Dear all,
I have a question regarding control function approach,
I understand that I need to first estimate a reduced-form equation of the endogenous variable, estimate the residuals then add the residuals to the structural equation of interest. I am wondering whether it is possible to add a stage in the beginning to deal with sample selection bias, the same way we can do in 2SLS models.
Thus run a model like this:
Stage (1):
Probit: Participation (X1 Z1)
Calculate IMILLS
Stage (2):
Regress: WAGES (X1 X2 Z2 IMILLS)
predict ERR, res
Stage (3):
OPROBIT: SATISFACTION (WAGES X1 X2 X3 ERR IMILLS)
Would this be considered consistent and improves on the efficiency of 2SLS or would it be considered redundant?
Thank you in advance.
I have a question regarding control function approach,
I understand that I need to first estimate a reduced-form equation of the endogenous variable, estimate the residuals then add the residuals to the structural equation of interest. I am wondering whether it is possible to add a stage in the beginning to deal with sample selection bias, the same way we can do in 2SLS models.
Thus run a model like this:
Stage (1):
Probit: Participation (X1 Z1)
Calculate IMILLS
Stage (2):
Regress: WAGES (X1 X2 Z2 IMILLS)
predict ERR, res
Stage (3):
OPROBIT: SATISFACTION (WAGES X1 X2 X3 ERR IMILLS)
Would this be considered consistent and improves on the efficiency of 2SLS or would it be considered redundant?
Thank you in advance.
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