Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand,” unpublished manuscript

Estimation of average treatment effects under unconfoundedness or selection on observ-ables is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trim-ming the sample or focused on subpopulations of interest. In this paper we develop formal methods for addressing such lack of overlap in which we sacrifice some external validity in exchange for improved internal validity. We characterize optimal subsamples where the average treatment effect can be estimated most precisely, as well optimally weighted average treatment effects. We show the problem of lack of overlap has important connections to the presence of treatment effect heterogeneity: under the assumption of constant conditional average treatment effects the treatment effect can be estimated much more precisely. The efficient estimator for the treatment effect under the assumption of a constant conditional average treatment effect is shown to be identical to the efficient estimator for the optimally weighted average treatment effect. We also develop tests for the null hypotheses of a con-stant and a zero conditional average treatment effect. The latter is in practice more powerful than the commonly used test for a zero average treatment effect. JEL Classification: C14, C21, C5