  The bootstrap, introduced by Efron (1982), has become a very popular method
for estimating variances and constructing confidence intervals. A key insight
is that one can approximate the properties of estimators by using the empirical
distribution function of the sample as an approximation for the true
distribution function. This approach views the uncertainty in the estimator as
coming exclusively from sampling uncertainty. We argue that for causal
estimands the uncertainty arises entirely, or partially, from a different
source, corresponding to the stochastic nature of the treatment received. We
develop a bootstrap procedure that accounts for this uncertainty, and compare
its properties to that of the classical bootstrap.
