  The conditional tail average treatment effect (CTATE) is defined as a
difference between the conditional tail expectations of potential outcomes,
which can capture heterogeneity and deliver aggregated local information on
treatment effects over different quantile levels and is closely related to the
notion of second-order stochastic dominance and the Lorenz curve. These
properties render it a valuable tool for policy evaluation. In this paper, we
study estimation of the CTATE locally for a group of compliers (local CTATE or
LCTATE) under the two-sided noncompliance framework. We consider a
semiparametric treatment effect framework under endogeneity for the LCTATE
estimation using a newly introduced class of consistent loss functions jointly
for the conditional tail expectation and quantile. We establish the asymptotic
theory of our proposed LCTATE estimator and provide an efficient algorithm for
its implementation. We then apply the method to evaluate the effects of
participating in programs under the Job Training Partnership Act in the US.
