Why is there no iv method when using logit?

[Flo Adriaansens]

Dear Stata users,

I am performing a regression using both logit and probit. I know they should give similar results in terms of marginal effects but that is one of the aspects I am trying to show so I still would like to use both estimations. I have good reasons to assume that one of my variables includes measurement error and I have found two instruments to correct for this. Furthermore, I know I can use probit together with IV, but I have found I cannot use logit with IV.

I was wondering if anyone can explain the technicalities behind the reason IV cannot be combined with logit? I am aware of the following post:
Re: st: ivlogit Function Question (stata.com)
but I don't find the answer very clear.

Thank you for your time.

[Joro Kolev]

I do not see any reason for why a Control Function handling endogeneity should not exist for the Logit model, as long as your endogenous regressor(s) are roughly continuous. See the user written by David Roodman command -cmp-. If there is anything that allows for logit with endogeneity it would be this command.

If I remember correctly for multinomial outcomes one needs the joint normality and this is why in this paper
Cupák, Andrej, Gueorgui I. Kolev, and Zuzana Brokešová. "Financial literacy and voluntary savings for retirement: novel causal evidence." The European Journal of Finance 25, no. 16 (2019): 1606-1625.
I had to revert to an ordered probit with endogeneity, although the referee wanted to see ordered logit with endogeneity.

But for binary outcomes I think one can do logit with a control function.

The thread you attach simply speaks of convenience of having something jointly-something distributed. E.g., in probit with endegeneity one can assume that the structural and the reduced form errors are jointly normal. I do not know how convenient is the joint logistic distribution function to work with (if such a thing exists at all).

[David Radwin]

You might also look at Alvarez, R. M., & Glasgow, G. (1999). Two-stage estimation of nonrecursive choice models. Political analysis, 8(2), 147-165 and related articles.