[Patrick Lang]

Jeff Wooldridge I would be curious about the solution when the EEV is binary. Can we still use the control function approach? Is it possible to use xtlogit in the first stage and then predict the residuals with the "score" option to obtain the generalized residuals? something like:

xtlogit y2 z1 ... zJ zJp1 ... zM i.year, fe
predict double v2h_fe, score
xtpoisson y1 y2 v2h_fe z1 ... zJ i.year, fe vce(robust)

Thank you.

[Vijayshree Jayaraman]

Dear Jeff,

I would be very curious about this "harder" solution if the EEV is not continuous. I am working on a problem with a binary EEV and directly implementing the method you suggest here (for continuous variables) seem to give strange results. Thanks in advance!

Best regards,
Olov

Hi Olov,

I am facing a similar problem, did you find a solution for question?

Regards

[Violette TT]

Thank you for the detailed thoughts, Prof. Wooldridge!

Following along the question from Olov, I'd like to learn about your solution on a binary endogenous variable in this case. We have a binary EEV as well as a binary IV. Does it only impact how we'd bootstrap to correct the standard errors, or that we have to completely follow a different procedure when estimating first stage?

Hi Dante:

Unfortunately, there is no statistical justification for the procedure you propose. It could suffer from the incidental parameters problem, although maybe using fixed effects in the second stage eliminates that. But I do know that to justify plugging in fitted values into an exponential function imposes strong assumptions.

What is the nature of X? Can it be treated as roughly a continuous variable? If so, I have an easy solution for you. If X is discrete, I have a somewhat harder solution for you (but not so hard for someone with decent Stata programming skills).

Best,
Jeff

Dear Jeff,

I would be very curious about this "harder" solution if the EEV is not continuous. I am working on a problem with a binary EEV and directly implementing the method you suggest here (for continuous variables) seem to give strange results. Thanks in advance!

Best regards,
Olov

[Marta Alvaro]

Hi Jeff Wooldridge ,

I'm wondering what's the solution you would suggest for panel data if the endogenous explanatory variable is count or binary, and the dependent variable is count. Also, the paper you posted is not longer available, and I have not been able to find it elsewhere. Would you mind re-sharing it?

Kind regards,
Marta

[Jeff Wooldridge]

See the attached slides, starting at slide 167. Ideally, one implement this using Stata's gmm command.

slides_12_exponential_2023.pdf

[Valentina Di Iasio]

Dear Jeff Wooldridge ,

Thank you very much for this explanation.

I found myself in a similar situation and was trying to access the paper where the method is outlined. However, the link posted in the previous post is no longer available (I guess that is because I am reading this discussion almost 4 years later). I wanted to ask whether there is an updated link and if it could be possible to share it.

Thanks in advance for your time

Valentina