The paper develops a statistical procedure to provide consistent estimators for the average impact of an intervention or treatment (e.g., earnings) among subjects of a target population (e.g., young high school dropouts). The procedures we study belong to a class of estimators which can be expressed as a DIFFERENCE between the average outcome in the treated sample and an adequately chosen weighted average of the outcomes in the control group. We refer to estimators in this class as D-estimators. We show that D-estimators should only be used in circumstances in which subjects are randomly assigned to treatment given the vector of observed covariates. This condition has been referred to as the \strongly ignorable assumption" or \selection on observable model". The consistency of D-estimators is proved under very weak restrictions on the distribution of the covariates.