# Heckman selection model: probit selection & logit outcome

I have a situation where I think I need to use a Heckman selection model to correct for endogeneity. I am interested in studying the effect of firm's market entry mode on its performance. Factors that influence a firm's performance could also be correlated with firm's choice of entry mode. So I am thinking I should use the Heckman model: first, model the choice of entry mode (selection equation) using a multinomial probit (since I have three entry modes in my context) and then model firm performance (outcome equation: success/failure in my context - hence logit).

My questions are as follows:

1. I think a key assumption of the Heckman selection model is that error terms of the selection and outcome equation are normally distributed. In my context, since I use a logit specification for my outcome equation, I think this assumption is violated. Is it right to the Heckman model in my situation? If not, is there a workaround?

2. Assuming I can use Heckman model, do I get two inverse Mills ratios given that I have three levels in my selection model? I have seen only examples of using inverse Mills ratio involving binary probit selection equation.

3. Again assuming I can use Heckman model, the outcome equation will be modeled on a panel data in my setting. Does that involve any complications/watchouts in using the inverse Mills ratio in the second stage?

4. Lastly, I am most comfortable with R, and is there any readymade solution available in R that I can use in my context? If not, I could also try out any Stata solutions. If neither, do I just run the models separately in two stages. In that case, is there a way to collect the Inverse Mills ratio manually from a multinomial probit model?

I really appreciate any suggestions to address my problem. Thanks.
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