y1 = a1 + b1*x1 + c1*x2 + d1*x3 + u1
y2 = a2 + b2*x1 + c2*x2 + d2*x3 + u2
y3 = a3 + b3*x1 + c3*x2 + d3*x3 + u3
If x1, x2, and x3 are in all three equations (as above) best estimates are just OLS
If not all x's in all equations but u1, u2, u3 are uncorrelated, best estimates are
just OLS.
Otherwise, can do better by using information in the covariance matrix of
the u's---generalized least squares (GLS).
If, say, b1 = b2 = b3, this constraint can be imposed when the system is estimated
by GLS.
If the u's are jointly normal, maximum likelihood can be used.