# st: regression on quartiles

 From Christopher F Baum To statalist@hsphsun2.harvard.edu Subject st: regression on quartiles Date Sat, 15 May 2004 09:17:29 -0400

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

*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/