Dear stata users,

As you know, the two-step multinomial logit estimation (McFadden correction), requires a multinomial logit (MNL) estimation in the first stage and a OLS estimation in the second stage.
This situation usually occurs when individuals select a choice in the first model and then a demand equation is estimated in the second (linear) model (demand which is conditional on the choice made by consumers in the first stage).

My problem is that I don't have a choice and a demand specifications, but rather two choice model specifications; that is, I would need to estimate a MNL both in the first and in the second stage (consumers make a choice in the second stage conditional on the choice made in the first stage).
The problem however is that I cannot perform (I think) the McFadden two-step correction procedure, since the second stage uses a MNL instead of a linear regression.

How could I proceed, then? I was not able to find any references on such a issue.

Besides, what if in the first stage I have a logit model? (which is basically a MNL reduced to two choices).

Many thanks in advance.

Jack