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

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  • Yue Fang
  • Geert Ridder

Abstract

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.

Suggested Citation

  • Yue Fang & Geert Ridder, 2025. "The Exact Variance of the Average Treatment Effect Estimator in Cluster Randomized Controlled Trials," Papers 2511.05801, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2511.05801
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    References listed on IDEAS

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