st: test for exogeneity

[Dragutin Culinovic <dragutin.culinovic@fsb.hr>]

I have one Structural equation and two reduced form equations:

Structural:   y=D1*g1 + D2*g2 + E1*b1 + E3*b3 + u
Reduced:     D1=E1*p11 + E2*p21 + E3*p31 + E4*p41 + v1
	     D2=E1*p12 + E2*p22 + E3*p32 + E4*p42 + v2

(coefficients are in small letters)
y* is unobservable, and we observe only y (0 or 1)

E's are all exogenous, and D's are (supposed) endogenous.

u, v1 and v2 have a joint normal distribution with mean zero and finite 
positive covariance matrix. How can I find that matrix.

How can I compute residuals for each observation and add it to that 
observation row?

For test of exogeneity i must to use residuals v1 and v2 in Structural 
equation, joint with D's and E's, because probit statistic of v1 and v2 
is a valid test of the null hypothesis that D's are exogenous.
How can I do this?

Thanks in advance.
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