Estimation of Heterogeneous Individual Treatment Effects With Endogenous Treatments

This article estimates individual treatment effects (ITE) and its probability distribution in a triangular model with binary-valued endogenous treatments. Our estimation procedure takes two steps. First, we estimate the counterfactual outcome and hence, the ITE for every observational unit in the sample. Second, we estimate the ITE density function of the whole population. Our estimation method does not suffer from the ill-posed inverse problem associated with inverting a nonlinear functional. Asymptotic properties of the proposed method are established. We study its finite sample properties in Monte Carlo experiments. We also illustrate our approach with an empirical application assessing the effects of 401(k) retirement programs on personal savings. Our results show that there exists a small but statistically significant proportion of individuals who experience negative effects, although the majority of ITEs is positive. Supplementary materials for this article are available online.本文针对含二元内生处理变量的三角模型，对个体处理效应（individual treatment effects, ITE）及其概率分布进行估计。本文的估计流程分为两个阶段：第一阶段，估计反事实结果，进而得到样本中每个观测单元的个体处理效应；第二阶段，估计全人群的个体处理效应密度函数。所提出的估计方法不会面临反转非线性泛函所引发的不适定逆问题。本文确立了该方法的渐近性质，并通过蒙特卡洛实验对其有限样本表现展开研究。此外，我们还借助一项实证应用案例阐释了所提方法的实际效果：评估401(k)退休计划对个人储蓄的影响。研究结果表明，尽管绝大多数个体处理效应为正值，但仍存在占比虽小但统计显著的群体受到了负面影响。本文的补充材料可在线获取。