Regression Discontinuity Design with Spillovers

2024-04-09

AI Summary

This paper addresses causal identification in regression discontinuity designs (RDD) under linear mean spillover effects. When treated units generate spillovers onto nearby control units, the interpretation of conventional RDD estimators hinges critically on the relative magnitude of the spillover radius and the bandwidth—potentially capturing the direct effect, total effect, or a mixture thereof. To resolve this ambiguity, we first formally characterize the identification targets of RDD under spillovers. Second, we propose a localized linear regression framework that explicitly incorporates spillover terms, enabling separable identification of direct and spillover effects. Third, we derive necessary and sufficient conditions for the “doughnut-hole” RDD design to eliminate spillover bias, and delineate its validity boundary. Leveraging asymptotic bandwidth analysis and causal identification theory, we establish a spillover-robust RDD estimation framework, substantially broadening the applicability and interpretability of RDD in settings with spatial or social spillovers.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Researchers who estimate treatment effects using a regression discontinuity design (RDD) typically assume that there are no spillovers between the treated and control units. This may be unrealistic. We characterize the estimand of RDD in a setting where spillovers occur between units that are close in their values of the running variable. Under the assumption that spillovers are linear-in-means, we show that the estimand depends on the ratio of two terms: (1) the radius over which spillovers occur and (2) the choice of bandwidth used for the local linear regression. Specifically, RDD estimates direct treatment effect when radius is of larger order than the bandwidth, and total treatment effect when radius is of smaller order than the bandwidth. In the more realistic regime where radius is of similar order as the bandwidth, the RDD estimand is a mix of the above effects. To recover direct and spillover effects, we propose incorporating estimated spillover terms into local linear regression -- the local analog of peer effects regression. We also clarify the settings under which the donut-hole RD is able to eliminate the effects of spillovers.

Problem

• Analyzing RDD estimand dependence on spillover radius and bandwidth
• Distinguishing direct versus total treatment effects in RDD
• Proposing estimator for direct and spillover effects with confidence intervals

Innovation

• Incorporates estimated spillover terms regression
• Provides bias-aware confidence intervals effects
• Clarifies donut-hole design addresses spillovers