Nothing
#' @import stats
NULL
###################################################################################
#' Outcome regression DiD estimator for the ATT, with repeated cross-section data
#' @description \code{reg_did_rc} computes the outcome regressions estimators for the average treatment effect on the
#' treated in difference-in-differences (DiD) setups with stationary repeated cross-sectional data.
#' @param y An \eqn{n} x \eqn{1} vector of outcomes from the both pre and post-treatment periods.
#' @param post An \eqn{n} x \eqn{1} vector of Post-Treatment dummies (post = 1 if observation belongs to post-treatment period,
#' and post = 0 if observation belongs to 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 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 OR DiD point estimate}
#' \item{se}{The OR 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 = FALSE, boot, boot.type, nboot, type="or")}
#'
#' @details
#'
#' The \code{reg_did_rc} function implements
#' outcome regression difference-in-differences (DiD) estimator for the average treatment effect
#' on the treated (ATT) defined in equation (2.2) of Sant'Anna and Zhao (2020) when stationary repeated cross-sectional
#' data are available. The estimator follows the same spirit of the nonparametric estimators proposed by Heckman, Ichimura and Todd (1997),
#' though here the the outcome regression models are assumed to be linear in covariates (parametric),
#'
#' The nuisance parameters (outcome regression coefficients) are estimated via ordinary least squares.
#' @references
#' \cite{Heckman, James J., Ichimura, Hidehiko, and Todd, Petra E. (1997),"Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme",
#' Review of Economic Studies, vol. 64(4), p. 605–654, \doi{10.2307/2971733}.
#' }
#'
#'
#' \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
#' # use the simulated data provided in the package
#' covX = as.matrix(sim_rc[,5:8])
#' # Implement OR DiD estimator
#' reg_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
#' covariates= covX)
#'
#' @export
reg_did_rc <-function(y, post, D, covariates, i.weights = NULL,
boot = FALSE, boot.type = "weighted", nboot = NULL,
inffunc = FALSE){
#-----------------------------------------------------------------------------
# D as vector
D <- as.vector(D)
# post as vector
post <- as.vector(post)
# Sample size
n <- length(D)
# outcome of interested
y <- as.vector(y)
# 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 Outcome regression for the control group at the pre-treatment period, using ols.
# reg.coeff.pre <- stats::coef(stats::lm(y ~ -1 + int.cov,
# subset = ((D==0) & (post==0)),
# weights = i.weights))
pre_filter <- (D == 0) & (post == 0)
reg.coeff.pre <- stats::coef(fastglm::fastglm(
x = int.cov[pre_filter, , drop = FALSE],
y = y[pre_filter],
weights = i.weights[pre_filter],
family = gaussian(link = "identity")
))
if(anyNA(reg.coeff.pre)){
stop("Outcome regression model coefficients have NA components. \n Multicollinearity of covariates is probably the reason for it.")
}
out.y.pre <- as.vector(tcrossprod(reg.coeff.pre, int.cov))
#-----------------------------------------------------------------------------
#Compute the Outcome regression for the control group at the pre-treatment period, using ols.
# reg.coeff.post <- stats::coef(stats::lm(y ~ -1 + int.cov,
# subset = ((D==0) & (post==1)),
# weights = i.weights))
post_filter <- (D == 0) & (post == 1)
reg.coeff.post <- stats::coef(fastglm::fastglm(
x = int.cov[post_filter, , drop = FALSE],
y = y[post_filter],
weights = i.weights[post_filter],
family = gaussian(link = "identity")
))
if(anyNA(reg.coeff.post)){
stop("Outcome regression model coefficients have NA components. \n Multicollinearity (or lack of variation) of covariates is probably the reason for it.")
}
out.y.post <- as.vector(tcrossprod(reg.coeff.post, int.cov))
#-----------------------------------------------------------------------------
#Compute the OR DiD estimators
# First, the weights
w.treat.pre <- i.weights * D * (1 - post)
w.treat.post <- i.weights * D * post
w.cont <- i.weights * D
reg.att.treat.pre <- w.treat.pre * y
reg.att.treat.post <- w.treat.post * y
reg.att.cont <- w.cont * (out.y.post - out.y.pre)
eta.treat.pre <- mean(reg.att.treat.pre) / mean(w.treat.pre)
eta.treat.post <- mean(reg.att.treat.post) / mean(w.treat.post)
eta.cont <- mean(reg.att.cont) / mean(w.cont)
reg.att <- (eta.treat.post - eta.treat.pre) - eta.cont
#-----------------------------------------------------------------------------
#get the influence function to compute standard error
#-----------------------------------------------------------------------------
# First, the influence function of the nuisance functions
# Asymptotic linear representation of OLS parameters in pre-period
weights.ols.pre <- i.weights * (1 - D) * (1 - post)
wols.x.pre <- weights.ols.pre * int.cov
wols.eX.pre <- weights.ols.pre * (y - out.y.pre) * int.cov
XpX_pre <- crossprod(wols.x.pre, int.cov)/n
# Check if XpX is invertible
if ( base::rcond(XpX_pre) < .Machine$double.eps) {
stop("The regression design matrix for pre-treatment is singular. Consider removing some covariates.")
}
XpX.inv.pre <- solve(XpX_pre)
asy.lin.rep.ols.pre <- wols.eX.pre %*% XpX.inv.pre
# Asymptotic linear representation of OLS parameters in post-period
weights.ols.post <- i.weights * (1 - D) * post
wols.x.post <- weights.ols.post * int.cov
wols.eX.post <- weights.ols.post * (y - out.y.post) * int.cov
XpX_post <- crossprod(wols.x.post, int.cov)/n
# Check if XpX is invertible
if ( base::rcond(XpX_post) < .Machine$double.eps) {
stop("The regression design matrix for post-treatment is singular. Consider removing some covariates.")
}
XpX.inv.post <- solve(XpX_post)
asy.lin.rep.ols.post <- wols.eX.post %*% XpX.inv.post
#-----------------------------------------------------------------------------
# Now, the influence function of the "treat" component
# Leading term of the influence function
inf.treat.pre <- (reg.att.treat.pre - w.treat.pre * eta.treat.pre) / mean(w.treat.pre)
inf.treat.post <- (reg.att.treat.post - w.treat.post * eta.treat.post) / mean(w.treat.post)
inf.treat <- inf.treat.post - inf.treat.pre
#-----------------------------------------------------------------------------
# Now, get the influence function of control component
# Leading term of the influence function: no estimation effect
inf.cont.1 <- (reg.att.cont - w.cont * eta.cont)
# Estimation effect from beta hat (OLS using only controls)
# Derivative matrix (k x 1 vector)
M1 <- base::colMeans(w.cont * int.cov)
# Now get the influence function related to the estimation effect related to beta's in post-treatment
inf.cont.2.post <- asy.lin.rep.ols.post %*% M1
# Now get the influence function related to the estimation effect related to beta's in pre-treatment
inf.cont.2.pre <- asy.lin.rep.ols.pre %*% M1
# Influence function for the control component
inf.control <- (inf.cont.1 + inf.cont.2.post - inf.cont.2.pre) / mean(w.cont)
#-----------------------------------------------------------------------------
#get the influence function of the DR estimator (put all pieces together)
reg.att.inf.func <- (inf.treat - inf.control)
#-----------------------------------------------------------------------------
if (boot == FALSE) {
# Estimate of standard error
se.reg.att <- stats::sd(reg.att.inf.func)/sqrt(n)
# Estimate of upper boudary of 95% CI
uci <- reg.att + 1.96 * se.reg.att
# Estimate of lower doundary of 95% CI
lci <- reg.att - 1.96 * se.reg.att
#Create this null vector so we can export the bootstrap draws too.
reg.boot <- NULL
}
if (boot == TRUE) {
if (is.null(nboot) == TRUE) nboot = 999
if(boot.type == "multiplier"){
# do multiplier bootstrap
reg.boot <- mboot.did(reg.att.inf.func, nboot)
# get bootstrap std errors based on IQR
se.reg.att <- stats::IQR(reg.boot) / (stats::qnorm(0.75) - stats::qnorm(0.25))
# get symmtric critival values
cv <- stats::quantile(abs(reg.boot/se.reg.att), probs = 0.95)
# Estimate of upper boudary of 95% CI
uci <- reg.att + cv * se.reg.att
# Estimate of lower doundary of 95% CI
lci <- reg.att - cv * se.reg.att
} else {
# do weighted bootstrap
reg.boot <- unlist(lapply(1:nboot, wboot_reg_rc,
n = n, y = y, post = post, D = D, int.cov = int.cov, i.weights = i.weights))
# get bootstrap std errors based on IQR
se.reg.att <- stats::IQR((reg.boot - reg.att)) / (stats::qnorm(0.75) - stats::qnorm(0.25))
# get symmtric critival values
cv <- stats::quantile(abs((reg.boot - reg.att)/se.reg.att), probs = 0.95)
# Estimate of upper boudary of 95% CI
uci <- reg.att + cv * se.reg.att
# Estimate of lower doundary of 95% CI
lci <- reg.att - cv * se.reg.att
}
}
if(inffunc == FALSE) reg.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 = FALSE,
boot = boot,
boot.type = boot.type,
nboot = nboot,
type = "or"
)
ret <- (list(ATT = reg.att,
se = se.reg.att,
uci = uci,
lci = lci,
boots = reg.boot,
att.inf.func = reg.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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