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

Joel A. Middleton

Papers from arXiv.org

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.

Date: 2021-09
New Economics Papers: this item is included in nep-ecm, nep-exp and nep-isf
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Citations: View citations in EconPapers (1)

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