Sharp Bounds on Continuous Treatment Effects under Unobserved Confounding

Abstract

We study partial identification of conditional treatment effects with a continuous treatment under unobserved confounding. We target the conditional average potential outcome (CAPO) E[Y_x|z] and the conditional average treatment effect (CATE) between two treatment levels. We assume a bounded outcome and Lipschitz continuity of the response functions and of the propensity scores given the latent confounder, and show that these conditions imply the smooth treatment response and smooth treatment selection conditions of Kim et al. (2018). The combined bound of Kim et al. uses only two reference points on the identified diagonal and is generally loose. Bounding through every diagonal reference point instead gives explicit bounds whose average is the sharp identified set of the CAPO at every treatment, inside or outside the observational support. Capping the difference between the upper and lower bounds gives sharp causal bounds on the CATE. These bounds are informative without monotonicity or overlap assumptions.

Doubly valid and doubly sharp sensitivity analysis to unobserved confounding for survival outcomes
Jean-Baptiste Baitairian, Bernard Sebastien, Rana Jreich +2
arXiv16 Sep 2026PreprintCC BY 4.0Full textStatisticsarXiv
Robust Design and Evaluation of Predictive Algorithms under Unobserved Confounding
Ashesh Rambachan, Amanda Coston, Edward H. Kennedy
The Review of Economics and Statistics18 Jun 2026Peer-reviewedLicence not statedFull text29 citedStatisticsOpenAlex
Causal Inference with Unobserved Confounding: A Mixture Learning Perspective
Mansi Sood, Devavrat Shah
arXiv19 Sep 2026PreprintarXiv licenceFull textStatisticsarXiv
Sharp Causal Bounds for Dynamic Treatment Regimes
Alexander Alvarez, Sebastian E. Ferrando
arXiv6 Sep 2026PreprintarXiv licenceFull textStatisticsarXiv
Estimating Group Average Treatment Effects in High-Risk Populations with Unobserved Target Membership
Shubo Zhang, Yinjun Zhao, Donglin Zeng +1
arXiv22 Oct 2026PreprintarXiv licenceFull textStatisticsarXiv

Cite

BibTeX RIS

BibTeX

@misc{zhang2026sharp,
  title = {{Sharp Bounds on Continuous Treatment Effects under Unobserved Confounding}},
  author = {Junzhe Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33278},
  eprint = {2610.33278},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33278},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Sharp Bounds on Continuous Treatment Effects under Unobserved Confounding
AU  - Junzhe Zhang
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33278
UR  - https://arxiv.org/abs/2610.33278
AB  - We study partial identification of conditional treatment effects with a continuous treatment under unobserved confounding. We target the conditional average potential outcome (CAPO) E[Y_x|z] and the conditional average treatment effect (CATE) between two treatment levels. We assume a bounded outcome and Lipschitz continuity of the response functions and of the propensity scores given the latent confounder, and show that these conditions imply the smooth treatment response and smooth treatment selection conditions of Kim et al. (2018). The combined bound of Kim et al. uses only two reference points on the identified diagonal and is generally loose. Bounding through every diagonal reference point instead gives explicit bounds whose average is the sharp identified set of the CAPO at every treatment, inside or outside the observational support. Capping the difference between the upper and lower bounds gives sharp causal bounds on the CATE. These bounds are informative without monotonicity or overlap assumptions.
ER  -

Abstract

Related

Cite