Re: st: Request for urgent response

["Roger B. Newson" <r.newson@imperial.ac.uk>]

Thanks to Stephen for the appreciation, The -scsomersd- package treats 
ties in the usual way for -somersd-. That is to say, the Gini 
coefficient is equal to

G = Pr(Y_1<Y_2) - Pr(Y_1>Y_2)

where Y_1 is the money of an individual sampled randomly and 
equiprobably from the population, and Y_2 is the money of an individual 
sampled randomly from the population with probability proportional to 
money. In other words, the Gini coefficient is the area above the Lorenz 
curve minus the area below the Lorenz curve, assuming that the Lorenz 
curve itself is a set of non-zero measure, defined as the event in which 
Y_1 and Y_2 are equal. As stated in Subsection 5.3 of Newson (2006), if 
the women in the -womenwage- data organise 2 lotteries, the first with 1 
ticket per woman and the second where each woman buys a number of 
tickets proportional to her wages, then there is a nonzero probability 
that the 2 lottery winners will have equal wages. In fact, they may even 
be the same woman, even if the lottery is not fixed, although the other 
women in the sample will probably not believe this if it happens.

I hope this helps.

Best wishes

Roger

References

Newson R. Confidence intervals for rank statistics: Somers' D and 
extensions. The Stata Journal 2006; 6(3): 309-334. Download from
http://www.stata-journal.com/article.html?article=snp15_6

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 23/08/2013 10:14, S.Jenkins@lse.ac.uk wrote:
> Date: Thu, 22 Aug 2013 20:22:57 +0530
> From: Soumitra Ghosh <soumitra@tiss.edu>
> Subject: st: Request for urgent response
>
> Hi,
>
> I have used the following commands to estimate the concentration index.
>
> glcurve income [aw=weight], pvar(rank) nograph
> qui sum yis [fw=intweight]
> scalar mean=r(mean)
> cor yis rank [fw=intweight], c
> sca c=(2/mean)*r(cov_12)
> sca list c
>
> Kindly let me know how to derive confidence interval for the
> concentration index calculated using the above STATA commands.
>
> ================
>
> In addition to the useful comments already received (including using informative Subject headers), please say where programs derive from. -glcurve- is on SSC.
>
> You have apparently not read the help file for -glcurve- properly. The second paragraph in the Notes explicitly warns you against using -glcurve- output to calculate concentration indices. There is the issue of using grouped versus unit record data, and also one has to be sure that ties in the data are treated correctly (proper calculation of fractional ranks). For proper calculation of concentration indices, see also the -sgini- package by Philippe Van Kerm at http://medim.ceps.lu/?id=software , with extensive pdf documentation. He also indicates how to derive bootstrapped standard errors.
>
> I have not checked the World Bank package that was cited (regression based), nor Roger Newson's, to see how they treat fractional ranks. (I hasten to say that in general I think very highly of Roger's -somersd- and related packages.)
>
> Stephen (-glcurve- co-author, with Philippe Van Kerm)
> ------------------
> Stephen P. Jenkins <s.jenkins@lse.ac.uk>
>
> Please access the attached hyperlink for an important electronic communications disclaimer: http://lse.ac.uk/emailDisclaimer
>
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