崩溃边界的推断
Inference on Breakdown Frontiers
摘要：
给定一组基线假设，细分边界是导致特定结论的一组假设与不导致特定结论的一组假设之间的边界。在具有二元治疗的潜在结果模型中，我们考虑两个结论：首先，ATE至少是一个特定值（例如，非负的）和第二受益于治疗的单位的比例至少是特定值（例如，至少50%）。对于这些结论，我们推导出两种假设的分解边界：一种是指基线随机分配治疗假设的松弛，另一种是指基线秩不变性假设的松弛。这些类别的假设嵌套的点识别假设的随机分配和秩不变性和相反的一端没有约束的治疗选择或潜在的结果之间的依赖结构。这一前沿提供了一个定量的衡量标准，衡量结论对基线点识别假设的放松的稳健性。我们推导出$\sqrt{N}$一致的样本模拟估计这些前沿。然后，我们提供了两个渐近有效的自助程序，用于构建较低的统一置信带的崩溃前沿。作为鲁棒性的度量，估计的击穿边界及其相应的置信带可以与在点识别假设下获得的传统点估计和置信区间一起呈现。我们说明了这种方法的实证应用的影响，儿童抚养工资。我们发现，充分弱的结论是鲁棒的秩不变和随机分配的同时失败，而一些更强的结论是相当强大的秩不变的失败，但不一定放松随机分配。
英文摘要：
Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50\%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes relaxations of the baseline random assignment of treatment assumption, and one which indexes relaxations of the baseline rank invariance assumption. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of robustness of conclusions to relaxations of the baseline point identifying assumptions. We derive $\sqrt{N}$-consistent sample analog estimators for these frontiers. We then provide two asymptotically valid bootstrap procedures for constructing lower uniform confidence bands for the breakdown frontier. As a measure of robustness, estimated breakdown frontiers and their corresponding confidence bands can be presented alongside traditional point estimates and confidence intervals obtained under point identifying assumptions. We illustrate this approach in an empirical application to the effect of child soldiering on wages. We find that sufficiently weak conclusions are robust to simultaneous failures of rank invariance and random assignment, while some stronger conclusions are fairly robust to failures of rank invariance but not necessarily to relaxations of random assignment.
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