The effectbounds package provides tools for estimating non-overlap
bounds for causal effects.
The identification of causal effects typically relies on the overlap assumption (also known as positivity), which requires that all units have a positive probability of being in either the treatment or control group.
When overlap fails in finite-samples, with some units having very small estimated probability of receiving the treatment (or control), then estimators of the causal effect can perform poorly.
Non-overlap bounds are an approach for estimating causal effects even when non-overlap is violated, by focusing on estimating bounds on the effect.
You can install the development version of effectbounds from GitHub:
# install.packages("devtools")
devtools::install_github("herbps10/effectbounds")The example estimates uniform 95% non-overlap bounds for the ATE using simulated data.
library(effectbounds)
dat <- simulate_ate_example(seed = 1, N = 5e2, alpha = 3, beta = 0.1, gamma = 1)
bounds <- ate_bounds(
dat,
X = c("X1", "X2"), A = "A", Y = "Y",
thresholds = c(10^seq(-3, -0.5, 0.1)),
smoothness = c(0.005)
)
plot(bounds, point_estimate = TRUE, main = "Non-overlap ATE Bounds", ylim = c(-0.3, 0.5))
The plot shows the non-overlap bounds (the black points) on the ATE axis for a range of propensity score thresholds. bounds are uniform 95% confidence intervals: this means you can pick any of the intervals, for any choice of threshold, and interpret it as a valid 95% confidence interval (CI) for the ATE.
The plot also shows a point estimate (the blue dot) and 95% CI (the blue line) for the ATE. The non-overlap bounds are, for the right choice of threshold, shorter than the 95% CI for the ATE point estimate.