Final Paper: IRFs by OLS
Set work directory
setwd("C:/Users/victo/Downloads/ECON 4310/Paper")Loading Packages
We are using various R packages that need to be installed and added. You might have to uncomment/run the chunk below. Alternatively, you may be able to install the missing packages through RStudio, selecting “packages” and “install”, entering the names.
#install.packages("invgamma")
library(invgamma)
#install.packages("matlib")
library(matlib)
#install.packages("MASS")
library(MASS)
#install.packages("MCMCpack")
library(MCMCpack) #for Inverse Wishart## Warning: package 'MCMCpack' was built under R version 4.2.3## Loading required package: coda## Warning: package 'coda' was built under R version 4.2.3## ##
## ## Markov Chain Monte Carlo Package (MCMCpack)## ## Copyright (C) 2003-2023 Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park## ##
## ## Support provided by the U.S. National Science Foundation## ## (Grants SES-0350646 and SES-0350613)
## ####
## Attaching package: 'MCMCpack'## The following objects are masked from 'package:invgamma':
##
## dinvgamma, rinvgamma#install.packages("mvtnorm")
library(mvtnorm) #for multivariate Normal
#install.packages("HypergeoMat")
library(HypergeoMat) #for multivariate gamma function (VAR-MDD calculation)## Warning: package 'HypergeoMat' was built under R version 4.2.3#install.packages("vars")
library(vars)## Warning: package 'vars' was built under R version 4.2.3## Loading required package: strucchange## Warning: package 'strucchange' was built under R version 4.2.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 4.2.3##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: sandwich## Warning: package 'sandwich' was built under R version 4.2.3## Loading required package: urca## Warning: package 'urca' was built under R version 4.2.3## Loading required package: lmtest## Warning: package 'lmtest' was built under R version 4.2.3Load Data
Load monthly data and trim to 1997, Q2 (max MPR data):
data <- read.csv("Chile_1986_Monthly.csv", header=TRUE)
# head(data)
#na.omit(as.numeric(data$CPI))
#na.omit(data$CPI)
UE <- ts(data$UE, frequency=12,start=c(1986,1))
CPI <- ts(data$CPI, frequency=12, start=c(1986,1))
UE <- window(UE,start=c(1997,2),end=c(2022,12))
CPI <- window(CPI,start=c(1997,2),end=c(2022,12))Convert monthly to quarterly data
MonthlyToQuarterly <- function(MonthlyData,start,namevec){
## Assume that first obs is first month of quarter
## Assume that last obs is last month of quarter
nobsMonth <- length(MonthlyData)
nobsQuart <- nobsMonth/3
firstyear <- start[1]
firstquarter <- ((start[2]-1) %/% 3)+1
QuarterlyData <- matrix(0,nrow=nobsQuart,ncol=1)
for(i in 1:nobsQuart){
QuarterlyData[i] <- mean(MonthlyData[(1+3*(i-1)):(3*i)],na.rm=FALSE)
}
QuarterlyData <- ts(QuarterlyData,frequency=4,start=c(firstyear,firstquarter),
names=namevec)
return(QuarterlyData)
}
UEq <- MonthlyToQuarterly(UE,c(1996,1),"UE")
UEq <- window(UEq,start=c(1997,2))
#print(UEq)
CPIq <- MonthlyToQuarterly(CPI,c(1996,1),"CPI")
CPIq <- window(CPIq,start=c(1997,2))
#print(CPIq)Load Monetary Policy Rate data (MPR)
data <- read.csv("Chile_MPR_monthly_F1997.csv", header = T)
MPR <- ts(data$MPR, frequency = 12, start = c(1997, 2))
MPRq <- MonthlyToQuarterly(MPR, c(1997,2), "MPR")
MPRq <- window(MPRq, start=c(1997,2), end=c(2021,3))
#print(MPRq)Load the GDP data (unnecessary for monetary policy shock)
data <- read.csv("Chile_1996_Quarterly.csv", header=TRUE)
GDP <- gsub(",","",data$GDP)
GDP <- as.numeric(GDP)
GDP <- ts(GDP, frequency=4, start=c(1997,2))
#head(GDP)
GDPlog <- log(GDP)
GDPlogdiff <- diff(GDPlog)
GDPgrowth <- 400*GDPlogdiff
GDPgrowth <- ts(GDPgrowth, frequency = 4,start=c(1997,2))VAR Estimation and IRFs
Tall <- length(UEq) # total number of observations, starting 1997:Q2
T1 <- (1+4) # estimation sample will start in T1
p <- 4 # number of lags
n <- 3 # number of variables
yyall <- cbind(MPRq, UEq, CPIq)
yy <- yyall[T1:Tall,]
xx <- matrix(1,nrow=(Tall-T1+1), ncol=(n*p+2))
xx[,2] <- 1:(Tall-T1+1)
for(i in 1:p){
# first column of xx is vector of 1s
# second column is time trend
# followed by y(t-1), y(t-2), ..., y(t-p)
xx[,(2+(i-1)*n+1):(2+i*n)] <- yyall[(T1-i):(Tall-i),]
}OLS/ML Estimation
Phi_hat <- solve(t(xx)%*%xx,t(xx)%*%yy)
Sigma_hat <- (t(yy)%*%yy - t(yy)%*%xx%*%Phi_hat)/(Tall-T1+1)
Sigma_hat_tr <- t(chol(Sigma_hat))
print(Phi_hat)## MPRq UEq CPIq
## [1,] 3.31589094 0.730720198 -0.29238156
## [2,] -0.01510097 -0.001359154 0.00275034
## [3,] 1.10667395 0.052127195 -0.05019767
## [4,] 0.06648655 1.293715152 -0.03237839
## [5,] 0.20931955 -0.151294608 0.27415532
## [6,] -0.36181610 -0.094764932 0.14551312
## [7,] -0.12095907 -0.494031308 0.01203095
## [8,] -0.06197169 0.310062429 0.06839104
## [9,] -0.04258664 0.047179841 -0.13794882
## [10,] 0.09925800 0.112450548 -0.04829436
## [11,] -0.27752248 0.029187200 -0.10705629
## [12,] 0.02657578 0.023185119 0.05200609
## [13,] -0.26468293 -0.021576992 0.10151634
## [14,] 0.88898678 0.217565970 0.31373781Impulse Responses
Hmax <- 36
shind <- 1 # Monetary Policy Rate shock is first
IRFmat <- matrix(0,nrow=(Hmax+1),ncol=n)
# response at impact is shind column of Sigma_hat_tr
IRFmat[1,] <- t(Sigma_hat_tr[,shind])
xxIRF <- matrix(0,nrow=1,ncol=p*n)
xxIRF[1,1:n] <- IRFmat[1,]
Phi_hat_no_const <- Phi_hat[3:(n*p+2),]
for(h in 1:Hmax){
IRFmat[(1+h),] <- xxIRF%*%Phi_hat_no_const
if(p > 1){
xxIRF[1,(n+1):(n*p)] <- xxIRF[1,1:(n*(p-1))]
}
xxIRF[1,1:n] <- IRFmat[(1+h),]
}
#par(mfrow=c(1,2),mar=c(2.2,2.2,2.2,2.2))
plot(0:Hmax,100*IRFmat[,1],ylim=c(-10,80),type="o",
col="blue",lwd=2,ylab="",xlab="")
title(main="MPR [%]")
abline(h=0,col="red")
plot(0:Hmax,100*IRFmat[,2],ylim=c(-1,10),type="o",
col="blue",lwd=2,ylab="",xlab="")
title(main="Unemployment Rate [%]")
abline(h=0,col="red")
plot(0:Hmax,100*IRFmat[,3],ylim=c(-5,10),type="o",
col="blue",lwd=2,ylab="",xlab="")
title(main="Inflation, CPI [%]")
abline(h=0,col="red")