Parag Pathak is clearly the researcher under age forty who has contributed most both to the general field of market design, and, in addition, to what has been its most important application in the last decade or so, that of education policy. Pathak’s applied work in market design has led to significant improvements in the application of market-design tools to the assignment of students to public schools. He has pushed the boundaries of known theory to make it sensitive to cognitive limits of participants and relevant to practical environments. Pathak has developed creative empirical tools to evaluate the impacts of various policy issues facing the educational environment; examples being the case for charter schools and the impact of exam schools and voucher systems. Pathak’s work blends institutional knowledge, theoretical sophistication, and careful empirical analysis to provide insights that are of immediate value to important public-policy issues.

Market Design and School Choice. Parag’s work on mechanism design and school choice began while he was still a graduate student. A paper by AbdulkadiroÄŸlu and Sönmez in the AER motivated the head of the Boston Public School system to contact a group working on mechanism design, and an allocation system that was not functioning well in New York City resulted in a similar request.

The first two papers were published in the Paper and Proceedings section of AER in 2005. The paper on “The Boston Public School Match” detailed the old allocation mechanism in Boston, explained the impact of the absence of incentives for students to report their preferences truthfully in that system, and outlined the way an incentive compatible system would work in the schooling context.

The second paper, entitled “The New York City High School Match” (with Abdulkadiroğlu and Roth) begins by describing the institutional details of the old New York City high school system and the congestion and manipulation problems that resulted from it. It then explains why New York chose the student proposing deferred acceptance algorithm. This is also dominant-strategy incentive compatible. It guarantees a stable match (but not a Pareto-efficient outcome). The paper also described the first year of operation of the match.

The Boston experience motivated Pathak to write the paper “Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism,” (American Economic Review, 2008). Pathak and co-author Sönmez documented the existence of substantial heterogeneous levels of sophistication among participants in the Boston school choice plan, motivating a framework that relaxes the strong rationality assumptions maintained in the theoretical market-design literature. The paper analyzes the Nash equilibria of the preference revelation game induced by the old Boston mechanism when there are two types of players. Sincere players are restricted to report their true preferences, while sophisticated players play a best response. The paper characterizes the set of Nash equilibrium outcomes as the set of stable matchings of an economy with a modified priority structure, where sincere students lose their priority to sophisticated students. A sophisticated student weakly prefers the assignment under the Pareto-dominant Nash equilibrium of the Boston mechanism to the assignment under the newly implemented student-optimal stable mechanism (based on the deferred acceptance algorithm). The paper formalizes a fairness rationale for strategy-proof mechanisms, which is particularly relevant for resource allocation in the public sector.

The New York City experience highlighted the importance of indifferences (many students having equal claims to attend a school) in models of student assignment. Pathak investigated this in the context of two mechanisms used for student placement. “Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match” (American Economic Review, 2009, with Abdulkadiroğlu and Roth) focuses on the new mechanism in New York City’s Main Round. It theoretically and empirically identifies tradeoffs between obtaining Pareto-efficient outcomes for students and maintaining incentives in the student-proposing deferred acceptance algorithm when schools may be indifferent between some applicants.

“School Admissions Reform in Chicago and England: Comparing Mechanisms by their Vulnerability to Manipulation” (American Economic Review, 2013, with Sönmez) proposes a way to rank mechanisms that are not strategy proof by their vulnerability to manipulation. One mechanism is less vulnerable to manipulation than another if an any environment in which the first can be manipulated, the second can also be manipulated. This article connects the theoretical results to events related to school-choice mechanisms that occurred in Chicago and England around the time they were writing the paper. The Chicago school district changed their assignment system in 2009, asking 14,000 participants to submit preferences under two different mechanisms. The rationale for the change was a concern that the matches were sensitive to unimportant details (“high-scoring kids were being rejected simply because of the order in which they listed their college prep preferences”). However, the change involved moving from one manipulable mechanism to another manipulable one. The paper explicitly ranks three mechanisms: a mechanism used in Boston (“first preference first”) in which students who listed a school first receive first priority and remaining places (if any) are filled by students who ranked the school second, and so on; an alternative where the iterations consider all choices prior to that iteration’s choice in assigning schools; and the Gale-Shapley student proposing algorithm that is truncated at different truncation points. Pathak and Sönmez show that the old Boston mechanism was the most manipulable mechanism. In England, by a 2007 Act of Parliament, the “first preferences first” mechanisms were ruled illegal. Just as in Chicago, new manipulable mechanisms were adopted, but Pathak and Sönmez show again that these mechanisms were less manipulable than their predecessor Their method to rank mechanisms has also applications across a wide range of applied mechanism design problems.

More recently, in “The Demise of Walk Zones: Priorities vs. Precedence in School Choice” (Journal of Political Economy 2016), Pathak and co-authors Dur, Kominers, and Sönmez identify unusual properties of two-sided matching mechanisms when priorities for school seats have a slot-specific nature. For example, in Boston, walk-zone priority applies at half of a school’s seats, while it does not at the other half. Students are allowed to apply to both halves, but the order of their application in both has an important effect on the overall assignment. Surprisingly, the fact that the slots are processed sequentially results in an assignment nearly identical to that without any walk-zone priority despite the perception that walk applicants gain an edge. The paper establishes formal results on priorities and precedence, and describes how transparency on these results contributed to the end of Boston’s walk-zone priority.

“Minimizing Justified Envy in School Choice: The Design of New Orleans OneApp” (March 2017, NBER Working Paper 23265, with with Abdulkadiroğlu, Che, Roth, and Tercieux) is a theoretical study that provides an argument for the top-trading cycle mechanism. Deferred acceptance algorithms are the most commonly allocation system. These mechanism are attractive because they generate stable outcomes (eliminating justified envy) while maintaining incentives for truthful revelation. They have the theoretical weakness that they do not provide Pareto-efficient matches. No incentive compatible mechanism can both eliminate justified envy and guarantee efficiency, but the deferred acceptance procedure comes close in the sense that it weakly dominates all other incentive compatible mechanisms that eliminate justified envy. This paper establishes a dual result for top-trading cycle mechanism. It shows that no incentive-compatible Pareto-efficient mechanism has less justified envy (fewer blocking pairs) than the top-trading cycle mechanism. Using data from New Orleans (which uses a top-trading cycle mechanism) the paper demonstrates (in a setting not covered by the paper’s theorem) the ability of top-trading cycle mechanisms to perform better than other procedures that are Pareto-efficient and incentive compatible. The practical message of the paper is a new argument for using top-trading cycle mechanisms when efficiency is the primary goal.

An interesting more recent and broader look at school choice that fits more squarely into the Public Finance literature is “The Distributional Consequences of Public School Choice” NBER Working Paper 21525). Here Pathak and co-author Avery develop a model to explore whether school choice improves access to high quality schools compared to residential-based assignment when housing markets are modeled explicitly. The key novel feature of the framework is that it captures how the introduction of choice programs affects the incentives of households to live in certain neighborhoods, a feature that may undermine the goals of choice programs. They show that the implementation of school-choice initiatives narrows the range between the highest and lowest quality schools compared to neighborhood assignment; they also illustrate how these changes are capitalized into housing prices. The resulting compressed distribution generates incentives for both the highest and lowest types to move out of cities with school choice, paradoxically producing worse outcomes for low types than neighborhood assignment. Even when choice results in improvement in the worst performing schools, the lowest type residents may not benefit.

Market Design in Large Markets Pathak has also written important papers on the performance of matching markets with a large number of participants. These results are relevant for the school-choice literature reviewed above, but are more broadly significant for applications of market design to other situations.

Kojima and Pathak’s paper “Incentives and Stability in Large Two-Sided Matching Markets,” (American Economic Review, 2009) analyzes the scope for manipulation in many-to-one matching markets under the student-optimal stable mechanism when the number of participants is large, but each participant only ranks a fixed number of “partners” (schools in school-choice applications). The limitation is descriptive of real-world school choice-problems. In general these mechanisms are subject to manipulation, but the paper shows that the fraction of participants with incentives to misrepresent their preferences when others are truthful approaches zero as the market becomes large.

Stable matches fail to exist in matching markets when participants on one side of the market have interdependent preferences. This possibility leads to problems in practice: Roth has shown that the existence of couples who wish to work in the same location causes instability in the residency match. In “Matching with Couples: Stability and Incentives in Large Markets” (Quarterly Journal of Economics, 2013), Kojima, Pathak, and Roth establish that a stable matching exists with high probability in large markets provided that there are relatively few couples and preference lists that not long compared to market size. Their paper also establishes stylized facts in the job market for psychologists, in which stable matchings exist for all years of the data, despite the presence of couples.

Economics of Education Pathak more recent work focuses on empirical work in the economics of education. “Accountability and Flexibility in Public Schools: Evidence from Boston’s Charters and Pilots” (Quarterly Journal of Economics 2011, with AbdulkadiroÄŸlu, Angrist, Dynarski, and Kane) examines charter schools and pilot schools, two competing models of school autonomy in Boston. Charter schools are treated as their own independent school districts and are not subject to the teachers’ union contract. Pilot schools have most of the flexibility of charter schools, but continue to be covered by the union contract provisions for the teachers. The authors use the random assignment nature of lotteries for entry into over-subscribed charter and pilot schools in Boston as a plausible identification strategy (that is, they compare students with similar backgrounds who applied and were not accepted to an oversubscribed school to an accepted student) and examine test score impacts three years after getting access to these schools. The results are striking. Winning the lottery to get into a charter school is associated consistently with large increases in test scores, but that getting into a pilot school does not improve student performance.

In joint research with Angrist, Dynarski, Kane, and Walters, Pathak conducted the first evaluation of a Knowledge is Power Program (KIPP) charter school using assignment lotteries. The KIPP schools are the so-called “No Excuses” schools and feature a long school day and year, selective teacher hiring, strict behavior norms, and encourage a strong student work ethic. They are the largest charter school system in the U.S. The KIPP schools in Lynn, Massachusetts were initially undersubscribed and then oversubscribed. Using the lottery system in the oversubscribed years to construct a quasi-experimental evaluation, “Who Benefits from KIPP?” (Journal of Policy Analysis and Management, 2012) provides evidence that that KIPP Lynn generated substantial score gains for lottery winners, with the estimates being remarkably similar to those reported for Boston charters.

These studies provide partial evidence that, at least in the Boston area, charter schools enhance student attainment. Partly as a result, Boston area residents voted in November 2016 on whether to increase the limit that had been put on Charter School attendance. Pathak’s research received popular attention prior to the election. The charters lost the vote, but there is now a lot more attention directed at the issue of charter schools in the Boston area. Pathak’s research has been central to the policy debates.

The studies also add to a growing body of evidence suggesting that urban charter schools have the potential to generate impressive achievement gains, especially for minority students living in high-poverty areas. A puzzling fact is that there is little evidence of achievement gains at charter schools outside of high-poverty urban areas. In “Explaining Charter School Effectiveness” (American Economic Journal: Applied Economics, 2013), Pathak and co-authors Angrist and Walters examine a large sample of charter schools throughout Massachusetts using the lottery research design. The paper documents treatment effect heterogeneity in a large sample of Massachusetts charter schools and develops a framework for interpreting this heterogeneity using both student- and school-level explanatory variables. The paper indicates that the relatively higher effectiveness of urban charter schools might be explained by adherence to the “No Excuses” approach to urban education discussed above.

“The Efficiency of Race-Neutral Alternatives to Race-Based Affirmative Action: Evidence from Chicago’s Exam Schools” (with Glenn Ellison, September 2016, NBER Working Paper 22589) measures the welfare costs of affirmative action programs. School districts wish to balance diversity goals with matching high-quality students to high-quality schools. Ellison and Pathak examine admissions procedures at elite public schools in Chicago. These schools have shifted from a system that used explicit race-based quotas to one in which schools admitted a fraction of their classes on the basis of performance measures only while allocating the remaining fraction to districts using (not directly race based) proxies of neighborhood socioeconomic status. The paper makes the straightforward theoretical observation that when racial diversity is valuable, limiting attention to race-neutral schemes is inefficient. It elaborates upon this observation with a convincing analysis of data from the Chicago school district that provides a quantitative measure of the efficiency costs. Diversity goals lead to a reduction in test scores of elite schools, but in the two schools that are the focus of this study, a race-based system would eliminate more than three quarters of the reduction caused by the school districts race-neutral procedure. The paper points out that Chicago’s current system even fails to achieve the socioeconomic diversity achieved by a system that takes race into account. Loosely, the efficiency losses arise because race-neutral system may give priority to low scorers in one district over higher scores from demographically similar districts. “Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation” (with AbdulkadiroÄŸlu, Angrist, and Narita, Econometrica 2017) estimates the causal effect of attending various school types in a setting where school assignments are partly random. The empirical challenge is to isolate the random aspect of the assignment with preferences and priorities that are part of the allocation mechanism. The paper isolates the lottery variation by conditioning on a propensity score and demonstrate that this score is relatively easy to compute in large-market approximations. The paper applies its technique to data from the Denver school district. Denver assigns to students to schools using a centralized deferred acceptance system. The paper finds a large positive effect of attending a charter school on test scores.

Parag’s most recent research focuses on evaluating different allocation mechanisms. “The Welfare Effects of Coordinated Assignment: Evidence from the New York High School Match” (with AbdulkadiroÄŸlu and Agarwal), AER 2017, is the first paper with comparisons of allocations before and after a centralized match. The analysis requires two related developments: a demand system, and a choice model in a non-incentive compatible environment. These developments enabled comparison of many mechanisms. The empirical results are striking. The gain from moving from no choice (neighborhood assignment) to the uncoordinated mechanism was worth 6.7 miles in their distance metric, the gain from the uncoordinated to the coordinated mechanism was 8.5 miles, and further gains to a full deferred acceptance was .11 miles and to Pareto-Efficient assignment (which abandons stability) was .5 miles. The children who gained the most from the movement to a coordinated system were the children who never got one of their choices in the uncoordinated system and had been administratively assigned. These results already motivated school systems in Denver and New Orleans to coordinate assignments for traditional, charter, and magnet schools.

Summary Parag Pathak’s research has lead to significant improvement in the assignment of students to public schools. He has carried out convincing analyzes of different policies designed to improve secondary education. Using innovative and sophisticated empirical and theoretical techniques, he has provided policy advice that has already positively influenced the lives of over one million public school students. He is a worthy candidate for the Clark Medal.

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