Re: st: stochastic dominance between two concentration curves

[Austin Nichols <austinnichols@gmail.com>]

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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