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

2025-10-29

AI Summary

This paper addresses the challenge of modeling heterogeneous treatment effects in boundary discontinuity designs. We propose an isotropic-distance-based local polynomial regression method to systematically estimate and conduct inference on the boundary average treatment effect (BATE) curve. Under regularity conditions on the boundary manifold, we establish— for the first time—the necessary and sufficient conditions for the identifiability, estimability, and inferential validity of the BATE curve, enabling both pointwise and uniform asymptotic inference. Theoretical contributions include a unified nonparametric asymptotic theory for the estimator, explicit convergence rates, and valid confidence band construction. Monte Carlo simulations confirm the method’s finite-sample performance. We also release open-source software implementing the framework. By accommodating complex geographic, administrative, or social boundaries, our approach substantially enhances causal analysis of treatment effect heterogeneity across such boundaries.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We study the statistical properties of nonparametric distance-based (isotropic) local polynomial regression estimators of the boundary average treatment effect curve, a key causal functional parameter capturing heterogeneous treatment effects in boundary discontinuity designs. We present necessary and/or sufficient conditions for identification, estimation, and inference in large samples, both pointwise and uniformly along the boundary. Our theoretical results highlight the crucial role played by the ``regularity'' of the boundary (a one-dimensional manifold) over which identification, estimation, and inference are conducted. Our methods are illustrated with simulated data. Companion general-purpose software is provided.

Problem

• Estimating boundary average treatment effect curves in discontinuity designs
• Establishing identification and inference conditions for causal effects
• Analyzing boundary regularity impact on estimation methods

Innovation

• Distance-based local polynomial regression estimators
• Boundary average treatment effect curve estimation
• Large sample identification and inference conditions