Dealing with limited overlap in estimation of average treatment effects

Estimation of average treatment effects under unconfounded orignorable treatment assignment is often hampered by lack ofoverlap in the covariate distributions between treatment groups.This lack of overlap can lead to imprecise estimates, and canmake commonly used estimators sensitive to the choice of specification.In such cases researchers have often used ad hoc methods fortrimming the sample. We develop a systematic approach to addressinglack of overlap. We characterize optimal subsamples for whichthe average treatment effect can be estimated most precisely.Under some conditions, the optimal selection rules depend solelyon the propensity score. For a wide range of distributions,a good approximation to the optimal rule is provided by thesimple rule of thumb to discard all units with estimated propensityscores outside the range [0.1,0.9].