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The variance of regression coefficients when the population is finite

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  • Startz, Richard
  • Steigerwald, Douglas G.

Abstract

Recent work has returned attention to the role of finite-population corrections in empirical settings. It is well established that if the only source of variation arises from the sampling design, then the asymptotic variance of regression estimators must include the proportion of the finite population that is sampled. If there is, in addition, a random shock to each element of the finite population, then it is commonly observed that the resulting super-population renders the finite-population correction moot. We explore this setting and find that this common observation does not fully capture the richness of the result. The fraction of the finite population that is sampled defines bounds on the variance of regression estimators. Ignoring the finite-population correction yields the upper bound, which can be quite conservative.

Suggested Citation

  • Startz, Richard & Steigerwald, Douglas G., 2024. "The variance of regression coefficients when the population is finite," Journal of Econometrics, Elsevier, vol. 240(1).
    • Handle: RePEc:eee:econom:v:240:y:2024:i:1:s0304407624000277
    DOI: 10.1016/j.jeconom.2024.105681
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    References listed on IDEAS

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    1. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2020. "Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis," Econometrica, Econometric Society, vol. 88(1), pages 265-296, January.
    2. 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.
    3. Alberto Abadie & Susan Athey & Guido W Imbens & Jeffrey M Wooldridge, 2023. "When Should You Adjust Standard Errors for Clustering?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(1), pages 1-35.
    4. Charles F. Manski & John V. Pepper, 2018. "How Do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity Using Bounded-Variation Assumptions," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 232-244, May.
    5. Richard Startz & Douglas G. Steigerwald, 2023. "Inference and extrapolation in finite populations with special attention to clustering," Econometric Reviews, Taylor & Francis Journals, vol. 42(4), pages 343-357, April.
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    More about this item

    Keywords

    Finite population; Potential outcomes; Variance estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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