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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.
    5. Thomas Barrios & Rebecca Diamond & Guido W. Imbens & Michal Kolesár, 2012. "Clustering, Spatial Correlations, and Randomization Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 578-591, June.
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    Citations

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    Cited by:

    1. Rajeev Dehejia & Cristian Pop-Eleches & Cyrus Samii, 2015. "From Local to Global: External Validity in a Fertility Natural Experiment," NBER Working Papers 21459, National Bureau of Economic Research, Inc.
    2. Olympia Bover & Jose Maria Casado & Sonia Costa & Philip Du Caju & Yvonne McCarthy & Eva Sierminska & Panagiota Tzamourani & Ernesto Villanueva & Tibor Zavadil, 2016. "The Distribution of Debt across Euro-Area Countries: The Role of Individual Characteristics, Institutions, and Credit Conditions," International Journal of Central Banking, International Journal of Central Banking, vol. 12(2), pages 71-128, June.
    3. 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.
    4. Abadie, Alberto & Athey, Susan & Imbens, Guido W. & Wooldridge, Jeffrey M., 2017. "Sampling-Based vs. Design-Based Uncertainty in Regression Analysis," Research Papers 3349, Stanford University, Graduate School of Business.
    5. Philip ME Garboden, 2019. "Sources and Types of Big Data for Macroeconomic Forecasting," Working Papers 2019-3, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    6. Paul Frijters & Benno Torgler & Christian Gillitzer & Jin Cong Wang, 2016. "Housing Wealth Effects: Cross-sectional Evidence from New Vehicle Registrations," The Economic Record, The Economic Society of Australia, vol. 92, pages 30-51, June.
    7. Cai, Hongbin & Chen, Yuyu & Gong, Qing, 2016. "Polluting thy neighbor: Unintended consequences of China׳s pollution reduction mandates," Journal of Environmental Economics and Management, Elsevier, vol. 76(C), pages 86-104.
    8. Victor Chernozhukov & Ivan Fernandez-Val & Martin Weidner, 2018. "Network and panel quantile effects via distribution regression," CeMMAP working papers CWP21/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Atila Abdulkadiroğlu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2017. "Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation," Econometrica, Econometric Society, vol. 85, pages 1373-1432, September.
    10. 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.
    11. Peter Ganong & Simon Jäger, 2018. "A Permutation Test for the Regression Kink Design," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 494-504, April.
    12. repec:hrv:faseco:34222894 is not listed on IDEAS
    13. 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.

    More about this item

    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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