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#' @import stats trust
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# Improved Doubly Robust DiD estimator with panel data
#' Improved locally efficient doubly robust DiD estimator for the ATT, with panel data
#'
#' @description \code{drdid_imp_panel} is used to compute the locally efficient doubly robust estimators for the ATT
#' in difference-in-differences (DiD) setups with panel data. The resulting estimator is also doubly robust
#' for inference; see Section 3.1 of Sant'Anna and Zhao (2020).
#'
#' @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 and regression 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 DiD point estimate.}
#' \item{se}{The DiD standard error.}
#' \item{uci}{The upper bound of the 95\% CI for the ATT.}
#' \item{lci}{The lower bound of the 95\% CI for the ATT}
#' \item{boots}{All Bootstrap draws of the ATT, in case bootstrap was used to conduct inference. Default is \code{NULL}.}
#' \item{ps.flag}{Convergence Flag for the propensity score estimation: =0 if \code{trust} algorithm converged,
#' =1 if IPW algorithm converged (in case it was used), =2 if GLM logit estimator was used (i.e., if both \code{trust} and IPT
#' did not converged).}
#' \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, estMethod = "imp", boot, boot.type, nboot, type="dr")}
#'
#' @references
#' \cite{Graham, Bryan, Pinto, Cristine, and Egel, Daniel (2012),
#' "Inverse Probability Tilting for Moment Condition Models with Missing Data."
#' Review of Economic Studies, vol. 79 (3), pp. 1053-1079, \doi{10.1093/restud/rdr047}}
#'
#'
#' \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}}
#'
#'
#' @details
#'
#' The \code{drdid_imp_panel} function implements the locally efficient doubly robust difference-in-differences (DiD)
#' estimator for the average treatment effect on the treated (ATT) defined in equation (3.1)
#' in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability
#' of being in the treated group, and of a linear regression model for the outcome evolution among the comparison units.
#'
#'
#' The nuisance parameters (propensity score and outcome regression parameters) are estimated using the methods
#' described in Sections 3.1 of Sant'Anna and Zhao (2020). In short, the propensity score parameters are estimated
#' using the inverse probability tilting estimator proposed by Graham, Pinto and Pinto (2012), and the outcome
#' regression coefficients are estimated using weighted least squares,where the weights depend on
#' the propensity score estimates; see Sant'Anna and Zhao (2020) for details.
#'
#'
#' The resulting estimator is not only locally efficient and doubly robust for the ATT,
#' but it is also doubly robust for inference; see Sant'Anna and Zhao (2020) for details.
#'
#'
#' @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$re74))
#'
#' # Implement improved DR locally efficient DiD with panel data
#' drdid_imp_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
#' D = eval_lalonde_cps$experimental,
#' covariates = covX)
#'
#' @export
drdid_imp_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)
#-----------------------------------------------------------------------------
#Compute the Pscore using the pscore.cal
pscore.ipt <- pscore.cal(D, int.cov, i.weights = i.weights, n = n)
ps.fit <- as.vector(pscore.ipt$pscore)
ps.fit <- pmin(ps.fit, 1 - 1e-6)
#Compute the Outcome regression for the control group
outcome.reg <- wols.br.panel(deltaY, D, int.cov, ps.fit, i.weights)
out.delta <- as.vector(outcome.reg$out.reg)
#Compute Bias-Reduced Doubly Robust DiD estimators
dr.att.summand.num <- as.vector((1 - (1 - D)/(1 - ps.fit)) * (deltaY - out.delta))
dr.att <- mean(i.weights * dr.att.summand.num)/mean(D * i.weights)
#get the influence function to compute standard error
dr.att.inf.func <- as.vector(i.weights * (dr.att.summand.num - D * dr.att) / mean(D * i.weights))
if (boot == FALSE) {
# Estimate of standard error
se.dr.att <- stats::sd(dr.att.inf.func)/sqrt(n)
# Estimate of upper boudary of 95% CI
uci <- dr.att + 1.96 * se.dr.att
# Estimate of lower doundary of 95% CI
lci <- dr.att - 1.96 * se.dr.att
#Create this null vector so we can export the bootstrap draws too.
dr.boot <- NULL
}
if (boot == TRUE) {
if (is.null(nboot) == TRUE) nboot = 999
if(boot.type == "multiplier"){
# do multiplier bootstrap
dr.boot <- mboot.did(dr.att.inf.func, nboot)
# get bootstrap std errors based on IQR
se.dr.att <- stats::IQR(dr.boot) / (stats::qnorm(0.75) - stats::qnorm(0.25))
# get symmtric critival values
cv <- stats::quantile(abs(dr.boot/se.dr.att), probs = 0.95)
# Estimate of upper boudary of 95% CI
uci <- dr.att + cv * se.dr.att
# Estimate of lower doundary of 95% CI
lci <- dr.att - cv * se.dr.att
} else {
# do weighted bootstrap
dr.boot <- unlist(lapply(1:nboot, wboot.dr.imp.panel,
n = n, deltaY = deltaY, D = D, int.cov = int.cov, i.weights = i.weights))
# get bootstrap std errors based on IQR
se.dr.att <- stats::IQR((dr.boot - dr.att)) / (stats::qnorm(0.75) - stats::qnorm(0.25))
# get symmtric critival values
cv <- stats::quantile(abs((dr.boot - dr.att)/se.dr.att), probs = 0.95)
# Estimate of upper boudary of 95% CI
uci <- dr.att + cv * se.dr.att
# Estimate of lower doundary of 95% CI
lci <- dr.att - cv * se.dr.att
}
}
if(inffunc == FALSE) dr.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,
estMethod = "imp",
boot = boot,
boot.type = boot.type,
nboot = nboot,
type = "dr"
)
ret <- (list(ATT = dr.att,
se = se.dr.att,
uci = uci,
lci = lci,
boots = dr.boot,
ps.flag = pscore.ipt$flag,
att.inf.func = dr.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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