Abstract

It has long been known that the inverse probability weighting (IPW) methods for estimating causal effects can be very unstable and can explode in certain settings, such as limited overlap. Several workarounds, such as trimming of the propensity scores, have been suggested in the recent literature, but the issue persists and goes hand in hand with the finite-sample bias of IPW -based estimators. To address the issue of bias, this paper proposes finite-sample ‘unbiased set-estimators’ (based on a generalization of the concept of unbiased point estimation) of heterogeneous causal effects in a common observational setting where unconfoundedness is plausible within fine strata (either predetermined or formed based on high-dimensional clustering algorithms) using large-scale data. These estimators are inspired by an in-depth investigation of a problematic ratio in causal inference: the reciprocal of the estimated propensity score. This paper also proposes asymptotically unbiased double-robust point-estimators in more general settings where causal effects are heterogeneous. Finite-sample and large-sample statistical inference methods are also proposed for quantifying statistical uncertainty. A byproduct of these methods is a finite-sample Fisherian frequentist alternative to the Bayesian posterior distribution for the causal effects. The proposed methods are empirically demonstrated using data from the widely analyzed National Supported Work program to enable empirical comparisons with other methods suggested in the literature. Simulation exercises are also conducted to evaluate the practical performance of the new procedures.