Wanna Get Away? Regression Discontinuity Estimation of Exam School Effects Away From the Cutoff

In regression discontinuity (RD) studies exploiting an award or admissions cutoff, causal effects are nonparametrically identified for those near the cutoff. The effect of treatment on inframarginal applicants is also of interest, but identification of such effects requires stronger assumptions than those required for identification at the cutoff. This article discusses RD identification and estimation away from the cutoff. Our identification strategy exploits the availability of dependent variable predictors other than the running variable. Conditional on these predictors, the running variable is assumed to be ignorable. This identification strategy is used to study effects of Boston exam schools for inframarginal applicants. Identification based on the conditional independence assumptions imposed in our framework yields reasonably precise and surprisingly robust estimates of the effects of exam school attendance on inframarginal applicants. These estimates suggest that the causal effects of exam school attendance for 9th grade applicants with running variable values well away from admissions cutoffs differ little from those for applicants with values that put them on the margin of acceptance. An extension to fuzzy designs is shown to identify causal effects for compliers away from the cutoff. Supplementary materials for this article are available online.

在依托获奖门槛或录取分数线开展的断点回归（Regression Discontinuity, RD）研究中，因果效应仅能对阈值邻域内的个体实现非参数识别。研究人员同样关注干预对边际外申请者的影响，但此类效应的识别所需假设相较于阈值处的效应识别更强。本文探讨了断点回归在阈值之外的识别与估计方法。我们的识别策略利用了除运行变量（running variable）之外的因变量预测因子；在控制这些预测因子的条件下，可假定运行变量满足可忽略性。本识别策略被用于探究波士顿选拔性中学对边际外申请者的影响。基于本文框架所设定的条件独立性假设得到的识别结果，可生成精度尚可且稳健性出人意料的选拔性中学就读对边际外申请者的效应估计值。这些估计结果显示，对于运行变量取值远离录取分数线的九年级申请者而言，选拔性中学就读的因果效应与处于录取边际的申请者的效应差异极小。本文还将该策略拓展至模糊断点设计（fuzzy designs），可实现对阈值之外的依从者（compliers）的因果效应识别。本文的补充材料可在线获取。