Doubly Robust Estimators with Weak Overlap

Doubly robust (DR) estimators guard against model misspecification but remain sensitive to weak covariate overlap. We show that trimming propensity scores reduces variance but eliminates double robustness. We introduce DR estimators that retain double robustness after trimming through bias correction, preserving the original causal targets across unconfoundedness, instrumental variables, and difference-in-differences designs. In four applications, the proposed estimator yields more precise estimates: ruling out large mortality effects of Medicaid expansion, detecting workforce growth from mental health reform, recovering the Black--White test score gap without strong functional form restrictions, and recovering a positive 401(k) savings effect consistent with the prior literature.