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Finite Population Causal Standard Errors

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Listed:
  • Alberto Abadie
  • Susan Athey
  • Guido W. Imbens
  • Jeffrey M. Wooldridge

Abstract

When a researcher estimates the parameters of a regression function using information on all 50 states in the United States, or information on all visits to a website, what is the interpretation of the standard errors? Researchers typically report standard errors that are designed to capture sampling variation, based on viewing the data as a random sample drawn from a large population of interest, even in applications where it is difficult to articulate what that population of interest is and how it differs from the sample. In this paper we explore alternative interpretations for the uncertainty associated with regression estimates. As a leading example we focus on the case where some parameters of the regression function are intended to capture causal effects. We derive standard errors for causal effects using a generalization of randomization inference. Intuitively, these standard errors capture the fact that even if we observe outcomes for all units in the population of interest, there are for each unit missing potential outcomes for the treatment levels the unit was not exposed to. We show that our randomization-based standard errors in general are smaller than the conventional robust standard errors, and provide conditions under which they agree with them. More generally, correct statistical inference requires precise characterizations of the population of interest, the parameters that we aim to estimate within such population, and the sampling process. Estimation of causal parameters is one example where appropriate inferential methods may differ from conventional practice, but there are others.

Suggested Citation

  • 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.
  • Handle: RePEc:nbr:nberwo:20325
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    References listed on IDEAS

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    14. 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.
    15. Bharat K. Chandar & Ali Hortaçsu & John A. List & Ian Muir & Jeffrey M. Wooldridge, 2019. "Design and Analysis of Cluster-Randomized Field Experiments in Panel Data Settings," NBER Working Papers 26389, National Bureau of Economic Research, Inc.
    16. Almond, Douglas & Sun, Yixin, 2017. "Son-biased sex ratios in 2010 US Census and 2011–2013 US natality data," Social Science & Medicine, Elsevier, vol. 176(C), pages 21-24.
    17. Ferman, Bruno, 2019. "Inference in Differences-in-Differences: How Much Should We Trust in Independent Clusters?," MPRA Paper 93746, University Library of Munich, Germany.
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    21. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
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    23. Liran Einav & Amy Finkelstein & Neale Mahoney, 2018. "Provider Incentives and Healthcare Costs: Evidence From Long‐Term Care Hospitals," Econometrica, Econometric Society, vol. 86(6), pages 2161-2219, November.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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