  We investigate the estimation of treatment effects from a sample that is
stratified on the binary treatment status. In the case of unconfounded
assignment where the potential outcomes are independent of the treatment given
covariates, we show that standard estimators of the average treatment effect
are inconsistent. In the case of an endogenous treatment and a binary
instrument, we show that the IV estimator is inconsistent for the local average
treatment effect. In both cases, we propose simple alternative estimators that
are consistent in stratified samples, assuming that the fraction treated in the
population is known or can be estimated.
