Simultaneous Equation with Identity

[fakephil]

Hello,

I have a system of simultaneous equations with the same regressors, simplified here
y1 ~ XB1 + c
y2 ~ XB2 + c

I also have an identity
y1 + y2 = y
where y, like y1 and y2, is a series for which I have data.

I'd like to estimate this system of equations simultaneously, but the system object doesn't accept identities. If I try to estimate
y ~ y1[XB1+c] + y2[XB2+c]
I get sensible answers, but the identity isn't satisfied all the time (there are errors \= 0).

How can I estimate this system+identity?

[EViews Gareth]

There's nothing to estimate in an identity. What's the goal?

[fakephil]

I want to see the impact of the regressors on y1 and y2. Using the identity should discipline the values of the regressors.

That is, I could naively estimate the two equations for y1 and y2 without the constraint. Then I could add the two coefficients that appear on the regressors in each equation
y1 ~ b11 x1 + ....
y2 ~ b12 x1 + .....
Then use b11+b12 as the coefficient on x1. But this doesn't use the identity.

[EViews Gareth]

I'm afraid, unless I'm missing something, what you're suggesting doesn't make sense mathematically/econometrically.