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Generalized Lee bounds

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  • Semenova, Vira

Abstract

Lee (2009) is a common approach to bound the average causal effect in the presence of selection bias, assuming the treatment effect on selection has the same sign for all subjects. This paper generalizes Lee bounds to allow the sign of this effect to be identified by pretreatment covariates, relaxing the standard (unconditional) monotonicity to its conditional analog. Asymptotic theory for generalized Lee bounds is proposed in low-dimensional smooth and high-dimensional sparse designs. The paper also generalizes Lee bounds to accommodate multiple outcomes. Focusing on JobCorps job training program, I first show that unconditional monotonicity is unlikely to hold, and then demonstrate the use of covariates to tighten the bounds.

Suggested Citation

  • Semenova, Vira, 2025. "Generalized Lee bounds," Journal of Econometrics, Elsevier, vol. 251(C).
    • Handle: RePEc:eee:econom:v:251:y:2025:i:c:s0304407625001095
    DOI: 10.1016/j.jeconom.2025.106055
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    Cited by:

    1. Gevorg Khandamiryan & Vira Semenova, 2026. "Adaptive Estimation of Aggregated Values of Conditional Linear Programs," Papers 2606.08359, arXiv.org.
    2. Daisuke Kurisu & Yuta Okamoto & Taisuke Otsu, 2026. "Lee Bounds for Random Objects," Papers 2601.09453, arXiv.org.
    3. Yingying Dong & Phillip Heiler, 2026. "Sharp Bounds and Inference in Sample Selection Models with Treatment Endogeneity," Papers 2606.09223, arXiv.org.
    4. Haoge Chang & Zeyang Yu, 2026. "Randomization Inference For the Always-Reporter Average Treatment Effect," Papers 2603.24970, arXiv.org, revised Mar 2026.
    5. Yanqin Fan & Carlos A. Manzanares & Hyeonseok Park & Yuan Qi, 2026. "A Sensitivity Analysis of the Surrogate Index Approach for Estimating Long-Term Treatment Effects," Papers 2603.00580, arXiv.org.
    6. Bruno Ferman & Davi Siqueira & Vitor Possebom, 2026. "Partial Identification under Stratified Randomization," Papers 2601.12566, arXiv.org.

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