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Finite Population Causal Standard Errors

Author

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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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. repec:mpr:mprres:6573 is not listed on IDEAS
    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. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
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    Cited by:

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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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