In this paper, we derive a new class of doubly robust estimators for treatment effect estimands that is also robust against weak covariate overlap. Our proposed estimator relies on trimming observations with extreme propensity scores and uses a bias correction device for trimming bias. Our framework accommodates many research designs, such as unconfoundedness, local treatment effects, and difference-in-differences. Simulation exercises illustrate that our proposed tools indeed have attractive finite sample properties, which are aligned with our theoretical asymptotic results.

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