Instrumental variables with xtlogit

[Kwasi Tabiri]

Hi
I am running an estimation with panel data for a binary dependent variable. However, my main regressor is endogenous, and therefore I plan to use an instrumental variable.
Is there a Stata command or routine that can help me run an instrumental variable regression with my data?

Thanks for your help!

[George Ford]

I know there's an xtivprobit

[Jeff Wooldridge]

Is the endogenous explanatory variable roughly continuous or discrete?

[Kwasi Tabiri]

Is the endogenous explanatory variable roughly continuous or discrete?

Thanks for your reply, Prof. Wooldridge. The endogenous explanatory variable is roughly continuous. It is a continuous index ranging between 0 and 1.

[Kwasi Tabiri]

I know there's an xtivprobit

Unfortunately I could not find xtivprobit as a built-in or user-written command. Could you kindly point me to the source of this command?
Thanks.

[Jeff Wooldridge]

Does it take values at the endpoints of 0 and 1? If not, then I have a simple control-function suggestion. More soon.

[Kwasi Tabiri]

Does it take values at the endpoints of 0 and 1? If not, then I have a simple control-function suggestion. More soon.

It does take on values at the endpoints. But those are relatively few.

[George Ford]

sorry. you're right.

xteprobit fits RE model.

also check this out:

  https://www.stata.com/meeting/germany14/abstracts/materials/de14_drukker_gsem.pdf

[Kwasi Tabiri]

Thank you, George! I really appreciate it.

[George Ford]

Maybe Jeff will get back. The CF may be your best option.

[Jeff Wooldridge]

If it's relatively few, I might bring those values just within the unit interval. Then, in the first stage, use the log-odds for the EEV -- call it w. Put the residuals in the probit in the second stage with w (not the log-odds, unless that's the variable you care about).

You can try just using a linear model for w itself in the first stage. That might be close enough if there aren't too many values near zero/one.

gen w_lodds = log(w/(1 - w))
reg w_lodds x1 ... xk z i.year
predict vhat, resid
probit y w vhat x1 ... xk i.year, vce(cluster id)
margins, dydx(w)

The cluster-robust t state on vhat tests the null of exogeneity. But you should bootstrap the two steps to get a valid standard error.

or

reg w x1 ... xk z i.year
predict vhat, resid
probit y w vhat x1 ... xk i.year, vce(cluster id)
margins, dydx(w)

If desired, you can square w or interact with x1, ..., xk for flexibility.

In my view xtprobit and gsem impose too many assumptions and are computationally difficult. Pooled probit with the CF imposes little.

[Kwasi Tabiri]

The cluster-robust t state on vhat tests the null of exogeneity. But you should bootstrap the two steps to get a valid standard error.

Thank you, Prof. Wooldridge! I appreciate you taking the time to provide this solution. So by two steps here, I presume you mean

 
 reg w_lodds x1 ... xk z i.year

and

 
 probit y w vhat x1 ... xk i.year, vce(cluster id)

Correct?