Control Function Approach in panel analysis

[Olanrewaju Adediran]

I use the control function method instead of 2SLS. I have a short panel dataset of two waves. I used pooled OLS regression for the first stage, predicted the residual, and plugged it in for the second stage. My question is, what is the appropriate estimator to use at the first and second stages? Is it appropriate to use regression in the first stage and panel regression in the second stage? Or is it advisable to use panel regression in the first and second stages?
reg autonomy iv xi a2
predict v,r
xtreg childhealth autonomy xi a2 v, vce(robust)
or
xtreg autonomy iv xi a2
predict v,r
xtreg childhealth autonomy xi a2 v, vce(robust)