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RE: st: stochastic dominance between two concentration curves


From   <S.Jenkins@lse.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: stochastic dominance between two concentration curves
Date   Wed, 2 May 2012 18:45:53 +0100

Existing Stata code? I don't know of any. (And, unfortunately, Austin -- I haven't got any!  I'm not sure Philippe has either.)

Complications: (i) testing for stochastic dominance is more complicated that testing differences in concentration (or inequality) indices; especially if (ii) you want to test null hypotheses of difference rather than equality. And of course there are correlated samples (the 2 curves being compared are for the same group of people).

I am away from my desk and library at present so don't have references to hand. But I would search for related papers in the health economics literature by Adam Wagstaff and collaborators on this topic -- there is an article I think by Wagstaff & Kakwani & maybe others, in the Journal of Econometrics, I think it is.)
More generally on testing for stochastic dominance with income data, go to the website of Russell Davidson -- he has some nice surveys (with reference lists!), I recall, as well as a pioneering paper with Jean-Yves Duclos in Econometrica. Also check out the webpage of Garry Barrett (U Sydney). 

I didn't know that the DASP program suite had disappeared. Maybe it has simply moved? I would start by looking for links off the web page of Jean-Yves Duclos.

I suspect Hewan may already know all this ...  

NB Hewan: what is the URL for the World Bank program code to which you referred?

Stephen

------------------------------

Date: Tue, 1 May 2012 10:30:30 -0700 (PDT)
From: Hewan Belay <hewan_belay@yahoo.com>
Subject: Re: st: stochastic dominance between two concentration curves

Thank you, I looked up the Jenkins paper (along by now with several others). I am worrying about the complexity of doing this in the absence of an existing command. 

Thus, I am wondering if it is fine to essentially do a ttest on the cdfs (i.e. ttest comparing the cdf of H with the cdf of E .... after all, they have the same underlying cdf(Y)--that is, they are both mapped against the same cumulative income). Then, if the results reveal that one mean is statistically larger than the other, one can take the next step and do the same ttests but for the different income quantiles, e.g. one ttest to compare cdf(H) with cdf(E) for each quantile (so if I use quintile, that would be 5 ttests). 

This may be slightly crude, but would it not essentially get at hte question? It would seem to deal with all of my four points below: (1) it's obviously a statistical test, (2)Â Â by looking at the cdf's rather than the variables themselves, I'm essentially capturing the difference in concentration curves, (3) ttest allows for matched pairs, and (4) there's obviously an official test for this.

Hewan

- ----- Original Message -----
From: Austin Nichols <austinnichols@gmail.com>
To: statalist@hsphsun2.harvard.edu
Cc: 
Sent: Tuesday, May 1, 2012 4:28 PM
Subject: Re: st: stochastic dominance between two concentration curves

Hewan Belay <hewan_belay@yahoo.com>:
Look up
Jenkins, Stephen. 1988. "Calculating Income Distribution Indices from
Micro Data." National Tax Journal 41: 139-42.
but note you want covariances, not correlations (my typo). You can
still estimate these via regression, but you will have autocorrelated
errors to deal with, too.  Might need some more thought.

I feel certain Jenkins and/or van Kerm must have already addressed
this problem in one of their papers...

On Tue, May 1, 2012 at 11:14 AM, Hewan Belay <hewan_belay@yahoo.com> wrote:
>
> Dear Austin,
>
> Thanks for this intuition. Just a question: If this "by hand" technique were used, wouldn't it be the case that one would need to regress the cdf of H on the cdf of Y (and cdf of E on cdf of Y), and then compare those coefficients? Rather than regressing H on cdf of Y? And if so, say the coefficient in the cdf(H) regression is statistically significantly larger, does that point to H's distribution being more progressive (or vice versa, does that mean E is more progressive?).
>
> Aside from this hands-on technique, is there any official stata or SSC command that looks at this question?
>
> Hewan
>
> ----- Original Message -----
> From: Austin Nichols <austinnichols@gmail.com>
> To: statalist@hsphsun2.harvard.edu
> Cc:
> Sent: Tuesday, May 1, 2012 2:26 PM
> Subject: Re: st: stochastic dominance between two concentration curves
>
> Hewan Belay <hewan_belay@yahoo.com>:
> Second-order stochastic dominance would be a comparison of
> concentration indices, which implies comparing the correlation of H
> and F(Y) with the correlation of E and F(Y), or comparing two
> regressions using standardized variables, with coefs compared via
> -suest-.
>
>
> On Tue, May 1, 2012 at 9:11 AM, Hewan Belay <hewan_belay@yahoo.com> wrote:
>> Dear statalist,
>>
>> I have what one would think is a very basic question, but scouring statalist and other sources has so far not yielded results for me. I want to to test stochastic dominance between two concentration curves. Let me give a simplified example of my data’s structure: We have say 1000 households, and there are three core variables: each household’s (a) income Y, (b) access to health services (a dummy) H, (c) access to education services (a dummy) E. First I plot the concentration curves for visual inspection, so that would be something like:
>>
>> glcurve H, pvar(x_H) glvar(y_H) sortvar(Y) nograph replace lorenz
>> glcurve E, pvar(x_E) glvar(y_E) sortvar(Y) nograph replace lorenz
>> twoway (line y_H x_H, sort ) (line y_E x_E, sort)
>>
>> The two concentration curves bulge up- and left-ward, i.e. are above the 45 degree line, thus the incidence of these two services is progressive. Health bulges a bit (but not much) more out, thus seems like it could be more progressive than education. Now, I want to test whether this dominance of health is confirmed statistically, going beyond the visual inspection.
>>
>> A few remarks (after having perused all other comments on the matter):
>>
>> 1. I am interested in statistical test of stochastic dominance, going beyond what plots tell the eyes (as important as that first visual investigation was).
>>
>> 2. I am looking for a test that treats these as the concentration curves that they are—i.e. the distribution of service access of households *against* these households’ income levels. Several tests (e.g. –signrank-, or –ksmirnov-, or –alorenz-) would seem to treat these simply as distributions of health and education, respectively (i.e. ignoring the fact that the observations should be ordered by their incomes, not by the services themselves). [by the way, -alorenz- has so many issues in how the help file is written, it would be great if that were edited some time…]
>>
>> 3. Furthermore, in tests like –signrank- the null is that these distributions are equal. It is unclear what rejecting the null says about which curve dominates over which. (Yes, in the above example of H vs E the visual inspection will give a clue, but I have cases that are less clear cut from eyeballing)
>>
>> 4. I would really rather only consider official or SSC commands. There’s a command out there called –dominance- written by World Bank folks, but it has not been inducted into SSC so I would rather not use it. And the DASP package in stata, by the way, seems to have been taken down. The url’s provided to the package all no longer work.
>>
>> I am hoping there is a technique in stata to undertake this pretty basic operation of testing dominance of two concentration curves? I am grateful for any thoughts!
>>
>> Hewan
>

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