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.

Two-sided matching markets are a cornerstone of modern economics. They model a wide range of applications such as ride-sharing, online dating, job positioning, school admissions, and many more. In many of those markets, monetary exchange does not play a role. For instance, the New York City public high school system is free of charge. Thus, the decision on how eighth-graders are assigned to public high schools must be made using concepts of fairness rather than price. There has been therefore a huge amount of literature, mostly in the economics community, defining various concepts of fairness in different settings and showing the existence of matchings that satisfy these fairness conditions. Those concepts have enjoyed wide-spread success, inside and outside academia. However, finding such matchings is as important as showing their existence. Moreover, it is crucial to have fast (i.e., polynomial-time) algorithms as the size of the markets grows. In many cases, modern algorithmic tools must be employed to tackle the intractability issues arising from the big data era. The aim of my research is to provide mathematically rigorous and provably fast algorithms to find solutions that extend and improve over a well-studied concept of fairness in two-sided markets known as stability. This concept was initially employed by the National Resident Matching Program in assigning medical doctors to hospitals, and is now widely used, for instance, by cities in the US for assigning students to public high schools and by certain refugee agencies to relocate asylum seekers. In the classical model, a stable matching can be found efficiently using the renowned deferred acceptance algorithm by Gale and Shapley. However, stability by itself does not take care of important concerns that arose recently, some of which were featured in national newspapers. Some examples are: how can we make sure students get admitted to the best school they deserve, and how can we enforce diversity in a cohort of students? By building on known and new tools from Mathematical Programming, Combinatorial Optimization, and Order Theory, my goal is to provide fast algorithms to answer questions like those above, and test them on real-world data. In Chapter 1, I introduce the stable matching problem and related concepts, as well as its applications in different markets. In Chapter 2, we investigate two extensions introduced in the framework of school choice that aim at finding an assignment that is more favorable to students -- legal assignments and the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) -- through the lens of classical theory of stable matchings. We prove that the set of legal assignments is exactly the set of stable assignments in another instance. Our result implies that essentially all optimization problems over the set of legal assignments can be solved within the same time bound needed for solving it over the set of stable assignments. We also give an algorithm that obtains the assignment output of EADAM. Our algorithm has the same running time as that of the deferred acceptance algorithm, hence largely improving in both theory and practice over known algorithms. In Chapter 3, we introduce a property of distributive lattices, which we term as affine representability, and show its role in efficiently solving linear optimization problems over the elements of a distributive lattice, as well as describing the convex hull of the characteristic vectors of the lattice elements. We apply this concept to the stable matching model with path-independent quota-filling choice functions, thus giving efficient algorithms and a compact polyhedral description for this model. Such choice functions can be used to model many complex real-world decision rules that are not captured by the classical model, such as those with diversity concerns. To the best of our knowledge, this model generalizes all those for which similar results were known, and our paper is the first that proposes efficient algorithms for stable matchings with choice functions, beyond classical extensions of the Deferred Acceptance algorithm. In Chapter 4, we study the discovery program (DISC), which is an affirmative action policy used by the New York City Department of Education (NYC DOE) for specialized high schools; and explore two other affirmative action policies that can be used to minimally modify and improve the discovery program: the minority reserve (MR) and the joint-seat allocation (JSA) mechanism. Although the discovery program is beneficial in increasing the number of admissions for disadvantaged students, our empirical analysis of the student-school matches from the 12 recent academic years (2005-06 to 2016-17) shows that about 950 in-group blocking pairs were created each year amongst disadvantaged group of students, impacting about 650 disadvantaged students every year. Moreover, we find that this program usually benefits lower-performing disadvantaged students more than top-performing disadvantaged students (in terms of the ranking of their assigned schools), thus unintentionally creating an incentive to under-perform. On the contrary, we show, theoretically by employing choice functions, that (i) both MR and JSA result in no in-group blocking pairs, and (ii) JSA is weakly group strategy-proof, ensures that at least one disadvantaged is not worse off, and when reservation quotas are carefully chosen then no disadvantaged student is worse-off. We show that each of these properties is not satisfied by DISC. In the general setting, we show that there is no clear winner in terms of the matchings provided by DISC, JSA, and MR, from the perspective of disadvantaged students. We however characterize a condition for markets, that we term high competitiveness, where JSA dominates MR for disadvantaged students. This condition is verified, in particular, in certain markets when there is a higher demand for seats than supply, and the performances of disadvantaged students are significantly lower than that of advantaged students. Data from NYC DOE satisfy the high competitiveness condition, and for this dataset our empirical results corroborate our theoretical predictions, showing the superiority of JSA. We believe that the discovery program, and more generally affirmative action mechanisms, can be changed for the better by implementing the JSA mechanism, leading to incentives for the top-performing disadvantaged students while providing many benefits of the affirmative action program.

This dissertation consists of three essays in public economics. The three chapters focus on interactions between public and private economic decisions. The first two chapters focus on unemployment insurance (UI) policy in the United States. The third discusses public-private interactions in the education market. The first chapter, a joint work with Arindrajit Dube, Calvin Jahnke, Raymond Kluender, Suresh Naidu, and Michael Stepner estimates the labor supply and spending responses to a large change in UI benefits during the pandemic. We examine the effects of the sudden withdrawal of expanded pandemic unemployment benefits in June 2021 using anonymized bank transaction data for 16,548 individuals receiving UI in April 2021. Comparing the difference in differences between states withdrawing and retaining expanded UI, we find that UI receipt falls 35 p.p. while employment rises by only 4.4 p.p. by early August. Average cumulative UI benefits fall by $1,385 while average cumulative earnings increase by only $93. Heterogeneity by unemployment duration implies that these effects are primarily driven by extensive margin expiration of benefits, rather than intensive margin reductions in the benefit level. The second chapter examines the role of gifts and loans from friends and family during unemployment. These transfers play a largely unstudied informal insurance role in high-income countries, making it difficult to assess their implications for social insurance policy. I present new results on informal insurance paid via person-to-person (P2P) payment platforms using a survey-linked administrative bank transaction dataset covering 130,502 low-income users from the US who were unemployed at least once between July 2019 and September 2020. Event study estimates show average monthly inflows from all P2P platforms increase by $30, or 2% of lost earnings, one month after job loss before returning to baseline over 10 months. Single mothers and the long-term unemployed receive the largest increases, as do those living in high-income areas. I exploit three plausibly exogenous changes to federal pandemic unemployment insurance (UI) policy to estimate that UI benefits crowd out at most $0.04 of informal P2P transfers. Using the social insurance framework introduced in Chetty & Saz (2010), my crowd-out estimates indicate negligible welfare consequences for an additional dollar of benefits. Altogether these results imply that public UI benefits can raise welfare by pooling risk across networks without reducing within-network targeting of informal insurance. The third chapter asks whether public school services fill in gaps left by private school failures. Specifically, it explores what type of schools enter the market and experience an increase in enrollment after reports of abuse by Catholic priests lead to Catholic Schools closures. I use a two-way fixed effects event study method to estimate a change in enrollments and number of different types of schools after a report of priest abuse within the same zip code, school district, or county. I find there are 0.2 fewer Catholic schools and Catholic school enrollment falls by 75 students after six years, which are offset by a 0.2 and 50-student increase in charter school counts and enrollments on average. These increases are unique to charter schools and is not observed in other public or non-Catholic private schools. Altogether, these results suggest that former Catholic schooled families show a preference for charter schools over other public schools, which may be due to the low-cost and similar emphasis on discipline and academic achievement.