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#' Calculate two-stage difference-in-differences following Gardner (2021)
#'
#' @import fixest
#'
#' @param data The dataframe containing all the variables
#' @param yname Outcome variable
#' @param first_stage Fixed effects and other covariates you want to residualize
#' with in first stage.
#' Formula following \code{\link[fixest:feols]{fixest::feols}}.
#' Fixed effects specified after "`|`".
#' @param second_stage Second stage, these should be the treatment indicator(s)
#' (e.g. treatment variable or event-study leads/lags).
#' Formula following \code{\link[fixest:feols]{fixest::feols}}.
#' Use `i()` for factor variables, see \code{\link[fixest:i]{fixest::i}}.
#' @param treatment A variable that = 1 if treated, = 0 otherwise
#' @param cluster_var What variable to cluster standard errors. This can be IDs
#' or a higher aggregate level (state for example)
#' @param weights Optional. Variable name for regression weights.
#' @param bootstrap Optional. Should standard errors be calculated using bootstrap?
#' Default is `FALSE`.
#' @param n_bootstraps Optional. How many bootstraps to run.
#' Default is `250`.
#' @param return_bootstrap Optional. Logical. Will return each bootstrap second-stage
#' estimate to allow for manual use, e.g. percentile standard errors and empirical
#' confidence intervals.
#' @param verbose Optional. Logical. Should information about the two-stage
#' procedure be printed back to the user?
#' Default is `TRUE`.
#'
#' @return `fixest` object with adjusted standard errors
#' (either by formula or by bootstrap). All the methods from `fixest` package
#' will work, including \code{\link[fixest:esttable]{fixest::esttable}} and
#' \code{\link[fixest:coefplot]{fixest::coefplot}}
#'
#' @section Examples:
#'
#' Load example dataset which has two treatment groups and homogeneous treatment effects
#'
#' ```{r, comment = "#>", collapse = TRUE}
#' # Load Example Dataset
#' data("df_hom")
#' ```
#'
#' ### Static TWFE
#'
#' You can run a static TWFE fixed effect model for a simple treatment indicator
#' ```{r, comment = "#>", collapse = TRUE}
#' static <- did2s(df_hom,
#' yname = "dep_var", treatment = "treat", cluster_var = "state",
#' first_stage = ~ 0 | unit + year,
#' second_stage = ~ i(treat, ref=FALSE))
#'
#' fixest::esttable(static)
#' ```
#'
#' ### Event Study
#'
#' Or you can use relative-treatment indicators to estimate an event study estimate
#' ```{r, comment = "#>", collapse = TRUE}
#' es <- did2s(df_hom,
#' yname = "dep_var", treatment = "treat", cluster_var = "state",
#' first_stage = ~ 0 | unit + year,
#' second_stage = ~ i(rel_year, ref=c(-1, Inf)))
#'
#' fixest::esttable(es)
#' ```
#'
#' ```{r, eval = F}
#' # plot rel_year coefficients and standard errors
#' fixest::coefplot(es, keep = "rel_year::(.*)")
#' ```
#'
#' ### Example from Cheng and Hoekstra (2013)
#'
#' Here's an example using data from Cheng and Hoekstra (2013)
#' ```{r, comment = "#>", collapse = TRUE}
#' # Castle Data
#' castle <- haven::read_dta("https://github.com/scunning1975/mixtape/raw/master/castle.dta")
#'
#' did2s(
#' data = castle,
#' yname = "l_homicide",
#' first_stage = ~ 0 | sid + year,
#' second_stage = ~ i(post, ref=0),
#' treatment = "post",
#' cluster_var = "state", weights = "popwt"
#' )
#' ```
#'
#' @export
did2s <- function(data, yname, first_stage, second_stage, treatment, cluster_var,
weights = NULL, bootstrap = FALSE, n_bootstraps = 250,
return_bootstrap = FALSE, verbose = TRUE) {
# Check Parameters ---------------------------------------------------------
if (!inherits(data, "data.frame")) stop("`did2s` requires a data.frame like object for analysis.")
# Extract vars from formula
if (inherits(first_stage, "formula")) first_stage <- as.character(first_stage)[[2]]
if (inherits(second_stage, "formula")) second_stage <- as.character(second_stage)[[2]]
# Check that treatment is a 0/1 or T/F variable
if (!all(
unique(data[[treatment]]) %in% c(1, 0, T, F)
)) {
stop(sprintf(
"'%s' must be a 0/1 or T/F variable indicating which observations are untreated/not-yet-treated.",
treatment
))
}
# Print --------------------------------------------------------------------
if (verbose) {
if (!bootstrap) cluster_msg <- paste0("- Standard errors will be clustered by `", cluster_var, "`\n")
if (bootstrap) cluster_msg <- paste0("- Standard errors will be block bootstrapped with cluster `", cluster_var, "`\n")
message(
paste(
"Running Two-stage Difference-in-Differences\n",
paste0("- first stage formula `", paste0("~ ", first_stage), "`\n"),
paste0("- second stage formula `", paste0("~ ", second_stage), "`\n"),
paste0("- The indicator variable that denotes when treatment is on is `", treatment, "`\n"),
cluster_msg,
collapse = "\n"
)
)
}
# Point Estimates ----------------------------------------------------------
est <- did2s_estimate(
data = data,
yname = yname,
first_stage = first_stage,
second_stage = second_stage,
treatment = treatment,
weights = weights,
bootstrap = bootstrap
)
# Analytic Standard Errors -------------------------------------------------
if (!bootstrap) {
# Subset data to the observations used in the second stage
# obsRemoved have - in front of rows, so they are deleted
removed_rows <- est$second_stage$obs_selection$obsRemoved
if (!is.null(removed_rows)) data <- data[removed_rows, ]
# Extract weights
if (is.null(weights)) {
weights_vector <- rep.int(1L, nrow(data))
} else {
weights_vector <- sqrt(data[[weights]])
}
# Extract first stage
first_u <- est$first_u
if (!is.null(removed_rows)) first_u <- first_u[removed_rows]
# x1 is matrix used to predict Y(0)
x1 <- did2s_sparse(data, est$first_stage, weights_vector)
# Extract second stage
second_u <- stats::residuals(est$second_stage)
x2 <- did2s_sparse(data, est$second_stage, weights_vector)
# multiply by weights
first_u <- weights_vector * first_u
x1 <- weights_vector * x1
second_u <- weights_vector * second_u
x2 <- weights_vector * x2
# x10 is matrix used to estimate first stage (zero out rows with D_it = 1)
x10 <- copy(x1)
# treated rows. Note dgcMatrix is 0-index !!
treated_rows = which(data[[treatment]] == 1L) - 1
idx = x10@i %in% treated_rows
x10@x[idx] <- 0
# x2'x1 (x10'x10)^-1
# Note: MatrixExtra makes transposing sparse matrices easy
# Note: SparseM relies on A (x10'x10) being positive symmetric for solving
V <- MatrixExtra::t_deep(
SparseM::solve(
Matrix::crossprod(x10),
MatrixExtra::t_shallow(Matrix::crossprod(x2, x1))
)
)
# Unique values of cluster variable
cl = data[[cluster_var]]
cls = split(1:length(cl), as.factor(cl))
for (i in 1:length(cls)) {
in_cl = cls[[i]]
x2_g = x2[in_cl, , drop = FALSE]
x10_g = x10[in_cl, , drop = FALSE]
first_u_g = first_u[in_cl]
second_u_g = second_u[in_cl]
W = Matrix::crossprod(x2_g, second_u_g) - V %*% Matrix::crossprod(x10_g, first_u_g)
# W' W
if(i == 1) {
meat_sum = Matrix::tcrossprod(W)
} else {
meat_sum = meat_sum + Matrix::tcrossprod(W)
}
}
# (X_2'X_2)^-1 (sum W_g W_g') (X_2'X_2)^-1
bread = SparseM::solve(Matrix::crossprod(x2))
cov <- as.matrix(bread %*% meat_sum %*% bread)
}
# Bootstrap Standard Errors ------------------------------------------------
if (bootstrap) {
message(paste0("Starting ", n_bootstraps, " bootstraps at cluster level: ", cluster_var, "\n"))
# Unique values of cluster variable
cl <- unique(data[[cluster_var]])
stat <- function(x, i) {
# select the observations to subset based on the cluster var
block_obs <- unlist(lapply(i, function(n) which(x[n] == data[[cluster_var]])))
# run regression for given replicate, return estimated coefficients
stats::coefficients(
did2s_estimate(
data = data[block_obs, ],
yname = yname,
first_stage = first_stage,
second_stage = second_stage,
treatment = treatment,
weights = weights,
bootstrap = TRUE
)$second_stage
)
}
boot <- boot::boot(cl, stat, n_bootstraps)
# Get estimates and fix names
estimates <- boot$t
colnames(estimates) <- names(stats::coef(est$second_stage))
# Bootstrap Var-Cov Matrix
cov <- stats::cov(estimates)
if (return_bootstrap) {
return(estimates)
}
}
# summary creates fixest object with correct standard errors and vcov
# Once fixest updates on CRAN
# rescale cov by G/(G-1) and use t(G-1) distribution
# G = length(cl)
# cov = cov * G/(G-1)
return(base::suppressWarnings(
# summary(
# est$second_stage,
# .vcov = list("Two-stage Adjusted" = cov),
# ssc = ssc(adj = FALSE, t.df = G-1)
# )
summary(est$second_stage, .vcov = cov)
))
}
# Point estimate for did2s
did2s_estimate <- function(data, yname, first_stage, second_stage, treatment,
weights = NULL, bootstrap = FALSE) {
## We'll use fixest's formula expansion macros to swap out first and second
## stages (see: ?fixest::xpd)
fixest::setFixest_fml(
..first_stage = first_stage,
..second_stage = second_stage
)
# First stage among untreated
untreat <- data[data[[treatment]] == 0, ]
if (is.null(weights)) {
weights_vector <- NULL
} else {
weights_vector <- untreat[[weights]]
}
first_stage <- fixest::feols(fixest::xpd(~ 0 + ..first_stage, lhs = yname),
data = untreat,
weights = weights_vector,
combine.quick = FALSE, # allows var1^var2 in FEs
warn = FALSE,
notes = FALSE
)
# Residualize outcome variable but keep same yname
first_u <- data[[yname]] - stats::predict(first_stage, newdata = data)
data[[yname]] <- first_u
# Zero out residual rows with D_it = 1 (for analytical SEs later on)
if (!bootstrap) first_u[data[[treatment]] == 1] <- 0
# Second stage
if (!is.null(weights)) weights_vector <- data[[weights]]
second_stage <- fixest::feols(fixest::xpd(~ 0 + ..second_stage, lhs = yname),
data = data,
weights = weights_vector,
warn = FALSE,
notes = FALSE
)
ret <- list(
first_stage = first_stage,
second_stage = second_stage
)
if (!bootstrap) {
ret <- list(
first_stage = first_stage,
second_stage = second_stage,
first_u = first_u
)
} else {
ret <- list(second_stage = second_stage)
}
return(ret)
}
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