Boundary Discontinuity Designs: Theory and Practice

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.