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Potential outcomes and finite-population inference for M-estimators

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  • Ruonan Xu

Abstract

SummaryWhen a sample is drawn from or coincides with a finite population, the uncertainty of the coefficient estimators is often reported assuming the population is effectively infinite. The recent literature on finite-population inference instead derives an alternative asymptotic variance of the ordinary least squares estimator. Here, I extend the results to the more general setting of M-estimators and also find that the usual robust ‘sandwich’ estimator is conservative. The proposed asymptotic variance of M-estimators accounts for two sources of variation. In addition to the usual sampling-based uncertainty arising from (possibly) not observing the entire population, there is also design-based uncertainty, which is usually ignored in the common inference method, resulting from lack of knowledge of the counterfactuals. Under this alternative framework, we can obtain smaller standard errors of M-estimators when the population is treated as finite.

Suggested Citation

  • Ruonan Xu, 2021. "Potential outcomes and finite-population inference for M-estimators," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 162-176.
    • Handle: RePEc:oup:emjrnl:v:24:y:2021:i:1:p:162-176.
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    File URL: http://hdl.handle.net/10.1093/ectj/utaa022
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    Cited by:

    1. Wooldridge, Jeffrey M., 2023. "What is a standard error? (And how should we compute it?)," Journal of Econometrics, Elsevier, vol. 237(2).
    2. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.
    3. Griffith, Alan & Noonen, Thomas, 2022. "The effects of public campaign funding: Evidence from Seattle’s Democracy Voucher program," Journal of Public Economics, Elsevier, vol. 211(C).

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