Working Papers

Extended Abstract to appear in EC 2022.

Abstract: This paper explores the dynamic relationship between school choices made at different educational stages and how it affects racial segregation across schools. We use New York City public school choice data to ask: "How does the middle school that a student attends affect her high school application and assignment?" We take two approaches to answer the question. First, we exploit quasi-random assignments to middle schools generated by the tie-breaking feature of the admissions system. We find evidence that students who attend high-achievement middle schools apply and are assigned to high-achievement high schools. Second, based on this empirical evidence, we develop and estimate a novel dynamic two-period model of school choice to decompose this effect and analyze the equilibrium consequences of counterfactual policies. In our setup, students applying to middle schools are aware that their choices may affect which high schools they eventually attend. Specifically, the middle schools that students attend can change how they rank high schools (the application channel) and how high schools rank their applications (the priority channel). We find that the application channel is quantitatively more important. Using the estimated model, we ask if an early affirmative action policy can address segregation in later stages. We find that a middle school-only affirmative action policy can alter students’ high school applications and thus their assignments, contributing to desegregating high schools. This finding suggests that early intervention in the form of middle school admissions reform can be a useful tool for desegregation.

"Leveraging Uncertainties to Infer Preferences: Robust Analysis of School Choice" (with Yeon-Koo Che and Yinghua He)

Draft available on request, Recording of presentation at ESWC 2020

Abstract: Recent evidence suggests that market participants make mistakes (even) in a strategically straightforward environment but seldom with significant payoff consequences. Uncertainties arising from the use of lotteries or other sources increase payoff consequences of certain mistakes, and force participants to take care to avoid them. Consequently, uncertainties limit the extent to which certain mistakes are made, thus making it possible for one to infer some preference relations reliably. We propose a novel method of exploiting the uncertainties present in a matching environment to systematically and robustly infer student preferences over schools based on their rank-order lists data. Our method consists of three steps: (i) simulating the underlying structure of uncertainties present in the environment, (ii) extracting preference relations revealed under the simulated uncertainties, and then (iii) extending the revealed preference relations via the axiom of transitivity. Depending on the type of uncertainties present, the method rationalizes a variety of procedures, ranging from truthful-reporting assumption at one extreme (full-support uncertainty) to the stability assumption at the other extreme (when there is little uncertainty). Further, we refine our method to strengthen the robustness of the revealed preferences in the presence of participants making even some payoff-relevant mistakes, and explore ways to optimally balance the tradeoff between robustness and efficiency in preference estimation. We apply our methods to estimate student preferences through a Monte Carlo analysis capturing canonical school choice environment with single tie-breaking lotteries. Finally, we apply our methods as well as other existing methods to New York City high school assignment data to explore their implications for preference estimation and counterfactual analysis under a possible policy intervention.

"Prestige Concerns in College Major Choice" (with Yeon-Koo Che, Jinwoo Kim, Se-jik Kim, Olivier Tercieux)

Draft available on request.

Abstract: We develop a signaling model of prestige seeking in competitive college applications. A prestigious program attracts competition from applicants, which in turn makes the program more selective in admitting students. This further increases the program's prestige and draws further competition, and so on. This amplifying effect of prestige seeking results in a program with little or no quality advantage enjoying a significant prestige in equilibrium. On the student side, the pursuit of prestige forces them to "sacrifice" their idiosyncratic preferences, or fits, for programs in application, resulting in a misallocation of program fits. The analysis of major choice data from Seoul National University provides evidence for the significant role played by the prestige concerns, for misallocation of major fits, and for its adverse effect on a student's academic performance in the chosen major, when majors are assigned through competitive screening---an important feature of college admissions adopted in many countries.

"Sorting, Commuting, and School Choice" (with Minseon Park)

Draft available on request.

Abstract: This paper studies how families use two margins to get a seat in their preferred school under school choice - 1) sorting into neighborhoods (choosing where to live) and 2) commuting to school (choosing which school to apply to). Using New York City student-level data, we present the evidence of both margins. We find a sharp discontinuity at school district boundaries: middle school applicants residing on the side of the boundary with better schools are 5pp less likely to be eligible for Free or Reduced Lunch compared to their peers on the other side. At the same time, students take advantage of choice options actively with significant heterogeneity. 24% of Black students commute across school district boundaries while 12% of White students do. We build and estimate a structural model where a household chooses where to live and then which school to apply to. Location and schools are tied through commuting cost and geography-based priority. We extend the Expectation-Maximization algorithm with Sequential Maximization step (Arcidiacono and Jones, 2003) to estimate the model. We incorporate Boundary Discontinuity Design to deal with the endogeneity of school characteristics. We find that families sort into neighborhoods based on both observable/unobserved taste over school characteristics. There is large individual heterogeneity in terms of which neighborhood gives the higher expected utility. The decomposition exercise shows that heterogeneity in location demand explains 80 percent of the gap in the mean test score of schools Black and White students are assigned to. Both extending the bus service across school districts and adopting free borough-wide choice undo the gap by 10 percent.

"What Makes NYC Specialized High Schools So Special?: Relating School Effectiveness and Student Preferences"

Draft available on request.

Abstract: New York City (NYC) specialized high schools are highly selective and popular among students and parents. Nevertheless, the reason why those schools are so popular compared to non-specialized high schools has not been studied yet. This paper aims to answer the question in the context of academic performance, by studying the relationship among three factors: preference of specialized high schools applicants, peer qualities and causal effectiveness of those schools. First, a unique feature of NYC public high school admission system enables me to link preferences on specialized high schools and non-specialized high schools and hence to jointly estimate those using students' rank-ordered lists. Next, I estimate the value-added of schools that corrects endogenous selection following Abdulkadiroglu et al. (2017), and finally link them to the estimated preference in the first step. I preliminarily find the additional valuation that students and parents put on specialized high schools relative to non-specialized high schools is mostly related with higher peer quality at specialized high schools.