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Studies of large policy interventions typically do not involve randomization. Adjustments, such as matching, can remove the bias due to observed covariates, but residual confounding remains a concern. In this paper we introduce two analytical strategies to bolster inferences of the effectiveness of policy interventions based on observational data. First, we identify how study groups may differ and then select a second comparison group on this source of difference. Second, we match subjects using a strategy that finely balances the distributions of key categorical covariates and stochastically balances on other covariates. An observational study of the effect of parity on the severely ill subjects enrolled in the Federal Employees Health Benefits (FEHB) Program illustrates our methods.