st: Difference between marginal effects from two survey-weighted regressions

["Hussein, Mustafa (Mustafa Hussien)" <mhussei4@uthsc.edu>]

Dear Statalisters,

I am estimating race-stratified regression models (gamma GLM and quantile regression) with difference-in-difference interaction terms. Post estimation, I use margins (with lincom) to estimate the difference-in-difference treatment effect in the treated group, by typing something like (my dataset is a complex survey):

margins, subpop(txgroup if post==1) at(txgroup=(1 0) post=(1 0)) vce(unconditional) post
lincom ..

My questions:
 
a) is it valid to compare the estimated marginal effects across the two models, that is calculate the difference between the effect in the "white" model and the effect in the "black" model? I am interested in finding the effect of the treatment on the disparity between blacks and whites

b) I found some literature that said it's okay to do so (on the basis that marginal effects are interpretable as random variables), via t test. I then used ttesti (the immediate form), plugging in actual not weighted sample sizes of each group. Assuming this is valid, I am concerned with the difference in sample size between the two groups (minority sample is 1/4th to 1/5th the size of white sample) that seems to render differences, even very large ones (ex. 60 to 1), non-significant. Is there a remedy to this?

c) Again, assuming taking a difference of marginal effects across models is valid for conditional mean regression, is it still valid with quantile regression? why/why not? (I imagine this might not be valid unless one is estimating unconditional quantile partial effects?) 

Any advice is greatly appreciated

Thanks,
Mustafa
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