Nonparametric Estimation of Truncated Conditional Expectation Functions

TL;DR

This paper introduces a novel two-stage nonparametric estimator for truncated conditional expectation functions, leveraging local linear methods and Neyman-orthogonal moments to improve inference robustness in economic applications.

Contribution

It proposes a new estimator that is insensitive to first-stage estimation errors, enabling reliable inference on truncated conditional expectations in various economic contexts.

Findings

Estimator performs well in empirical applications

Robust inference methods are adaptable to the proposed estimator

Extension to estimated truncation quantiles enhances flexibility

Abstract

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.