st: regression on quartiles

[Christopher F Baum <baum@bc.edu>]

> I don't think sureg is what you want -- sureg is used for models 
> estimated
> on the same sample.  What you want is more like a Chow test or, 
> preferably,
> just create interaction terms on the slope (and/or intercept).  This 
> latter
> approach can be done for you by xi.  For example, if you create zquart 
> to
> hold the quartiles of Z, then you could
>
> xi: reg Y X i.zquart*X
>
>
> and then look at the significance of the _I terms and perform tests on 
> them
>
>
> Michael Blasnik
> michael.blasnik@verizon.net
>
>
> ----- Original Message -----
> From: "Vuri, Daniela" <Daniela.Vuri@iue.it>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Thursday, May 13, 2004 4:43 AM
> Subject: st: compare coefficients after sureg
>
>
> > Dear Stata users,
> > I have the following problem.
> > I have a regression of Y on X and Z and I want to see if the effect 
> of Z
> is different across quartile of Z.
> > I do the following:
> >
> > gen quart=1 if Z is in the first quartile
> > replace quart=2 if Z is in the second quartile
> > replace quart=3 if Z is in the third quartile
> > replace quart=4 if Z is in the fourth quartile
> >
> > and then I do the following
> >
> > bysort quart: sureg(Y X)
> >
> > at this point I would like to test whether the beta coefficient I 
> get in
> the first equation (the first quartile) is equal to the beta 
> coefficient I
> get in the second equation (the second quartile) and so on.
> >
> > Is sureg the right command?  and how can I get the test of equality 
> of the
> coefficients across quartiles?
> >
> > thanks
> > daniela
> >

There are two approaches that one could follow here. Michael's 
suggestion implies a linear regression model  in which there is a 
single intercept term and four different slopes (one for each 
quartile). Since the number of observations are equal (assuming 
mod(N,4)=0) in each quartile, Daniela could reshape the data wide by 
quart, and then run sureg on the four different "equations": eqn_i 
contains the Y and X from quartile i, etc. In the SUR context, one can 
then test that the slopes are equal across equations. This model would 
allow for different slopes, intercepts, and sigma^2 for each quartile. 
An intermediate form would be to follow Michael's suggestion and allow 
for quartile-specific intercepts; that form still assumes that the 
errors are homoskedastic across quartiles.

Kit
 
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