I personally would recommend the jackknife confidence interval for the Gini coefficient. The Gini coefficient is a special case of Somers' D, which is one of the best-behaved statistics known to science in its rate of convergence to a Normal form under the Central Limit Theorem. However, I would recommend using the delta-jackknife, with the Normalizing and variance-stabilizing hyperbolic arctangent transformation advocated by Edwardes (1995), especially if one or other of the income distributions being compared is expected to be very unequal, with a large Gini coefficient. Newson (2006) gives a worked example of calculating a confidence interval for the Gini coefficient, using the Stata package -somersd-, which can be downloaded from SSC.
If the 2 samples are independent, then you can calculate confidence intervals for the difference between the 2 Gini coefficients, or for the back-transformed difference between the 2 hyperbolic arctangents, using the -parmby- and -metaparm- modules of the -parmest- package, which you can also download from SSC using the -ssc- command in Stata.
I hope this helps.
Roger
References
Edwardes, M. D. d. B. A confidence interval for Pr(X < Y) − Pr(X > Y) estimated from simple cluster samples. Biometrics 1995; 51: 571–578.
Newson R. Confidence intervals for rank statistics: Somers' D and extensions. The Stata Journal 2006; 6(3): 309-334. Download pre-publication draft from
http://www.imperial.ac.uk/nhli/r.newson/
Roger Newson
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: [email protected]
www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Stas Kolenikov
Sent: 11 April 2007 04:21
To: [email protected]
Subject: Re: st: Testing Equality of Gini Coefficients
Are your two samples independent? If yes, that's a simple two-sample
z-test; if not, then it is next to impossible to get this right and
straight. I would even doubt the jackknife-based estimates, as the
Gini (and that's a last name) coefficient is not a smooth function of
the data.
On 4/10/07, Zachary Neal <[email protected]> wrote:
> All,
>
> I am trying to conduct a test of the difference between gini
> coefficients from two samples. I am able to run several of the
> available ADOs that provide both bootstrap and jackknife confidence
> intervals. Of course, I can infer that the gini coefficients from
> the two populations are significantly different if their CIs do not
> overlap. But, I would prefer to directly test this. Does anyone
> know either:
>
> 1. How to compute the 'standard error of the difference of ginis'
> from the bookstrap/jackknife standard errors of two sample?
>
> OR
>
> 2. How to use the bookstrap or jackknife commands in conjunction
> with an existing ADO to directly cumpute the standard error of the
> difference?
>
> Thanks in advance.
>
>
> Zachary Neal
> Managing Editor, City & Community
> ------------------------------
> Department of Sociology (M/C 312)
> University of Illinois at Chicago
> 1007 West Harrison Street
> Chicago, IL 60607
> http://www2.uic.edu/~zneal2
>
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>
--
Stas Kolenikov
http://stas.kolenikov.name
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