ABSTRACT 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.

中文翻译：

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用内源性治疗估计异质个体治疗效果

摘要 本文在具有二值内源性治疗的三角模型中估计了个体治疗效果 (ITE) 及其概率分布。我们的估计过程需要两个步骤。首先，我们估计反事实结果，从而估计样本中每个观察单元的 ITE。其次，我们估计整个人口的 ITE 密度函数。我们的估计方法不会遇到与非线性函数求逆相关的不适定逆问题。建立了所提出方法的渐近性质。我们在蒙特卡罗实验中研究了它的有限样本特性。我们还通过评估 401(k) 退休计划对个人储蓄的影响的实证应用来说明我们的方法。我们的结果表明，尽管大多数 ITE 是积极的，但仍有一小部分人受到负面影响，但在统计上却显着。本文的补充材料可在线获取。