具有潜在秩不变性的分布处理效应
Distributional Treatment Effect with Latent Rank Invariance
AI总结：
本文提出基于潜在秩不变性假设的分布处理效应估计方法，利用非负矩阵分解和Neyman正交性推导估计量的极限分布，解决处理效应异质性问题。
摘要：
在评估政策影响时，处理效应异质性是一个重要关注点：“处理是否是帕累托改进的？”，“在处理下境况变好的人的比例是多少？”等。然而，即使在二元随机处理的简单情况下，由于对于给定单位我们无法同时观察到处理潜在结果和未处理潜在结果这一根本限制，现有分析大多局限于平均处理效应或分位数处理效应。本文假设一个条件独立性假设，即两个潜在结果在给定标量潜在变量的情况下相互独立。通过严格递增条件期望的具体例子，我将该潜在变量标记为“潜在秩”，并将这一识别假设称为“潜在秩不变性”。在实现中，我假设潜在变量具有有限支撑，并提出一种基于非负矩阵分解的估计策略。利用Neyman正交性，推导出了分布处理效应估计量的极限分布。
英文摘要：
Treatment effect heterogeneity is of great concern in policy evaluation. However, existing analyses have mostly been limited to summary measures such as an average treatment effect, due to the fundamental limitation that we cannot simultaneously observe both potential outcomes for a given unit. In this paper, I identify and estimate moment-identified distributional treatment effect (DTE) parameters, such as the marginal distribution of treatment effect. The key identifying assumption is that the two potential outcomes are conditionally independent given a latent variable. Interpreting this latent variable as underlying individual-level heterogeneity, I motivate the identifying assumption as `latent rank invariance.' In the conditional independence framework, the DTE parameters are identified given two proxy variables. In implementation, I assume a finite support on the latent variable, imposing a finite mixture structure on the identifying assumption. Using Neyman orthogonality, I establish asymptotic normality of the estimator, enabling inference for DTE parameters.
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