*. simpsel1 pdv, sel() exog() very()

/*Observed data are n observations of p,d,y,z,v,x;
                         The model is
                         p = (yB + e)d,  E(ez)=0, d = I(0 < v + M* < A*), v = xA + eta
                         p is the observed outcome, is zero when d=0.
                         d is the discrete selection indicator
                         v is the very exogenous regressor.
                         y is varlist in sel()
                         z is varlist in exog(), instruments for p model
                         x is varlist in very(), regressors in d and v models.
                         e = outcome error, 
                         M* and A* are latent variables (A* can be infinity)
                         M*, e, and X can be related in unknown ways, but are all independent of eta.
                         eta = v model error*/

cap pro drop simpsel1
pro def simpsel1, eclass

local varlist "required existing max(3) min(3)"
local if "optional "
local options "sel(string) exog(string) very( string)"
parse "`*'"
                           
preserve
tokenize "`varlist'"
di in g "Regression of `3' on `very'"
reg `3' `very'

tempvar eta sigma f w ww  
predict `eta' if e(sample), resid
gen `sigma'=sqrt(e(rss)/(_N))
gen `f'=normden(`eta', 0, `sigma')            /* assume v model error is normal, estimate the density*/

zrnd `f'                                      /* round the near zero density away from zero*/                    
gen `w'=`2'/`f'                               /* generate weight*/
qui sum `w'
gen `ww'=`w'/r(mean)                          /* normalize weight*/

di "                                  "
di in g "Based on conditional normal density of `v', sample selection is corrected."
di "                                  "

di in g "Structure model parameters are estimated by 2SLS."
ivreg `1' (`sel'=`exog') [iw=`ww']

di in g "Note the Std. Err. and Conf. Interval are wrong! "
di  "                              "
di in g "Bootstrap command can be used to get correct Std Err. and Conf. Interval."
di "                                      "
di in y `"Try it, :)) -  bs "simpsel1 varlist" _b, size() level() rep() saving() replace"'

end