Control Function (2SRI) approach with (binary) logit

[steny rapheal]

Hi
I am working around the endogeneity problem where both the outcome variable and endogenous independent variable are dichotomous. I did run ivregress 2SLS model and got meaningful results. I am also thinking of pursuing a control function approach instrumenting the endogenous predictor in the first step using logit and then including the residuals in the second step, logit model. The recommended way of doing this seems to be bootstrapping, but I am not sure whether the procedure below is correct.

1) Will this procedure (i.e. bootstrapping the whole program) lead to a reasonable estimate of the standard errors for the model?
2) Is estimating logit in both stages fine?
3) Will these commands entail two-stage residual inclusion with logit?

I am working with DHS data and am using Stata 17.

outcome variable: (d108)
binary endogenous regressor: whether woman is engaged paid work (occp)
instrument variable: cluster average of women's working status (occp-adj)

program bsses
preserve
svy: logistic occp occp_adj
predict pvhat,p
gen uhat = occp - pvhat
test occp_adj
svy: logistic d108 i.occp uhat                                                        
drop uhat
restore
end program
bootstrap, reps(50): bsses

Any advice will be helpful. Thanking you.

[steny rapheal]

Any advice will be of great help to me... I am also confused if bootstrapping can be combined with the svy command.