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# Generalized Impulse Response Function (GIR) as in Peseran and Shin 1996
#
# input
# x ... a gvar object
# n ... number of periods, in the GVAR literature often set to 40
# shock.var ... list of vectors of length 2, first element specifies the country to be shocked, second element the variable in the country (e.g. shock.var=c(13,3) third variable in US is going to be shocked)
# shock.dir ... a list of scalars, set to 1 or -1, for a (negative) 1sd shock, where sd refers to the country specific residuals. Alternatively, if scal = TRUE, any number submitted indicates
# the magnitude of the resulting first period shock, e.g. -0.01 for a 1% decrease in the first quarter
# scal ... TRUE if shock.dir indicates resulting value of shock
#
# output
# psi ... matrix of impulse responses
# Fmat ... coefficient matrix of ar1 representation of the system, important to check stability of system via its eigenvalues
# G ... G
# H ... H
# U ... U (residual matrix of the gvar system)
# shock.dir ... contains the submitted shock (either in standard deviations or in other magnitudes that get standardized within GIR)
# sigma.il ... residual standard deviation (i.e. magnitude of the shock if not elsewise specified)
GIR=function (x, n=40, shock.var, shock.dir=-1,scal=FALSE){
endoN=sapply(x$we.vecms,function(x) x$n)
G <- x$G
U <- x$U
H.list <- x$H
H <- H.list[[1]]
p = x$arguments$p
q = x$arguments$q
l <- length(x$subsys)
if ((x$arguments$exo.type!="from.sub" || is.null(x$arguments$exo.type)) && x$arguments$exo.var==TRUE) l <- l-1
if (max(p, q) > 1) {
for (i in 2:max(p, q)) {
H <- cbind(H, H.list[[i]])
}
I.n <- diag(ncol(H) - ncol(H.list[[max(p, q)]]))
Zeros <- matrix(0, nrow = ncol(H) - ncol(H.list[[max(p,
q)]]), ncol = ncol(H.list[[max(p, q)]]))
H <- rbind(H, cbind(I.n, Zeros))
G <- rbind(cbind(G, t(Zeros)), cbind(Zeros, I.n))
U <- rbind(U, matrix(0, nrow(Zeros), ncol(U)))
}
G_inv=solve(G)
Fmat <- G_inv %*% H
UtU= cov(t(U))
# define shock / either in terms of sd or %
s.j <- rep(0, dim(U)[1])
ind.j <- rep(0, dim(U)[1])
sigma.il <- vector()
for (i in 1:length(shock.dir))
{
if (shock.var[[i]][1] == 1) {
j <- shock.var[[i]][2]
}
else {
j <- sum(endoN[1:(shock.var[[i]][1] - 1)]) + shock.var[[i]][2]
}
# define variables once
sigma.il[i] <- sqrt(UtU[j, j])
if(scal){
# shock=as.numeric(unlist(strsplit(shock.dir,"/sd"))[[1]])*cons*(1/G_inv[j,j])
shock <- shock.dir[[i]]*sigma.il[i]/(G_inv%*%UtU)[j,j]
}
else{
shock <- shock.dir[[i]]
}
if(!is.numeric(shock)){
stop("For the argument shock.dir please submit either a volume shock (e.g. shock.dir='0.003/sd') or a standard deviation shock (e.g. shock.dir='-1').")
}
s.j[j] <- shock
ind.j[j] <- 1
}
cons <- 1/sqrt(as.vector(t(ind.j)%*%UtU%*%ind.j))
# cons <- 1/sqrt(as.vector(t(s.j)%*%UtU%*%s.j))
psi.m <- matrix(nrow = nrow(U), ncol = n + 1)
F.n <- diag(nrow(Fmat))
psi.m[, 1] <- cons * F.n %*% G_inv %*% UtU %*%s.j
# browser()
for (i in 1:n) {
F.n <- F.n %*% Fmat
psi.m[, (i + 1)] <- cons* F.n %*% G_inv %*% UtU %*%s.j
}
psi <- list()
psi[[1]] <- t(psi.m[1:endoN[1],])
rownames(psi[[1]]) <- 0:n
colnames(psi[[1]]) <- colnames(x$Data[[1]])
for (i in 2:l)
{
psi[[i]] <- t(psi.m[(sum(endoN[1:(i-1)])+1):(sum(endoN[1:i])),])
rownames(psi[[i]]) <- 0:n
colnames(psi[[i]]) <- colnames(x$Data[[i]])
}
names(psi) <- x$subsys[1:l]
# calculate cumulated effects
psi.cum=lapply(psi,function(x) apply(x,2,cumsum))
names(psi.cum)=names(psi)
res <- list(psi = psi, psi.cum=psi.cum,Fmat = Fmat, G = G, H = H, U = U,shock.dir=shock.dir,sigma.il=sigma.il)
return(res)
}
#testGIR1 <- GIR(varM_epepsus,n=40,list(c(1,1)),shock.dir=list(-0.01),scal=TRUE)
#testGIR2 <- GIR(varM_epepsus,n=40,list(c(2,1)),shock.dir=list(-0.00000000000000000001),scal=TRUE)
#testGIR3 <- GIR(varM_epepsus,n=40,list(c(1,1),c(2,1)),shock.dir=list(-0.01,-0.00000000000000000001),scal=TRUE)
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