Random serial dictatorship and the core from random endowments in house allocation problems

Parents gauge school quality in part by the level of student achievement and a school's racial and socioeconomic mix. The importance of school characteristics in the housing market can be seen in the jump in house prices at school district boundaries where peer characteristics change. The question of whether schools with more attractive peers are really better in a value-added sense remains open, however. This paper uses a fuzzy regression-discontinuity design to evaluate the causal effects of peer characteristics. Our design exploits admissions cutoffs at Boston and New York City's heavily over-subscribed exam schools. Successful applicants near admissions cutoffs for the least selective of these schools move from schools with scores near the bottom of the state SAT score distribution to schools with scores near the median. Successful applicants near admissions cutoffs for the most selective of these schools move from above-average schools to schools with students whose scores fall in the extreme upper tail. Exam school students can also expect to study with fewer nonwhite classmates than unsuccessful applicants. Our estimates suggest that the marked changes in peer characteristics at exam school admissions cutoffs have little causal effect on test scores or college quality.

A central issue in school choice is the design of a student assignment mechanism. Education literature provides guidance for the design of such mechanisms but does not offer specific mechanisms. The flaws in the existing school choice plans result in appeals by unsatisfied parents. We formulate the school choice problem as a mechanism design problem and analyze some of the existing school choice plans including those in Boston, Columbus, Minneapolis, and Seattle. We show that these existing plans have serious shortcomings, and offer two alternative mechanisms each of which may provide a practical solution to some critical school choice issues.

Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over‐subscribed schools using randomly assigned lottery numbers, non‐lottery tie‐breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores and other criteria to rank applicants at the city's screened schools, combined with lottery tie‐breaking at the rest. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity methods to allow for multiple treatments and multiple running variables, some of which are randomly assigned. The key to this generalization is a local propensity score that quantifies the school assignment probabilities induced by lottery and non‐lottery tie‐breakers. The utility of the local propensity score is demonstrated in an assessment of the predictive value of New York City's school report cards. Schools that earn the highest report card grade indeed improve SAT math scores and increase graduation rates, though by much less than OLS estimates suggest. Selection bias in OLS estimates of grade effects is egregious for screened schools.

School choice may lead to improvements in school productivity if parents’ choices reward effective schools and punish ineffective ones. This mechanism requires parents to choose schools based on causal effectiveness rather than peer characteristics. We study relationships among parent preferences, peer quality, and causal effects on outcomes for applicants to New York City’s centralized high school assignment mechanism. We use applicants’ rank-ordered choice lists to measure preferences and to construct selection-corrected estimates of treatment effects on test scores, high school graduation, college attendance, and college quality. Parents prefer schools that enroll high-achieving peers, and these schools generate larger improvements in short- and long-run student outcomes. Preferences are unrelated to school effectiveness and academic match quality after controlling for peer quality.

Coordinated single-offer school assignment systems are a popular education reform. We show that uncoordinated offers in NYC's school assignment mechanism generated mismatches. One-third of applicants were unassigned after the main round and later administratively placed at less desirable schools. We evaluate the effects of the new coordinated mechanism based on deferred acceptance using estimated student preferences. The new mechanism achieves 80 percent of the possible gains from a no-choice neighborhood extreme to a utilitarian benchmark. Coordinating offers dominates the effects of further algorithm modifications. Students most likely to be previously administratively assigned experienced the largest gains in welfare and subsequent achievement.

Charter takeovers are traditional public schools restarted as charter schools. We develop a grandfathering instrument for takeover attendance that compares students at schools designated for takeover with a matched sample of students attending similar schools not yet taken over. Grandfathering estimates from New Orleans show substantial gains from takeover enrollment. In Boston, grandfathered students see achievement gains at least as large as the gains for students assigned charter seats in lotteries. A non-charter Boston turnaround intervention that had much in common with the takeover strategy generated gains as large as those seen for takeovers, while other more modest turnaround interventions yielded smaller effects.

Despite its widespread use, the Boston mechanism has been criticized for its poor incentive and welfare performances compared to the Gale-Shapley deferred acceptance algorithm (DA). By contrast, when students have the same ordinal preferences and schools have no priorities, we find that the Boston mechanism Pareto dominates the DA in ex ante welfare, that it may not harm but rather benefit participants who may not strategize well, and that, in the presence of school priorities, the Boston mechanism also tends to facilitate greater access than the DA to good schools for those lacking priorities at those schools.

The design of the New York City (NYC) high school match involved trade-offs among efficiency, stability, and strategy-proofness that raise new theoretical questions. We analyze a model with indifferences—ties—in school preferences. Simulations with field data and the theory favor breaking indifferences the same way at every school—single tiebreaking—in a student-proposing deferred acceptance mechanism. Any inefficiency associated with a realized tiebreaking cannot be removed without harming student incentives. Finally, we empirically document the extent of potential efficiency loss associated with strategy-proofness and stability, and direct attention to some open questions.

mechanism to match over 90,000 entering students to public high schools each year. This paper makes a very preliminary report on the design process and the first year of operation, in academic year 2003-04, for students entering high school in Fall 2004. In the first year, only about 3,000 students had to be assigned to a school for which they had not indicated a preference, which is only 10 % of the number of such assignments the previous year. New York City has the largest public school system in the country, with over a million students. In 1969 the system was decentralized into over thirty community school districts. In the 1990s, the city began to take more centralized control, and in 2002, a newly reorganized NYCDOE began to reform many aspects of the school system. In May 2003, Dr. Jeremy Lack, then the NYCDOE Director of Strategic Planning, contacted one of us for advice on designing a new high school matching process. The NYCDOE was aware of the matching process for American physicians, the National Resident Matching Program (Roth 1984; Roth and Peranson 1999). They wanted to know if it could be appropriately adapted to the city’s schools. The three authors of the present paper (and, at several crucial junctures, also Tayfun Sönmez) advised (and often convinced) Dr.