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Robust Inference Using Inverse Probability Weighting

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  • Xinwei Ma
  • Jingshen Wang

Abstract

Inverse probability weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of “small denominators,” trimming is routinely employed as a regularization strategy. However, ad hoc trimming of the observations renders usual inference procedures invalid for the target estimand, even in large samples. In this article, we first show that the IPW estimator can have different (Gaussian or non-Gaussian) asymptotic distributions, depending on how “close to zero” the probability weights are and on how large the trimming threshold is. As a remedy, we propose an inference procedure that is robust not only to small probability weights entering the IPW estimator but also to a wide range of trimming threshold choices, by adapting to these different asymptotic distributions. This robustness is achieved by employing resampling techniques and by correcting a non-negligible trimming bias. We also propose an easy-to-implement method for choosing the trimming threshold by minimizing an empirical analogue of the asymptotic mean squared error. In addition, we show that our inference procedure remains valid with the use of a data-driven trimming threshold. We illustrate our method by revisiting a dataset from the National Supported Work program. Supplementary materials for this article are available online.

Suggested Citation

  • Xinwei Ma & Jingshen Wang, 2020. "Robust Inference Using Inverse Probability Weighting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1851-1860, December.
  • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:532:p:1851-1860
    DOI: 10.1080/01621459.2019.1660173
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    Cited by:

    1. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised Feb 2024.
    2. 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.
    3. Yumou Qiu & Jing Tao & Xiao‐Hua Zhou, 2021. "Inference of heterogeneous treatment effects using observational data with high‐dimensional covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 1016-1043, November.
    4. Yukun Ma & Pedro H. C. Sant'Anna & Yuya Sasaki & Takuya Ura, 2023. "Doubly Robust Estimators with Weak Overlap," Papers 2304.08974, arXiv.org, revised Apr 2023.
    5. Benjamin Lu & Eli Ben-Michael & Avi Feller & Luke Miratrix, 2023. "Is It Who You Are or Where You Are? Accounting for Compositional Differences in Cross-Site Treatment Effect Variation," Journal of Educational and Behavioral Statistics, , vol. 48(4), pages 420-453, August.
    6. 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.

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