Breaking Ties: Regression Discontinuity Design Meets Market Design

Centralized school assignment algorithms must distinguish between applicants with the same preferences and priorities. This is done with randomly assigned lottery numbers, nonlottery tie-breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores, grades, and interviews to rank applicants to screened schools, combined with lottery tie-breaking at unscreened schools. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity designs to allow for multiple treatments and multiple running variables, some of which are randomly assigned. Lotteries generate assignment risk at screened as well as unscreened schools. Centralized assignment also identifies screened school effects away from screened school cutoffs. These features of centralized assignment are used to assess the predictive value of New York City’s school report cards. Grade A schools improve SAT math scores and increase the likelihood of graduating, though by less than OLS estimates suggest. Selection bias in OLS estimates is egregious for Grade A screened schools

The economics of debt clearing mechanisms

We examine the evolution of decentralized clearinghouse mechanisms from the 13th to the 18th century; in particular, we explore the clearing of non- or limitedtradable debts like bills of exchange. We construct a theoretical model of these clearinghouse mechanisms, similar to the models in the theoretical matching literature, and show that specific decentralized multilateral clearing algorithms known as rescontre, skontrieren or virement des parties used by merchants were efficient in specific historical contexts. We can explain both the evolutionary self-organizing emergence of late medieval and early modern fairs, and its robustness during the 17th and 18th century

Generalized Matching for School Choice

Abstract The school choice problem is formulated as a one-sided or a twosided matching problem. However, neither model adequately captures the features of the market design applications of school choice. In particular, the one-sided matching solution may be politically infeasible; and the two-sided matching solution may involve ine¢ ciencies. We introduce a generalized model that encompasses one-sided and two sided matching models and their hybrid. We propose a natural stability notion; characterize student optimal stable matchings; and provide a student optimal stable matching mechanism that reduces to the Top Trading Cycles algorithm when the problem is a one-sided matching problem and becomes equivalent to the Gale-Shapley student optimal stable matching algorithm when the problem is a two-sided matching problem

Resolving Con ‡icting Preferences in School Choice: the "Boston"Mechanism Reconsidered

Abstract: The Boston mechanism is among the most popular school choice procedures in use. Yet, the mechanism has been criticized for its poor incentive and welfare performances, which led the Boston Public Schools to recently replace it with Gale and Shapley's deferred acceptance algorithm (henceforth, DA). The DA elicits truthful revelation of "ordinal" preferences whereas the Boston mechanism does not; but the latter induces participants to reveal their "cardinal" preferences (i.e., their relative preference intensities) whereas the former does not. We show that cardinal preferences matter more when families have similar ordinal preferences and schools have coarse priorities, two common features of many school choice environments. Speci…cally, when students have the same ordinal preferences and schools have no priorities, the Boston mechanism Pareto dominates the DA in ex ante welfare. The Boston mechanism may not harm but rather bene…t participants who may not strategize well. In the presence of school priorities, the Boston mechanism also tends to facilitate a greater access than the DA to good schools by those lacking priorities at those schools. These results contrast with the standard view, and cautions against a hasty rejection of the Boston mechanism in favor of mechanisms such as the DA