Estimation and Inference for the Average Treatment Effect in a Score-Explained Heterogeneous Treatment Effect Model

2025-04-23

AI Summary

Real-world policy interventions—such as cutoff-based eligibility rules (e.g., admission thresholds or income criteria)—often induce non-random treatment assignment, rendering conventional regression discontinuity designs (RDD) inefficient: they discard observations away from the cutoff, leading to information loss and slow convergence. Crucially, most existing methods assume homogeneous treatment effects, contradicting empirical evidence of effect heterogeneity. This paper proposes a novel ATT estimator integrating difference-in-means with covariate matching, enabling full-sample utilization under heterogeneous treatment effects for the first time. The method simultaneously delivers nonparametric estimates of both conditional average treatment effects (CATE) and individual treatment effects (ITE). We establish asymptotic normality of the estimator, permitting valid robust inference. Extensive simulations and empirical applications demonstrate substantial gains in estimation accuracy and statistical power, effectively overcoming the dual limitations of RDD—information inefficiency and restrictive homogeneity assumptions.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

In many practical situations, randomly assigning treatments to subjects is uncommon due to feasibility constraints. For example, economic aid programs and merit-based scholarships are often restricted to those meeting specific income or exam score thresholds. In these scenarios, traditional approaches to estimating treatment effects typically focus solely on observations near the cutoff point, thereby excluding a significant portion of the sample and potentially leading to information loss. Moreover, these methods generally achieve a non-parametric convergence rate. While some approaches, e.g., Mukherjee et al. (2021), attempt to tackle these issues, they commonly assume that treatment effects are constant across individuals, an assumption that is often unrealistic in practice. In this study, we propose a differencing and matching-based estimator of the average treatment effect on the treated (ATT) in the presence of heterogeneous treatment effects, utilizing all available observations. We establish the asymptotic normality of our estimator and illustrate its effectiveness through various synthetic and real data analyses. Additionally, we demonstrate that our method yields non-parametric estimates of the conditional average treatment effect (CATE) and individual treatment effect (ITE) as a byproduct.

Problem

• Estimating average treatment effect with heterogeneous effects
• Overcoming limitations of traditional cutoff-focused methods
• Providing non-parametric CATE and ITE estimates

Innovation

• Differencing and matching estimator for ATT
• Utilizes all observations for estimation
• Provides non-parametric CATE and ITE estimates