We model household choice of schools under the Boston mechanism (BM) and
develop a new method, applicable to a broad class of mechanisms, to fully solve the
choice problem even if it is infeasible via the traditional method. We estimate the
joint distribution of household preferences and sophistication types using adminis-
trative data from Barcelona. Counterfactual policy analyses show that a change
from BM to the Deferred Acceptance mechanism would decrease average welfare
by 1,020 euros, while a change to the top trading cycles mechanism would increase
average welfare by 460 euros.