The Exact Variance of the Average Treatment Effect Estimator in Cluster Randomized Controlled Trials
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| Format: | Preprint |
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2025
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| _version_ | 1866917148128968704 |
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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 |