Hello,
I am trying to run a model with a binary endogenous regressor. I am still learning econometrics so I am sorry if this may be a trivial question.
In particular, I am trying to implement the procedure explained by Woooldridge 2010 at p. 939 (Procedure 21.1)
Would this be a correct approach?

Code:
* first I run a probit model on the binary variable (BV) I want to instrument. X  are all included regressors and (Z)  is my valid instrument 
probit BV X Z, cluster(id)
* create fitted values
predict prb_hat
* use fitted values as instruments (it is a lagged dv model)
 xtivreg Y L.Y X (BV=prb_hat)
My question is whether this is the (or a) correct way to run an instrumental variable regregression with an endogenous binary variable or whether I should use the a simpler approach as the following.

Code:
 xtivreg Y L.Y X (BV=Z)
My issue with this latter approach is that the instrument is weak hence is not valid. while is I use prb_hat my instrument is strong and significant.

Thanks a lot in advance for your help


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