Title: Essays on Empirical School Choice
Description: This dissertation empirically studies market design based centralized school choice. Chapter 1 explores the dynamic relationship between school choices made at different educational stages and how it affects racial segregation across schools. It uses New York City (NYC) public school choice data to ask: "How does the middle school that a student attends affect her high school application and assignment?" The paper takes two approaches to answer the question. First, it exploits quasi-random assignments to middle schools generated by the tie-breaking feature of the admissions system. It finds evidence that students who attend high-achievement middle schools apply and are assigned to high-achievement high schools. Second, based on this empirical evidence, the paper develops and estimates a novel dynamic two-period model of school choice to decompose this effect and analyze the equilibrium consequences of counterfactual policies. In the model, 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). It finds that the application channel is quantitatively more important. Using the estimated model, the paper asks if an early affirmative action policy can address segregation in later stages. It finds 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. Chapter 2 studies the relationship between the popularity of selective exam schools and their academic performance measures. 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 the NYC public high school admission system enables linking applicants' preferences on specialized high schools and non-specialized high schools and hence jointly estimating those using their rank-ordered lists. Next, it estimates the value-added measures of high schools and finally links them back to the estimated preference in the first step. The paper finds that the additional valuation that students/parents put on specialized high schools relative to non-specialized high schools is mostly related to the higher peer quality of specialized high schools. Chapter 3 develops a method of inferring students' preferences from school choice data. Recent evidence suggests that market participants make mistakes (even) in a strategically straightforward environment but seldom with significant payoff consequences.

This paper explores the implications of such payoff-insignificant mistakes for inferring students' preferences from school choice data. Uncertainties arise from the use of lotteries or other sources in a typical school choice setting; they make certain mistakes more costly than others, thus making some preferences---those whose misrepresentation would be more costly and would thus be avoided by students---more reliably inferable than others. The paper proposes a novel method of exploiting the structure of the uncertainties present in a matching environment to robustly infer student preferences under the Deferred-Acceptance mechanism. Monte Carlo simulations show that the method is superior to existing alternative approaches.