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Semiparametric Difference-in-Differences Estimation With Missing Not at Random Data: A Shadow Variable Approach

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  • Junjie Li
  • Dongyuan Mu

Abstract

This paper considers a semiparametric difference-in-differences (DID) framework for identifying and estimating treatment effects on the treated (ATT) when outcomes are missing not at random (MNAR), and a fully observed shadow variable is available. The shadow variable is assumed to be associated with the outcome evolution but independent of the missingness process, conditional on covariates and the possibly unobserved outcome evolution. We establish the identification conditions, derive the corresponding identification results and estimation algorithm, and evaluate the finite-sample performance of the proposed estimator through simulation studies and a real data application.

Suggested Citation

  • Junjie Li & Dongyuan Mu, 2026. "Semiparametric Difference-in-Differences Estimation With Missing Not at Random Data: A Shadow Variable Approach," Papers 2606.08474, arXiv.org.
    • Handle: RePEc:arx:papers:2606.08474
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    References listed on IDEAS

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    1. repec:mpr:mprres:8160 is not listed on IDEAS
    2. Eric J. Tchetgen Tchetgen & Kathleen E. Wirth, 2017. "A general instrumental variable framework for regression analysis with outcome missing not at random," Biometrics, The International Biometric Society, vol. 73(4), pages 1123-1131, December.
    3. Jiwei Zhao & Yanyuan Ma, 2022. "A Versatile Estimation Procedure Without Estimating the Nonignorable Missingness Mechanism," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1916-1930, October.
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