Bounding Treatment Effects by Pooling Limited Information across Observations

Abstract

We provide novel bounds on average treatment effects (on the treated) that are valid under an unconfoundedness assumption. Our bounds are designed to be robust in challenging situations, for example, when the conditioning variables take on a large number of different values in the observed sample, or when the overlap condition is violated. This robustness is achieved by only using limited "pooling" of information across observations. Namely, the bounds are constructed as sample averages over functions of the observed outcomes such that the contribution of each outcome only depends on the treatment status of a limited number of observations. No information pooling across observations leads to so-called "Manski bounds", while unlimited information pooling leads to standard inverse propensity score weighting. We explore the intermediate range between these two extremes and provide corresponding inference methods.We show in Monte Carlo experiments and through an empirical application that our bounds are indeed robust and informative in practice.

Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap

“…29 My FPW approach is similar in spirit to that of Lee and Weidner (2021), but they consider a broader setting where the parameters of interest may not even be point-identified, so the set-estimators they propose are generally wider. Under my assumptions, the parameters are indeed point-identified.…”

“…In the presence of limited overlap, some researchers suggest focusing attention instead on alternative estimands and parameters that can be estimated efficiently using heavy trimming or winsorization of the propensity scores (Crump et al, 2009;Zhou et al, 2020) or using other weighting procedures. 6 Lee and Weidner (2021) propose partial identification methods. Ma and Wang (2020) develop bias-correction and robust inference procedures for trimmed IPW estimators.…”

“…I define a notion of finite-sample unbiasedness for set-estimators (a generalization of the usual concept for point-estimators), and I show that the property holds for the FPW set-estimator. An interesting feature of the FPW set-estimator is that it actually reduces to a point-estimator for many practical purposes and thus serves as a simpler alternative to other available set-estimators that are wider (see, e.g., Lee and Weidner, 2021) in the (high-dimensional) strata setting.…”