The Exact Variance of the Average Treatment Effect Estimator in Cluster Randomized Controlled Trials

Fuente: arXiv
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Main Authors: Fang, Yue, Ridder, Geert
Format: Preprint
Published: 2025
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author Fang, Yue
Ridder, Geert
author_facet Fang, Yue
Ridder, Geert
contents In cluster randomized controlled trials (CRCT) with a finite populations, the exact design-based variance of the Horvitz-Thompson (HT) estimator for the average treatment effect (ATE) depends on the joint distribution of unobserved cluster-aggregated potential outcomes and is therefore not point-identifiable. We study a common two-stage sampling design-random sampling of clusters followed by sampling units within sampled clusters-with treatment assigned at the cluster level. First, we derive the exact (infeasible) design-based variance of the HT ATE estimator that accounts jointly for cluster- and unit-level sampling as well as random assignment. Second, extending Aronow et al (2014), we provide a sharp, attanable upper bound on that variance and propose a consistent estimator of the bound using only observed outcomes and known sampling/assignment probabilities. In simulations and an empirical application, confidence intervals based on our bound are valid and typically narrower than those based on cluster standard errors.
format Preprint
id arxiv_https___arxiv_org_abs_2511_05801
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Exact Variance of the Average Treatment Effect Estimator in Cluster Randomized Controlled Trials
Fang, Yue
Ridder, Geert
Econometrics
In cluster randomized controlled trials (CRCT) with a finite populations, the exact design-based variance of the Horvitz-Thompson (HT) estimator for the average treatment effect (ATE) depends on the joint distribution of unobserved cluster-aggregated potential outcomes and is therefore not point-identifiable. We study a common two-stage sampling design-random sampling of clusters followed by sampling units within sampled clusters-with treatment assigned at the cluster level. First, we derive the exact (infeasible) design-based variance of the HT ATE estimator that accounts jointly for cluster- and unit-level sampling as well as random assignment. Second, extending Aronow et al (2014), we provide a sharp, attanable upper bound on that variance and propose a consistent estimator of the bound using only observed outcomes and known sampling/assignment probabilities. In simulations and an empirical application, confidence intervals based on our bound are valid and typically narrower than those based on cluster standard errors.
title The Exact Variance of the Average Treatment Effect Estimator in Cluster Randomized Controlled Trials
topic Econometrics
url https://arxiv.org/abs/2511.05801