#===============================================================================================#
# Metody Ekonometryczne
# Zadanie 8. 
# Michal Gradzewicz & Jakub Mućk 
#===============================================================================================#
library(AER)

N = 200
sigma_t = 0.2;sigma_z = 0.1; sigma_x = 0.1;sigma_y = 0.1
m_t = 10;m_z = 20;m_x = 5;m_y = 7

t = rnorm(N, m_t, sigma_t)
z = rnorm(N, m_z, sigma_z)
x = t + z + rnorm(N, m_x, sigma_x)
y = t + rnorm(N, m_y, sigma_y)

DATA = data.frame(t, z, x, y)

# Regresja z pkt (ii)
summary(lm(y ~ x, data = DATA))
# Regresja z pkt (iii)
summary(lm(y ~ x + t, data = DATA))
# IV z punktu (iv)
summary(ivreg(y ~ x | z, data = DATA), diagnostics = TRUE)