We characterize welfare gains from government intervention when the private sector provides partial insurance. We analyze models in which adverse selection, pre-existing information, or imperfect optimization create a role for government intervention. We derive formulas that map existing empirical estimates into quantitative predictions for optimal policy. When private insurance generates moral hazard, standard formulas for optimal government insurance must be modified to account for fiscal externalities. In contrast, standard formulas are unaffected by "informal" private insurance that does not generate moral hazard. Applications to health and unemployment show that formal private market insurance can significantly reduce optimal government benefit rates. (JEL D82, G22, H21, H23, J65)
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