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On equivalencies between design-based and regression-based variance estimators for randomized experiments

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  • Samii, Cyrus
  • Aronow, Peter M.

Abstract

This paper demonstrates that the randomization-based “Neyman” and constant-effects estimators for the variance of estimated average treatment effects are equivalent to a variant of the White “heteroskedasticity-robust” estimator and the homoskedastic ordinary least squares (OLS) estimator, respectively.

Suggested Citation

  • Samii, Cyrus & Aronow, Peter M., 2012. "On equivalencies between design-based and regression-based variance estimators for randomized experiments," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 365-370.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:365-370
    DOI: 10.1016/j.spl.2011.10.024
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    References listed on IDEAS

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    1. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    2. Middleton, Joel A., 2008. "Bias of the regression estimator for experiments using clustered random assignment," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2654-2659, November.
    3. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    4. Gadbury G. L., 2001. "Randomization Inference and Bias of Standard Errors," The American Statistician, American Statistical Association, vol. 55, pages 310-313, November.
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    Citations

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    Cited by:

    1. Joel A. Middleton, 2021. "Unifying Design-based Inference: On Bounding and Estimating the Variance of any Linear Estimator in any Experimental Design," Papers 2109.09220, arXiv.org.
    2. Ding Peng & Li Xinran & Miratrix Luke W., 2017. "Bridging Finite and Super Population Causal Inference," Journal of Causal Inference, De Gruyter, vol. 5(2), pages 1-8, September.
    3. Daniel Oto-Peralías & Diego Romero-Ávila, 2016. "The economic consequences of the Spanish Reconquest: the long-term effects of Medieval conquest and colonization," Journal of Economic Growth, Springer, vol. 21(4), pages 409-464, December.
    4. Susan Athey & Guido Imbens, 2016. "The Econometrics of Randomized Experiments," Papers 1607.00698, arXiv.org.
    5. Middleton Joel A. & Aronow Peter M., 2015. "Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments," Statistics, Politics and Policy, De Gruyter, vol. 6(1-2), pages 39-75, December.
    6. Lu, Jiannan & Deng, Alex, 2017. "On randomization-based causal inference for matched-pair factorial designs," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 99-103.
    7. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2014. "Finite Population Causal Standard Errors," NBER Working Papers 20325, National Bureau of Economic Research, Inc.
    8. Eszter Czibor & David Jimenez‐Gomez & John A. List, 2019. "The Dozen Things Experimental Economists Should Do (More of)," Southern Economic Journal, John Wiley & Sons, vol. 86(2), pages 371-432, October.
    9. Abadie, Alberto & Athey, Susan & Imbens, Guido W. & Wooldridge, Jeffrey M., 2017. "Sampling-Based vs. Design-Based Uncertainty in Regression Analysis," Research Papers 3349, Stanford University, Graduate School of Business.
    10. Zach Branson & Tirthankar Dasgupta, 2020. "Sampling‐based Randomised Designs for Causal Inference under the Potential Outcomes Framework," International Statistical Review, International Statistical Institute, vol. 88(1), pages 101-121, April.
    11. Clara Bicalho & Adam Bouyamourn & Thad Dunning, 2022. "The Power of Prognosis: Improving Covariate Balance Tests with Outcome Information," Papers 2205.10478, arXiv.org, revised Oct 2025.
    12. Aronow Peter M. & Middleton Joel A., 2013. "A Class of Unbiased Estimators of the Average Treatment Effect in Randomized Experiments," Journal of Causal Inference, De Gruyter, vol. 1(1), pages 135-154, June.
    13. Lu, Jiannan, 2016. "On randomization-based and regression-based inferences for 2K factorial designs," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 72-78.
    14. Haoge Chang & Joel Middleton & P. M. Aronow, 2021. "Exact Bias Correction for Linear Adjustment of Randomized Controlled Trials," Papers 2110.08425, arXiv.org, revised Oct 2021.

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