Identification and Estimation in Fuzzy Regression Discontinuity Designs with Covariates

2026-02-01

AI Summary

This study addresses potential bias in conventional local average treatment effect (LATE) estimation under fuzzy regression discontinuity designs when compliance rates are heterogeneous and covariates influence treatment effects. To mitigate this issue, the authors propose a conditional weighted LATE (CWLATE) estimator that leverages covariate information through a Wald ratio identification strategy, weighting by the squared first-stage jump. This approach enhances estimation stability and accuracy. For discrete covariates, they develop a simple yet robust bias-corrected inference procedure. Theoretical analysis and simulation studies demonstrate that CWLATE substantially reduces mean squared error under heterogeneous compliance. Empirical application to Uruguay’s conditional cash transfer program for pregnant women yields a more precise estimate of the program’s impact on low birth weight outcomes.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study fuzzy regression discontinuity designs with covariates and characterize the weighted averages of conditional local average treatment effects (WLATEs) that are point identified. Any identified WLATE equals a Wald ratio of conditional reduced-form and first-stage discontinuities. We highlight the Compliance-Weighted LATE (CWLATE), which weights cells by squared first-stage discontinuities and maximizes first-stage strength. For discrete covariates, we provide simple estimators and robust bias-corrected inference. In simulations calibrated to common designs, CWLATE improves stability and reduces mean squared error relative to standard fuzzy RDD estimators when compliance varies. An application to Uruguayan cash transfers during pregnancy yields precise RDD-based effects on low birthweight.

Problem

• fuzzy regression discontinuity
• covariates
• local average treatment effect
• compliance
• identification

Innovation

• Fuzzy Regression Discontinuity Design
• Local Average Treatment Effect
• Compliance-Weighted LATE
• Covariate Adjustment
• Bias-Corrected Inference