questions about constrained v.s. unconstrained coefficients in seemingly unrelated regression, thanks

[Huan Gao]

Dear all,

I have used the 'sureg' package in STATA to run a system of regression equations.
e.g.
Y1 = b1*X1 + b2*X2 + error
Y2 = c1*X1 + c2*X2 + error

Ideally, b1 + c1 = 1
However, if I do not set the constrains on the coefficients, then （b1+c1）is much smaller than 1,
After I have set the constraints on the coefficients b1 + c1 =1, then the results show that (b1+c1) suddenly very close to 1, around 0.99.

I am not sure about why such large difference can happen.
Can anyone give me some explanations?
or, how can I test whether or not the constrains on coefficients are valid? are those constraints reasonable statistically?

Before I did this SUR model, I had never set constraints on regression coefficients.
Therefore, although I understand the economic meaning behind such constraints, I do not understand about such setting statistically.

Many thanks!

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a helpful answer if you follow the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data using dataex.
I don't see why you'd be surprised. If you constrain b1+c1 to equal 1, then Stata applies that constraint - if forces them to add to 1 (or very close to it). When you don't constrain the parameters, Stata just gives the estimates it gets normally. Whether is makes sense to apply a constraint that substantially changes the results would depend on your substantive question. While they do change the results, the constraints could be appropriate.

[Eddie Oczkowski]

You can use the test command after sureg to test the plausibility of the constraint. If without the constraint b1 + c1 is not close to unity, then chances are the contraint will be rejected.