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.
翻译:有条件预期功能是一系列广泛的经济应用中感兴趣的对象,包括收入不平等计量、金融风险管理和影响评价,通常涉及缩短其有条件分布的某些四分位数以上或以下的结果变量。在本文中,根据当地线性方法,提出了这种功能的新颖的、两阶段的非参数性估计值。在这一估算问题中,有条件的量化功能是一个在第一阶段必须估算的干扰参数。提议的估算器对第一阶段估算错误不敏感,原因是在第二阶段使用了内曼-orthogoinal时刻。这一构建确保为标准非参数回归而开发的推论方法可以很容易地调整,以便根据临时有条件期望进行推论。作为扩展,将考虑估计的变速孔度水平估算值。拟议的估算器应用于两个经验性环境:精确回归不连续状态设计,在抽样选择中操纵进行可变和随机实验。