1-A , the Gini coefficient has a very simple form:

G = X - A

It can be further shown, that within the legal values G < X < 1 , the minimum of the rich-to-poor per capita income occures when X = 0.5 ( 1 + G ) and equals ((1+G)/(1-G))^2

Some values of the minimum ratios of rich-to-poor per capita incomes for different Gini values:

G = 0.25 (Sweden) : R/P (min) = 2.8 , for 63% of people earning 38% of the total income

G = 0.41 (USA) .... : R/P (min) = 5.7 , for 71% of people earning 30% of the total income

G = 0.55 (Clile) ..... : R/P (min) = 11.9 , for 78% of people earning 23% of the total income

G = 0.74 (Namibia) : R/P (min) = 45 , for 87% of people earning 13% of the total income

More details (in bulgarian) here: http://rigas.forumotion.com/iauanoai-f4/iaaaoiaoiaie-iiaeie-t147-750.htm#27809

More generally, with two income groups, poor and rich, Gini = (share of poor in population) - (share of poor's income in total income). I don't have a ref for it but it's just a simple calculation. Perhaps it should be added.radek (talk) 19:18, 11 May 2009 (UTC)

credit risk model

I propose to include a section on the use of the Gini Coefficient as part of credit risk model build. There are several different intrepretations of the formulae and also its application. I would like to clear it up and publish for other users. MaryGowenBOI (talk) 10:17, 8 October 2008 (UTC)

I'm not familiar with this, but if it's used that way it might be a good addition. Just make sure your new info is sourced. CRETOG8(t/c) 13:35, 8 October 2008 (UTC)

I moved your addition plus the credit risk stuff from the lead to a new section. CRETOG8(t/c) 13:45, 8 October 2008 (UTC)

Can you provide (maybe here on the talk page) a more complete reference for "Analytics of risk model validation"--author, pages, and such? Also, does the whole idea come from that book? Which parts of your addition should get referenced by it? If you put that stuff here, I'll update the reference in the article. CRETOG8(t/c) 17:00, 8 October 2008 (UTC)

His source is The Analytics of Risk Model Valuation by George Christodoulakis and Stephen Satchell, Academic Press, 2007. If, like me, you don't have that book, you can get an idea of how the gini coefficient can be used for credit scoring measurement from this journal article: Assessing the Discriminatory Power of Credit Scores (very technical, from page 13 onwards). - Marcika (talk) 15:16, 14 October 2008 (UTC)

I'm also a bit unfamiliar with this but I looked at the above paper and it makes sense. You basically use the Gini to construct a statistical estimator. That part's fine. The part that bothers me is "In this case, negative Gini Coefficient values are possible." Maybe it's just not explained well, but the Gini, by definition (and by formula G1) cannot be negative, otherwise it's not a Gini. Note that this is also true in the paper provided above. It cannot be negative because you cannot have a negative area and the Gini's a ratio of two areas.radek (talk) 15:45, 14 October 2008 (UTC)

This may help: Deutsche Bundesbank, Do banks diversify loan portfolios?, 2005 (Usage of e.g. the Gini coefficient for risc evaluation of loan portefolios) --DL5MDA (talk) 21:55, 29 October 2008 (UTC)

It's still + in that paper - between 0 and 22/23.radek (talk) 20:29, 9 December 2008 (UTC)

free market nations

In the first paragraph the article mentions "free market" nations. As far as I'm aware there are no nations that adhere to the free market. There are some that are more liberalised then others (countries such as Singapore and Hong Kong being the most liberalised). This should be changed.

Gini coeff over time.

In regard to the fact tag on the statement: "It is possible for a given economy to have a higher Gini coefficient at any one point in time than another economy, while the Gini coefficient calculated over individuals' lifetime income is actually lower (or even more higher) than the "more equal" (at a given point in time) economy's.". I think this possibility is just intuitive. Consider two economies. In both economies individuals live for two periods, young, then old and the proportion of young to old in both is 1/2, 1/2. In the first economy 1/2 of people (young and old) always have income of 1 regardless of whether they're old or young, while the other 1/2 have income of 2/3. In the second economy all the young (also 1/2 of total pop) have income of 1/5 but all the old have (1/2) have income of 4/5. Then the first economy will have a lower Gini at any point in time, while the second Gini will have a Gini of zero based on lifetime income (since everybody's lifetime income is 1).radek (talk) 19:38, 13 April 2009 (UTC)

EU Gini

I removed speculation about the EU gini being "surprisingly low" because it's not clear how Eurostat calculated the EU-wide gini. It's possible that it was calculated by weighting the country specific Ginis by population shares (this, unfortunately, is how it's often done) but this method is invalid as the section on disadvantages of the Gini points out.radek (talk) 03:01, 23 April 2009 (UTC)

Figure caption is wrong

The caption on the figure illustrating the curve says "Graphical representation of the Gini coefficient; (The area of the whole triangle is defined as 1, not 0.5)"

The area of the triangle, i.e.: the area under the 45deg line, IS 0.5. The Gini coefficient is the area between the 45deg line and the Lorenz curve AS A PERCENTAGE OF the area under the 45deg line, 0.5.

The section in the body describes it correctly. A/(A+B), where A is the area between the curves and B is the area below the Lorenz curve. A+B = 0.5, since that's the area of the triangle (b*h*1/2 = 1*1*1/2 = 0.5), so the coefficient is A/0.5 = 2A, where A = 1/2 (area of triangle) - B (area below Lorenz curve). —Preceding unsigned comment added by 204.178.86.60 (talk) 15:37, 19 May 2009 (UTC)