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#' @import stats
NULL
###################################################################################
# Standardized version of Abadie's IPW DiD estimator
#' Standardized inverse probability weighted DiD estimator, with panel data
#' @description \code{std_ipw_did_panel} is used to compute inverse probability weighted (IPW) estimators for the ATT
#' in difference-in-differences (DiD) setups with panel data. IPW weights are normalized to sum up to one, that is,
#' the estimator is of the Hajek type.
#'
#' @param y1 An \eqn{n} x \eqn{1} vector of outcomes from the post-treatment period.
#' @param y0 An \eqn{n} x \eqn{1} vector of outcomes from the pre-treatment period.
#' @param D An \eqn{n} x \eqn{1} vector of Group indicators (=1 if observation is treated in the post-treatment, =0 otherwise).
#' @param covariates An \eqn{n} x \eqn{k} matrix of covariates to be used in the propensity score estimation.
#' If covariates = NULL, this leads to an unconditional DiD estimator.
#' @param i.weights An \eqn{n} x \eqn{1} vector of weights to be used. If NULL, then every observation has the same weights. The weights are normalized and therefore enforced to have mean 1 across all observations.
#' @param boot Logical argument to whether bootstrap should be used for inference. Default is FALSE.
#' @param boot.type Type of bootstrap to be performed (not relevant if \code{boot = FALSE}). Options are "weighted" and "multiplier".
#' If \code{boot = TRUE}, default is "weighted".
#' @param nboot Number of bootstrap repetitions (not relevant if \code{boot = FALSE}). Default is 999.
#' @param inffunc Logical argument to whether influence function should be returned. Default is FALSE.
#'
#' @return A list containing the following components:
#' \item{ATT}{The IPW DiD point estimate.}
#' \item{se}{ The IPW DiD standard error}
#' \item{uci}{Estimate of the upper bound of a 95\% CI for the ATT}
#' \item{lci}{Estimate of the lower bound of a 95\% CI for the ATT}
#' \item{boots}{All Bootstrap draws of the ATT, in case bootstrap was used to conduct inference. Default is NULL}
#' \item{att.inf.func}{Estimate of the influence function. Default is NULL}
#' \item{call.param}{The matched call.}
#' \item{argu}{Some arguments used (explicitly or not) in the call (panel = TRUE, normalized = TRUE, boot, boot.type, nboot, type="ipw")}
#' @references
#' \cite{Abadie, Alberto (2005), "Semiparametric Difference-in-Differences Estimators",
#' Review of Economic Studies, vol. 72(1), p. 1-19, \doi{10.1111/0034-6527.00321}.
#' }
#'
#'
#' \cite{Sant'Anna, Pedro H. C. and Zhao, Jun. (2020),
#' "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122,
#' \doi{10.1016/j.jeconom.2020.06.003}}
#'
#'
#' @examples
#' # Form the Lalonde sample with CPS comparison group
#' eval_lalonde_cps <- subset(nsw, nsw$treated == 0 | nsw$sample == 2)
#' # Further reduce sample to speed example
#' set.seed(123)
#' unit_random <- sample(1:nrow(eval_lalonde_cps), 5000)
#' eval_lalonde_cps <- eval_lalonde_cps[unit_random,]
#' # Select some covariates
#' covX = as.matrix(cbind(eval_lalonde_cps$age, eval_lalonde_cps$educ,
#' eval_lalonde_cps$black, eval_lalonde_cps$married,
#' eval_lalonde_cps$nodegree, eval_lalonde_cps$hisp,
#' eval_lalonde_cps$re74))
#' # Implement normalized IPW DiD with panel data
#' std_ipw_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
#' D = eval_lalonde_cps$experimental,
#' covariates = covX)
#'
#' @export
std_ipw_did_panel <-function(y1, y0, D, covariates, i.weights = NULL,
boot = FALSE, boot.type = "weighted", nboot = NULL,
inffunc = FALSE){
#-----------------------------------------------------------------------------
# D as vector
D <- as.vector(D)
# Sample size
n <- length(D)
# generate deltaY
deltaY <- as.vector(y1 - y0)
# Add constant to covariate vector
int.cov <- as.matrix(rep(1,n))
if (!is.null(covariates)){
if(all(as.matrix(covariates)[,1]==rep(1,n))){
int.cov <- as.matrix(covariates)
} else {
int.cov <- as.matrix(cbind(1, covariates))
}
}
# Weights
if(is.null(i.weights)) {
i.weights <- as.vector(rep(1, n))
} else if(min(i.weights) < 0) stop("i.weights must be non-negative")
# Normalize weights
i.weights <- i.weights/mean(i.weights)
#-----------------------------------------------------------------------------
#Pscore estimation (logit) and also its fitted values
#PS <- suppressWarnings(stats::glm(D ~ -1 + int.cov, family = "binomial", weights = i.weights))
PS <- suppressWarnings(parglm::parglm(D ~ -1 + int.cov, family = "binomial", weights = i.weights))
if(PS$converged == FALSE){
warning("Propernsity score estimation did not converge.")
}
ps.fit <- as.vector(PS$fitted.values)
# Do not divide by zero
ps.fit <- pmin(ps.fit, 1 - 1e-6)
#-----------------------------------------------------------------------------
#Compute IPW estimator
# First, the weights
w.treat <- i.weights * D
w.cont <- i.weights * ps.fit * (1 - D)/(1 - ps.fit)
att.treat <- w.treat * deltaY
att.cont <- w.cont * deltaY
eta.treat <- mean(att.treat) / mean(w.treat)
eta.cont <- mean(att.cont) / mean(w.cont)
ipw.att <- eta.treat - eta.cont
#-----------------------------------------------------------------------------
#get the influence function to compute standard error
#-----------------------------------------------------------------------------
# Asymptotic linear representation of logit's beta's
score.ps <- i.weights * (D - ps.fit) * int.cov
Hessian.ps <- stats::vcov(PS) * n
asy.lin.rep.ps <- score.ps %*% Hessian.ps
#-----------------------------------------------------------------------------
# Now, the influence function of the "treat" component
# Leading term of the influence function: no estimation effect
inf.treat <- (att.treat - w.treat * eta.treat)/mean(w.treat)
# Now, get the influence function of control component
# Leading term of the influence function: no estimation effect
inf.cont.1 <- (att.cont - w.cont * eta.cont)
# Estimation effect from gamma hat (pscore)
# Derivative matrix (k x 1 vector)
M2 <- base::colMeans(w.cont *(deltaY - eta.cont) * int.cov)
# Now the influence function related to estimation effect of pscores
inf.cont.2 <- asy.lin.rep.ps %*% M2
# Influence function for the control component
inf.control <- (inf.cont.1 + inf.cont.2) / mean(w.cont)
#get the influence function of the DR estimator (put all pieces together)
att.inf.func <- inf.treat - inf.control
#-----------------------------------------------------------------------------
if (boot == FALSE) {
# Estimate of standard error
se.att <- stats::sd(att.inf.func)/sqrt(n)
# Estimate of upper boudary of 95% CI
uci <- ipw.att + 1.96 * se.att
# Estimate of lower doundary of 95% CI
lci <- ipw.att - 1.96 * se.att
#Create this null vector so we can export the bootstrap draws too.
ipw.boot <- NULL
}
if (boot == TRUE) {
if (is.null(nboot) == TRUE) nboot = 999
if(boot.type == "multiplier"){
# do multiplier bootstrap
ipw.boot <- mboot.did(att.inf.func, nboot)
# get bootstrap std errors based on IQR
se.att <- stats::IQR(ipw.boot) / (stats::qnorm(0.75) - stats::qnorm(0.25))
# get symmtric critival values
cv <- stats::quantile(abs(ipw.boot/se.att), probs = 0.95)
# Estimate of upper boudary of 95% CI
uci <- ipw.att + cv * se.att
# Estimate of lower doundary of 95% CI
lci <- ipw.att - cv * se.att
} else {
# do weighted bootstrap
ipw.boot <- unlist(lapply(1:nboot, wboot.std.ipw.panel,
n = n, deltaY = deltaY, D = D, int.cov = int.cov, i.weights = i.weights))
# get bootstrap std errors based on IQR
se.att <- stats::IQR(ipw.boot - ipw.att) / (stats::qnorm(0.75) - stats::qnorm(0.25))
# get symmtric critival values
cv <- stats::quantile(abs((ipw.boot - ipw.att)/se.att), probs = 0.95)
# Estimate of upper boudary of 95% CI
uci <- ipw.att + cv * se.att
# Estimate of lower doundary of 95% CI
lci <- ipw.att - cv * se.att
}
}
if(inffunc == FALSE) att.inf.func <- NULL
#---------------------------------------------------------------------
# record the call
call.param <- match.call()
# Record all arguments used in the function
argu <- mget(names(formals()), sys.frame(sys.nframe()))
boot.type <- ifelse(argu$boot.type=="multiplier", "multiplier", "weighted")
boot <- ifelse(argu$boot == TRUE, TRUE, FALSE)
argu <- list(
panel = TRUE,
normalized = TRUE,
boot = boot,
boot.type = boot.type,
nboot = nboot,
type = "ipw"
)
ret <- (list(ATT = ipw.att,
se = se.att,
uci = uci,
lci = lci,
boots = ipw.boot,
att.inf.func = att.inf.func,
call.param = call.param,
argu = argu))
# Define a new class
class(ret) <- "drdid"
# return the list
return(ret)
}
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