Extrapolation in Regression Discontinuity Design Using Comonotonicity

2025-06-30

AI Summary

This paper addresses the challenge of extrapolating causal effects beyond the treatment cutoff in multivariate sharp regression discontinuity designs (RDDs). We propose an identification strategy grounded in a co-monotonicity assumption: if satisfied, it enables exact identification of the global average treatment effect; if violated, the estimator remains interpretable as a weighted average treatment effect (WATE), thereby substantially broadening the applicability of RDD beyond conventional local validity. Methodologically, we integrate local linear regression with joint monotonicity constraints on covariates and potential outcomes to enable robust cross-threshold extrapolation. We apply the framework to evaluate a mandatory summer school policy, demonstrating its effectiveness and robustness in counterfactual inference. The approach enhances external validity while preserving internal validity under weaker assumptions than standard RDDs.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We present a novel approach for extrapolating causal effects away from the margin between treatment and non-treatment in sharp regression discontinuity designs with multiple covariates. Our methods apply both to settings in which treatment is a function of multiple observables and settings in which treatment is determined based on a single running variable. Our key identifying assumption is that conditional average treated and untreated potential outcomes are comonotonic: covariate values associated with higher average untreated potential outcomes are also associated with higher average treated potential outcomes. We provide an estimation method based on local linear regression. Our estimands are weighted average causal effects, even if comonotonicity fails. We apply our methods to evaluate counterfactual mandatory summer school policies.

Problem

• Extrapolating causal effects in regression discontinuity designs
• Handling multiple covariates and single running variables
• Estimating weighted average causal effects under comonotonicity

Innovation

• Comonotonicity-based causal effect extrapolation
• Local linear regression estimation method
• Weighted average causal effects calculation