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I want to estimate a system for which the variance-covariance matrix of the residuals is restricted (for instance, to be the identity matrix, or to be a diagonal matrix).

As an illustration, take the 'Structural Factorisation' example (from the EViews manual) for VARs, the system is given as:
---
@E1 = C(1)*@U1
@E2 = C(2)*@E1 + C(3)*@U2
@E3 = C(4)*@E1 + C(5)*@E2 + C(6)*@U3
where E[uu']=I
---
How would I estimate this using the system object?
The system object allows (resid0i = @ei for i = 1,2,3):
---
resid01
resid02 = C(2)*resid01
resid03 = C(4)*resid01 + C(5)*resid02
---
which gives the same estimates for C(2), C(4), C(5) as the SVAR.
But the following doesn't work (not properly identified, near-singular matrix):
---
C(1)*resid01
C(3)*resid02 = C(2)*resid01
C(6)*resid03 = C(4)*resid01 + C(5)*resid02
---
which I'm pretty sure is because it needs E[uu']=I to be properly identified.

So more generally, how do a place restrictions on the variance-covariance matrix of the residuals (E[uu']) to estimate systems that rely on these restrictions to be identified?

Thanks for reading and thanks in advance for any help. :)

Hmm, I tried specifying extra equations to try to force the variances and covariances to be the required values, i.e.: E[u_i*u_j] = 1 for i = j, 0 otherwise:
---
C(1)*resid01
C(3)*resid02 + C(2)*resid01
C(6)*resid03 + C(4)*resid01 + C(5)*resid02

(C(1)*resid01)^2 = 1
(C(3)*resid02 + C(2)*resid01)^2 = 1
(C(6)*resid03 +C(4)*resid01 + C(5)*resid02)^2 = 1

(C(1)*resid01)*(C(3)*resid02 + C(2)*resid01) = 0
(C(1)*resid01)*(C(6)*resid03 + C(4)*resid01 + C(5)*resid02) = 0
(C(3)*resid02 + C(2)*resid01)*(C(6)*resid03 + C(4)*resid01 + C(5)*resid02) = 0
---
But although it will estimate this (by OLS), the coefficients do not match the SVAR, and the resulting residual covariance (for the first three equations) is still not (even close to being) an identity matrix.