arXiv 8 Nov 2025 · Econometrics
arXiv:2511.05801 · PDF · DOI · OpenAlex · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Abadie, Alberto and Athey, Susan and Imbens, Guido W and Wooldridge,… (2023) When should you adjust standard errors for clustering? | 1.000 | 10 | 3 | 100% |
| 2 | Su, Fangzhou and Ding, Peng (2021) Model-assisted analyses of cluster-randomized experiments | 0.950 | 7 | 4 | 86% |
| 3 | Aronow, Peter M and Green, Donald P and Lee, Donald KK (2014) SHARP BOUNDS ON THE VARIANCE IN RANDOMIZED EXPERIMENTS | 0.935 | 11 | 6 | 82% |
| 4 | Chauvet, Guillaume and Vallée, Audrey-Anne (2020) Inference for two-stage sampling designs | 0.928 | 5 | 4 | 80% |
| 5 | Dhar, Diva and Jain, Tarun and Jayachandran, Seema (2022) Reshaping adolescents' gender attitudes: Evidence from a school-based experiment in India | 0.928 | 4 | 3 | 100% |
| 6 | Ohlsson, Esbjörn (1989) Asymptotic normality for two-stage sampling from a finite population | 0.843 | 4 | 3 | 75% |
| 7 | Abadie, Alberto and Athey, Susan and Imbens, Guido W and Wooldridge,… (2020) Sampling-based versus design-based uncertainty in regression analysis | 0.644 | 4 | 1 | 100% |
| 8 | Li, Xinran and Ding, Peng (2017) General forms of finite population central limit theorems with applications to causal inference | 0.644 | 3 | 2 | 67% |
| 9 | Middleton, Joel A and Aronow, Peter M (2015) Unbiased estimation of the average treatment effect in cluster-randomized experiments | 0.644 | 2 | 2 | 100% |
| 10 | Attanasio, Orazio and Cattan, Sarah and Fitzsimons, Emla and Meghir,… (2020) Estimating the production function for human capital: results from a randomized controlled trial in Colombia | 0.405 | 1 | 1 | 100% |
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