The boundary discontinuity (BD) design is a non-experimental method for identifying causal effects that exploits a thresholding rule based on a bivariate score and a boundary curve. This widely used method generalizes the univariate regression discontinuity design but introduces unique challenges arising from its multidimensional nature. We synthesize over 80 empirical papers that use the BD design, tracing the method's application from its formative stages to its implementation in modern research. We also overview ongoing theoretical and methodological research on identification, estimation, and inference for BD designs employing local polynomial regression, and offer recommendations for practice.

翻译：边界断点（BD）设计是一种基于二元评分与边界曲线的阈值规则来识别因果效应的非实验方法。这一广泛应用的方法推广了单变量断点回归设计，但也因其多维特性引入了独特的挑战。我们综合分析了80余篇采用BD设计的实证论文，追溯了该方法从形成阶段到现代研究中的应用历程。同时，我们概述了当前关于采用局部多项式回归的BD设计在识别、估计与推断方面的理论与方法学研究，并为实践应用提供了建议。