We consider a functional parameter called the conditional average treatment effect (CATE), designed to capture heterogeneity of a treatment effect across subpopulations when the unconfoundedness assumption applies. In contrast to quantile regressions, the subpopulations of interest are defined...

We propose inverse probability weighted estimators for the the local average treatment effect (LATE) and the local average treatment effect for the treated (LATT) under instrumental variable assumptions with covariates. We show that these estimators are asymptotically normal and efficient, and...