This paper studies nonparametric identification and estimation of causal effects in centralized school assignment. In many centralized assignment algorithms, students face both lottery-driven variation and regression discontinuity- (RD) driven variation. We characterize the full set of identified atomic treatment effects (aTEs), defined as the conditional average treatment effect between a pair of schools given student characteristics. Atomic treatment effects are the building blocks of more aggregated treatment contrasts, and common approaches to estimating aTE aggregations can mask important heterogeneity. In particular, many aggregations of aTEs put zero weight on aTEs driven by RD variation, and estimators of such aggregations put asymptotically vanishing weight on the RD-driven aTEs. We provide a diagnostic and recommend new aggregation schemes. Lastly, we provide estimators and asymptotic results for inference on these aggregations.

翻译：本文研究了集中式学校分配中因果效应的非参数化识别与估计。在许多集中式分配算法中，学生既面临彩票驱动的变异，也面临断点回归驱动的变异。我们刻画了所有已识别的原子处理效应的完整集合，该集合定义为给定学生特征下成对学校间的条件平均处理效应。原子处理效应是更聚合处理对比的基础构件，而估计原子处理效应聚合的常见方法可能掩盖重要的异质性。特别地，许多原子处理效应的聚合对断点回归驱动的原子处理效应赋予零权重，而此类聚合的估计量对断点回归驱动的原子处理效应赋予渐近消失的权重。我们提供了一种诊断方法并推荐了新的聚合方案。最后，我们为这些聚合的推断提供了估计量及渐近结果。