*******  AULA PRATICA - LATE/VI   ****
** BASEADA NO TEXTO
/*The Stata Journal (2014) 14, Number 3, pp. 453–480
ivtreatreg: A command for fitting binary treatment models with heterogeneous response
to treatment and unobservable selection
Author: Giovanni Cerulli   */

cd "C:\FEA_OwnCloud\guilherme\FEARP\mestrado\avaliação\late-vi"
use "fertil2.dta", clear

/*"fertil2.dta is a collection of cross-sectional data on 4,361 women
of childbearing age in Botswana. This dataset contains 28 variables on various female
and family characteristics. 
We are particularly interested in evaluating the impact of the variable "educ7" 
(taking value 1 if a woman has seven years of education or more and 0 otherwise)
 on the number of family children (children). Several conditioning
(or confounding) observable factors are included in the dataset, such as the age
of the woman (age), whether or not the family owns a TV (tv), and whether or not the
woman lives in a city (urban). To inquire about the relationship between education and
fertility, following Wooldridge (2010), we estimate the following specification:*/

*gerando "educ7"
gen educ7=0
replace educ7=1 if educ>=7&educ~=.

 
*diferença de média ingenua
reg children educ7
estimates store ttest

*regressão múltipla
reg children educ7 age agesq evermarr urban electric tv
estimates store mqo

* tem que instalar o comando 
* ssc install ivtreatreg

*rodando o comando para VI
/*frsthalf é a variável instrumental que assume valor 1 se a mulher nasceu no primeiro 
semestre do ano e 0 caso contrário. Essa variável é parcialmente correlacionada
com educ7, mas não deveria ter nenhum efeito direto sobre a fertilidade */

reg children educ7 age agesq evermarr urban electric tv
 estimates store mqo
 
ivtreatreg children educ7 age agesq evermarr urban electric tv, ///
iv(frsthalf) model(probit-2sls) graphic
estimates store probit_2sls

ivtreatreg children educ7 age agesq evermarr urban electric tv, ///
iv(frsthalf) model(direct-2sls) graphic
estimates store direct_2sls
 
ivtreatreg children educ7 age agesq evermarr urban electric tv, ///
iv(frsthalf) model(probit-ols) graphic
estimates store probit_ols

ivreg 2sls children age agesq evermarr urban electric tv (educ7=frsthalf) 
estimates store ivregr

estimates table mqo probit_ols direct_2sls probit_2sls ivregr,b(%9.2f) keep(educ7 G_fv) star

/*G_fv é a probabilidade predita a partir de modelo probit, condicional nas observáveis*/

/*probit-ols
1. Apply a probit of w on x and z, thus getting pw, the predicted probability of w.
2. Run an OLS of y on {1, x, pw, pw(x - µx)}.*/

/*direct_2sls
1. Run an OLS regression of w on x and z, thus getting the predicted values of wi,
indicated by wfv,i.
2. Run a second OLS of y on {x, wfv,i, wfv,i(x - µx)}. 

/*probit-2sls
1. Apply a probit of w on x and z, thus getting pw, the predicted probability of w.
2. Run an OLS of w on (1, x, pw), thus getting the fitted values w2fv,i.
3. Run a second OLS of y on {1, x, w2fv,i, w2fv,i(x - µx)}.*/

/*The coefficient of w2fv,i is a more efficient estimator of ATE compared 
with direct-2sls. Furthermore, to achieve consistency, this procedure does 
not require that the process generating w is correctly specified; 
thus, it is more robust than probit-ols.*/