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Doubly weighted M-estimation for nonrandom assignment and missing outcomes

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  • Negi Akanksha

    (Department of Econometrics and Business Statistics, Monash University, Wellington Road, Clayton, Victoria 3800, Australia)

Abstract

This article proposes a class of M-estimators that double weight for the joint problems of nonrandom treatment assignment and missing outcomes. Identification of the main parameter of interest is achieved under unconfoundedness and missing at random assumptions with respect to the treatment and sample selection problems, respectively. Given the parametric framework, the asymptotic theory of the proposed estimator is outlined in two parts: first, when the parameter solves an unconditional problem, and second, when it solves a stronger conditional problem. The two parts help to summarize the misspecification scenarios permissible under the given framework and the role played by double weighting in each. As illustrative examples, the article also discusses the estimation of causal parameters like average and quantile treatment effects. With respect to the average treatment effect, this article shows that the proposed estimator is doubly robust. Finally, a detailed application to Calónico and Smith’s (The women of the national supported work demonstration. J Labor Econom. 2017;35(S1):S65–S97.) reconstructed sample from the National Supported Work training program is used to demonstrate the estimator’s performance in empirical settings.

Suggested Citation

  • Negi Akanksha, 2024. "Doubly weighted M-estimation for nonrandom assignment and missing outcomes," Journal of Causal Inference, De Gruyter, vol. 12(1), pages 1-25.
    • Handle: RePEc:bpj:causin:v:12:y:2024:i:1:p:25:n:1007
    DOI: 10.1515/jci-2023-0016
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    References listed on IDEAS

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    1. Hitomi, Kohtaro & Nishiyama, Yoshihiko & Okui, Ryo, 2008. "A Puzzling Phenomenon In Semiparametric Estimation Problems With Infinite-Dimensional Nuisance Parameters," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1717-1728, December.
    2. Sebastian Calónico & Jeffrey Smith, 2017. "The Women of the National Supported Work Demonstration," Journal of Labor Economics, University of Chicago Press, vol. 35(S1), pages 65-97.
    3. Akanksha Negi & Jeffrey M. Wooldridge, 2021. "Revisiting regression adjustment in experiments with heterogeneous treatment effects," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 504-534, April.
    4. Słoczyński, Tymon & Wooldridge, Jeffrey M., 2018. "A General Double Robustness Result For Estimating Average Treatment Effects," Econometric Theory, Cambridge University Press, vol. 34(1), pages 112-133, February.
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