probit and counterfactual outcomes between groups

[Ikechukwu Nwaka]

Hello,
I have some issues regarding the estimation of counterfactual treatment effects regression for binary outcome variable, food insecurity=1 vs food secured=0 each for male (MHH) and female (FHH) headed families using random effects probit model. My main aim is to analyze food counterfactual food insecurity levels of FHH – 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 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:
probit fd_insec yrsch_hd age_hd hhsize occp_hd if MHH==0 // presenting the actual estimates for female headed families
probit 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 command that can be used to estimate a counterfactual probit model by interchanging the characteristics of MHH into those of the FHHs?
Your kind help will be highly appreciated.
Ikechukwu

[Jeff Wooldridge]

Ikechukwu: This may not be quite what you want, but I think it's close. First, you didn't actually do random effects -- and I wouldn't actually recommend it. Just use probit as you've done. What I think you want are the fitted values for all units, so that you can summarize what happens when you plug in the covariates for a FHH into the MHH and vice versa. The Stata "predict" command is very handy for this.

probit fd_insec yrsch_hd age_hd hhsize occp_hd if MHH==0
predict fd_F
probit fd_insec yrsch_hd age_hd hhsize occp_hd if MHH==1
predict fd_M

Now you'll have fitted values for every unit across the two counterfactuals, and you can summarize them as you wish. I also believe the user-written command nldecompose essentially does this because it is for the Blinder_Oaxaca decomposition for nonlinear models. But I haven't used it.

For example, the "average treatment effect" from having FHH versus MHH is obtained as

gen te = fd_F - fd_M
sum te

If you want the ATE and a proper standard error, you should use teffects and use the probit option.

teffects ra (fd_insec hd_age hhsize occp_hd, probit) (FHH)

[Ikechukwu Nwaka]

You are amazing Jeff - thank you so much! This is just what I need. Further clarifications please - by your response "...you can summarize what happens when you plug in the covariates for a FHH into the MHH and vice versa.."; is it safe to apply the

sum

command for the counterfactual outcomes

sum fd_F if MHH==1
sum fd_M if MHH==0

[Jeff Wooldridge]

Yes, that's exactly right.

[Ikechukwu Nwaka]

Thank you, Jeff, but one more question. Any idea on how to obtain the heterogeneous effects from the average predicted probabilities? This obtains from the fact that "MHHs and FHHs may not have the same food security status even if they have the same observed characteristics or even if they have the same returns on their respective observed characteristics...." (Aryal et al 2019)