This paper develops a class of potential outcomes models characterized by three main features: (i) Unobserved heterogeneity can be represented by a vector of potential outcomes and a type describing the manner in which an instrument determines the choice of treatment; (ii) The availability of an instrumental variable that is conditionally independent of unobserved heterogeneity; and (iii) The imposition of convex restrictions on the distribution of unobserved heterogeneity. The proposed class of models encompasses multiple classical and novel research designs, yet possesses a common structure that permits a unifying analysis of identification and estimation. In particular, we establish that these models share a common necessary and sufficient condition for identifying certain causal parameters. Our identification results are constructive in that they yield estimating moment conditions for the parameters of interest. Focusing on a leading special case of our framework, we further show how these estimating moment conditions may be modified to be doubly robust. The corresponding double robust estimators are shown to be asymptotically normally distributed, bootstrap based inference is shown to be asymptotically valid, and the semi-parametric efficiency bound is derived for those parameters that are root-n estimable. We illustrate the usefulness of our results for developing, identifying, and estimating causal models through an empirical evaluation of the role of mental health as a mediating variable in the Moving To Opportunity experiment.

翻译：本文发展了一类具有三个主要特征的潜在结果模型：（i）未观测异质性可通过一个潜在结果向量和一个描述工具变量如何决定处理选择的类型来表示；（ii）存在一个与未观测异质性条件独立的工具变量；（iii）对未观测异质性分布施加凸性约束。所提出的模型类涵盖多种经典与新颖的研究设计，但共享一个统一结构，允许对识别与估计进行统一分析。具体而言，我们证明这些模型在识别特定因果参数时具有共同的必要且充分条件。我们的识别结果是建设性的，因为它们为目标参数提供了估计矩条件。聚焦于本框架的一个主要特例，我们进一步展示了如何修改这些估计矩条件以实现双重稳健性。相应的双重稳健估计量被证明是渐近正态分布的，基于自助法的推断被证明是渐近有效的，并且对于可进行根号n估计的参数导出了半参数效率界。通过一项关于心理健康作为"搬向机遇"实验中介变量的实证评估，我们展示了这些结果在发展、识别及估计因果模型中的实用性。