Boundary Discontinuity Designs: Theory and Practice
Matias D. Cattaneo, Rocio Titiunik, Ruiqi Rae Yu
TL;DR
The Boundary Discontinuity design extends the regression discontinuity framework to a two-dimensional score by leveraging a boundary curve to separate treatment from control, yielding rich identification and inference challenges tied to boundary geometry. The authors synthesize the BD literature, contrasting pooling-based methods that generate a boundary-wide average effect with boundary-point estimators that recover a boundary-wise effect curve, $\tau(\mathbf{x})$, along $\mathcal{B}$. They summarize recent theoretical advances that formalize identification, estimation, and inference for pooling (via tubular neighborhoods) and for distance- and location-based heterogeneity analyses (via BATEC, WBATE, and LBATE), and provide practical recommendations and software tools (rdrobust, rdmulti, rd2d) to implement robust, bias-corrected inference. The work highlights the importance of boundary geometry, suggests robust bias-corrected, interaction-inclusive specifications, and advocates focusing on the richer boundary-level heterogeneity to inform policy decisions and future methodological development.
Abstract
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.