mlogit with a binary endogenous variable? Control function approach?

[Cooper Felix]

Is it possible to adopt the control function approach in this case? Can I apply a linear probability in the first stage to obtain the residuals and then plug the residuals to the mlogit model in the second stage?

If not, can you suggest a Stata command for this scenario? Thanks!

[Cooper Felix]

According to Angrist and Pischke (p. 198 of their well-known book "Mostly Harmless Econometrics), "The arguments in favor of conventional OLS with LDVs apply with equal force to 2SLS and models with endogenous variables."

I guess I can just apply 2SLS to my data with nominal outcome and binary endogenous variable. Can anyone please correct me if I am wrong?