Using SUR regressions and the Wald test in Stata

[Dirk Harmelink]

Hi all,
I've read in a paper that after running Seemingly Unrelated regressions (SUR), they use the Wald test to test the following:
H0: beta(r1) = beta(r2) versus Ha: beta(r1) > beta(r2)

where r1 denotes the beta of first ran regression and r2 denotes the beta for the second regression.
This is exactly what i need, however I do not know how to perform both the SUR and Wald tests in Stata (I have a panel dataset: N=520, T=983).

Therefore my question, how to test this?
thanks in advance!

[George Ford]

just -test- or -lincom- after sureg should work. no?

[George Ford]

use auto, clear

sureg (price mpg headroom) (weight mpg trunk displacement)
lincom [price]mpg - [weight]mpg

[Dirk Harmelink]

Hi George,
First I want to say that I highly appreciate the helpful responses on both posts!

Regarding the Stata command, I came across the following: Suest can be used for my purposes, however, xtreg is not supported by Suest.
Moreover, sureg can indeed by used but as shown below, my ylist and xlist are the same for all regressions and therefore (I think) I get the error: covariance matrix of errors is singular
so both options are not achievable, is there any alternative to this problem?

below i'll show the commands and the subsequent errors

Option1 (using Suest)
xtreg $ylist $xlist if LL_group == 1, fe
est store model1
xtreg $ylist $xlist if LL_group == 2, fe
est store model2
xtreg $ylist $xlist if LL_group == 3, fe
est store model3
suest model1 model2 model3
test [model1_mean]x1 - [model2_mean]x1 = 0

"xtreg is not supported by suest"

Option2 (using sureg)
sureg ($ylist $xlist if LL_group == 1)($ylist $xlist if LL_group == 3)

"covariance matrix of errors is singular"

[George Ford]

if your x's are the same, there's no benefit to sureg.

you can use reg and just i.x your fixed effects. The SE are a little different since xtreg demeans before estimation affecting the degrees of freedom. You could do the same manually and use reg.

As you've written it, you don't need 3 models. All of those are nested.

So create group variable g1, g2, g3 (you could use i.LL_group instead, but it will look a little different but give you the same margins in the end).

reg y x2 x2 x3 g2 c.g2#(c.x1 c.x2 c.x3) g3 c.g3#(c.x1 c.x2 c.x3)

The interaction terms are a direct test of a difference.

[George Ford]

you can use xtreg as well. same setup.

[Dirk Harmelink]

Thankyou very much George, I found what I was looking for!