Robust Inference Using Inverse Probability Weighting
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Inverse Probability Weighting (IPW) is widely used in program evaluation and other empirical economics applications. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization strategy. However, ad hoc trimming of the observations renders usual inference procedures invalid for the target estimand, even in large samples. In this paper, we propose an inference procedure that is robust not only to small probability weights entering the IPW estimator, but also to a wide range of trimming threshold choices. Our inference procedure employs resampling with a novel bias correction technique. Specifically, we show that both the IPW and trimmed IPW estimators can have different (Gaussian or non-Gaussian) limiting distributions, depending on how "close to zero" the probability weights are and on the trimming threshold. Our method provides more robust inference for the target estimand by adapting to these different limiting distributions. This robustness is partly achieved by correcting a non-negligible trimming bias. We demonstrate the finite-sample accuracy of our method in a simulation study, and we illustrate its use by revisiting a dataset from the National Supported Work program.
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