Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods
Abstract
Boundary discontinuity designs are used to learn about causal treatment effects along a continuous assignment boundary that splits units into control and treatment groups according to a bivariate location score. We analyze location-based local polynomial treatment effect estimators that directly employ the bivariate score of each unit. We develop pointwise and uniform estimation and inference methods for the \textit{Boundary Average Treatment Effect Curve} (BATEC), as well as for two aggregated causal parameters: the \textit{Weighted Boundary Average Treatment Effect} (WBATE) and the \textit{Largest Boundary Average Treatment Effect} (LBATE). Our results cover both sharp and fuzzy (imperfect compliance) designs. We illustrate the methods with an empirical application, and provide companion general-purpose software. The supplemental appendix includes additional substantive theoretical results, methodological details, and simulation evidence.
Cite
@article{arxiv.2505.05670,
title = {Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods},
author = {Matias D. Cattaneo and Rocio Titiunik and Ruiqi Rae Yu},
journal= {arXiv preprint arXiv:2505.05670},
year = {2026}
}