That is when the system is triangular such that Y2 does NOT depend on Y1, but we believe it is weakly endogenous because the disturbances are correlated between the equations. For this case, in the first stage we could regress on any list of instruments that are sufficient to identify the system. Now, we will have to perform the adjustment to the covariance matrix ourselves. Let's do this in Stata. In particular, the hard part is to get the Standard Errors to account for the fact that some of the right hand side variables in the second stage are estimated.
Any suggestion is appreciated.
Thank you very much.