st: SUR, constraints, and normalization

[Daniel Muluwork Atsbeha <daniel.atsbeha@umb.no>]

Dear all,

I have a question about the effect of normalization on hypothesis testing in SUR. My understanding is that normalization results in re-scaling of data and therefore must not have an effect on z-scores and that's what I get below:
sysuse auto
sum price
gen p= price /r(mean)
sum length
gen l = length /r(mean)
sum mpg
gen m= mpg /r(mean)
sum weight
gen w = weight /r(mean)
sureg (price length) (mpg  weight)
sureg (p l) (m w)

However, once constraints are involved, the above assertion is no longer valid, for example:
constraint 1 [price]length = [mpg]weight
constraint 2 [p]l = [m]w
sureg (price  length) (mpg  weight), c(1)
sureg (p l) (m w), c(2)

Does this mean one shouldn't normalize data when constraints are involved? Or should the normalization be done in some other way?

Thanks.

Daniel

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