Talk:Income inequality metrics

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Merge with Economic Inequality[edit]

This article pretty much deals with the same subject matter as economic inequality. Should they be merged?

This article is on metrics. However, there wasn't too much metrics in it. So I added the spreadsheet for the Gini index, the Robin Hood index and the Theil index. --DL5MDA (talk) 01:24, 31 October 2008 (UTC)
I saw the redirects to this article and now can understand the proposal to merge the article. However, as for now, the article really deserves its title "income ineqiality metrics". So rather the redirects should change. --DL5MDA (talk) 10:13, 2 November 2008 (UTC)

Improvement drive[edit]

A related topic, Grameen Bank, has been nominated on Wikipedia:This week's improvement drive. Contribute your expertise and vote for Grameen Bank on Wikipedia:This week's improvement drive!--Fenice 06:47, 10 August 2005 (UTC)

Absolute measures[edit]

  1. Absolute measures often give very different results than relative measures. For example, in measuring inequality changes due to the development of less developed countries, absolute measures typically show improvements as the general income level rises, but it is also common for relative measures to deteriorate as the new wealth becomes concentrated in the hands of the upper percentiles. The diverging results can be a problem if they are used inappropriately or interpreted incorrectly.

I cut it, because it claims as a fact that developed countries often have higher income inequality, while the empirical data seems to show a completely opposite trend. Almost universally, the less developed the country, the higher its income inequality. Seriously, it should be backed by some data if it is to stay.

Here's a map: World Map Gini coefficient.png Taw 13:58, 25 January 2006 (UTC)

Why?[edit]

Would someone mind putting in a section iterating why income equality is important? Fephisto 18:49, 9 September 2006 (UTC)

I put in a link to economic inequality, which covers those issues. -- Beland 20:30, 11 February 2007 (UTC)
It's an important issue. But the relation between inequality an e.g. growth is non-linear. There may be an optimum range of inequality. I assume, it is between (a) Theil index and Hoover index being equal and (b) Theil index minus Hoover index having a minimum. --DL5MDA (talk) 01:12, 31 October 2008 (UTC)

Another inc.ineq. index[edit]

Please accept my apology if what I'm doing is improper: I made another wealth distribution index, which I hope is better then Gini etc, or at least can be of use. Now I'm unclear on whether Wikipedia (should) list "common" knowledge, or "all" knowledge. In the first case, it should probably not be listed, though I'm neither sure whether this index already exists. I can imagine someone might view this as an attempt to make advertisements. Please don't be insulted, I'm only trying to improve things.

Index: 2 * Sum { .5 ^ ( Average-Data / Element-Data ) } / Total-Elements-N

I've converted this into a C program (free[soft]ware) for convenience: http://www.xs4all.nl/~joshb/cc/distribution.html I've called it "naddi", ``normalized average data distribution index. Since it might be unknown (unproven), please verify before adding. Jos Boersema (joshb@ -REDUCESPAM- xs4all.nl) —The preceding unsigned comment was added by 80.127.225.147 (talk) 12:31, 4 February 2007 (UTC).

Uh. Oh. In Philip B. Coulter's Measuring Inequality (1989) you can find about 50 inequality measures. I think, one should focus on the Gini index (for the sake of tradition), the Theil index (probably representing the most realistic ressource distribution model) and the Hoover index (for the sake of simplicity). The Atkinson index can be represented as a transformation of the Theil index. That should be enough. --DL5MDA (talk) 01:24, 31 October 2008 (UTC)
I agree with DL5MDA here. In fact the article should start off right after the lead (or maybe even in the lead) by listing those 3 (or 4 if you count Atkinson) indices and defining them. On the other hand, the present section on 'Absolute income criteria' should be removed, as it is not about inequality at all but rather poverty, which is an altogether different concept. In fact another thing that belongs in the lead or right after it is a list of 'properties' that generally a measure of inequality should posses, as found in the literature (briefly; anonymity, scale independence, population independence and the Dalton-Pigou principle). Then these assumptions could be used to contrast the notion of 'inequality' with 'poverty' (difference in the DP principle) or even fairness (anonymity assumption).radek (talk) 02:28, 1 November 2008 (UTC)
As for "...the article should start off right after the lead (or maybe even in the lead) by listing those 3 (or 4 if you count Atkinson) indices and defining them...": I did that in the German wikipedia (de:Ungleichverteilungsmaße) in order to provide a "less mathematical" explanation of the three important inequality metrics. I fear, I presently do not have the time, to do this here as well. --DL5MDA (talk) 07:54, 1 November 2008 (UTC)
Theil index is the special case of Atkinson index. So rather than giving a special case, we should give the more general Atkinson formulation. Frankly, despite my earlier work in income distribution economics, I could not wrap my head around Hoover index. I've never seen it used there. Atkinson index and generalized entropy indices are used for serious analysis with group decompositions; Gini index and percentile ratios are used because they are easy to explain, although they are lousy measures of inequality. Please take a look at my updates on Atkinson index, and feel free to steal the mathematical formulations from there :)). Stas K (talk) 15:29, 26 March 2010 (UTC)
I think that's known in the economics literature as Kakutani index. I had a reference Kakutani (1978) off the top of my head, but Google scholar did not give anything meaningful :(. Stas K (talk) 15:29, 26 March 2010 (UTC)

Income distribution measures[edit]

The concept of inoome distribution and inequaliity is very important and one that needs further research....I hoped to see the content cover measures that have been presented and used at least mention, how these are used and whether important. Growth economists are interested in analytic forms that can be incorporated into growth models - since income distribution is of paramount importance to long term economic growth along with aging / demographics. 1- why important, 2- how measured, 3- what are the measures, 4- how are they used.

Analytically the important properties are 1- range of the measure - capable of describing extremes normally encountered in economies, 2- scalability - the measure remains the same if all recipients receive the same % increase in incomes, 3- captures wealth transfers

Beyond Lorenz curves and Ginis the analytic forms that have been used include

lognormal log logistic Singh Maddala Dagum 4 parameter Champernowne 5 parameter

Dbecher-hamburg 22:31, 3 December 2007 (UTC)

Well, as for the amount of inequality metrics see above ;-) --DL5MDA (talk) 01:24, 31 October 2008 (UTC)

Rewrote first para after lead[edit]

First let me say that it's not OR, though I have not had time to properly cite it. The stuff on the four basic properties of inequality indices can be found in any economics textbook which deals with inequality in a serious manner, for example most development econ books. The transfer principle (or the Dalton-Pigou principle) is central and it probably should have its own page. At the moment I'm not sure whether or not the Hoover index satisfies this principle and am too tired to think about it - since it's the area between the line of equality and the Lorenz curve though, it should. Second, I though it was important to distinguish inequality from poverty and fairness and including the four properties right at the beginning allows one to do that in a natural manner. Also I have this vague recollection of a paper which showed that the Theil index and its derivatives are the only (if and only if) class of inequality metrics which satisfy the four properties plus the decomposability one but that was way back in grad school. Finally this article could also benefit from a discussion of how inequality is actually measured in practice (very, very sloppily) and how entire income distributions are extrapolated from a limited number of data points. I don't have time to review that literature right now so help from others would be greatly appreciated.radek (talk) 09:21, 1 November 2008 (UTC)

I like your edit. By the way, the Hoover index satisfies anonymity, scale independence, population independence and the strong form of the Dalton-Pigou criterion. I add that to the article. --DL5MDA (talk) 10:17, 1 November 2008 (UTC)

Some hefty rearranging[edit]

@Radeksz: By http://en.wikipedia.org/w/index.php?title=Income_inequality_metrics&diff=249080070&oldid=248968702 I rearranged some of your and my edits and added a briefing on the 3 important inequality measures. Please check, wether I got your statements on quintiles wrong. --DL5MDA (talk) 22:27, 1 November 2008 (UTC)

Looks good. I made some minor spelling and stylistic changes. In terms of the article as a whole, the section on the Theil index maybe be a little too long relative to the other sections, particularly since most of that information should be in the relevant article. I'm also not clear on what this phrase means: "techniques used to make judgments within the concept of poverty and fairness". Can you clarify? Another thought; it might be worthwhile to (briefly) mention the Foster-Greer-Thorbecke measure (and red link it for now) as a measure which combines measurement of poverty and inequality (for some values of FGT alpha).radek (talk) 00:10, 2 November 2008 (UTC)
I simply removed the "techniques" thing.
As for FGT: I had a look into http://rspas.anu.edu.au/papers/asarc/2003_02.pdf and http://sedac.ciesin.columbia.edu/povmap/contribute/ds_defs_vars.jsp. The FGT measure clearly is a powerty measure. Does that fit into an article on inequality measures? --DL5MDA (talk) 01:46, 2 November 2008 (UTC)
It's a poverty measure that also takes into account (with alpha=2) the inequality among the poor. It can be written as a function of a poor-only Gini and a poor-only coefficient of variation. I'll try to look some stuff up on it.radek (talk) 02:08, 2 November 2008 (UTC)
I comparison to the inequality measures, when using FGT measures, of course the powerty line z and the amount q of poor people within a society with the size N has to be determined before the computation. Computing FGT measures requires more decisions than what is requirde to decide before computing the Gini index, the Theil index or the Hoover index. In order to determine the poverty line, you either could use the median or (better) welfare functions, which again requires to compute inequality measures.
FGT refers to a whole class of measures. Probably that deserves a separate article.
--DL5MDA (talk) 09:11, 2 November 2008 (UTC)
I created an article on the FGT. It's just a beginning for now.radek (talk) 10:31, 2 November 2008 (UTC)

Theil index[edit]

The paragraph is a bit longer again. But (in contrary to the article dedicated to the Theil index) here I did not torture the readers with formulas. Also it compares the Theil index with the Hoover index, which due to its nature very well can serve as a contrast to the Theil index. --DL5MDA (talk) 10:09, 2 November 2008 (UTC)

Redundancy[edit]

Because this article covers issues which are also covered in separate articles on the Gini coefficient, the Theil index and the Hoover index, I would like to mention an important difference between this article and the articles dedicated to single inequality measures: In this article I avoid formulas. Only in the spreadsheet you find formulas, but there they serve as applied tools and not as an explanation. --DL5MDA (talk) 20:31, 2 November 2008 (UTC)

Why is few academic infos available for the term....[edit]

from Google scholar point of view ...???

--222.64.18.96 (talk) 06:02, 8 October 2009 (UTC)

Graph of countries / US[edit]

I'd like to see a plot of countries on a Gini coefficient (or whichever measure is chosen) vs. log GDP per capita chart. As I recall, the trend is very strong: there is a strip of egalitarian countries with low to high wealth, and a strip of poor countries with low to high inequality. The notable outlier in the graph is the United States. Surely this effect has been noticed in WP:RS; if anyone has seen this I think it would make a good (sub)section.

CRGreathouse (t | c) 15:45, 21 January 2010 (UTC)

See this blog posting? - Bhyde (talk) 17:28, 21 January 2010 (UTC)

Thanks for that, interesting reading. CRGreathouse (t | c) 02:54, 22 January 2010 (UTC)