atebounds: Bounding the average treatment effect (ATE)

In ATbounds: Bounding Treatment Effects by Limited Information Pooling

Bounding the average treatment effect (ATE)

Description

Bounds the average treatment effect (ATE) under the unconfoundedness assumption without the overlap condition.

Usage

atebounds(
  Y,
  D,
  X,
  rps,
  Q = 3L,
  studentize = TRUE,
  alpha = 0.05,
  x_discrete = FALSE,
  n_hc = NULL
)

Arguments

Y	n-dimensional vector of binary outcomes
D	n-dimensional vector of binary treatments
X	n by p matrix of covariates
rps	n-dimensional vector of the reference propensity score
Q	bandwidth parameter that determines the maximum number of observations for pooling information (default: Q = 3)
studentize	TRUE if the columns of X are studentized and FALSE if not (default: TRUE)
alpha	(1-alpha) nominal coverage probability for the confidence interval of ATE (default: 0.05)
x_discrete	TRUE if the distribution of X is discrete and FALSE otherwise (default: FALSE)
n_hc	number of hierarchical clusters to discretize non-discrete covariates; relevant only if x_discrete is FALSE. The default choice is n_hc = ceiling(length(Y)/10), so that there are 10 observations in each cluster on average.

Value

An S3 object of type "ATbounds". The object has the following elements.

call	a call in which all of the specified arguments are specified by their full names
type	ATE
cov_prob	Confidence level: 1-alpha
y1_lb	estimate of the lower bound on the average of Y(1), i.e. E[Y(1)]
y1_ub	estimate of the upper bound on the average of Y(1), i.e. E[Y(1)]
y0_lb	estimate of the lower bound on the average of Y(0), i.e. E[Y(0)]
y0_ub	estimate of the upper bound on the average of Y(0), i.e. E[Y(0)]
est_lb	estimate of the lower bound on ATE, i.e. E[Y(1) - Y(0)]
est_ub	estimate of the upper bound on ATE, i.e. E[Y(1) - Y(0)]
est_rps	the point estimate of ATE using the reference propensity score
se_lb	standard error for the estimate of the lower bound on ATE
se_ub	standard error for the estimate of the upper bound on ATE
ci_lb	the lower end point of the confidence interval for ATE
ci_ub	the upper end point of the confidence interval for ATE

References

Sokbae Lee and Martin Weidner. Bounding Treatment Effects by Pooling Limited Information across Observations. Forthcoming at the Journal of Econometrics.

Examples

  Y <- RHC[,"survival"]
  D <- RHC[,"RHC"]
  X <- RHC[,c("age","edu")]
  rps <- rep(mean(D),length(D))
  results_ate <- atebounds(Y, D, X, rps, Q = 3)

ATbounds documentation built on May 8, 2026, 1:06 a.m.