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Bridging Finite and Super Population Causal Inference

Author

Listed:
  • 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)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:causin:v:5:y:2017:i:2:p:8:n:7
    DOI: 10.1515/jci-2016-0027
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    References listed on IDEAS

    as
    1. 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.
    2. Rosenbaum, Paul R., 2010. "Design Sensitivity and Efficiency in Observational Studies," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 692-702.
    3. 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.
    4. 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.
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