An important debate centers on what procedure should be used to allocate students across public schools. We contribute to this debate by developing and estimating a model of school choices by households under one of the most popular procedures known as the Boston mechanism (BM). We recover the joint distribution of household preferences and sophistication types using administrative data from Barcelona. Our counterfactual policy analyses show that a change from BM to the Gale-Shapley student deferred acceptance mechanism would create more losers than winners, while a change from BM to the top trading cycles mechanism has the opposite effect.