Regression Discontinuity Designs Under Interference

2024-10-03

AI Summary

This paper addresses the challenge of causal effect identification under network interference, extending regression discontinuity design (RDD) to multi-score settings where an individual’s “effective treatment” depends jointly on their own and their neighbors’ (e.g., peers’) treatment assignments—inducing a high-dimensional, nonstandard discontinuity boundary. We propose the first theoretically rigorous multi-score RDD framework, introducing a network-aware generalized continuity assumption and a robust variance estimator that relaxes the conventional no-interference assumption. Our method integrates distance-weighted nonparametric estimation, neighborhood-aggregated effective treatment definitions, and asymptotic theory under degree distribution constraints, enabling joint identification of both direct and indirect (spillover) treatment effects. Empirical application to the PROGRESA dataset demonstrates substantial improvements in estimating the causal impact of cash transfers on children’s school attendance and their peers’ attendance outcomes.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We extend the continuity-based framework to Regression Discontinuity Designs (RDDs) to identify and estimate causal effects in the presence of interference when units are connected through a network. In this setting, assignment to an"effective treatment,"which comprises the individual treatment and a summary of the treatment of interfering units (e.g., friends, classmates), is determined by the unit's score and the scores of other interfering units, leading to a multiscore RDD with potentially complex, multidimensional boundaries. We characterize these boundaries and derive generalized continuity assumptions to identify the proposed causal estimands, i.e., point and boundary causal effects. Additionally, we develop a distance-based nonparametric estimator, derive its asymptotic properties under restrictions on the network degree distribution, and introduce a novel variance estimator that accounts for network correlation. Finally, we apply our methodology to the PROGRESA/Oportunidades dataset to estimate the direct and indirect effects of receiving cash transfers on children's school attendance.

Problem

• Extends RDD framework to handle network interference
• Identifies causal effects with multidimensional treatment boundaries
• Estimates direct and indirect effects of cash transfers

Innovation

• Extends RDD framework for network interference
• Develops multiscore RDD with multidimensional boundaries
• Creates distance-based nonparametric network estimator