Obtaining Counterfactual estimates after xtprobit in exogenous switching regression model

[Ikechukwu Nwaka]

Dear Statalisters,
I have some issues regarding the estimation of counterfactual treatment effects regression for the binary outcome variable, food insecurity=1 vs food secured=0 each for male (MHH) and female (FHH) headed families using random effects xtprobit model. My main aim is to analyze counterfactual food insecurity of FHHs – reflecting what food insecurity of FHH would be when the returns of the MHH characteristics are swapped into the FHHs
First, model is simplified to run separate random effects probit models each for MHH and FHH families as such:
MHH_Fd_insec=B_MHH X_MHH + U_MHH if MHH=1 for male-headed families
FHH_Fd_insec = B_FHH X_FHH + U_FHH if MHH=0 for female-headed families
I tried the following:
xtprobit fd_insec yrsch_hd age_hd hhsize occp_hd if MHH==0 // presenting the actual estimates for female-headed families
xtprobit fd_insec yrsch_hd age_hd hhsize occp_hd if MHH==1 // presenting the actual estimates for male-headed families

Please, is there any STATA commands that can be implemented to estimate a counterfactual xtprobit model by interchanging the characteristics of MHH into those of the FHHs? Are there other means of resolving this, please?

Any kind of help will be highly appreciated.

Ikechukwu