Abstract :
In this paper, we propose nonparametric estimators of sharp bounds on the distribution
of treatment effects of a binary treatment and establish their asymptotic distributions.
We note the possible failure of the standard bootstrap with the same sample
size and apply the fewer-than-n bootstrap to making inferences on these bounds.
The finite sample performances of the confidence intervals for the bounds based on
normal critical values, the standard bootstrap, and the fewer-than-n bootstrap are
investigated via a simulation study. Finally we establish sharp bounds on the treatment
effect distribution when covariates are available.
