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

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.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-11-08

• Fields of study

  Economics

• Identifiers
  arXiv 2511.05801
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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