attbounds {ATbounds}

Bounding the average treatment effect on the treated (ATT)

Description

Bounds the average treatment effect on the treated (ATT) under the unconfoundedness assumption without the overlap condition.

Usage

attbounds(
  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 X is studentized elementwise 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

ATT

cov_prob

Confidence level: 1-alpha

est_lb

estimate of the lower bound on ATT, i.e. E[Y(1) - Y(0) | D = 1]

est_ub

estimate of the upper bound on ATT, i.e. E[Y(1) - Y(0) | D = 1]

est_rps

the point estimate of ATT using the reference propensity score

se_lb

standard error for the estimate of the lower bound on ATT

se_ub

standard error for the estimate of the upper bound on ATT

ci_lb

the lower end point of the confidence interval for ATT

ci_ub

the upper end point of the confidence interval for ATT

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_att <- attbounds(Y, D, X, rps, Q = 3)