Yuehao Bai, Xun Huang, Joseph P. Romano, Azeem M. Shaikh, Max Tabord-Meehan
arXiv 10 Aug 2026 · Econometrics
arXiv:2608.10177 · PDF · Extracted main text
This paper considers design-based inference on the average treatment effect in finely stratified experiments, where uncertainty arises only from the randomized treatment assignment. We focus on settings in which units are first stratified into groups of fixed size according to baseline covariates and, then within each group, exactly one unit is assigned to treatment. In this setting, we introduce a class of graph-Laplacian variance estimators in which strata form the vertices of a weighted graph and edge weights determine how between-stratum comparisons are aggregated. The canonical estimator of Imai (2008) corresponds to a complete graph with edge weights normalized so that each stratum has weighted degree one, while a paired-stratum estimator arises from a perfect matching graph. For the subclass of degree-calibrated graphs, in which each vertex has weighted degree one, we derive an exact bias identity showing that the corresponding estimators are upward-biased, with bias governed by squared differences in the true stratum-level treatment effects across adjacent strata. As a result, any such estimator may be used for valid inference. The identity further suggests that paired-stratum estimators constructed from a covariate-based perfect matching can induce small biases when treatment effects vary smoothly with the covariates. Without such smoothness, however, we show that paired-stratum estimators can exhibit large worst-case bias, and that, within the class of degree-calibrated estimators, the complete-graph estimator is minimax optimal for normalized bias under a weak bound on treatment-effect heterogeneity. Motivated by this contrast, we propose a regularized graph estimator that controls worst-case normalized bias while preserving much of the locality of the paired-stratum estimator. Simulations illustrate the resulting tradeoff between locality and worst-case protection.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Imai, Kosuke (2008) Variance identification and efficiency analysis in randomized experiments under the matched-pair design | 0.928 | 4 | 3 | 100% |
| 2 | Cytrynbaum, Max (2024) Optimal stratification of survey experiments | 0.843 | 5 | 3 | 60% |
| 3 | De Chaisemartin, Clément and Ramirez-Cuellar, Jaime (2024) At what level should one cluster standard errors in paired and small-strata experiments? | 0.843 | 3 | 3 | 100% |
| 4 | Fogarty, Colin B (2018) On mitigating the analytical limitations of finely stratified experiments | 0.822 | 9 | 4 | 56% |
| 5 | Pashley, Nicole E and Miratrix, Luke W (2021) Insights on variance estimation for blocked and matched pairs designs | 0.811 | 4 | 2 | 100% |
| 6 | Bai, Yuehao and Romano, Joseph P. and Shaikh, Azeem M (2022) Inference in Experiments With Matched Pairs self | 0.737 | 3 | 2 | 100% |
| 7 | Bai, Yuehao and Liu, Jizhou and Tabord-Meehan, Max (2024) Inference for Matched Tuples and Fully Blocked Factorial Designs self | 0.737 | 3 | 2 | 100% |
| 8 | Abadie, Alberto and Imbens, Guido W (2008) Estimation of the Conditional Variance in Paired Experiments | 0.644 | 2 | 2 | 100% |
| 9 | Imai, Kosuke and King, Gary and Nall, Clayton (2009) The Essential Role of Pair Matching in Cluster-Randomized Experiments, with Application to the Mexican Universal Health Insuranc… | 0.644 | 2 | 2 | 100% |
| 10 | Zhu, Ke and Liu, Hanzhong and Yang, Yuehan (2024) Design-Based Theory for Lasso Adjustment in Randomized Block Experiments and Rerandomized Experiments | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 35 scored citations.