# Variaveis instrumentais no R I 
# Prof. Raphael B. Corbi/ Monitor Alan Leal

# Pacotes utilizados neste código:
if(!require(tidyverse)){install.packages("tidyverse");require(tidyverse)}
if(!require(AER)){install.packages("AER");require(AER)}
if(!require(stargazer)){install.packages("stargazer");require(stargazer)}

# Lendo a base agora:
# Lendo a base:
card <- haven::read_stata("https://raw.github.com/scunning1975/mixtape/master/card.dta") %>% 
  filter(if_all(c(lwage,educ,exper,black,south,married,smsa,nearc4),~!is.na(.)))

# Iremos criar agora as tres matrizes de interesse, X, Z e y:
y <- card$lwage
X <- cbind(1,card$educ,card$exper,card$black,card$south,card$married,card$smsa)
Z <- cbind(1,card$nearc4,card$exper,card$black,card$south,card$married,card$smsa)

# Vamos agora as estimativas de mqo e iv:
beta_ols <- solve(t(X)%*%X)%*%t(X)%*%y
beta_iv <- solve(t(Z)%*%X)%*%t(Z)%*%y
cbind(beta_ols,beta_iv)

# Faremos esse mesmo procedimento por dois estágios:
frst_stg <- lm(educ~nearc4+exper+black+south+married+smsa,data=card)
summary(frst_stg)
card$educ_hat <- predict(frst_stg)
# Segundo estágio:
scnd_stg <- lm(lwage~educ_hat+exper+black+south+married+smsa,data=card)
summary(scnd_stg)
# usando o comando próprio do R:
ivreg_card <- ivreg(lwage~educ+exper+black+south+married+smsa|nearc4+exper+black+south+married+smsa,data=card)
summary(ivreg_card)


# Vamos comparar o resultado do ivreg com o resultado de dois estágios:
stargazer(scnd_stg,ivreg_card,type="text")

# Usando o "diagnostics" do ivreg:
summary(ivreg_card,diagnostics = TRUE)