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Optimality of Matched-Pair Designs in Randomized Controlled Trials

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  • Yuehao Bai

Abstract

In randomized controlled trials, treatment is often assigned by stratified randomization. I show that among all stratified randomization schemes that treat all units with probability one half, a certain matched-pair design achieves the maximum statistical precision for estimating the average treatment effect. In an important special case, the optimal design pairs units according to the baseline outcome. In a simulation study based on datasets from ten randomized controlled trials, this design lowers the standard error for the estimator of the average treatment effect by 10 percent on average, and by up to 34 percent, relative to the original designs.

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  • Yuehao Bai, 2022. "Optimality of Matched-Pair Designs in Randomized Controlled Trials," American Economic Review, American Economic Association, vol. 112(12), pages 3911-3940, December.
    • Handle: RePEc:aea:aecrev:v:112:y:2022:i:12:p:3911-40
    DOI: 10.1257/aer.20201856
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    Cited by:

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    3. George Gui & Seungwoo Kim, 2025. "Leveraging LLMs to Improve Experimental Design: A Generative Stratification Approach," Papers 2509.25709, arXiv.org.
    4. Yuehao Bai & Meng Hsuan Hsieh & Jizhou Liu & Max Tabord-Meehan, 2022. "Revisiting the Analysis of Matched-Pair and Stratified Experiments in the Presence of Attrition," Papers 2209.11840, arXiv.org, revised Oct 2023.
    5. Jiang, Liang & Phillips, Peter C.B. & Tao, Yubo & Zhang, Yichong, 2023. "Regression-adjusted estimation of quantile treatment effects under covariate-adaptive randomizations," Journal of Econometrics, Elsevier, vol. 234(2), pages 758-776.
    6. Laurent Davezies & Guillaume Hollard & Pedro Vergara Merino, 2024. "Revisiting Randomization with the Cube Method," Papers 2407.13613, arXiv.org, revised Jul 2025.
    7. Jinglong Zhao, 2023. "Adaptive Neyman Allocation," Papers 2309.08808, arXiv.org, revised Sep 2025.
    8. Yuehao Bai & Jizhou Liu & Azeem M. Shaikh & Max Tabord-Meehan, 2023. "On the Efficiency of Finely Stratified Experiments," Papers 2307.15181, arXiv.org, revised Nov 2025.
    9. Guillermo Cruces & Dario Tortarolo & Gonzalo Vazquez-Bare, 2022. "Design of two-stage experiments with an application to spillovers in tax compliance," IFS Working Papers W22/32, Institute for Fiscal Studies.
    10. Bugni, Federico A. & Gao, Mengsi, 2023. "Inference under covariate-adaptive randomization with imperfect compliance," Journal of Econometrics, Elsevier, vol. 237(1).
    11. Cai, Yong & Rafi, Ahnaf, 2024. "On the performance of the Neyman Allocation with small pilots," Journal of Econometrics, Elsevier, vol. 242(1).
    12. Max Cytrynbaum, 2024. "Finely Stratified Rerandomization Designs," Papers 2407.03279, arXiv.org, revised Jan 2025.
    13. Jinglong Zhao, 2024. "Experimental Design For Causal Inference Through An Optimization Lens," Papers 2408.09607, arXiv.org, revised Aug 2024.
    14. Bai, Yuehao & Liu, Jizhou & Shaikh, Azeem M. & Tabord-Meehan, Max, 2024. "Inference in cluster randomized trials with matched pairs," Journal of Econometrics, Elsevier, vol. 245(1).
    15. Yuehao Bai & Azeem M. Shaikh & Max Tabord-Meehan, 2024. "A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances," Papers 2405.03910, arXiv.org, revised Apr 2025.
    16. Yuehao Bai & Xun Huang & Joseph P. Romano & Azeem M. Shaikh & Max Tabord-Meehan, 2025. "A New Design-Based Variance Estimator for Finely Stratified Experiments," Papers 2503.10851, arXiv.org, revised May 2025.
    17. Jizhou Liu, 2023. "Inference for Two-stage Experiments under Covariate-Adaptive Randomization," Papers 2301.09016, arXiv.org, revised Oct 2024.
    18. James J. Heckman & Jin Zhou, 2025. "A Study of the Microdynamics of Early Childhood Learning," NBER Working Papers 34294, National Bureau of Economic Research, Inc.
    19. Yuehao Bai & Meng Hsuan Hsieh & Jizhou Liu & Max Tabord‐Meehan, 2024. "Revisiting the analysis of matched‐pair and stratified experiments in the presence of attrition," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(2), pages 256-268, March.
    20. Yuehao Bai & Jizhou Liu & Max Tabord‐Meehan, 2024. "Inference for matched tuples and fully blocked factorial designs," Quantitative Economics, Econometric Society, vol. 15(2), pages 279-330, May.
    21. Yuehao Bai & Jizhou Liu & Max Tabord-Meehan, 2022. "Inference for Matched Tuples and Fully Blocked Factorial Designs," Papers 2206.04157, arXiv.org, revised Nov 2023.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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