#Import data
setwd("C:/Andrzej/Dydaktyka/econometric_methods/")
dataset <- read.csv("lecture_9_ecm.csv", sep = ";", dec = ",")
#Convert series into time series objects
l_real_wage <- ts(dataset$l_real_wage)
l_productivity <- ts(dataset$l_productivity)
unemployment <- ts(dataset$unemployment)

#Unit root test sequences for 3 series to verify the necessary condition for cointegration
#install.packages("fUnitRoots")
library(fUnitRoots)
#One can also use the function ur.df from package urca, where the lag length is selected based on info criteria for test regression.
adfTest(l_real_wage, lags = 4, type = "c")
adfTest(diff(l_real_wage, differences = 1) , lags = 4, type = "c")
adfTest(l_productivity, lags = 4, type = "c")
adfTest(diff(l_productivity, differences = 1) , lags = 4, type = "c")
adfTest(unemployment, lags = 4, type = "c")
adfTest(diff(unemployment, differences = 1) , lags = 4, type = "c")

#Verifying the sufficient condition for cointegration
coint.equation <- lm(l_real_wage ~ l_productivity + unemployment)
summary(coint.equation)
#The following is AN INCORRECT way to test residuals for nonstationarity (usual ADF):
adfTest(resid(coint.equation), lags = 4, type = "c")
#The following is THE CORRECT way to test residuals for nonstationarity (CIDF):
#install.packages("aTSA")
library(aTSA)
coint.test(y = dataset$l_real_wage, X = as.matrix(cbind(dataset$l_productivity, dataset$unemployment)))

#Estimating the error correction model
ECT <- resid(coint.equation)
plot(ECT)
dataset.ts <- ts(cbind(dataset[, -1], ECT), frequency = 4, start = c(1967, 1))
library(dynlm)
ECM.equation <- dynlm(d(l_real_wage) ~ L(ECT, 1) + d(l_productivity) + d(unemployment), data = dataset.ts)
summary(ECM.equation)