library(AER) # CigarettesSW

data("CigarettesSW")
#?CigarettesSW
View(CigarettesSW)

# iba rok 1995
data <- CigarettesSW[CigarettesSW$year == "1995", ]
data$rprice <- data$price / data$cpi # "normalizovane" ceny
View(data)
# packs ... pocet predanych balikov v US statoch, per capita
# rprice ... cena baliku / consumer price index

# Obycajna regresia
cig_lm <- lm(log(packs) ~ log(rprice), data = data)
summary(cig_lm)
# beta: -1.21, signifikantna

# IV:
data$salestax <- (data$taxs - data$tax) / data$cpi # sales tax (~ spotrebna dan)
View(data)

cor(data$salestax, data$rprice) # slusne korelovane s cenou
# (treba poriadnejsie otestovat)

# Instrumental-variable regression
?ivreg # y ~ x | IV
cig_ivreg <- ivreg(log(packs) ~ log(rprice) | salestax, data = data)
summary(cig_ivreg)
# beta: -1.0836, signifikantna