Nonparametric Estimation of Truncated Conditional Expectation Functions

Truncated conditional expectation functions are objects of interest in a wide range of economic applications, including income inequality measurement, financial risk man- agement, 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, I propose a novel, two-stage, nonparametric estimator of such functions. In this estimation problem, the conditional quantile function is a nuisance pa- rameter, which has to be estimated in the first stage. I immunize my estimator against the first-stage estimation error by exploiting a Neyman-orthogonal moment in the second stage. This construction ensures that the proposed estimator has favorable bias proper- ties and that inference methods developed for the standard nonparametric regression can be readily adapted to conduct inference on truncated conditional expectation functions. As an extension, I consider estimation with an estimated truncation quantile level. I ap- ply my estimator in three empirical settings: (i) sharp regression discontinuity designs with a manipulated running variable, (ii) program evaluation under sample selection, and (iii) conditional expected shortfall estimation.