Boundary Discontinuity Designs: Theory and Practice

2025-11-09

AI Summary

Conventional univariate regression discontinuity design (RDD) struggles with multidimensional threshold-based decision rules. Method: We propose boundary discontinuity design (BD design), a novel framework focusing on treatment assignment along arbitrary boundary curves in two-dimensional score space. We develop a unified identification theory characterizing local identifiability conditions, bandwidth selection challenges, and sources of estimation bias, and integrate local polynomial estimation with robust inference procedures. Contribution/Results: Synthesizing over 80 empirical studies, we trace methodological evolution and provide the first theoretical guide and practical implementation protocol for BD design. Our approach substantially improves estimation accuracy of causal effects under multidimensional cutoffs and enhances the reliability and applicability of nonexperimental causal inference in complex policy settings—such as school district zoning and credit approval—where decisions depend on multiple criteria.

Technology Category

• Reasoning under Uncertainty: Causality
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Causal Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Generalizes regression discontinuity designs using bivariate scores and boundaries
• Addresses identification and estimation challenges in multidimensional causal inference
• Systematically reviews empirical applications and provides practical implementation guidance

Innovation

• Generalizes regression discontinuity with bivariate scoring
• Exploits threshold-based treatment assignment rules
• Addresses multi-dimensional identification and estimation challenges