  Truncated conditional expectation functions are objects of interest in a wide
range of economic applications, including income inequality measurement,
financial risk management, and impact evaluation. They typically involve
truncating the outcome variable above or below certain quantiles of its
conditional distribution. In this paper, based on local linear methods, a
novel, two-stage, nonparametric estimator of such functions is proposed. In
this estimation problem, the conditional quantile function is a nuisance
parameter that has to be estimated in the first stage. The proposed estimator
is insensitive to the first-stage estimation error owing to the use of a
Neyman-orthogonal moment in the second stage. This construction ensures that
inference methods developed for the standard nonparametric regression can be
readily adapted to conduct inference on truncated conditional expectations. As
an extension, estimation with an estimated truncation quantile level is
considered. The proposed estimator is applied in two empirical settings: sharp
regression discontinuity designs with a manipulated running variable and
randomized experiments with sample selection.
