Public housing benefits are rationed through wait lists. Theoretical work on public housing allocation has debated how much choice applicants should have over units, identifying a possible trade-off between efficiency and redistribution. This paper empirically establishes the existence and economic importance of this trade-off using wait list data from Cambridge, Massachusetts. I estimate a model of public housing preferences in a setting where heterogeneous apartments are rationed through waiting time. Eliminating choice would improve targeting but reduce tenant welfare by more than 30 percent. Such a change is only justified on targeting grounds by a strong social preference for redistribution.

Waitlists are often used to ration scarce resources, but the trade-offs in designing these mechanisms depend on agents' preferences. We study equilibrium allocations under alternative designs for the deceased donor kidney waitlist. We model the decision to accept an organ or wait for a preferable one as an optimal stopping problem and estimate preferences using administrative data from the New York City area. Our estimates show that while some kidney types are desirable for all patients, there is substantial match-specific heterogeneity in values. We then develop methods to evaluate alternative mechanisms, comparing their effects on patient welfare to an equivalent change in donor supply. Past reforms to the kidney waitlist primarily resulted in redistribution, with similar welfare and organ discard rates to the benchmark first come first served mechanism. These mechanisms and other commonly studied theoretical benchmarks remain far from optimal. We design a mechanism that increases patient welfare by the equivalent of an 18.2 percent increase in donor supply.