Boundary Discontinuity Designs: Theory and Practice

We review the literature on boundary discontinuity (BD) designs, a powerful non-experimental research methodology that identifies causal effects by exploiting a thresholding treatment assignment rule based on a bivariate score and a boundary curve. This methodology generalizes standard regression discontinuity designs based on a univariate score and scalar cutoff, and has specific challenges and features related to its multi-dimensional nature. We synthesize the empirical literature by systematically reviewing over $80$ empirical papers, tracing the method's application from its formative uses to its implementation in modern research. In addition to the empirical survey, we overview the latest methodological results on identification, estimation and inference for the analysis of BD designs, and offer recommendations for practice.