atebounds {ATbounds}

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.

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)