This paper develops a theoretical explanation why it may be optimal for higher-level governments to pay categorical block grants or closed-ended matching grants to local governments. We consider a federation with two types of local governments which differ in the cost of providing public goods. The federal government redistributes between jurisdictions, but cannot observe the type of a jurisdiction. In this asymmetric information setting, it is shown that the second-best optimum can be implemented with the help of categorical block grants and closed-ended matching grants, but not with unconditional block grants or open-ended matching grants.