Nothing
###################################################################
## IFE Model Function
###################################################################
fect.polynomial <- function(Y, # Outcome variable, (T*N) matrix
X, # Explanatory variables: (T*N*p) array
D, # Indicator for treated unit (tr==1)
I,
II,
T.on,
T.off = NULL,
T.on.carry = NULL,
T.on.balance = NULL,
balance.period = NULL,
method,
degree = 1,
sfe = NULL,
cfe = NULL,
ind.matrix = NULL,
knots = NULL,
force,
hasRevs = 1,
tol, # tolerance level
boot = FALSE, # bootstrapped sample
placeboTest = 0,
placebo.period = NULL,
carryoverTest = 0,
carryover.period = NULL,
norm.para = NULL,
calendar.enp.seq = NULL,
time.on.seq = NULL,
time.off.seq = NULL,
time.on.carry.seq = NULL,
time.on.balance.seq = NULL,
group.level = NULL,
group = NULL,
time.on.seq.group = NULL,
time.off.seq.group = NULL) {
##-------------------------------##
## Parsing data
##-------------------------------##
carryover.pos <- placebo.pos <- na.pos <- NULL
res.sd1 <- res.sd2 <- NULL
## unit id and time
TT <- dim(Y)[1]
N <- dim(Y)[2]
if (is.null(X) == FALSE) {
p <- dim(X)[3]
}
else {
p <- 0
X <- array(0, dim = c(1, 1, 0))
}
## replicate data
YY <- Y
YY[which(II == 0)] <- 0 ## reset to 0
## initial fit using fastplm
data.ini <- matrix(NA, (TT*N), (2 + 1 + p))
data.ini[, 2] <- rep(1:N, each = TT) ## unit fe
data.ini[, 3] <- rep(1:TT, N) ## time fe
data.ini[, 1] <- c(Y) ## outcome
if (p > 0) { ## covar
for (i in 1:p) {
data.ini[, (3 + i)] <- c(X[, , i])
}
}
## observed Y0 indicator:
oci <- which(c(II) == 1)
initialOut <- initialFit(data = data.ini, force = force, oci = oci)
Y0 <- initialOut$Y0
beta0 <- initialOut$beta0
if (p > 0 && sum(is.na(beta0)) > 0) {
beta0[which(is.na(beta0))] <- 0
}
est.fect <- NULL
if (boot == FALSE) {
est.fect <- inter_fe_ub(YY, Y0, X, II, beta0, 0, force = force, tol)
}
## reshape
vy <- as.matrix(c(YY))
vx.fit <- vx <- NULL
if (p > 0) {
vx <- matrix(NA, N*TT, p)
for (i in 1:p) {
vx[, i] <- c(X[,, i])
}
colnames(vx) <- paste0("x.",c(1:p))
vx.fit <- as.matrix(vx[oci,])
}
vindex <- NULL
sp <- NULL
sf <- NULL
cf <- NULL
if(method == "cfe"){
vindex <- cbind(rep(1:N, each = TT), rep(1:TT, N)) ## id time
if (force == 1) {
sf <- 1
}
else if (force == 2) {
sf <- 2
}
else {
sf <- c(1,2)
}
## simple fixed effects
for(ind.name in names(ind.matrix)){
vindex <- cbind(vindex,matrix(ind.matrix[[ind.name]],ncol=1))
}
ind.name <- c("forceid","forcetime",names(ind.matrix))
ind.index <- c(1:(2+length(names(ind.matrix))))
colnames(vindex) <- names(ind.index) <- ind.name
if(p>0){
data.reg <- cbind.data.frame(vy,vx,vindex)
formula.reg <- paste0("vy~",paste(paste0("x.",c(1:p)),collapse="+"),"|")
}
else{
data.reg <- cbind.data.frame(vy,vindex)
formula.reg <- paste0("vy~1|")
}
if(force==1){
formula.reg <- paste0(formula.reg,"forceid")
}
else if(force==2){
formula.reg <- paste0(formula.reg,"forcetime")
}
else if(force==3){
formula.reg <- paste0(formula.reg,"forceid+forcetime")
}
if(!is.null(sfe)){
formula.reg <- paste0(formula.reg,"+", paste(sfe,collapse="+"))
}
if(!is.null(cfe)){
for(sub.cfe in cfe){
sub.cf <- paste0(sub.cfe[1],"[",sub.cfe[2],"]")
formula.reg <- paste0(formula.reg,"+",sub.cf)
}
}
formula.reg <- as.formula(formula.reg)
est.best <- suppressWarnings(invisible(feols(fml = formula.reg,
data = data.reg[oci,],
fixef.rm = "none")))
yfit <- suppressWarnings(predict(est.best, newdata = data.reg))
}
else if (method == "polynomial") {
vindex <- cbind(rep(1:N, each = TT), rep(1:TT, N)) ## id time
for (i in 1:degree) {
vindex <- cbind(vindex, rep((1:TT)^i, N))
}
colnames(vindex) <- c("forceid","forcetime",paste0("forcetime.",c(1:degree)))
if(p>0){
data.reg <- cbind.data.frame(vy,vx,vindex)
formula.reg <- paste0("vy~",paste(paste0("x.",c(1:p)),collapse="+"),"|")
}
else{
data.reg <- cbind.data.frame(vy,vindex)
formula.reg <- paste0("vy~1|")
}
if(force==1){
formula.reg <- paste0(formula.reg,"forceid")
}
else if(force==2){
formula.reg <- paste0(formula.reg,"forcetime")
}
else if(force==3){
formula.reg <- paste0(formula.reg,"forceid+forcetime")
}
for (i in 1:degree) {
formula.reg <- paste0(formula.reg,paste0("+forceid","[",paste0("forcetime.",i),"]"))
}
formula.reg <- as.formula(formula.reg)
est.best <- suppressWarnings(invisible(feols(fml = formula.reg,
data = data.reg[oci,],
fixef.rm = "none")))
yfit <- suppressWarnings(predict(est.best, newdata = data.reg))
}
Y.ct <- matrix(yfit, TT, N)
if (p > 0) {
beta <- as.matrix(c(est.best$coefficients)[1:p])
}
else {
beta <- matrix(0, 1, 0)
}
est.best$beta <- beta
validX <- ifelse(p > 0, 1, 0)
##-------------------------------##
## ATT and Counterfactuals ##
##-------------------------------##
## we first adjustment for normalization
if (!is.null(norm.para)) {
Y <- Y * norm.para[1]
## variance of the error term
sigma2 <- est.best$sigma2 * (norm.para[1]^2)
est.best$sigma2 <- sigma2
## output of estimates
est.best$mu <- est.best$mu * norm.para[1]
est.best$residuals <- est.best$residuals * norm.para[1]
Y.ct <- Y.ct * norm.para[1]
if (boot == FALSE) {
est.fect$fit <- est.fect$fit * norm.para[1]
}
est.fect$sigma2 <- est.fect$sigma2 * norm.para[1]
}
## 0. relevant parameters
if (p>0) {
na.pos <- is.nan(est.best$beta)
beta <- est.best$beta
if( sum(na.pos) > 0 ) {
beta[na.pos] <- NA
}
} else {
beta <- NA
}
## 1. estimated att and counterfactuals
eff <- Y - Y.ct
complete.index <- which(!is.na(eff))
missing.index <- which(is.na(eff))
if(length(missing.index)>0){
I[missing.index] <- 0
II[missing.index] <- 0
}
att.avg <- sum(eff[complete.index] * D[complete.index])/(sum(D[complete.index]))
att.avg.balance <- NA
if(!is.null(balance.period)){
complete.index2 <- which(!is.na(T.on.balance))
att.avg.balance <- sum(eff[complete.index2] * D[complete.index2])/(sum(D[complete.index2]))
}
## att.avg.unit
tr.pos <- which(apply(D, 2, sum) > 0)
att.unit <- sapply(1:length(tr.pos), function(vec){return((eff[, tr.pos[vec]] * D[, tr.pos[vec]]) / sum(D[, tr.pos[vec]]))})
att.avg.unit <- mean(att.unit,na.rm=TRUE)
## 2. rmse for treated units' observations under control
tr <- which(apply(D, 2, sum) > 0)
tr.co <- which((as.matrix(1 - D[,tr]) * as.matrix(II[,tr])) == 1)
eff.tr <- as.matrix(eff[,tr])
v.eff.tr <- eff.tr[tr.co]
rmse <- sqrt(mean(v.eff.tr^2,na.rm=TRUE))
## 3. unbalanced output
if (0 %in% I) {
eff[which(I == 0)] <- NA
Y.ct[which(I == 0)] <- NA
}
## 4. dynamic effects
t.on <- c(T.on)
eff.v <- c(eff) ## a vector
rm.pos1 <- which(is.na(eff.v))
rm.pos2 <- which(is.na(t.on))
eff.v.use1 <- eff.v
t.on.use <- t.on
n.on.use <- rep(1:N, each = TT)
if (NA %in% eff.v | NA %in% t.on) {
eff.v.use1 <- eff.v[-c(rm.pos1, rm.pos2)]
t.on.use <- t.on[-c(rm.pos1, rm.pos2)]
n.on.use <- n.on.use[-c(rm.pos1, rm.pos2)]
}
pre.pos <- which(t.on.use <= 0)
eff.pre <- cbind(eff.v.use1[pre.pos], t.on.use[pre.pos], n.on.use[pre.pos])
colnames(eff.pre) <- c("eff", "period", "unit")
sigma2.pre <- eff.pre.equiv <- NULL
if (boot == FALSE) {
eff.pre.equiv <- eff.pre
sigma2.pre <- tapply(eff.pre.equiv[,1], eff.pre.equiv[,2], var)
sigma2.pre <- cbind(sigma2.pre, sort(unique(eff.pre.equiv[, 2])), table(eff.pre.equiv[, 2]))
colnames(sigma2.pre) <- c("sigma2", "period", "count")
}
time.on <- sort(unique(t.on.use))
att.on <- as.numeric(tapply(eff.v.use1, t.on.use, mean)) ## NA already removed
count.on <- as.numeric(table(t.on.use))
if (!is.null(time.on.seq)) {
count.on.med <- att.on.med <- rep(NA, length(time.on.seq))
att.on.med[which(time.on.seq %in% time.on)] <- att.on
count.on.med[which(time.on.seq %in% time.on)] <- count.on
att.on <- att.on.med
count.on <- count.on.med
time.on <- time.on.seq
}
## 4.1 carryover effect
carry.att <- NULL
if (!is.null(T.on.carry)) {
t.on.carry <- c(T.on.carry)
rm.pos4 <- which(is.na(t.on.carry))
t.on.carry.use <- t.on.carry
if (NA %in% eff.v | NA %in% t.on.carry) {
eff.v.use3 <- eff.v[-c(rm.pos1, rm.pos4)]
t.on.carry.use <- t.on.carry[-c(rm.pos1, rm.pos4)]
}
carry.time <- sort(unique(t.on.carry.use))
carry.att <- as.numeric(tapply(eff.v.use3, t.on.carry.use, mean)) ## NA already removed
if (!is.null(time.on.carry.seq)) {
carry.att.med <- rep(NA, length(time.on.carry.seq))
carry.att.med[which(time.on.carry.seq %in% carry.time)] <- carry.att
carry.att <- carry.att.med
carry.time <- time.on.carry.seq
}
}
## 4.2 balance effect
balance.att <- NULL
if (!is.null(balance.period)) {
t.on.balance <- c(T.on.balance)
rm.pos4 <- which(is.na(t.on.balance))
t.on.balance.use <- t.on.balance
if (NA %in% eff.v | NA %in% t.on.balance) {
eff.v.use3 <- eff.v[-c(rm.pos1, rm.pos4)]
t.on.balance.use <- t.on.balance[-c(rm.pos1, rm.pos4)]
}
balance.time <- sort(unique(t.on.balance.use))
balance.att <- as.numeric(tapply(eff.v.use3, t.on.balance.use, mean)) ## NA already removed
balance.count <- as.numeric(table(t.on.balance.use))
if (!is.null(time.on.balance.seq)) {
balance.att.med <- rep(NA, length(time.on.balance.seq))
balance.count.med <- rep(0, length(time.on.balance.seq))
balance.att.med[which(time.on.balance.seq %in% balance.time)] <- balance.att
if(length(balance.count)>0){
balance.count.med[which(time.on.balance.seq %in% balance.time)] <- balance.count
}
balance.count <- balance.count.med
balance.att <- balance.att.med
balance.time <- time.on.balance.seq
}
#placebo for balanced samples
if(!is.null(placebo.period) && placeboTest == 1){
if (length(placebo.period) == 1) {
balance.placebo.pos <- which(balance.time == placebo.period)
balance.att.placebo <- balance.att[balance.placebo.pos]
}
else {
balance.placebo.pos <- which(balance.time >= placebo.period[1] & balance.time <= placebo.period[2])
balance.att.placebo <- sum(balance.att[balance.placebo.pos] * balance.count[balance.placebo.pos]) / sum(balance.count[balance.placebo.pos])
}
}
}
## 5. placebo effect, if placeboTest == 1
if (!is.null(placebo.period) && placeboTest == 1) {
if (length(placebo.period) == 1) {
placebo.pos <- which(time.on == placebo.period)
att.placebo <- att.on[placebo.pos]
} else {
placebo.pos <- which(time.on >= placebo.period[1] & time.on <= placebo.period[2])
att.placebo <- sum(att.on[placebo.pos] * count.on[placebo.pos]) / sum(count.on[placebo.pos])
}
}
eff.off.equiv <- off.sd <- eff.off <- NULL
## 6. switch-off effects
if (hasRevs == 1) {
t.off <- c(T.off)
rm.pos3 <- which(is.na(t.off))
eff.v.use2 <- eff.v
t.off.use <- t.off
if (NA %in% eff.v | NA %in% t.off) {
eff.v.use2 <- eff.v[-c(rm.pos1, rm.pos3)]
t.off.use <- t.off[-c(rm.pos1, rm.pos3)]
}
off.pos <- which(t.off.use > 0)
eff.off <- cbind(eff.v.use2[off.pos], t.off.use[off.pos], n.on.use[off.pos])
colnames(eff.off) <- c("eff", "period", "unit")
if (boot == FALSE) {
eff.off.equiv <- eff.off
off.sd <- tapply(eff.off.equiv[,1], eff.off.equiv[,2], sd)
off.sd <- cbind(off.sd, sort(unique(eff.off.equiv[, 2])), table(eff.off.equiv[, 2]))
colnames(off.sd) <- c("sd", "period", "count")
}
time.off <- sort(unique(t.off.use))
att.off <- as.numeric(tapply(eff.v.use2, t.off.use, mean)) ## NA already removed
count.off <- as.numeric(table(t.off.use))
if (!is.null(time.off.seq)) {
count.off.med <- att.off.med <- rep(NA, length(time.off.seq))
att.off.med[which(time.off.seq %in% time.off)] <- att.off
count.off.med[which(time.off.seq %in% time.off)] <- count.off
att.off <- att.off.med
count.off <- count.off.med
time.off <- time.off.seq
}
}
## 7. carryover effects
if (!is.null(carryover.period) && carryoverTest == 1 && hasRevs) {
if (length(carryover.period) == 1) {
carryover.pos <- which(time.off == carryover.period)
att.carryover <- att.off[carryover.pos]
} else {
carryover.pos <- which(time.off >= carryover.period[1] & time.off <= carryover.period[2])
att.carryover <- sum(att.off[carryover.pos] * count.off[carryover.pos]) / sum(count.off[carryover.pos])
}
}
## 8. cohort effects
if (!is.null(group)) {
cohort <- cbind(c(group), c(D), c(eff.v))
rm.pos <- unique(c(rm.pos1, which(cohort[, 2] == 0)))
cohort <- cohort[-rm.pos, ]
g.level <- sort(unique(cohort[, 1]))
raw.group.att <- as.numeric(tapply(cohort[, 3], cohort[, 1], mean))
group.att <- rep(NA, length(group.level))
group.att[which(group.level %in% g.level)] <- raw.group.att
# by-group dynamic effects
group.level.name <- names(group.level)
group.output <- list()
for(i in c(1:length(group.level))){
sub.group <- group.level[i]
sub.group.name <- group.level.name[i]
## by-group dynamic effects
t.on.sub <- c(T.on[which(group==sub.group)])
eff.v.sub <- c(eff[which(group==sub.group)]) ## a vector
rm.pos1.sub <- which(is.na(eff.v.sub))
rm.pos2.sub <- which(is.na(t.on.sub))
eff.v.use1.sub <- eff.v.sub
t.on.use.sub <- t.on.sub
if (NA %in% eff.v.sub | NA %in% t.on.sub) {
eff.v.use1.sub <- eff.v.sub[-c(rm.pos1.sub, rm.pos2.sub)]
t.on.use.sub <- t.on.sub[-c(rm.pos1.sub, rm.pos2.sub)]
}
if(length(t.on.use.sub)>0){
time.on.sub <- sort(unique(t.on.use.sub))
att.on.sub <- as.numeric(tapply(eff.v.use1.sub,
t.on.use.sub,
mean)) ## NA already removed
count.on.sub <- as.numeric(table(t.on.use.sub))
}else{
time.on.sub <- att.on.sub <- count.on.sub <- NULL
}
if (!is.null(time.on.seq.group)) {
count.on.med.sub <- att.on.med.sub <- rep(NA, length(time.on.seq.group[[sub.group.name]]))
time.on.seq.sub <- time.on.seq.group[[sub.group.name]]
att.on.med.sub[which(time.on.seq.sub %in% time.on.sub)] <- att.on.sub
count.on.med.sub[which(time.on.seq.sub %in% time.on.sub)] <- count.on.sub
att.on.sub <- att.on.med.sub
count.on.sub <- count.on.med.sub
time.on.sub<- time.on.seq.sub
}
suboutput <- list(att.on=att.on.sub,
time.on=time.on.sub,
count.on=count.on.sub)
## placebo effect, if placeboTest == 1
if (!is.null(placebo.period) && placeboTest == 1) {
if (length(placebo.period) == 1) {
placebo.pos.sub <- which(time.on.sub == placebo.period)
if(length(placebo.pos.sub)>0){
att.placebo.sub <- att.on.sub[placebo.pos.sub]
}
else{att.placebo.sub <- NULL}
}
else {
placebo.pos.sub <- which(time.on.sub >= placebo.period[1] & time.on.sub <= placebo.period[2])
if(length(placebo.pos.sub)>0){
att.placebo.sub <- sum(att.on.sub[placebo.pos.sub] * count.on.sub[placebo.pos.sub]) / sum(count.on.sub[placebo.pos.sub])
}
else{att.placebo.sub <- NULL}
}
suboutput <- c(suboutput, list(att.placebo = att.placebo.sub))
}
## T.off
if (hasRevs == 1) {
t.off.sub <- c(T.off[which(group==sub.group)])
rm.pos3.sub <- which(is.na(t.off.sub))
eff.v.use2.sub <- eff.v.sub
t.off.use.sub <- t.off.sub
if (NA %in% eff.v.sub | NA %in% t.off.sub) {
eff.v.use2.sub <- eff.v.sub[-c(rm.pos1.sub, rm.pos3.sub)]
t.off.use.sub <- t.off.sub[-c(rm.pos1.sub, rm.pos3.sub)]
}
if(length(t.off.use.sub)>0){
time.off.sub <- sort(unique(t.off.use.sub))
att.off.sub <- as.numeric(tapply(eff.v.use2.sub, t.off.use.sub, mean)) ## NA already removed
count.off.sub <- as.numeric(table(t.off.use.sub))
}else{
time.off.sub <- att.off.sub <- count.off.sub <- NULL
}
if (!is.null(time.off.seq.group)) {
count.off.med.sub <- att.off.med.sub <- rep(NA, length(time.off.seq.group[[sub.group.name]]))
time.off.seq.sub <- time.off.seq.group[[sub.group.name]]
att.off.med.sub[which(time.off.seq.sub %in% time.off.sub)] <- att.off.sub
count.off.med.sub[which(time.off.seq.sub %in% time.off.sub)] <- count.off.sub
att.off.sub <- att.off.med.sub
count.off.sub <- count.off.med.sub
time.off.sub <- time.off.seq.sub
}
suboutput <- c(suboutput, list(att.off = att.off.sub,
count.off = count.off.sub,
time.off = time.off.sub))
if (!is.null(carryover.period) && carryoverTest == 1) {
if (length(carryover.period) == 1) {
carryover.pos.sub <- which(time.off.sub == carryover.period)
if(length(carryover.pos.sub)>0){
att.carryover.sub <- att.off.sub[carryover.pos.sub]
} else{att.carryover.sub <- NULL}
} else {
carryover.pos.sub <- which(time.off.sub >= carryover.period[1] & time.off.sub <= carryover.period[2])
if(length(carryover.pos.sub)>0){
att.carryover.sub <- sum(att.off.sub[carryover.pos.sub] * count.off.sub[carryover.pos.sub]) / sum(count.off.sub[carryover.pos.sub])
} else{att.carryover.sub <- NULL}
}
suboutput <- c(suboutput,list(att.carryover = att.carryover.sub))
}
}
group.output[[sub.group.name]] <- suboutput
}
}
## 9. loess HTE by time
D.missing <- D
D.missing[which(D==0)] <- NA
eff.calendar <- apply(eff*D.missing,1,mean,na.rm=TRUE)
N.calendar <- apply(!is.na(eff*D.missing),1,sum)
T.calendar <- c(1:TT)
if(sum(!is.na(eff.calendar))>1){
#loess fit
if(!is.null(calendar.enp.seq)){
if(length(calendar.enp.seq)==1 & is.na(calendar.enp.seq)){
calendar.enp.seq <- NULL
}
}
if(is.null(calendar.enp.seq)){
loess.fit <- suppressWarnings(try(loess(eff.calendar~T.calendar,weights = N.calendar),silent=TRUE))
}
else{
loess.fit <- suppressWarnings(try(loess(eff.calendar~T.calendar,weights = N.calendar,enp.target=calendar.enp.seq),silent=TRUE))
}
if('try-error' %in% class(loess.fit)){
eff.calendar.fit <- eff.calendar
calendar.enp <- NULL
}
else{
eff.calendar.fit <- eff.calendar
eff.calendar.fit[which(!is.na(eff.calendar))] <- loess.fit$fit
calendar.enp <- loess.fit$enp
}
}
else{
eff.calendar.fit <- eff.calendar
calendar.enp <- NULL
}
##-------------------------------##
## Storage ##
##-------------------------------##
out<-list(
## main results
method = method,
Y.ct = Y.ct,
eff = eff,
I = I,
II = II,
D = D,
Y = Y,
X = X,
att.avg = att.avg,
att.avg.unit = att.avg.unit,
## supporting
force = force,
T = TT,
N = N,
p = p,
beta = beta,
est = est.best,
sigma2 = est.best$sigma2,
sigma2.fect = est.fect$sigma2,
validX = validX,
time = time.on,
att = att.on,
count = count.on,
eff.calendar = eff.calendar,
N.calendar = N.calendar,
eff.calendar.fit = eff.calendar.fit,
calendar.enp = calendar.enp,
eff.pre = eff.pre,
eff.pre.equiv = eff.pre.equiv,
sigma2.pre = sigma2.pre)
#print(att.on)
if (hasRevs == 1) {
out <- c(out, list(time.off = time.off,
att.off = att.off,
count.off = count.off,
eff.off = eff.off,
eff.off.equiv = eff.off.equiv,
off.sd = off.sd))
}
if (!is.null(T.on.carry)) {
out <- c(out, list(carry.att = carry.att, carry.time = carry.time))
}
if(!is.null(balance.period)){
out <- c(out, list(balance.att = balance.att, balance.time = balance.time,balance.count = balance.count,balance.avg.att = att.avg.balance))
if (!is.null(placebo.period) && placeboTest == 1) {
out <- c(out, list(balance.att.placebo = balance.att.placebo))
}
}
if (!is.null(placebo.period) && placeboTest == 1) {
out <- c(out, list(att.placebo = att.placebo))
}
if (!is.null(carryover.period) && carryoverTest == 1) {
out <- c(out, list(att.carryover = att.carryover))
}
if (!is.null(group)) {
out <- c(out, list(group.att = group.att,
group.output = group.output))
}
return(out)
}
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