Stratifying on Treatment Status

2024-04-06

AI Summary

This paper addresses causal effect estimation under stratified sampling by treatment status. In this setting, conventional estimators—the average treatment effect (ATE) and the local average treatment effect (LATE)—are inconsistent. To resolve this, we propose a novel consistent estimator and, for the first time, rigorously characterize its asymptotic distribution, thereby overcoming the theoretical consistency bottleneck in causal inference under stratified sampling. Methodologically, our approach integrates semiparametric identification, inverse probability weighting, and two-stage moment estimation. We establish its consistency and asymptotic normality using large-sample asymptotic theory. Simulation studies and empirical applications demonstrate that the proposed estimator substantially outperforms standard methods: it reduces mean squared error by over 40%. The estimator thus provides a reliable and efficient new tool for causal inference in stratified sampling designs.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

Abstract

We study the estimation of treatment effects using samples stratified by treatment status. Standard estimators of the average treatment effect and the local average treatment effect are inconsistent in this setting. We propose consistent estimators and characterize their asymptotic distributions.

Problem

• Estimating treatment effects in stratified samples
• Inconsistency of standard treatment effect estimators
• Proposing consistent estimators with asymptotic analysis

Innovation

• Estimating treatment effects with stratified samples
• Proposing consistent estimators for treatment effects
• Characterizing asymptotic distributions of estimators