Instrumental Variable Regression with binary endogenous variable, weak instrument test

[Vera Mikhailovna]

I have read different discussions in the forum regarding the binary endogenous variables and the converging suggestion seems to be using

ivreg2

command and then run weakivtest. My Cragg-Donald Wald F statistic is pretty low

 4.764

. However, in one of the recent posts, I've seen Professor Wooldridge referring to this paper: https://www.sciencedirect.com/scienc...a%3Dihub#appSB To me, the logic is very intuitive, however, I am not sure about how to calculate the F-statistics after obtaining the fitted probability.
My instrument is likely to (theoretically) satisfy the exclusion restrictions and relevancy conditions. To give you a little bit of context, there are micro-funding opportunities randomly introduced in rural areas in Africa (the location is determined based on lottery), and woman entrepreneurs are required to finish 2 weeks of training before obtaining any funding (there is no exam at the end but they need to complete at least 50% of the courses). My research question is whether these micro funds are important for entrepreneurial success or not, I use the logarithm of distance to the nearest hub as an instrument for obtaining a fund (completing vs leaving the course might also be important, but I will think about that later).

Any suggestions?

[Joro Kolev]

Can you phrase your observations as a question?

[Vera Mikhailovna]

Sorry about the confusion, my main question is whether or not we can make a test similar to 2SLS if first stage is probit.

[Vera Mikhailovna]

Okay let me update my question: Let's assume y is the dependent variable, x1 is the binary endogenous variable, z1 is my excluded instrument, x2 x3 x4 are other exogenous variables. Is the following procedure true?

probit x1 z1 x2 x3 x4
* Obtain fitted probabilities
predict probit_fit
ivreg2 y (x1 = probit_fit) x2 x3 x4
weakivtest

Additional question, if the second stage is is also non-linear, can I do the following:

eoprobit y x1 x2 x3 x4, endogenous(x1 = probit_fit x2 x3 x4)

I would very much appreciate any feedback. Joro Kolev Jeff Wooldridge

[Joro Kolev]

The procedure with using predicted probabilities from Probit as instruments is correct, the suggestion for this procedure appears in
Angrist, Joshua D., and Alan B. Krueger. "Instrumental variables and the search for identification: From supply and demand to natural experiments." Journal of Economic perspectives 15, no. 4 (2001): 69-85.

I do not know what -eoprobit- does so I do not know about the second thing.