It is widely believed that politicians allocate public resources in ways to maximize political gains. But what is less clear is whether this comes at a cost to welfare; and if so, whether alternative electoral rules can help reduce these costs. In this paper, we address both of these questions by modeling and estimating politicians' decisions to allocate public funds. We use data from Brazil's federal legislature, which grants each federal legislator a budget to fund public projects in his state. We find that 26 percent of the public funds are distorted relative to a social planner's allocation. We then use the model to simulate several potential policies reforms to the electoral system, including adopting approval voting and implementing term limits. We find that an approval voting system reduces the distortions by 7.5 percent. Term limits also reduce distortions, but come at the cost of more corruption, which makes it a welfare-reducing policy.