Control Function approach for binary endogenous variable and count dependent variable

[Neha Bhardwaj Up]

Dear All,

I was hoping to receive some confirmation here. I would like to use the control function approach for the following design.

Count dependent y ; Endogenous w (binary) ; exogenous covariates x_j ; and IVs z_h. Dataset is panel type with N=150 and T=25.

 xtlogit w x1 x2 ... xk z1 ... zm i.year , fe vce(jack)

predict vhat, p

xtpoisson y w vhat x1 ... xk i.year, fe vce(jack)

I understand that I cannot simply use

ivpoisson y (w=z1) x1 x2 ... xk 

as it is not workable for a fixed effects model.

Please suggest.

[Joro Kolev]

In general the control function approach is not appropriate for binary endogenous regressor, it needs the endogenous regressor to be roughly continuous.

If I am not wrong, in this paper Wooldridge, Jeffrey M. "Control function methods in applied econometrics." Journal of Human Resources 50, no. 2 (2015): 420-445,
Professor Wooldridge speaks of some controversial approach where you use a generalised residual.

You can check the paper for the section in question. I cannot say much more because I have never done this "generalised residual" estimation.

[Neha Bhardwaj Up]

Thank you Joro !