Boundary discontinuity designs are used to learn about causal treatment effects along a continuous assignment boundary that splits units into control and treatment groups according to a bivariate location score. We analyze location-based local polynomial treatment effect estimators that directly employ the bivariate score of each unit. We develop pointwise and uniform estimation and inference methods for the \textit{Boundary Average Treatment Effect Curve} (BATEC), as well as for two aggregated causal parameters: the \textit{Weighted Boundary Average Treatment Effect} (WBATE) and the \textit{Largest Boundary Average Treatment Effect} (LBATE). Our results cover both sharp and fuzzy (imperfect compliance) designs. We illustrate the methods with an empirical application, and provide companion general-purpose software. The supplemental appendix includes additional substantive theoretical results, methodological details, and simulation evidence.

翻译：边界断点设计用于学习沿着一条连续分配边界上的因果处理效应，该边界根据双变量位置得分将单位划分为控制组和处理组。我们分析了直接利用每个单位双变量得分的基于位置局部多项式处理效应估计量。我们为“边界平均处理效应曲线”（BATEC）以及两个聚合因果参数——即“加权边界平均处理效应”（WBATE）和“最大边界平均处理效应”（LBATE）——开发了点态与一致的估计与推断方法。我们的结果涵盖精确设计（sharp）和模糊设计（fuzzy，即不完全依从）两种情况。我们通过实证应用展示了这些方法，并提供了配套的通用软件。补充附录包含额外的实质性理论结果、方法学细节以及模拟证据。