Boundary Discontinuity Designs: Theory and Practice

TL;DR

Boundary Discontinuity Designs are a versatile non-experimental approach for causal inference using threshold-based rules in multidimensional settings, with extensive empirical and theoretical research guiding their application.

Contribution

This paper synthesizes over 80 empirical applications of BD design, reviews ongoing theoretical developments, and provides practical recommendations for researchers.

Findings

BD design extends regression discontinuity to multidimensional scores

Empirical applications span various fields and demonstrate the method's versatility

Theoretical research advances identification, estimation, and inference techniques

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.