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Inference on finite-population treatment effects under limited overlap

Author

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  • Han Hong
  • Michael P Leung
  • Jessie Li

Abstract

SummaryThis paper studies inference on finite-population average and local average treatment effects under limited overlap, meaning that some strata have a small proportion of treated or untreated units. We model limited overlap in an asymptotic framework, sending the propensity score to zero (or one) with the sample size. We derive the asymptotic distribution of analogue estimators of the treatment effects under two common randomization schemes: conditionally independent and stratified block randomization. Under either scheme, the limit distribution is the same and conventional standard error formulas remain asymptotically valid, but the rate of convergence is slower the faster the propensity score degenerates. The practical import of these results is two-fold. When overlap is limited, standard methods can perform poorly in smaller samples, as asymptotic approximations are inadequate owing to the slower rate of convergence. However, in larger samples, standard methods can work quite well even when the propensity score is small.

Suggested Citation

  • Han Hong & Michael P Leung & Jessie Li, 2020. "Inference on finite-population treatment effects under limited overlap," The Econometrics Journal, Royal Economic Society, vol. 23(1), pages 32-47.
    • Handle: RePEc:oup:emjrnl:v:23:y:2020:i:1:p:32-47.
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    File URL: http://hdl.handle.net/10.1093/ectj/utz017
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    Citations

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    Cited by:

    1. Chen, Xiaohong & Liu, Ying & Ma, Shujie & Zhang, Zheng, 2024. "Causal inference of general treatment effects using neural networks with a diverging number of confounders," Journal of Econometrics, Elsevier, vol. 238(1).
    2. George Gui & Harikesh Nair & Fengshi Niu, 2021. "Auction Throttling and Causal Inference of Online Advertising Effects," Papers 2112.15155, arXiv.org, revised Feb 2022.
    3. Pengzhou Wu & Kenji Fukumizu, 2021. "$\beta$-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap," Papers 2110.05225, arXiv.org.
    4. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    5. Phillip Heiler & Michael C. Knaus, 2021. "Effect or Treatment Heterogeneity? Policy Evaluation with Aggregated and Disaggregated Treatments," Papers 2110.01427, arXiv.org, revised Aug 2023.

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