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Unifying Design-based Inference: On Bounding and Estimating the Variance of any Linear Estimator in any Experimental Design

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  • Joel A. Middleton

Abstract

This paper provides a design-based framework for variance (bound) estimation in experimental analysis. Results are applicable to virtually any combination of experimental design, linear estimator (e.g., difference-in-means, OLS, WLS) and variance bound, allowing for unified treatment and a basis for systematic study and comparison of designs using matrix spectral analysis. A proposed variance estimator reproduces Eicker-Huber-White (aka. "robust", "heteroskedastic consistent", "sandwich", "White", "Huber-White", "HC", etc.) standard errors and "cluster-robust" standard errors as special cases. While past work has shown algebraic equivalences between design-based and the so-called "robust" standard errors under some designs, this paper motivates them for a wide array of design-estimator-bound triplets. In so doing, it provides a clearer and more general motivation for variance estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2109.09220
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    File URL: http://arxiv.org/pdf/2109.09220
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    References listed on IDEAS

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    1. Peter Z. Schochet, "undated". "Is Regression Adjustment Supported by the Neyman Model for Causal Inference? (Presentation)," Mathematica Policy Research Reports abfc39d59c714499b2fe42f68, Mathematica Policy Research.
    2. Peter Z. Schochet, "undated". "Is Regression Adjustment Supported By the Neyman Model for Causal Inference?," Mathematica Policy Research Reports 782da2242fba458eb61752f96, Mathematica Policy Research.
    3. Hansen, Ben B. & Bowers, Jake, 2009. "Attributing Effects to a Cluster-Randomized Get-Out-the-Vote Campaign," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 873-885.
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    5. 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.
    6. 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.
    7. Xinran Li & Peng Ding, 2017. "General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1759-1769, October.
    8. repec:mpr:mprres:6573 is not listed on IDEAS
    9. 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.
    10. Lu, Jiannan, 2016. "Covariate adjustment in randomization-based causal inference for 2K factorial designs," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 11-20.
    11. Arceneaux, Kevin & Nickerson, David W., 2009. "Modeling Certainty with Clustered Data: A Comparison of Methods," Political Analysis, Cambridge University Press, vol. 17(2), pages 177-190, April.
    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.
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    Cited by:

    1. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.

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