Sharp Instrumental Variable Bounds under The Marginal Sensitivity Model
Abstract
Marginal sensitivity models bound the degree of unmeasured confounding but do not incorporate instrumental-variable restrictions, even when an instrument is available. We develop a framework combining these models with instrumental-variable assumptions to sharpen inference on population treatment effects without requiring treatment monotonicity or treatment-effect homogeneity. For continuous and finite ordered outcomes, we characterize sharp identified sets for potential-outcome means and the average treatment effect, together with observable restrictions implied jointly by the instrumental-variable and sensitivity assumptions. The bounds admit explicit formulas for finite ordered outcomes, while optimization over prespecified threshold classes provides tractable outer bounds for continuous outcomes. We develop cross-fitted one-step estimators that accommodate flexible nuisance estimation. Under suitable conditions, the resulting outward confidence sets asymptotically cover the sharp identified interval without requiring optimal threshold estimation. Stronger conditions yield semiparametric efficient estimation and inference for restricted-class bounds. Numerical experiments show narrower confidence sets when incorporating an instrument and compare the performance of outward inference and inference for individual bounds. We apply the framework to the Oregon Health Insurance Experiment to illustrate how combining instrumental-variable assumptions with restrictions on the degree of unmeasured confounding can strengthen conclusions about the effect of Medicaid coverage on emergency-department use.
Related
- BGM-IV: AI-Powered Bayesian Generative Modeling for Instrumental Variable Regression with High-Dimensional Covariates
- Bridging Local and Population Causal Effects: A Proximal Instrumental Variable Approach
- Identifying Causal Effects in Experiments with Latent Treatments: An Instrumental Variable Approach
- Instrumental Variable Analysis in Underrepresented Subpopulations Powered by Knowledge Transfer
- One-Sample Mendelian Randomization and Instrumental Variable Analyses in R and Stata: The OneSampleMR and ivonesamplemr Packages
BibTeX
@misc{olivasmartinez2026sharp,
title = {{Sharp Instrumental Variable Bounds under The Marginal Sensitivity Model}},
author = {Antonio Olivas-Martinez and Eric Tchetgen Tchetgen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22513},
eprint = {2610.22513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22513},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp Instrumental Variable Bounds under The Marginal Sensitivity Model
AU - Antonio Olivas-Martinez
AU - Eric Tchetgen Tchetgen
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22513
UR - https://arxiv.org/abs/2610.22513
AB - Marginal sensitivity models bound the degree of unmeasured confounding but do not incorporate instrumental-variable restrictions, even when an instrument is available. We develop a framework combining these models with instrumental-variable assumptions to sharpen inference on population treatment effects without requiring treatment monotonicity or treatment-effect homogeneity. For continuous and finite ordered outcomes, we characterize sharp identified sets for potential-outcome means and the average treatment effect, together with observable restrictions implied jointly by the instrumental-variable and sensitivity assumptions. The bounds admit explicit formulas for finite ordered outcomes, while optimization over prespecified threshold classes provides tractable outer bounds for continuous outcomes. We develop cross-fitted one-step estimators that accommodate flexible nuisance estimation. Under suitable conditions, the resulting outward confidence sets asymptotically cover the sharp identified interval without requiring optimal threshold estimation. Stronger conditions yield semiparametric efficient estimation and inference for restricted-class bounds. Numerical experiments show narrower confidence sets when incorporating an instrument and compare the performance of outward inference and inference for individual bounds. We apply the framework to the Oregon Health Insurance Experiment to illustrate how combining instrumental-variable assumptions with restrictions on the degree of unmeasured confounding can strengthen conclusions about the effect of Medicaid coverage on emergency-department use.
ER -