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At What Level Should One Cluster Standard Errors in Paired and Small-Strata Experiments?

Author

Listed:
  • Clément de Chaisemartin

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Jaime Ramirez-Cuellar

    (Microsoft - Microsoft Research [Cambridge] - Microsoft Research)

Abstract

In clustered and paired experiments, to estimate treatment effects, researchers often regress their outcome on the treatment and pair fixed effects, clustering standard errors at the unit-ofrandomization level. We show that even if the treatment has no effect, a 5%-level t-test based on this regression will wrongly conclude that the treatment has an effect up to 16.5% of the time, an error rate much larger than the researcher's 5% target. To achieve their targeted error rate, researchers should instead cluster standard errors at the pair level. Using simulations, we show that similar results apply to clustered experiments with small strata.

Suggested Citation

  • Clément de Chaisemartin & Jaime Ramirez-Cuellar, 2022. "At What Level Should One Cluster Standard Errors in Paired and Small-Strata Experiments?," SciencePo Working papers Main hal-03873897, HAL.
    • Handle: RePEc:hal:spmain:hal-03873897
    DOI: 10.2139/ssrn.3520820
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03873897
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    Cited by:

    1. Federico Bugni & Ivan Canay & Azeem Shaikh & Max Tabord-Meehan, 2022. "Inference for Cluster Randomized Experiments with Non-ignorable Cluster Sizes," Papers 2204.08356, arXiv.org, revised Apr 2024.
    2. Clément de Chaisemartin & Jaime Ramirez-Cuellar, 2024. "At What Level Should One Cluster Standard Errors in Paired and Small-Strata Experiments?," American Economic Journal: Applied Economics, American Economic Association, vol. 16(1), pages 193-212, January.
    3. 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.
    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. Lafortune, Jeanne & Pugatch, Todd & Tessada, José & Ubfal, Diego, 2022. "Can Interactive Online Training Make High School Students More Entrepreneurial? Experimental Evidence from Rwanda," IZA Discussion Papers 15064, Institute of Labor Economics (IZA).
    6. Ferman, Bruno & Lima, Lycia & Riva, Flávio, 2021. "Artificial Intelligence, Teacher Tasks and Individualized Pedagogy," SocArXiv qw249, Center for Open Science.
    7. Damon Jones & David Molitor & Julian Reif, 2024. "Incentives and Habit Formation in Health Screenings: Evidence from the Illinois Workplace Wellness Study," NBER Working Papers 32745, National Bureau of Economic Research, Inc.
    8. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Testing for the appropriate level of clustering in linear regression models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2027-2056.
    9. Bruno Ferman, 2019. "Assessing Inference Methods," Papers 1912.08772, arXiv.org, revised Oct 2022.
    10. Dominik Stelzeneder, 2023. "Does Schooling Affect Political Attitudes? Quasi-Experimental Evidence," Vienna Economics Papers vie2301, University of Vienna, Department of Economics.
    11. Denis Agniel & Jonathan H. Cantor & Johanna Catherine Maclean & Kosali I. Simon & Erin Taylor, 2023. "Insurance Coverage and Provision of Opioid Treatment: Evidence from Medicare," NBER Working Papers 31884, National Bureau of Economic Research, Inc.
    12. Fonseca, Julia & Matray, Adrien, 2024. "Financial inclusion, economic development, and inequality: Evidence from Brazil," Journal of Financial Economics, Elsevier, vol. 156(C).
    13. Fenoll, Ainoa Aparicio & Moscarola, Flavia Coda & Zaccagni, Sarah, 2021. "Mathematics camps: A gift for gifted students?," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 738-751.
    14. Meinzen-Dick, Laura, 2020. "Decentralization and Elections in Burkina Faso," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304447, Agricultural and Applied Economics Association.
    15. Alice Guerra & Tatyana Zhuravleva, 2022. "Do women always behave as corruption cleaners?," Public Choice, Springer, vol. 191(1), pages 173-192, April.
    16. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.
    17. 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

    Keywords

    clustered standard errors; clustering; paired experiments; stratified experiments; randomized experiments; RCT;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • O16 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Financial Markets; Saving and Capital Investment; Corporate Finance and Governance
    • O18 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Urban, Rural, Regional, and Transportation Analysis; Housing; Infrastructure

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