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Re: st: gini coeff


From   Jenkins S P <stephenj@essex.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: gini coeff
Date   Sun, 7 Mar 2004 13:55:38 +0000 (GMT)

On Sat, 6 Mar 2004, Do, Phoenix wrote:

> I am calculating a gini coeff for each tract in my census dataset. The
> observations are at the blockgroup level and I have 3 counties.
>
> This is my command:
>
> ginidesc  percapi, bygroup(tract)
>
>
> However, when I use only a subset of my data, some of the ginicoeff
> change. I thought the ginicoeffs were not influenced by the composition
> of other tracts. In other words, the ginicoeff of tractA depends only on
> the income distribution of the blockgroups within tractA and is
> independent of the income distributions of other tracts. I am finding
> this to not be the case.
>

The Gini coefficient depends on the (normalised)  ranking by income of
each observation. An observation's ranking in the population (which
depends on everyone from all the groups) differs from an individual's
ranking within a given group. This is also why the Gini coefficient does
not neatly decompose into a sum of Within-Group + Between-Group Inequality
(cf. the generalised entropy indices) -- there is an additional term
summarising overlapping between groups. (Put another way, the issue you
draw attention to, is precisely why the majority of analysts do not rely
on the Gini coefficient for inequality decomposition by population
subgroups.)

If, however, you are simply interested in simply getting a Gini for each
subgroup (tract) and storing it, then it is straightforward to do with
several programs, including my -ineqdeco- (or -ineqdec0-):

levels tract, local(reg)
ge gini_reg = .

foreach r of local reg {
  ineqdeco percapi if tract == `r'
  replace gini_reg = $S_gini if tract == `r'
}

-ineqdeco income, by(region)- would produce output showing inequality
indices for each region, but the results by region would not be saved.
It would however, show the Within/Between decomposition for a range of
indices, though not for the Gini (for the reasons given above). -ginidesc-
provides the special Within/Between/Overlapping decomposition for the
Gini. (Note too that -ginidesc- stores its results in matrices rather than
in global macros.)

The same principles (-foreach- and so on) could be used to get and save
poverty index estimates using -povdeco-.

PS ensure you have the latest version of -povdeco- (version 1.3 Feb 2001)
and -ineqdeco- (version 1.6 April 2001). Get them using the -ssc- command.


Stephen
=============================================
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research (ISER)
University of Essex, Colchester CO4 3SQ, UK
Phone: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
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