Bridging Finite and Super Population Causal Inference

Ding Peng (), Li Xinran () and Miratrix Luke W. ()
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Ding Peng: Department of Statistics, University of California Berkeley, Berkeley, USA
Li Xinran: Department of Statistics, Harvard University, Cambridge, MA 02138, USA
Miratrix Luke W.: Graduate School of Education and Department of Statistics, Harvard University, Cambridge, MA 02138, USA

Journal of Causal Inference, 2017, vol. 5, issue 2, 8

Abstract: There are two general views in causal analysis of experimental data: the super population view that the units are an independent sample from some hypothetical infinite population, and the finite population view that the potential outcomes of the experimental units are fixed and the randomness comes solely from the treatment assignment. These two views differs conceptually and mathematically, resulting in different sampling variances of the usual difference-in-means estimator of the average causal effect. Practically, however, these two views result in identical variance estimators. By recalling a variance decomposition and exploiting a completeness-type argument, we establish a connection between these two views in completely randomized experiments. This alternative formulation could serve as a template for bridging finite and super population causal inference in other scenarios.

Keywords: completeness; finite population correction; potential outcomes; simple random sample; variance of individual causal effects (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:5:y:2017:i:2:p:8:n:7

DOI: 10.1515/jci-2016-0027

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