Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods

TL;DR

This paper develops new estimation and inference methods for boundary discontinuity designs using location-based local polynomial estimators, applicable to sharp and fuzzy cases, with software and empirical illustration.

Contribution

It introduces pointwise and uniform methods for the Boundary Average Treatment Effect Curve and related parameters, advancing boundary discontinuity analysis.

Findings

Methods applicable to sharp and fuzzy designs.

Provides software and empirical application.

Includes theoretical, simulation, and methodological results.

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.