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.

翻译：暂无翻译