The New York City High School Match

Economic

Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match

The design of the New York City (NYC) High School match involved tradeoffs 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 tie breaking-- in a student-proposing deferred acceptance mechanism. Any inefficiency associated with a realized tie breaking 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.

The Boston Public School Match

Economic

The Elite Illusion: Achievement Effects at Boston and New York Exam Schools

Talented students compete fiercely for seats at Boston and New York exam schools. These schools are characterized by high levels of peer achievement and a demanding curriculum tailored to each district's highest achievers. While exam school students do very well in school, the question of whether an exam school education adds value relative to a regular public education remains open. We estimate the causal effect of exam school attendance using a regression-discontinuity design, reporting both parametric and non- parametric estimates. The outcomes studied here include scores on state standardized achievement tests, PSAT and SAT participation and scores, and AP scores. Our estimates show little effect of exam school offers on most students' achievement. We use two-stage least squares to convert reduced form estimates of the effects of exam school offers into estimates of peer and tracking effects, arguing that these appear to be unimportant in this context. Finally, we explore the external validity of RD estimates, arguing that as best we can tell, there is little effect of an exam school education on achievement even for the highest-ability marginal applicants and for applicants to the right of admissions cutoffs. On the other hand, a Boston exam school education seems to have a modest effect on high school English scores for minority applicants. A small group of 9th grade applicants also appears to do better on SAT Reasoning. These localized gains notwithstanding, the intense competition for exam school seats does not appear to be justified by improved learning for a broad set of students.

Social Welfare in One-sided Matching Markets without Money

We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent's utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first non-trivial performance guarantees for these natural mechanisms

Pareto-optimal matching allocation mechanisms for boundedly rational agents

Is the Pareto optimality of matching mechanisms robust to the introduction of boundedly rational behavior? To address this question I define a restrictive and a permissive notion of Pareto optimality and consider the large set of hierarchical exchange mechanisms which contains serial dictatorship as well as Gale’s top trading cycles. Fix a housing problem with boundedly rational agents and a hierarchical exchange mechanism. Consider the set of matchings that arise with all possible assignments of agents to initial endowments in the given mechanism. I show that this set is nested between the sets of Pareto optima according to the restrictive and the permissive notion. These containment relations are generally strict, even when deviations from rationality are minimal. In a similar vein, minimal deviations from rationality suffice for the set of outcomes of Gale’s top trading cycles with all possible initial endowments to differ from the set of outcomes of serial dictatorship with all possible orders of agents as dictators. © 2016 The Author(s