  Inverse propensity weighting (IPW) is a popular method for estimating
treatment effects from observational data. However, its correctness relies on
the untestable (and frequently implausible) assumption that all confounders
have been measured. This paper introduces a robust sensitivity analysis for IPW
that estimates the range of treatment effects compatible with a given amount of
unobserved confounding. The estimated range converges to the narrowest possible
interval (under the given assumptions) that must contain the true treatment
effect. Our proposal is a refinement of the influential sensitivity analysis by
Zhao, Small, and Bhattacharya (2019), which we show gives bounds that are too
wide even asymptotically. This analysis is based on new partial identification
results for Tan (2006)'s marginal sensitivity model.
