R/MSWfunction.R
In martinbaumgaertner/varexternal: Vector autoregression with external instruments
Defines functions
MSWfunction
Documented in
MSWfunction
#' MARep
#'
#'Reports the confidence interval for IRF coefficients described in Montiel-Olea, Stock, and Watson (2017).
#'
#' @param confidence confidence level
#' @param nvar variable defining the normalization
#' @param scale scale of the shock
#' @param horizons Number of horizons for the IRF
#' @param RForm reduced-form structure
#' @param display_on dummy variable
#'
#' @return InferenceMSW: Structure containing the MSW weak-iv robust confidence interval
#' @return Plugin: Structure containing standard plug-in inference
#' @return Chol: Cholesky IRFs
#'
#' @seealso https://github.com/jm4474/SVARIV
#' @seealso https://uc4384f22718973d3d912d614f2e.dl.dropboxusercontent.com/cd/0/inline2/Aslwi_FA9z6v37dfxMeUP3mEaP-a4ZA8RFrXd5h_EymM1lqGy-UUwGJB3TxqRxluMhE9ebnvHEMZktfcUmJ1v4mGSxeS_ZEDJBCrjGvyopAnP44ClPLJ6kmM36F557kHnqKQjn___0XTNvPaWvXnkEC0Btt3MpVhn41q0ddL4qtZ1g9l2ooeVweHH9X5xCAaG3R28lpzivQzj8AZRVSPHs98yseh0L9I10-G0frVqteUkjuQJQNAmFlEPpqegmDhpPo_vaMScx1w1ivQ--mxoZli2uvBI1Pnen-nGIyD3qT_oT-0r3K6bjwk1vI71fgMtGw6ZhWWFuWv48Oq-vg7lN1fKgPEyvcJMcdIISnra0z-1w/file
#'
#' @export
#'
#'
MSWfunction <-function(confidence,nvar,scale,horizons,RForm) {
irfs<-list()
for(a in 1:length(confidence)){
confi<-confidence[a]
critval = stats::qnorm(1 - ((1 - confi) / 2), 0, 1) ^ 2
Caux = cbind(diag(RForm$n), MARep(RForm$AL, RForm$p, horizons))
C = array(Caux, c(RForm$n, RForm$n, horizons + 1))
for (i in 2:dim(C)[3]) {
if (i == 2) {
Ccum <- cbind(C[, 1:dim(C)[2], 2])
} else{
Ccum <- cbind(Ccum, C[, 1:dim(C)[2], i])
}
}
Ccum <- array(Ccum, c(dim(C)[1], dim(C)[2], dim(C)[3]))
G <-Gmatrices(RForm$AL,
MARep(RForm$AL, RForm$p, horizons),
RForm$p,
horizons,
RForm$n)$G
Gcum <-Gmatrices(RForm$AL,
MARep(RForm$AL, RForm$p, horizons),
RForm$p,
horizons,
RForm$n)$Gcum
B1chol = t(chol(RForm$Sigma))
B1chol = scale * (B1chol[, 1] / B1chol[nvar, 1])
Chol <- array(numeric(), c(0, 0, 2))
Chol[, , 1] = colSums(aperm(sweep(C, 2, t(B1chol), FUN = "*"), c(2, 1, 3)))
Chol[, , 2] = colSums(aperm(sweep(Ccum, 2, t(B1chol), FUN = "*"), c(2, 1, 3)))
W1 = RForm$WHat[1:((RForm$n ^ 2) * RForm$p), 1:((RForm$n ^ 2) *RForm$p)]
W12 = RForm$WHat[1:((RForm$n ^ 2) * RForm$p), (1 + (RForm$n ^2) * RForm$p):(ncol(RForm$WHat))]
W2 = RForm$WHat[(1 + (RForm$n ^ 2) * RForm$p):nrow(RForm$WHat), (1 +(RForm$n ^ 2) * RForm$p):ncol(RForm$WHat)]
n = RForm$n
Ti = dim(RForm$eta)[2]
e = diag(n)
ahat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
bhat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
chat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Deltahat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
MSWlbound = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
MSWubound = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
casedummy = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
lambdahat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
DmethodVar = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Dmethodlbound = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Dmethodubound = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
ahatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
bhatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
chatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Deltahatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
MSWlboundcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
MSWuboundcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
casedummycum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
lambdahatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
DmethodVarcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Dmethodlboundcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Dmethoduboundcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
for (j in 1:n) {
for (ih in 1:(horizons + 1)) {
ahat[j, ih] = (Ti %*% (RForm$Gamma[nvar, 1] ^ 2)) - (critval %*% W2[nvar, nvar])
bhat[j, ih] = -2 * Ti * scale * (t(e[, j]) %*% C[, , ih] %*% RForm$Gamma) %*%RForm$Gamma[nvar, 1] +
2 * critval * scale * kronecker(t(RForm$Gamma), t(e[, j])) %*% G[, , ih] %*%W12[, nvar] +
2 * critval * scale * t(e[, j]) %*% C[, , ih] %*% W2[, nvar]
chat[j, ih] = ((Ti ^ .5) * scale * t(e[, j]) %*% C[, , ih] %*% RForm$Gamma) ^2 -
critval * (scale ^ 2) * (kronecker(t(RForm$Gamma), t(e[, j]))) %*%G[, , ih] %*% W1 %*% t((kronecker(t(RForm$Gamma), t(e[, j]))) %*% G[, , ih]) -
2 * critval * (scale ^ 2) * (kronecker(t(RForm$Gamma), t(e[, j]))) %*%G[, , ih] %*% W12 %*% t(C[, , ih]) %*% e[, j] -
critval * (scale ^ 2) * t(e[, j]) %*% C[, , ih] %*% W2 %*% t(C[, , ih]) %*%e[, j]
Deltahat[j, ih] = bhat[j, ih] ^ 2 - (4 * ahat[j, ih] * chat[j, ih])
if (ahat[j, ih] > 0 && Deltahat[j, ih] > 0) {
casedummy[j, ih] = 1
MSWlbound[j, ih] = (-bhat[j, ih] - (Deltahat[j, ih] ^ 0.5)) / (2 *ahat[j, ih])
MSWubound[j, ih] = (-bhat[j, ih] + (Deltahat[j, ih] ^ 0.5)) / (2 *ahat[j, ih])
} else if (ahat[j, ih] < 0 && Deltahat[j, ih] > 0) {
casedummy[j, ih] = 2
MSWlbound[j, ih] = (-bhat[j, ih] + (Deltahat[j, ih] ^ 0.5)) / (2 *ahat[j, ih])
MSWubound[j, ih] = (-bhat[j, ih] - (Deltahat[j, ih] ^ 0.5)) / (2 *ahat[j, ih])
} else if (ahat[j, ih] > 0 && Deltahat[j, ih] < 0) {
casedummy[j, ih] = 3
MSWlbound[j, ih] = NA
MSWubound[j, ih] = NA
} else{
casedummy[j, ih] = 4
MSWlbound[j, ih] = -Inf
MSWubound[j, ih] = Inf
}
}
}
MSWlbound[nvar, 1] = scale
MSWubound[nvar, 1] = scale
InferenceMSW <- list(
ahat = ahat,
bhat = bhat,
chat = chat,
Deltahat = Deltahat,
casedummy = casedummy,
MSWlbound = MSWlbound,
MSWubound = MSWubound,
Ti = Ti
)
for (ih in 1:(horizons + 1)) {
for (ivar in 1:n) {
lambdahat[ivar, ih] = scale * t(e[, ivar]) %*% C[, , ih] %*% RForm$Gamma /RForm$Gamma[nvar, 1]
d1 = ((kronecker(t(RForm$Gamma), t(e[, ivar])) *scale) %*% G[, , ih])
d2 = (scale * t(e[, ivar]) %*% C[, , ih]) -(lambdahat[ivar, ih] %*% t(e[, nvar]))
d = t(cbind(d1, d2))
DmethodVar[ivar, ih] = t(d) %*% RForm$WHat %*% d
Dmethodlbound[ivar, ih] = lambdahat[ivar, ih] - ((critval / Ti) ^0.5) * (DmethodVar[ivar, ih] ^ 0.5) / abs(RForm$Gamma[nvar, 1])
Dmethodubound[ivar, ih] = lambdahat[ivar, ih] + ((critval / Ti) ^0.5) * (DmethodVar[ivar, ih] ^ 0.5) / abs(RForm$Gamma[nvar, 1])
rm(d1)
rm(d2)
rm(d)
}
}
IRF = lambdahat
IRFstderror = (DmethodVar ^ 0.5) / ((Ti ^ 0.5) * abs(RForm$Gamma[nvar, 1]))
for (j in 1:n) {
for (ih in 1:(horizons + 1)) {
ahatcum[j, ih] = (Ti %*% (RForm$Gamma[nvar, 1] ^ 2)) - (critval %*% W2[nvar, nvar])
bhatcum[j, ih] = -2 * Ti * scale * (t(e[, j]) %*% Ccum[, , ih] %*% RForm$Gamma) %*%RForm$Gamma[nvar, 1] +
2 * critval * scale * kronecker(t(RForm$Gamma), t(e[, j])) %*% Gcum[, , ih] %*%W12[, nvar] +
2 * critval * scale * t(e[, j]) %*% Ccum[, , ih] %*% W2[, nvar]
chatcum[j, ih] = ((Ti ^ 0.5) * scale * t(e[, j]) %*% Ccum[, , ih] %*%RForm$Gamma) ^ 2 -
critval * (scale ^ 2) * (kronecker(t(RForm$Gamma), t(e[, j]))) %*%Gcum[, , ih] %*% W1 %*% t((kronecker(t(RForm$Gamma), t(e[, j]))) %*% Gcum[, , ih]) -
2 * critval * (scale ^ 2) * (kronecker(t(RForm$Gamma), t(e[, j]))) %*%Gcum[, , ih] %*% W12 %*% t(Ccum[, , ih]) %*% e[, j] -
critval * (scale ^ 2) * t(e[, j]) %*% Ccum[, , ih] %*% W2 %*% t(Ccum[, , ih]) %*%e[, j]
Deltahatcum[j, ih] = bhatcum[j, ih] ^ 2 - (4 * ahatcum[j, ih] * chatcum[j, ih])
if (ahatcum[j, ih] > 0 & Deltahatcum[j, ih] > 0) {
casedummycum[j, ih] = 1
MSWlboundcum[j, ih] = (-bhatcum[j, ih] - (Deltahatcum[j, ih] ^ 0.5)) /(2 * ahatcum[j, ih])
MSWuboundcum[j, ih] = (-bhatcum[j, ih] + (Deltahatcum[j, ih] ^ 0.5)) /(2 * ahatcum[j, ih])
} else if (ahatcum[j, ih] < 0 & Deltahatcum[j, ih] > 0) {
casedummycum[j, ih] = 2
MSWlboundcum[j, ih] = (-bhatcum[j, ih] + (Deltahatcum[j, ih] ^ 0.5)) /(2 * ahatcum[j, ih])
MSWuboundcum[j, ih] = (-bhatcum[j, ih] - (Deltahatcum[j, ih] ^ 0.5)) /(2 * ahatcum[j, ih])
} else if (ahatcum[j, ih] > 0 & Deltahatcum[j, ih] < 0) {
casedummycum[j, ih] = 3
MSWlboundcum[j, ih] = NA
MSWuboundcum[j, ih] = NA
} else{
casedummycum[j, ih] = 4
MSWlboundcum[j, ih] = -Inf
MSWuboundcum[j, ih] = Inf
}
}
}
MSWlboundcum[nvar, 1] = scale
MSWuboundcum[nvar, 1] = scale
for (ih in 1:(horizons + 1)) {
for (ivar in 1:n) {
lambdahatcum[ivar, ih] = scale * t(e[, ivar]) %*% Ccum[, , ih] %*% RForm$Gamma /RForm$Gamma[nvar, 1]
d1 = ((kronecker(t(RForm$Gamma), t(e[, ivar])) *scale) %*% Gcum[, , ih])
d2 = (scale * t(e[, ivar]) %*% Ccum[, , ih]) -(lambdahatcum[ivar, ih] %*% t(e[, nvar]))
d = t(cbind(d1, d2))
DmethodVarcum[ivar, ih] = t(d) %*% RForm$WHat %*% d
Dmethodlboundcum[ivar, ih] = lambdahatcum[ivar, ih] - ((critval / Ti) ^0.5) * (DmethodVarcum[ivar, ih] ^ 0.5) / abs(RForm$Gamma[nvar, 1])
Dmethoduboundcum[ivar, ih] = lambdahatcum[ivar, ih] + ((critval / Ti) ^0.5) * (DmethodVarcum[ivar, ih] ^ 0.5) / abs(RForm$Gamma[nvar, 1])
rm(d1)
rm(d2)
rm(d)
}
}
IRFstderrorcum = (DmethodVarcum ^ 0.5) / ((Ti ^ 0.5) * abs(RForm$Gamma[nvar, 1]))
Waldstat = (((Ti ^ 0.5) * RForm$Gamma[[nvar, 1]]) ^ 2) / RForm$WHat[((n ^2) * RForm$p) +
nvar, ((n ^ 2) * RForm$p) + nvar]
irfs[[a]]<-list(
plugin=list(point=lambdahat,
lower=lambdahat-IRFstderror,
upper=lambdahat+IRFstderror),
delta=list(point=lambdahat,
lower=Dmethodlbound,
upper=Dmethodubound),
msw=list(point=lambdahat,
lower=MSWlbound,
upper=MSWubound,
Waldstat=Waldstat,
critval=critval),
plugin_cum=list(point=lambdahatcum,
lower=lambdahatcum-IRFstderrorcum,
upper=lambdahatcum+IRFstderrorcum),
delta_cum=list(point=lambdahatcum,
lower=Dmethodlboundcum,
upper=Dmethodubound),
msw_cum=list(point=lambdahatcum,
lower=MSWlboundcum,
upper=Dmethoduboundcum,
Waldstat=Waldstat,
critval=critval)
)
}
names(irfs)<-confidence
return(irfs)
}
martinbaumgaertner/varexternal documentation built on April 27, 2022, 1:31 a.m.
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Defines functions MSWfunction
Documented in MSWfunction
#' MARep
#'
#'Reports the confidence interval for IRF coefficients described in Montiel-Olea, Stock, and Watson (2017).
#'
#' @param confidence confidence level
#' @param nvar variable defining the normalization
#' @param scale scale of the shock
#' @param horizons Number of horizons for the IRF
#' @param RForm reduced-form structure
#' @param display_on dummy variable
#'
#' @return InferenceMSW: Structure containing the MSW weak-iv robust confidence interval
#' @return Plugin: Structure containing standard plug-in inference
#' @return Chol: Cholesky IRFs
#'
#' @seealso https://github.com/jm4474/SVARIV
#' @seealso https://uc4384f22718973d3d912d614f2e.dl.dropboxusercontent.com/cd/0/inline2/Aslwi_FA9z6v37dfxMeUP3mEaP-a4ZA8RFrXd5h_EymM1lqGy-UUwGJB3TxqRxluMhE9ebnvHEMZktfcUmJ1v4mGSxeS_ZEDJBCrjGvyopAnP44ClPLJ6kmM36F557kHnqKQjn___0XTNvPaWvXnkEC0Btt3MpVhn41q0ddL4qtZ1g9l2ooeVweHH9X5xCAaG3R28lpzivQzj8AZRVSPHs98yseh0L9I10-G0frVqteUkjuQJQNAmFlEPpqegmDhpPo_vaMScx1w1ivQ--mxoZli2uvBI1Pnen-nGIyD3qT_oT-0r3K6bjwk1vI71fgMtGw6ZhWWFuWv48Oq-vg7lN1fKgPEyvcJMcdIISnra0z-1w/file
#'
#' @export
#'
#'
MSWfunction <-function(confidence,nvar,scale,horizons,RForm) {
irfs<-list()
for(a in 1:length(confidence)){
confi<-confidence[a]
critval = stats::qnorm(1 - ((1 - confi) / 2), 0, 1) ^ 2
Caux = cbind(diag(RForm$n), MARep(RForm$AL, RForm$p, horizons))
C = array(Caux, c(RForm$n, RForm$n, horizons + 1))
for (i in 2:dim(C)[3]) {
if (i == 2) {
Ccum <- cbind(C[, 1:dim(C)[2], 2])
} else{
Ccum <- cbind(Ccum, C[, 1:dim(C)[2], i])
}
}
Ccum <- array(Ccum, c(dim(C)[1], dim(C)[2], dim(C)[3]))
G <-Gmatrices(RForm$AL,
MARep(RForm$AL, RForm$p, horizons),
RForm$p,
horizons,
RForm$n)$G
Gcum <-Gmatrices(RForm$AL,
MARep(RForm$AL, RForm$p, horizons),
RForm$p,
horizons,
RForm$n)$Gcum
B1chol = t(chol(RForm$Sigma))
B1chol = scale * (B1chol[, 1] / B1chol[nvar, 1])
Chol <- array(numeric(), c(0, 0, 2))
Chol[, , 1] = colSums(aperm(sweep(C, 2, t(B1chol), FUN = "*"), c(2, 1, 3)))
Chol[, , 2] = colSums(aperm(sweep(Ccum, 2, t(B1chol), FUN = "*"), c(2, 1, 3)))
W1 = RForm$WHat[1:((RForm$n ^ 2) * RForm$p), 1:((RForm$n ^ 2) *RForm$p)]
W12 = RForm$WHat[1:((RForm$n ^ 2) * RForm$p), (1 + (RForm$n ^2) * RForm$p):(ncol(RForm$WHat))]
W2 = RForm$WHat[(1 + (RForm$n ^ 2) * RForm$p):nrow(RForm$WHat), (1 +(RForm$n ^ 2) * RForm$p):ncol(RForm$WHat)]
n = RForm$n
Ti = dim(RForm$eta)[2]
e = diag(n)
ahat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
bhat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
chat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Deltahat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
MSWlbound = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
MSWubound = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
casedummy = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
lambdahat = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
DmethodVar = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Dmethodlbound = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Dmethodubound = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
ahatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
bhatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
chatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Deltahatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
MSWlboundcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
MSWuboundcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
casedummycum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
lambdahatcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
DmethodVarcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Dmethodlboundcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
Dmethoduboundcum = matrix(0,n,horizons+1,dimnames = list(RForm$names,NULL))
for (j in 1:n) {
for (ih in 1:(horizons + 1)) {
ahat[j, ih] = (Ti %*% (RForm$Gamma[nvar, 1] ^ 2)) - (critval %*% W2[nvar, nvar])
bhat[j, ih] = -2 * Ti * scale * (t(e[, j]) %*% C[, , ih] %*% RForm$Gamma) %*%RForm$Gamma[nvar, 1] +
2 * critval * scale * kronecker(t(RForm$Gamma), t(e[, j])) %*% G[, , ih] %*%W12[, nvar] +
2 * critval * scale * t(e[, j]) %*% C[, , ih] %*% W2[, nvar]
chat[j, ih] = ((Ti ^ .5) * scale * t(e[, j]) %*% C[, , ih] %*% RForm$Gamma) ^2 -
critval * (scale ^ 2) * (kronecker(t(RForm$Gamma), t(e[, j]))) %*%G[, , ih] %*% W1 %*% t((kronecker(t(RForm$Gamma), t(e[, j]))) %*% G[, , ih]) -
2 * critval * (scale ^ 2) * (kronecker(t(RForm$Gamma), t(e[, j]))) %*%G[, , ih] %*% W12 %*% t(C[, , ih]) %*% e[, j] -
critval * (scale ^ 2) * t(e[, j]) %*% C[, , ih] %*% W2 %*% t(C[, , ih]) %*%e[, j]
Deltahat[j, ih] = bhat[j, ih] ^ 2 - (4 * ahat[j, ih] * chat[j, ih])
if (ahat[j, ih] > 0 && Deltahat[j, ih] > 0) {
casedummy[j, ih] = 1
MSWlbound[j, ih] = (-bhat[j, ih] - (Deltahat[j, ih] ^ 0.5)) / (2 *ahat[j, ih])
MSWubound[j, ih] = (-bhat[j, ih] + (Deltahat[j, ih] ^ 0.5)) / (2 *ahat[j, ih])
} else if (ahat[j, ih] < 0 && Deltahat[j, ih] > 0) {
casedummy[j, ih] = 2
MSWlbound[j, ih] = (-bhat[j, ih] + (Deltahat[j, ih] ^ 0.5)) / (2 *ahat[j, ih])
MSWubound[j, ih] = (-bhat[j, ih] - (Deltahat[j, ih] ^ 0.5)) / (2 *ahat[j, ih])
} else if (ahat[j, ih] > 0 && Deltahat[j, ih] < 0) {
casedummy[j, ih] = 3
MSWlbound[j, ih] = NA
MSWubound[j, ih] = NA
} else{
casedummy[j, ih] = 4
MSWlbound[j, ih] = -Inf
MSWubound[j, ih] = Inf
}
}
}
MSWlbound[nvar, 1] = scale
MSWubound[nvar, 1] = scale
InferenceMSW <- list(
ahat = ahat,
bhat = bhat,
chat = chat,
Deltahat = Deltahat,
casedummy = casedummy,
MSWlbound = MSWlbound,
MSWubound = MSWubound,
Ti = Ti
)
for (ih in 1:(horizons + 1)) {
for (ivar in 1:n) {
lambdahat[ivar, ih] = scale * t(e[, ivar]) %*% C[, , ih] %*% RForm$Gamma /RForm$Gamma[nvar, 1]
d1 = ((kronecker(t(RForm$Gamma), t(e[, ivar])) *scale) %*% G[, , ih])
d2 = (scale * t(e[, ivar]) %*% C[, , ih]) -(lambdahat[ivar, ih] %*% t(e[, nvar]))
d = t(cbind(d1, d2))
DmethodVar[ivar, ih] = t(d) %*% RForm$WHat %*% d
Dmethodlbound[ivar, ih] = lambdahat[ivar, ih] - ((critval / Ti) ^0.5) * (DmethodVar[ivar, ih] ^ 0.5) / abs(RForm$Gamma[nvar, 1])
Dmethodubound[ivar, ih] = lambdahat[ivar, ih] + ((critval / Ti) ^0.5) * (DmethodVar[ivar, ih] ^ 0.5) / abs(RForm$Gamma[nvar, 1])
rm(d1)
rm(d2)
rm(d)
}
}
IRF = lambdahat
IRFstderror = (DmethodVar ^ 0.5) / ((Ti ^ 0.5) * abs(RForm$Gamma[nvar, 1]))
for (j in 1:n) {
for (ih in 1:(horizons + 1)) {
ahatcum[j, ih] = (Ti %*% (RForm$Gamma[nvar, 1] ^ 2)) - (critval %*% W2[nvar, nvar])
bhatcum[j, ih] = -2 * Ti * scale * (t(e[, j]) %*% Ccum[, , ih] %*% RForm$Gamma) %*%RForm$Gamma[nvar, 1] +
2 * critval * scale * kronecker(t(RForm$Gamma), t(e[, j])) %*% Gcum[, , ih] %*%W12[, nvar] +
2 * critval * scale * t(e[, j]) %*% Ccum[, , ih] %*% W2[, nvar]
chatcum[j, ih] = ((Ti ^ 0.5) * scale * t(e[, j]) %*% Ccum[, , ih] %*%RForm$Gamma) ^ 2 -
critval * (scale ^ 2) * (kronecker(t(RForm$Gamma), t(e[, j]))) %*%Gcum[, , ih] %*% W1 %*% t((kronecker(t(RForm$Gamma), t(e[, j]))) %*% Gcum[, , ih]) -
2 * critval * (scale ^ 2) * (kronecker(t(RForm$Gamma), t(e[, j]))) %*%Gcum[, , ih] %*% W12 %*% t(Ccum[, , ih]) %*% e[, j] -
critval * (scale ^ 2) * t(e[, j]) %*% Ccum[, , ih] %*% W2 %*% t(Ccum[, , ih]) %*%e[, j]
Deltahatcum[j, ih] = bhatcum[j, ih] ^ 2 - (4 * ahatcum[j, ih] * chatcum[j, ih])
if (ahatcum[j, ih] > 0 & Deltahatcum[j, ih] > 0) {
casedummycum[j, ih] = 1
MSWlboundcum[j, ih] = (-bhatcum[j, ih] - (Deltahatcum[j, ih] ^ 0.5)) /(2 * ahatcum[j, ih])
MSWuboundcum[j, ih] = (-bhatcum[j, ih] + (Deltahatcum[j, ih] ^ 0.5)) /(2 * ahatcum[j, ih])
} else if (ahatcum[j, ih] < 0 & Deltahatcum[j, ih] > 0) {
casedummycum[j, ih] = 2
MSWlboundcum[j, ih] = (-bhatcum[j, ih] + (Deltahatcum[j, ih] ^ 0.5)) /(2 * ahatcum[j, ih])
MSWuboundcum[j, ih] = (-bhatcum[j, ih] - (Deltahatcum[j, ih] ^ 0.5)) /(2 * ahatcum[j, ih])
} else if (ahatcum[j, ih] > 0 & Deltahatcum[j, ih] < 0) {
casedummycum[j, ih] = 3
MSWlboundcum[j, ih] = NA
MSWuboundcum[j, ih] = NA
} else{
casedummycum[j, ih] = 4
MSWlboundcum[j, ih] = -Inf
MSWuboundcum[j, ih] = Inf
}
}
}
MSWlboundcum[nvar, 1] = scale
MSWuboundcum[nvar, 1] = scale
for (ih in 1:(horizons + 1)) {
for (ivar in 1:n) {
lambdahatcum[ivar, ih] = scale * t(e[, ivar]) %*% Ccum[, , ih] %*% RForm$Gamma /RForm$Gamma[nvar, 1]
d1 = ((kronecker(t(RForm$Gamma), t(e[, ivar])) *scale) %*% Gcum[, , ih])
d2 = (scale * t(e[, ivar]) %*% Ccum[, , ih]) -(lambdahatcum[ivar, ih] %*% t(e[, nvar]))
d = t(cbind(d1, d2))
DmethodVarcum[ivar, ih] = t(d) %*% RForm$WHat %*% d
Dmethodlboundcum[ivar, ih] = lambdahatcum[ivar, ih] - ((critval / Ti) ^0.5) * (DmethodVarcum[ivar, ih] ^ 0.5) / abs(RForm$Gamma[nvar, 1])
Dmethoduboundcum[ivar, ih] = lambdahatcum[ivar, ih] + ((critval / Ti) ^0.5) * (DmethodVarcum[ivar, ih] ^ 0.5) / abs(RForm$Gamma[nvar, 1])
rm(d1)
rm(d2)
rm(d)
}
}
IRFstderrorcum = (DmethodVarcum ^ 0.5) / ((Ti ^ 0.5) * abs(RForm$Gamma[nvar, 1]))
Waldstat = (((Ti ^ 0.5) * RForm$Gamma[[nvar, 1]]) ^ 2) / RForm$WHat[((n ^2) * RForm$p) +
nvar, ((n ^ 2) * RForm$p) + nvar]
irfs[[a]]<-list(
plugin=list(point=lambdahat,
lower=lambdahat-IRFstderror,
upper=lambdahat+IRFstderror),
delta=list(point=lambdahat,
lower=Dmethodlbound,
upper=Dmethodubound),
msw=list(point=lambdahat,
lower=MSWlbound,
upper=MSWubound,
Waldstat=Waldstat,
critval=critval),
plugin_cum=list(point=lambdahatcum,
lower=lambdahatcum-IRFstderrorcum,
upper=lambdahatcum+IRFstderrorcum),
delta_cum=list(point=lambdahatcum,
lower=Dmethodlboundcum,
upper=Dmethodubound),
msw_cum=list(point=lambdahatcum,
lower=MSWlboundcum,
upper=Dmethoduboundcum,
Waldstat=Waldstat,
critval=critval)
)
}
names(irfs)<-confidence
return(irfs)
}
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