A generalization of the balancing property of the propensity score

Propensity score matching is a nonparametric technique frequently used for estimating average treatment effects. Yet its applicability is not confined to treatment evaluation. In this paper the propensity score property is generalized to the setting of selection on unobservables. It is shown that propensity score matching can be used to decompose effects due to observables and due to unobservables; which can be used, for example, to analyze racial or sexual discrimination. Furthermore, the generalized propensity score property justifies the use of propensity score matching in difference-in-difference treatment evaluation.