In an endogenous switching model, if there is an additional endogenous explanatory variable, I think we can either follow a control function approach (Murtazashvili and Wooldridge 2016), or a full information maximum likelihood approach. I tried both, but the full information maximum likelihood approach does not work out. I suspect I've made some stupid mistakes in writing up the likelihood function or the Stata codes. Hope someone can help me with this.
For editing reasons, I posted my question here on StackExchange.