the second term enforces the equality conditions. The estimator $\hat{\theta}_{MEI}$ minimizes this
objective function, and marginal confidence intervals can be constructed using the
procedure developed by Bugni et al. (2017).

2.3.6 Selecting Among Alternative Preference Inference Hypotheses

Each of the preference estimation approaches reviewed above relies on distinct
identifying assumptions grounded in revealed preference restrictions. A natural
question is whether empirical tests can distinguish between these alternatives. The
answer depends critically on the richness of the data and the degree of structure
one is willing to impose on preferences and behavior.

**Overcoming the limitations of administrative data.** Inference based solely on administrative data from centralized school choice or college admission systems faces fundamental limitations. Absent behavioral or parametric restrictions, it is generally not possible to empirically test the identifying assumptions underlying different estimation approaches. For instance, in the portfolio choice framework, Agarwal and Somaini (2018, Theorem A.1) show that any ROL can be rationalized as optimal for some utility vector, as long as each ranked school has strictly positive assignment probability. This flexibility makes it impossible to separately identify heterogeneity in preferences from heterogeneity in strategic sophistication without additional structure. Likewise, it is always possible to find a utility vector that is consistent with both truth-telling and stability, making it difficult to discriminate between these assumptions using administrative data alone.

To address these limitations, several complementary strategies have emerged. One line of research uses laboratory experiments to examine how individuals report preferences in controlled matching environments, offering insights into the determinants of preference misrepresentation under both manipulable and strategy-proof mechanisms (see the reviews by Hakimov and Kübler, 2021 and Rees-Jones and Shorrer, 2023). Complementing this experimental evidence, a growing number of field studies exploit institutional features of real-world matching systems, such as the joint determination of admissions and financial aid, to detect preference misrepresentation using administrative data from strategy-proof mechanisms (Hassidim et al., 2021; Artemov et al., 2023; Shorrer and Sóvágó, 2023, e.g.).

A second approach relies on field surveys administered to participants in school
choice or college admissions systems to elicit their preferences and beliefs (e.g.,
Budish and Cantillon, 2012; Chen and Pereyra, 2019; Kapor et al., 2020; Larroucau
and Rios, 2020; Hassidim et al., 2021; Arteaga et al., 2022; Bobba et al., 2023; De Haan et al., 2023; Corradini and Idoux, 2025; Larroucau et al., 2025). These surveys have documented systematic biases in beliefs about admission probabilities, limited knowledge of available options and their characteristics, misunderstanding of the assignment mechanism, and evidence of optimization failures (see Sections 3.1.2 and 3.1.3). This survey evidence is increasingly being combined with administrative data to estimate structural models of application behavior and conduct counter-factual policy simulations (e.g., Kapor et al., 2020; De Haan et al., 2023; Ajayi and Sidibé, 2024; Ajayi et al., 2025; Larroucau et al., 2025).

As discussed in Sections 2.1 and 2.2, this body of work has directly informed the development of methods that relax the assumption of full rationality in preference estimation. These include approaches that allow for heterogeneous levels of strategic sophistication among applicants (Hwang, 2015; He, 2017; Agarwal and Somaini, 2018; Calsamiglia et al., 2020; Kapor et al., 2020; Bayraktar and Hwang, 2024); models in which agents fail to fully internalize continuation values when constructing their ROL (Idoux, 2023; Wang et al., 2025); and frameworks that accommodate strategic mistakes even in strategy-proof environments (Artemov et al., 2023; Che et al., 2023).

**Leveraging the nesting structure of identifying assumptions.** When relying solely on administrative data, the plausibility of the assumptions underlying different preference estimation approaches must be carefully evaluated in context. For instance, assuming rational expectations in the portfolio choice framework is more credible when participants have access to reliable information about the competitiveness of various schools than when this information is not publicly available. In DA settings, WTT is more plausible when students face significant uncertainty about their priorities and can rank an unlimited number of schools at no cost. Conversely, when list-length restrictions or application costs are present, stability may be more compelling than truth-telling, especially in large markets where admission cutoffs are easier to predict.

In some cases, the nesting structure of identifying assumptions allows for specification tests. Fack et al. (2019) exploit this feature to propose a test of WTT against stability in strict-priority DA settings.<fnref n="49" /> Because WTT implies stability but not vice versa, WTT imposes over-identifying restrictions under the stability framework.

<footnote n="49">⁴⁹For a generalization of this test to settings with priority uncertainty, see Che et al. (2023). Fack et al. (2019) also propose a test of stability against the undominated-strategies assumption, which involves checking whether the identified set from the moment (in)equality model (12) is empty, using the specification test developed by Bugni et al. (2015). However, current moment (in)equalities techniques tend to yield conservative confidence sets, limiting the power of such tests.</footnote>
This allows for a Hausman-type test: under the null hypothesis that applicants are weakly truth-telling, both the WTT and stability estimators, $\hat{\theta}_{WTT}$ and $\hat{\theta}_{Stability}$, are consistent; under the alternative—that WTT is violated but the assignment is stable—only $\hat{\theta}_{Stability}$ remains consistent. A test statistic can thus be constructed as:

$$ (\hat{\theta}_{Stability} - \hat{\theta}_{WTT})' (V(\hat{\theta}_{Stability}) - V(\hat{\theta}_{WTT}))^{-1} (\hat{\theta}_{Stability} - \hat{\theta}_{WTT}), $$

where $V(\cdot)$ denotes the covariance matrix of the estimator. Under the null, the statistic is asymptotically $\chi^2_{|\theta|}$ distributed, and rejection indicates that the data are inconsistent with WTT, assuming correct model specification.

This test has been applied across a range of DA settings and has generally led to rejection of WTT in favor of stability (Fack et al., 2019; Arslan, 2021; Che et al., 2023; Andersson et al., 2024; Ngo and Dustan, 2024). For example, using data from 15 Swedish school districts over multiple years, Andersson et al. (2024) find that WTT is rejected in 66 of 75 datasets. A caveat, however, is that rejection of WTT in favor of stability does not definitely rule out truth-telling, as the test is conditional on the model's parametric assumptions. In the presence of misspecification, the test may simply favor the less restrictive model. Developing non-parametric methods to formally compare and select among competing identification assumptions represents a promising direction for future research.

## 3 Empirical Insights from Centralized School Choice

The methods reviewed in the previous section, together with researchers' growing access to rich administrative data from centralized school assignment systems, have fueled a rapidly expanding empirical literature applying the tools of market design to school choice. This section provides an overview of some of the main insights that have emerged from this body of work.

While the broader empirical literature on school choice has traditionally focused on the effects of competition between public, private, charter, and voucher schools on school productivity, student sorting, and academic outcomes (see Hoxby, 2003a; Bettinger, 2011; Epple et al., 2016; Urquiola, 2016; Cohodes and Parham, 2021, for surveys), the empirical market design literature places greater emphasis on the organization of the choice process itself. This line of research builds on theoretical advances in matching theory to study the design of centralized assignment systems, how families respond to their core features, and how these design choices affect individual welfare and distributional outcomes. Methodologically, it com-
bines reduced-form and structural approaches, leveraging detailed administrative data from these assignment systems to estimate student preferences, assess the performance of matching mechanisms, and conduct counterfactual analyses under alternative policy designs. Our review builds on earlier syntheses by Cantillon (2017), Pathak (2017), and Agarwal and Somaini (2020), while incorporating more recent empirical contributions and policy applications. Where relevant, we also draw on evidence from centralized college admissions, as findings from these settings provide useful perspectives for the design of school choice systems.

We organize the discussion around three central themes. First, we examine how families form preferences and make application decisions, with particular attention to information frictions and behavioral deviations from full rationality (Section 3.1). Second, we explore the design trade-offs in school choice systems, including the degree of centralization, the choice of assignment mechanisms, and the use of decision-support tools (Section 3.2). Third, we assess the broader effectiveness of centralized school choice reforms, focusing on their market-level impacts, distributional consequences, and interactions with other household decisions such as residential choice (Section 3.3).

## 3.1 Preferences and Application Behavior

A central question in the empirical school choice literature is how families form preferences and translate them into application decisions. This section reviews the evidence along three dimensions that jointly shape how families engage with centralized assignment systems and help explain observed disparities in outcomes: (i) the determinants of parental preferences; (ii) the distorting effects of information gaps on decision-making; and (iii) the influence of bounded rationality on application behavior.

### 3.1.1 Drivers of Preferences and Preference Heterogeneity

A consistent finding across empirical studies of school choice is that families' reported preferences correlate with both proximity to schools and a range of school attributes (e.g., Hastings et al., 2009; Burgess et al., 2015; Akyol and Krishna, 2017; Pathak and Shi, 2021; Beuermann et al., 2023). These attributes include not only academic performance indicators and peer composition, but also more idiosyncratic features such as school denomination and educational philosophy (e.g., Borghans et al., 2015).
A key trade-off parents face is between school quality and geographic proximity. Because the set of available alternatives varies in quality and distance, parents must often choose between a nearby school and one with stronger academic outcomes. This trade-off is particularly pronounced for low-socioeconomic status (low-SES) families, who are more constrained in their options due to residential sorting. In England, Burgess et al. (2015) estimate that differences in geographic constraints explain approximately two-thirds of the observed SES gap in the quality of chosen schools. Geography thus remains a major obstacle to equalizing access to high-performing schools.

Even when proximity and school availability are held constant, substantial heterogeneity in parental preferences persists. Numerous studies document systematic differences in school preferences by socioeconomic status and race (e.g., Hastings et al., 2009; Borghans et al., 2015; Burgess et al., 2015; Oosterbeek et al., 2021; Ajayi, 2024; Laverde, 2024; Corradini and Idoux, 2025), as well as by gender (e.g., Ngo and Dustan, 2024). For instance, in their landmark study of school choice in the Charlotte-Mecklenburg School Public School District (CMS), North Carolina, Hastings et al. (2009) show that higher-SES families place greater weight on test scores, whereas lower-SES and minority families balance academic quality against preferences for schools with predominantly same-race peers. Vignette experiments in New York City (Corradini and Idoux, 2025) confirm that families favor schools with peer groups that match their own racial background. In Amsterdam, Oosterbeek et al. (2021) estimate that such preference heterogeneity accounts for 40% of ethnic segregation and 25% of income segregation across secondary schools. These findings underscore a core limitation of school choice as a tool for integration: even when access is formally equalized, segregation may persist or even intensify if preferences remain stratified by social group.

A central policy concern is whether parents value a school's causal effectiveness (value-added) or merely its peer composition. If families prioritize peers over instructional quality, Barseghyan et al. (2019) show that school choice reforms may fail to generate competitive pressure for academic improvement, and could even reduce overall welfare. For choice to raise productivity, it must reward schools for effective teaching, not for attracting already high-achieving students. Yet this distinction is often blurred in practice. In New York City, Abdulkadiroğlu et al. (2020b) find that parental preferences correlate with both peer quality and value-added, but are uncorrelated with true effectiveness once peer composition is controlled for. This suggests that parents tend to penalize schools serving lower-achieving peers regardless of the actual instructional value they provide, weakening the intended
incentive structure of school choice policies.

Whether parents value school effectiveness may depend on context, particularly
the information environment and the multidimensional nature of school output.
Evidence from Beuermann et al. (2023) underscores this point. Using administrative
and survey data on public secondary school choice in Trinidad and Tobago, the
authors estimate the causal effects of attending specific schools on a wide array of
academic and non-academic outcomes, including dropout, arrests, teen motherhood,
and labor market participation. They find that schools' causal effects on student
performance in the high-stakes tests taken at the end of secondary school are
only weakly correlated with their effects on longer-term non-academic outcomes,
highlighting the limitations of relying on test scores as the sole measure of school
effectiveness. Linking these causal estimates to parents' school rankings, they show
that parents do value schools that raise test scores, but also prefer those that reduce
crime and teen births and improve labor market outcomes. Notably, families of
low-achieving students place greater weight on non-academic impacts, whereas
high-achieving students' families prioritize test score gains. These results indicate
that, in some settings, parents recognize and act upon a broader conception of school
quality—one that extends beyond test scores—which highlights the importance of
accounting for a wider range of school contributions when designing and evaluating
school choice policies.

Together, these findings raise a deeper question: to what extent do application
patterns reflect genuine preferences, as opposed to differences in the information
families possess and how they process it when forming and reporting school
rankings? This distinction has spurred a growing body of work on informational
frictions and bounded rationality in school choice.

3.1.2 Information Frictions

Across a wide range of contexts, school choice participants are often found to be
misinformed about key aspects of the matching process, such as the characteristics
of schools, the full menu of available options, and their chances of admission. These
information frictions carry important implications for both the efficiency and equity
of assignment outcomes.

A consistent finding in the literature is that many families lack accurate infor-
mation about school attributes, which can lead to suboptimal application decisions
(e.g., Hastings and Weinstein, 2008; Ainsworth et al., 2023; Agte et al., 2024; Campos,
2024; Corradini, 2024; Ajayi et al., 2025; Corradini and Idoux, 2025; Larroucau et al.,
2025). In a seminal study leveraging both natural and field experimental variation in the CMS District, Hastings and Weinstein (2008) show that providing low-income families with information about school test scores increases their likelihood of applying to higher-scoring schools and leads to improved outcomes for their children. These findings illustrate that disadvantaged households may fail to consider high-performing schools simply due to lack of information, even when those schools are accessible.

Other studies highlight persistent racial and social gaps in the quality of information families possess. In New York City, Corradini (2024) documents that Black and Hispanic families apply to lower value-added high schools than White and Asian families, and attributes part of this gap to inaccurate beliefs about school quality. This is evidenced by the fact that the introduction of a letter-grade rating system shifted their choices more than those of white and Asian families, reducing racial gaps in both enrollment at high-quality schools and subsequent academic achievement. Complementing this, Corradini and Idoux (2025) find that racial disparities in application behavior also stem from differences in school awareness, i.e., the extent to which families know that certain schools exist.

Social interactions play a critical role in shaping how families access and interpret school-related information. Campos (2024) finds that parents tend to underestimate school value-added and overestimate peer quality. But when provided with accurate information, both they and their neighbors adjust their preferences in favor of higher value-added schools. This pattern reveals not only a latent demand for school effectiveness but also the powerful mediating role of social networks in transmitting information and influencing choices. In a similar vein, Corradini and Idoux (2025) show that exposure to more diverse middle school peers reduces racial gaps in high school applications by broadening families' awareness of available school options and shifting preferences toward greater peer diversity. Their evidence suggests that racial disparities in school choice are not only driven by homophily in preferences but also by unequal information environments mediated by social exposure. Together, these findings highlight that social context and peer environments can reinforce or mitigate informational inequalities, with important implications for both segregation and access to high-quality schools.

Information frictions can also arise from the difficulty of navigating a complex menu of options. When families face high search and processing costs, they may make poorly informed decisions upfront and revise their preferences only after experiencing their initial match. Narita (2018) provides evidence of this dynamic in New York City's high school choice system, where families dissatisfied with their
initial match can participate in a discretionary reapplication process. He finds that over 70% of reapplicants reverse their original school rankings, with most changes reflecting genuine updates in preferences driven by learning rather than strategic misreporting. These shifts in demand undermine the welfare performance of the initial match, which assumes stable and well-informed preferences. Narita (2018) further shows that a centralized reapplication mechanism could significantly outperform the existing discretionary process, highlighting the importance of aftermarket design to accommodate evolving preferences.

Alongside misperceptions of school attributes, families also hold inaccurate beliefs about admission chances (e.g., Kapor et al., 2020; Agte et al., 2024; Ajayi and Sidibé, 2024; Arteaga et al., 2022). In environments that require strategic decision-making, such errors can be particularly costly because they directly influence how applicants rank schools. In New Haven, Kapor et al. (2020) find that families frequently misperceive their admission probabilities, with average absolute deviations from rational expectations reaching 37 percentage points. A common misconception is failing to understand that placing a school lower in one's ROL reduces the chance of admission. These belief errors are not merely anecdotal: Kapor et al. estimate that they lead to a 24% welfare loss compared to a best-case scenario in which families are fully informed and play the Bayes-Nash equilibrium in the game induced by the New Haven mechanism.

Importantly, such distortions also arise under strategy-proof mechanisms and can induce suboptimal behavior by distorting how applicants conduct their school search. Using data from a large-scale survey of participants in Chile's centralized school choice system, Arteaga et al. (2022) find that applicants systematically overestimate their admission probabilities, especially when the true likelihood of placement is low. This leads to premature termination of the search process and the submission of overly narrow application portfolios. More broadly, Agte et al. (2024) show that misperceptions about school availability, quality, and admission probabilities interact to reduce search effort and lower match quality relative to a full-information benchmark.

These findings have motivated the development of school choice platforms and interventions aimed at helping families navigate the complexity of the application process and conduct a more effective school search. We return to these policy implications and design innovations in Section 3.2.1.
### 3.1.3 Bounded Rationality

While information frictions contribute to suboptimal decisions in centralized school choice, a growing body of evidence suggests that participants also deviate from fully rational decision-making in ways that go beyond informational constraints.

A longstanding concern in school choice design is that families differ in their ability to understand the assignment rules and optimize their application strategies accordingly. This heterogeneity in strategic sophistication has motivated the widespread adoption of strategy-proof mechanisms, which aim to protect participants who may lack the cognitive resources for complex reasoning. As discussed in Section 1.6, mechanisms that reward strategic play may yield inequitable outcomes when some families are better equipped to navigate the strategic environment than others. This concern is empirically illustrated by Abdulkadiroğlu et al. (2006a,b), who show that under Boston's former IA mechanism, families differed markedly in their ability to anticipate capacity constraints. While some adjusted their sub-missions strategically, others failed to do so, leading to avoidable non-assignments. Further evidence comes from lab experiments by Basteck and Mantovani (2018), who find that under manipulable mechanisms, participants with lower cognitive ability are more likely to be matched to lower-quality schools.

Notably, even in strategy-proof settings with readily accessible information, many applicants continue to misrepresent their preferences. This pattern has been documented in both laboratory and field settings (see Section 2.2.1), and in some cases results in meaningful welfare losses. These findings raise concerns about the real-world effectiveness of non-manipulable mechanisms and suggest that their theoretical benefits may not always be realized in practice. In response, a growing literature in behavioral market design seeks to identify the sources of preference misrepresentation in strategy-proof environments. While the full policy implications have yet to be fully explored, incorporating behavioral insights into system design is increasingly seen as essential for ensuring that school choice mechanisms are not only theoretically robust but also practically effective and equitable.

Rees-Jones and Shorrer (2023) provide a comprehensive review of this emerging literature and identify three broad categories of behavioral explanations for preference misrepresentation in strategy-proof environments.

The first centers on incorrect processing of incentives, where participants fail to fully grasp the strategic properties of the mechanisms. This includes failures of contingent reasoning (Niederle and Vespa, 2023), reliance on faulty heuristics (Hassidim et al., 2017; Rees-Jones and Shorrer, 2023), and misunderstandings of
continuation value (Idoux, 2023; Wang et al., 2025).

The second category involves non-standard preferences. These include report-
dependent preferences, where individuals are averse to rejection and derive utility
from being assigned to a school they actively ranked, leading them to apply to
schools with higher admission likelihoods (Meisner, 2022; Kloosterman and Troyan,
2024); and expectations-based reference dependence, where students form psycho-
logical attachments to schools they expect to attend and avoid ranking high-value
but unlikely options to minimize potential disappointment (Dreyfuss et al., 2022b;
Meisner and van Wangenheim, 2023).

The third category stems from models of incorrect processing of admission
probabilities. A common example is overconfidence in admission chances (Pan,
2019; Kapor et al., 2020; Arteaga et al., 2022; Larroucau et al., 2025), which can lead
students to under- or over-apply to certain schools. Another documented bias is
correlation neglect, where applicants fail to recognize that admission probabilities
are correlated across schools, causing them to omit viable fallback options from
their application portfolios (Rees-Jones et al., 2024).

These behavioral insights are increasingly being integrated into empirical meth-
ods for preference estimation, either by allowing for certain types of mistakes in the
stability-based approach (Artemov et al., 2023; Che et al., 2023), or by embedding
psychological structure into the portfolio choice models (Idoux, 2023; Wang et al.,
2025). Beyond estimation, they have begun to inform the design of interventions,
such as simplified application platforms, nudges, and targeted information provi-
sion, aimed at mitigating welfare losses from cognitive and behavioral frictions. As
discussed in the next section, this research agenda opens promising avenues for
policy innovation in the design and implementation of school choice systems.

## 3.2 Market Design Trade-offs

Closely linked to the extensive theoretical literature on matching mechanisms in
education, a substantial body of empirical research has investigated the trade-offs
involved in the design of centralized assignment systems.

3.2.1 Centralized vs. Decentralized Choice

One of the main theoretical motivations for adopting centralized, single-offer school
assignment systems is their ability to reduce misallocation caused by congestion
and matching frictions in decentralized and uncoordinated processes. However,
empirically comparing the allocative efficiency of centralized and decentralized
systems is challenging, as the latter rarely produce the kind of systemic data needed
to directly assess student welfare across regimes.

Abdulkadiroğlu et al. (2017a) address this challenge by analyzing New York City's transition from an uncoordinated high school admissions system to one based on the DA mechanism in 2003. Using data from the new centralized system to estimate student preferences, they find that it achieved approximately 80% of the welfare gains attainable by moving from a neighborhood-based assignment to a utilitarian optimal allocation, while the uncoordinated system achieved at most 35% of these gains. The largest improvements accrued to students who were most likely to remain unassigned in the previous system and were administratively placed after the main round. These results suggest that congestion and ad hoc placement were key sources of inefficiency in the uncoordinated system. Notably, the efficiency gains occurred in a context where families were already familiar with school choice, as both systems used a common application. This implies that even greater benefits from coordination may be possible in settings with less structured markets or less experienced participants.

Further support for centralization comes from studies of the welfare effects of off-platform options in centralized assignment mechanisms—i.e., alternatives available to participants but operating outside the centralized platform. The existing evidence comes primarily from college admissions. In Chile, Kapor et al. (2024) show that off-platform programs generate negative externalities, as applicants forgo centralized offers in favor of alternatives, leading to greater waitlisting and aftermarket frictions. Exploiting a 2012 reform that expanded the centralized platform's capacity by 40%, they find substantial welfare gains and higher graduation rates conditional on enrollment. In Albania, Vrioni (2024) studies the integration of private colleges into the centralized platform and reports more nuanced effects: while the reform improved the matching outcomes of low-SES students relative to their high-SES peers, it was associated with an overall welfare loss, driven by strict list-length constraints and admission uncertainty that encouraged overly cautious application portfolios. These findings highlight the importance of relaxing list-length limits and improving information about admission probabilities to fully realize the benefits of centralization.

These lessons, however, may not be directly applicable to K–12 school choice,
where institutions and participation margins differ. In the United States, many
districts operate opt-in systems, whereby families default to a neighborhood school
unless they actively participate in a centralized process. This design resembles an off-
platform setting and raises important but understudied questions: Which schools
are included on the platform, who chooses to opt in, and how do information
frictions and application costs shape participation? More evidence is needed to
assess how these factors affect both equity and efficiency, and to clarify the trade-offs
between partial and full centralization in K-12 settings.

3.2.2 Trade-offs between Assignment Mechanisms

A central insight from the theoretical literature on market design is that selecting
a student assignment mechanism involves inherent trade-offs between efficiency,
fairness, and strategy-proofness (see Section 1).

A prominent illustration of these trade-offs is the long-standing debate sur-
rounding the use of IA vs. DA in centralized assignment systems. While IA has
been widely criticized for its poor incentive properties compared to DA, its com-
parative efficiency remains theoretically ambiguous. As discussed in Section 1.6,
Abdulkadiroğlu et al. (2011b) show that when applicants have correlated ordinal
preferences over schools and priorities are determined purely by lotteries, IA can
Pareto dominate DA in terms of cardinal welfare. The intuition is that IA enables
applicants to signal the intensity of their preferences through strategic play: only
those with strong preferences will apply to highly competitive schools. As a result,
IA tends to allocate seats to applicants who value them the most, leading to higher
average welfare ex ante (i.e., before lottery tie-breakers are realized). However, this
potential efficiency advantage must be weighed against the risks that IA poses to
participants who lack the information or the sophistication to strategize effectively.

To inform this debate, the empirical literature has evaluated the performance of
IA in real-world settings—including Amsterdam, Barcelona, Beijing, Boston, New
Haven, and Wake County—focusing on its implications for efficiency and equity
relative to DA. Comparing these mechanisms is empirically challenging due to
the difficulty of recovering preferences from data generated under manipulable
mechanisms. Researchers have addressed this challenge using a range of strategies
(see Section 2.1).

Studies that estimate preferences using submitted ROLs generally find that IA
dominates DA in terms of average welfare (typically measured in distance units).
This result holds under a range of modeling assumptions: when applicants are
assumed to have rational or adaptive expectations (Agarwal and Somaini, 2018),
when they are modeled as a mix of naive and sophisticated players (Agarwal
and Somaini, 2018; Calsamiglia et al., 2020; Xu and Hammond, 2024), or when
restrictions are imposed based on the assumption that participants do not play
dominated strategies (Hwang, 2015; He, 2017; Bayraktar and Hwang, 2024).

However, a key limitation in comparing the welfare implications of IA and DA
is the sensitivity of these analyses to assumptions about applicants' beliefs and
decision-making behavior. To address this, a complementary line of research incor-
porates survey data on beliefs and stated preferences (Kapor et al., 2020; De Haan
et al., 2023), or relies on direct measures of strategic sophistication (Dur et al., 2018a).
These studies consistently find that in IA settings, applicants frequently hold inaccu-
rate beliefs about their admission chances, and that socially disadvantaged students
are less likely to behave strategically. Such belief and optimization errors are critical
to the welfare comparison between IA and DA. In New Haven, Kapor et al. (2020)
show that accounting for applicants' subjective belief errors reverses the welfare
ranking: switching from IA to DA would increase average welfare, whereas assum-
ing rational expectations would imply the opposite. Similarly, De Haan et al. (2023)
find that in Amsterdam, incorporating strategic mistakes—whether due to biased
beliefs or suboptimal choices given those beliefs—reverses the welfare ordering of
IA and DA relative to the rational expectations benchmark. These findings suggest
that, in practice, the costs of strategic mistakes under manipulable mechanisms
tend to outweigh the benefits of increased expressiveness. Such concerns have been
central to the adoption of strategy-proof mechanisms in districts such as Amsterdam,
Boston, New Haven, and Wake County, all of which transitioned from IA to DA.

Theoretical work by Shorrer (2019), Calsamiglia et al. (2021), and Akbarpour et al. (2022) demonstrates that manipulable mechanisms such as IA raise equity concerns not only because participants differ in strategic sophistication, but also because these mechanisms systematically favor those with better outside options (such as access to private school alternatives), thereby fostering endogenous segregation (see Section 1.6). Empirical evidence supports these predictions. For example, Calsamiglia and Güell (2018) show that while only 4% of schools in Barcelona are private, 14% of families who adopt risky application strategies end up enrolling in a private school when not admitted to their preferred public option. This suggests that access to outside options is disproportionately concentrated among families willing to take greater strategic risks. Likewise, Akbarpour et al. (2022) document that prior to New Haven's switch from IA to DA, students with outside options were significantly more likely to rank oversubscribed, highly rated schools. This behavioral gap disappeared after the reform, reinforcing the idea that access to outside options amplifies strategic distortions under IA and exacerbates existing inequalities among participants.
However, evidence from Terrier et al. (2025) underscores that the equity implications of strategic behavior are highly context-dependent. In particularly competitive environments, such as local authorities in England with selective schools, IA can lead high-SES families to strategically avoid ranking overdemanded schools where they could, in fact, have gained admission. Consistent with the example in footnote 17, this behavior lowers competition for the most sought-after schools, thereby improving access for low-SES students. Because of this “competition-for-top-schools” effect, replacing IA with DA can, in some settings, reduce access to high-quality options for disadvantaged groups by intensifying competition. The experience in England illustrates this risk: Terrier et al. find that banning IA led to a deterioration in both school quality and peer composition for low-SES students.

While much of the empirical literature has focused on IA and DA, comparatively less is known about TTC, which has rarely been implemented in practice. To our knowledge, the New Orleans Recovery School District is the only system to have adopted TTC, before switching to DA after one year. According to Pathak (2017), this change was partly motivated by the difficulty of explaining how TTC handled priorities, which created confusion among families and administrators. Existing evaluations, based primarily on counterfactual simulations (Abdulkadiroğlu et al., 2017a, 2020a; Calsamiglia et al., 2020; Xu and Hammond, 2024), generally find that TTC yields only modest welfare gains relative to DA. For example, Abdulkadiroğlu et al. (2017a) show that while TTC outperforms DA in some respects, the bulk of welfare improvements in New York City’s school choice reform came from moving to a coordinated system—highlighting that the gains from centralization often exceed those from switching assignment mechanisms within a centralized framework.

As DA has gained widespread adoption, recent research has increasingly turned to how specific design features shape its performance. One key consideration is the use of list-length constraints, which are common in practice. Beyond undermining the strategy-proofness of DA, such constraints can generate significant welfare losses by increasing the risk of non-assignment and reducing match quality. This pattern has been documented in both school choice contexts (Ajayi and Sidibé, 2017) and college admissions (Luflade, 2019; Hernández-Chanto, 2021; Ekbatani, 2022), underscoring the potential gains from relaxing list-size limits or helping students better target feasible options.

Another influential design choice concerns the implementation of DA in sequential rather than static form. A growing body of theoretical and experimental work shows that sequential versions of strategy-proof mechanisms encourage more truthful reporting (Li, 2017; Klijn et al., 2019; Bó and Hakimov, 2020) and reduce the
impact of behavioral biases such as loss aversion (Meisner and van Wangenheim, 2021; Dreyfuss et al., 2022a). Moreover, building on an emerging literature that investigates the implications of costly information acquisition for the design of matching markets (e.g., Bade, 2015; Immorlica et al., 2020; Artemov, 2021; Bucher and Caplin, 2021; Chen and He, 2021, 2022; Noda, 2022; Hakimov et al., 2023; Koh and Lim, 2025), there is increasing evidence that sequential implementations of DA facilitate more effective learning by allowing students to update their admission chances and refine their preferences accordingly.

Empirical studies support this view across a variety of contexts. Luflade (2019) shows that in Tunisia's sequential DA college match, where students are assigned by priority tiers over multiple rounds, disclosing program vacancies between rounds enables applicants to update their expectations about admission chances and improves final allocations. In Chile, Larroucau et al. (2025) find that providing real-time personalized information about college applicants' admission probabilities, alongside warning messages and cutoff scores for all programs in the centralized system—resembling a one-shot implementation of the iterative DA algorithm described by Bó and Hakimov (2022)—reduces application mistakes and enhances student matching outcomes. Using data from the German college match—where the initial stages of the college-proposing DA mechanism are implemented in real time, allowing students to hold multiple offers—Grenet et al. (2022) show that multioffer mechanisms raise expected utility by enabling applicants to learn their preferences more efficiently.

Sequential assignment procedures can also mitigate inefficiencies caused by off-platform options, which arise when students reject centralized offers in favor of outside opportunities, leaving vacancies in programs that other applicants would have preferred over their own match. Using data from France's former three-round centralized college admissions system, which reallocated offers declined by students opting for off-platform alternatives, De Groote et al. (2025) estimate a dynamic model of application and acceptance decisions that captures students' trade-off between waiting for a better offer and the cost of delayed certainty. Despite substantial waiting costs, counterfactual simulations indicate that the sequential mechanism outperforms a standard one-round alternative in terms of match quality, graduation rates, and student welfare.
### 3.2.3 Choice Support

While the design of matching mechanisms is central to the functioning of centralized assignment systems, optimizing the mechanism alone is not sufficient. Equally important is ensuring that participants can navigate the system effectively and make informed decisions. The information frictions documented in Section 3.1.2 have spurred growing interest in integrating informational interventions into school choice and college admissions platforms. These developments raise important questions for market design: what kinds of information best support families’ decision-making, and how should that information be communicated?

A substantial empirical literature highlights the value of interventions that inform families about key school characteristics. Field experiments that provide accessible data on test scores (Hastings and Weinstein, 2008; Andrabi et al., 2017) or graduation rates (Corcoran et al., 2018; Cohodes et al., 2022) show that families are generally responsive to such information, shifting applications toward higher-performing schools. In several cases, these shifts translate into improved student outcomes. For example, Hastings and Weinstein (2008) find that access to school performance data increases academic achievement, while in Pakistan, Andrabi et al. (2017) document gains in both primary school enrollment and student test scores.

Much of the early focus in this literature was on raw performance metrics, rather than school effectiveness as measured by value-added. This distinction matters, since efficiency gains in school choice hinge more on rewarding instructional quality than on sorting by peer characteristics. Moreover, because school value-added is only weakly correlated with the racial and socioeconomic composition of schools (Angrist et al., 2024b), providing families with effectiveness data may also help mitigate segregation in enrollment patterns. Recent evidence supports this potential. In Romania, Ainsworth et al. (2023) show that access to accurate value-added data leads families, particularly those of low-achieving students, to make higher-quality school choices. Campos (2024) finds similar patterns, with value-added information more influential when disseminated through social networks. Still, Ainsworth et al. (2023) emphasize that even under full information, families place substantial weight on peer composition and curriculum, limiting the extent to which they prioritize school effectiveness. In their setting, improved information closed only about one-quarter of the gap between actual and optimal school choices in terms of value-added.

Beyond value-added metrics, another promising line of research focuses on supporting applicants through real-time feedback on admission probabilities. Us-
ing experimental and quasi-experimental designs in the Chilean and New Haven
centralized school choice systems, Arteaga et al. (2022) show that “smart matching
platforms,” which provide live risk assessments based on the evolving distribution
of submitted applications, significantly reduce non-placement rates and increase
the value-added of students’ final assignments. Similarly, Larroucau et al. (2025)
find that personalized admission probability feedback in Chilean college admissions
reduces application errors and substantially improves matching outcomes, particu-
larly for students at risk of going unmatched or undermatched. Moreover, using
randomized interventions and administrative data from Chile’s nationwide school
choice process, Agte et al. (2024) show that combining personalized feedback on
admission chances with information on the quality of nearby schools leads students
to match to higher-quality schools and closes the gap between low- and high-SES
students.

Providing performance feedback also shows promise. In Mexico, Bobba et al. (2023) show that offering students from low socioeconomic backgrounds individuated information about their academic standing helps align their school choices and placement with their demonstrated abilities. Three years later, students who received this feedback were 4 percentage points more likely to graduate from high school.

Yet while these interventions can improve decision-making and match qual-
ity, they do not necessarily reduce opportunity gaps. Studies by Corcoran et al.
(2018) and Cohodes et al. (2022) show that both advantaged and disadvantaged
students benefit from improved information, and in some cases, more advantaged
students benefit disproportionately. Corradini (2024) emphasizes the importance
of general equilibrium considerations in assessing the distributional consequences
of information. In her structural analysis of New York City’s 2007 introduction of
a high school letter-grade system, she finds that enrollment outcomes improved
for Black and Hispanic students largely because white and Asian families—due to
their stronger preferences for peer demographics—were less responsive to the new
quality ratings. However, her counterfactual simulations reveal that if all families
responded primarily to academic quality and commute time, the distributional
effects would reverse: the quality of school offers would improve for white and
Asian students, while minority students would receive lower-quality offers due
to intensified competition for high-rated schools. To mitigate this displacement
risk, Corradini proposes a targeted information design that releases coarse quality
ratings (e.g., letter grades) while providing more precise signals only for schools
that are disproportionately chosen by disadvantaged families. Such a design can
help preserve access by dampening excess competition for the highest-performing schools.

These findings underscore the need to account for general equilibrium effects when assessing the welfare consequences of large-scale information interventions. Addressing this challenge, Allende et al. (2019) embed a field experiment targeting public Pre-K families in Chile within a structural model of school choice and school-side responses. Their counterfactual simulations show that while capacity constraints cut in half the average quality gains induced by information provision for low-SES families, endogenous responses by schools—in terms of quality improvement, expansion, and pricing—partially offset these effects, resulting in a net positive average treatment effect.

Finally, it is important to recognize that even well-designed informational interventions may fall short when other structural barriers constrain behavior. This is especially true in developing-country contexts, where geographic, financial, and logistical challenges can limit families’ ability to act on improved information. In Ghana, for instance, Ajayi et al. (2025) show that despite receiving detailed information on high school quality and selectivity, many students ultimately fail to matriculate due to constraints such as travel distance, cost, or prior commitments made before the information arrived.

In sum, information interventions have considerable promise for improving match quality and expanding access to high-performing schools, particularly when they incorporate value-added measures and personalized guidance. But their impact depends critically on thoughtful design, attention to equilibrium effects, and complementary policies that address structural barriers. Understanding how to best deploy these interventions remains an important frontier for research and policy.

## 3.3 School Choice Effectiveness

Having examined how families form school preferences and how market design can help improve the allocation of students to schools, we now turn to the broader question of school choice effectiveness: to what extent do school choice policies expand access to high-quality education, and for whom? Addressing this requires a market-level perspective that considers not only the behavior of families, but also schools’ supply-side responses, the distributional consequences across socioeconomic groups, and the interactions between overlapping markets. These include both vertical linkages across educational levels (e.g., primary, secondary, and higher education) and horizontal linkages with other domains, such as housing.
### 3.3.1 Market-Level Effects of School Choice and Supply-Side Responses

A central rationale for moving away from traditional neighborhood-based assign-
ment toward centralized school choice is its potential to enhance both the efficiency
of student-school matches and the incentives faced by schools. By allowing families
to select from a wider range of options, choice policies aim to better align students
with schools that fit their needs and preferences, thereby improving allocative effi-
ciency. At the same time, expanding choice introduces competitive pressure that
may encourage schools to raise academic performance, adopt innovations, and
respond more effectively to parental demand (Friedman, 1955; Hoxby, 2000, 2003b).
From this dual perspective, school choice offers the prospect not only of more
effective matching but also of dynamic improvements in school quality and overall
system performance.

Empirically identifying these market-level effects, however, remains a significant
challenge, largely due to the difficulty of observing credible counterfactuals across
different market structures. Much of the existing evidence therefore focuses either on
the individual-level impacts of school choice (e.g., Cullen et al., 2006; Abdulkadiroğlu
et al., 2011a; Deming et al., 2014; Abdulkadiroğlu et al., 2018), or on cross-district
and cross-municipality comparisons (Hoxby, 2000, 2003b; Hsieh and Urquiola, 2006;
Rothstein, 2006, 2007), which yield mixed results. A related body of research
examines competition across school sectors—such as Catholic, charter, or voucher
schools—which often operate alongside traditional public schools and compete for
students across district lines (e.g., Neal, 1997; Card et al., 2010). While informative,
these studies typically do not capture the systemic, equilibrium effects of introducing
centralized school choice within an integrated public school system.

Campos and Kearns (2024) directly address this gap by exploiting a natural
experiment within the Los Angeles Unified School District's Zones of Choice (ZOC)
program. Unlike much of the existing literature, which focuses on individual-
level impacts or cross-district comparisons, this study evaluates the market-level
consequences of introducing centralized choice within a single, unified system. In
2012, approximately one-third of the district was restructured into local choice zones,
while the remainder continued to operate under traditional neighborhood-based
assignment. Using a difference-in-differences strategy embedded in a structural
model of school competition and family preferences, the authors find that the
ZOC program led to substantial gains in both student achievement and college
enrollment. The largest improvements occurred in previously low-performing
schools, driven not only by improved student-school matching but also by increases
in school value-added, consistent with quality improvements spurred by competitive pressure. The study further documents a reduction in between-neighborhood inequality in educational outcomes and shows that families in high-choice settings tend to prioritize school effectiveness over peer composition. This latter finding may partly reflect the relative demographic homogeneity across schools within ZOC zones, where student populations are predominantly from socially disadvantaged backgrounds, which likely reduces parental concerns about peer composition. Taken together, these results offer some of the strongest empirical evidence to date that centralized school choice can generate meaningful gains in both allocative efficiency and school quality via supply-side responses.

While these findings are compelling, further research is needed to evaluate how broadly they generalize across districts with differing demographic and institutional environments. The increasing adoption of centralized assignment systems presents new opportunities in this regard, enabling researchers to exploit variation in policy implementation and leverage detailed administrative data to gain deeper insight into both parental preferences and the incentive structures shaping supply-side responses.

### 3.3.2 Distributional Effects

As illustrated in Section 1.1, a central motivation for school choice reforms is to decouple educational opportunity from residential location, with the aim of promoting more equitable access to high-quality schools. Proponents argue that giving families the freedom to choose schools can reduce socioeconomic and racial segregation and potentially close achievement gaps by expanding access to better educational environments. Yet empirical evidence on these distributional effects remains mixed, highlighting the need to better understand how school choice systems can be designed to more effectively achieve their equity objectives.

Geographic constraints continue to pose a major barrier to equitable access. An illustrative case is provided by Laverde (2024), who shows that in Boston's pre-kindergarten system, Black students are disproportionately assigned to lower-rated schools, even under a choice-based assignment. Cross-racial gaps in assigned school quality are no smaller than under a hypothetical neighborhood-based allocation, suggesting that commuting burdens, especially for Black families, limit the effectiveness of choice systems in expanding access to high-quality options. Ajayi (2024) documents similar dynamics in a developing-country context: in Ghana, disadvantaged students are more likely to apply to lower-performing secondary
schools than more advantaged peers with similar exam scores. This pattern is partly
driven by longer travel distances to high-quality schools, coupled with a stronger
preference for proximity among disadvantaged families. Taken together, these
studies underscore that residential sorting and mobility costs can severely constrain
the equalizing potential of school choice. Formal equalization of access may have
limited effects on enrollment outcomes or segregation unless such structural barriers
are explicitly addressed.

Within the constraints imposed by geography, priority rules nonetheless play
a central role in affecting distributional outcomes (e.g., Kessel and Olme, 2018;
Burgess et al., 2020; Nguyen, 2021; Oosterbeek et al., 2021; Calsamiglia and Miralles,
2023; Idoux, 2023; Gortázar et al., 2023; Pariguana and Ortega-Hesles, 2025). In New
York City, Idoux (2023) estimates that roughly half of the racial segregation among
public middle schools can be attributed to admission criteria—primarily those based
on geographic proximity and, to a lesser extent, academic screening—with the
remainder explained by parental preferences and residential sorting. While these
findings point to the potential for admissions policies to reduce segregation, the
analysis also stresses that their effectiveness depends critically on how families
respond. Evidence from two local middle school reforms in NYC, which curtailed
academic screening and expanded access to selective schools, illustrates the impor-
tance of behavioral reactions: Idoux shows that in both cases, families adjusted
their application strategies in ways that reinforced the reforms’ integrative effects,
resulting in school offers that were three times less segregated. However, these
gains were partially offset by increased exit from the public system among white
and high-income families. These findings highlight the importance of anticipating
demand-side responses when designing equity-oriented admissions policies, as
family reactions may amplify or undermine policy goals.

One potential tool for promoting equity through admission criteria is the use
of priority rules that give preferential treatment to disadvantaged groups, such
as quotas and reserves. While such policies aim to expand access for underrep-
resented students, theoretical insights show that, under certain combinations of
preferences and priorities, instruments like majority quotas or minority reserves can
unintentionally make some disadvantaged students worse off by assigning them to
less preferred schools (see Section 1.7 for details). A separate concern arises from
the “mismatch hypothesis,” which posits that students placed in more selective
schools or colleges than they would otherwise attend may struggle academically
if the environment is not well aligned with their prior preparation (Sander, 2004;
Sander and Taylor Jr, 2012; Arcidiacono and Lovenheim, 2016).
These concerns highlight the need for empirical evaluation to assess whether such policies achieve their equity objectives in practice. In higher education, evidence from large-scale implementations of quota-based affirmative action in India and Brazil suggests broadly positive results. Studies of engineering schools in India (Bagde et al., 2016) and federal universities in Brazil (Francis-Tan and Tannuri-Pianto, 2018; Mello, 2022; Barahona et al., 2023) find that these policies significantly improved access for marginalized students without compromising overall efficiency. In particular, Barahona et al. (2023) show that a nationwide policy reserving 50% of seats for disadvantaged groups substantially boosted their enrollment in selective programs, with no evidence of negative spillovers for non-targeted students.

In contrast, evidence from K-12 settings is more mixed. For instance, studies of Chicago's place-based affirmative action policy in elite public high schools document unintended negative effects on low-SES students' academic performance and four-year college enrollment. Possible explanations include within-school rank effects (Barrow et al., 2020) and the diversion of students from higher-performing alternatives such as charter schools (Angrist et al., 2023b). These findings caution that the success of affirmative action policies depends on the broader institutional context and the set of counterfactual options available to targeted students. This calls for further empirical investigation across a wider range of implementation settings, especially in school choice systems where the use of affirmative action policies within centralized assignment mechanisms has received less attention than in higher education.

While mobility costs and admission criteria are important levers for promoting integration through school choice reforms, empirical evidence suggests that even when such reforms lead to greater integration, they may not substantially reduce racial or socioeconomic achievement gaps. This concern is illustrated by Angrist et al. (2024a), who study the effects of non-neighborhood school enrollment in Boston and New York City. Using conditionally randomized school offers as instruments, they find that although commuting to non-neighborhood schools reduces minority students' isolation and increases their enrollment in schools with fewer minority peers, these integrative effects translate into minimal gains in test scores. In New York City, they even observe negative effects on on-time high school graduation and college enrollment. These disappointing outcomes are attributed to two main factors: the destination schools offer little added value relative to nearby alternatives, and in New York, the additional travel burden appears to negatively affect longer-term outcomes, independent of school quality.

These findings highlight the limitations of relying on school mobility alone as
a lever for equity, and point to the need for policies that both raise the quality of
schooling options and help families identify schools that offer genuine value. In
this context, information frictions emerge as a critical constraint. Building on this
idea, Lee and Son (2024) use data from New York City's high school choice system
to show how limited awareness of available options and inaccurate beliefs about
admission chances influence students' application behavior. Their analysis reveals
that such frictions disproportionately affect Black and Hispanic students, limiting
their access to high-performing schools and reducing the overall welfare gains
from school choice. Counterfactual simulations suggest that personalized school
recommendations, designed to align with families' preferences and awareness, could
recover between 20% and 36% of the lost welfare. These findings are consistent with
the previously discussed evidence from Allende et al. (2019) and Corradini (2024),
which highlight the potential for well-designed information interventions to shift
demand toward more effective schools, particularly among disadvantaged students.

3.3.3 Dynamic Effects of School Choice and Interactions with Other Markets

A growing body of empirical research is opening up a new agenda by moving
beyond static models of school choice to recognize the dynamic and interdependent
nature of families' decisions. Rather than selecting schools in isolation, households
make a series of interconnected choices over time and across markets, considering
how residential location shapes access to schools, how current school choices influ-
ence future academic options, and how public school choice options interact with
alternatives such as private schooling. These interdependencies call for a dynamic
framework to more fully capture the welfare and distributional consequences of
school choice reforms.

One important line of research investigates the interaction between school choice and residential location. While most empirical models in the school choice literature treat housing location as fixed, households often select neighborhoods strategically, in part to gain access to preferred schools. Several theoretical studies have formalized this joint decision-making process, embedding school choice within models of neighborhood sorting (e.g., Xu, 2019; Avery and Pathak, 2021; Grigoryan, 2023). Empirical work on this interaction, however, has only begun to take shape.

A notable contribution is Park and Hahm (2023), who develop a model in which
both residential location and the decision to pursue alternative schooling options
are endogenously determined. Using boundary discontinuity variation in New
York City, they show that up to 30% of the racial gap in school quality reflects
differences in residential choices driven by the expected utility of accessible schools, with non-minority households being more sensitive to the average test score of nearby schools than minority households. These endogenous location decisions have important implications for both policy design and empirical identification. On the methodological front, the study cautions against treated school proximity as orthogonal to unobserved preferences. In their setting, families choose where to live in part to improve their children's chances of getting into desirable schools. If this self-selection is ignored, researchers may mistakenly attribute too much importance to travel distance in determining school preferences. Indeed, the authors find that failing to account for this leads to a 15% overestimate of commuting costs, because proximity affects both travel time and the likelihood of admission. From a policy perspective, Park and Hahm's results suggest that residential mobility can substantially undermine the effectiveness of admissions reforms. In a counterfactual exercise, they show that replacing priority-based admissions with a pure lottery at high-performing Manhattan schools would reduce racial disparities in assignments by 7%, but this impact is cut in half once location responses are taken into account. Ignoring the interaction between school choice and residential sorting thus risks overstating the equity gains from centralized assignment reforms.

Agostinelli et al. (2024) reach similar conclusions in a different context. They develop a spatial equilibrium model of residential sorting and school choice in Wake County, North Carolina, to evaluate two common equity-oriented policies: expanding the set of school options available to disadvantaged families (a “place-based” approach) and offering housing vouchers to help them relocate to more affluent neighborhoods (“people-based”). While both policies modestly improve peer environments for targeted students, they result in aggregate welfare losses. These losses stem in part from negative spillovers: families who previously paid to reside near high-performing schools experience a decline in peer quality and face limited options to avoid it—especially low-income families just able to afford these neighborhoods. The model also sheds light on how geography and zoning regulations affect who bears the costs of integration: schools in remote or tightly zoned areas are largely insulated from new inflows, shifting the integration burden onto a narrower set of schools. These results highlight the importance of accounting for neighborhood structure and general equilibrium effects when evaluating the broader consequences of school choice expansions.

Another strand of work explores the dynamic linkages between educational stages, showing that earlier school choices influence later ones, and that policies can leverage this sequentiality to enhance their overall impact. Building on this
idea, Hahm and Park (2024) develop a dynamic framework to analyze how middle school assignments affect subsequent high school choices and outcomes. Using quasi-random variation from New York City's middle school admissions process, they show that students who attend top-rated middle schools are more likely to subsequently apply to and be assigned to high-performing high schools. Through structural modeling, the authors disentangle two mechanisms: a "priority channel," through which middle school affects a student's admissions chances, and an "application channel," through which it changes preferences and application behavior. Strikingly, the application channel accounts for 80% of the observed effect on high school quality. Their counterfactual simulations show that eliminating geography-based eligibility rules for top middle schools would improve both efficiency and equity at the high school level, and that these effects are amplified by up to 50% when combined with parallel reforms in high school admissions. These results suggest that policies targeting earlier educational stages can generate meaningful downstream benefits, even when reforms at later stages appear less effective in isolation.

A further dimension of dynamic interaction involves the relationship between centralized public school choice systems and the private education sector. As public choice systems expand, private providers may respond by adjusting tuition, admissions criteria, or even their market participation. Dinerstein and Smith (2021) offer compelling evidence of such responses in the context of a large-scale public school funding reform in New York City: increased resources for public schools triggered a significant contraction in private school enrollment. While this reform was not directly related to school choice, it illustrates how public sector policies can reshape the education market as a whole. Previous studies have documented private school responses to voucher programs (Hsieh and Urquiola, 2006; Böhlmark and Lindahl, 2015) and charter school growth (Chakrabarti and Roy, 2016), but there is limited evidence on how private providers react specifically to the expansion of centralized public school choice. This gap presents a promising direction for future research, particularly given its implications for equity and competition in education markets.

Finally, school choice policies may affect other connected markets, such as the labor market for teachers. By shifting enrollment patterns and redistributing students across schools, these policies can alter teacher demand across schools, potentially influencing teacher sorting, compensation, and quality. Although empirical evidence in this area remains limited, it represents a fruitful avenue for future research with important implications for the long-term effectiveness of school choice systems.
A fuller understanding of these broader market interactions will be essential to
informed policy design.
<table><caption>Table 1 – Preference Estimation in Centralized School Choice and College Admissions: Survey of Empirical Studies</caption><thead><tr><th>Study</th><th>Matching market</th><th>Country or city</th><th>Assignment mechanism</th><th>List-length restrictions</th><th>Priorities</th><th>Empirical approach(es)</th><th>Model(s)</th><th>Estimation method(s)</th></tr></thead><tbody><tr><td colspan="9">Panel A. Immediate Acceptance and Other Strategic Mechanisms</td></tr><tr><td>Agarwal and Somaini (2018)</td><td>High S</td><td>Cambridge (MA)</td><td>Cambridge<sup>a</sup></td><td>Yes</td><td>Coarse+lottery</td><td>WTT/Portfolio</td><td>Probit</td><td>Gibbs</td></tr><tr><td>Hastings et al. (2009)</td><td>Elem. S</td><td>Charlotte-Meckl. (NC)</td><td>Charlotte<sup>b</sup></td><td>Yes</td><td>Coarse+lottery</td><td>WTT</td><td>Mixed logit</td><td>MSL</td></tr><tr><td>Campos (2024)</td><td>High S</td><td>Los Angeles (CA)</td><td>IA</td><td>No</td><td>Coarse+lottery</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Campos and Kearns (2024)</td><td>High S</td><td>Los Angeles (CA)</td><td>IA</td><td>No</td><td>Coarse+lottery</td><td>WTT/Portfolio</td><td>Logit/Probit</td><td>MLE/Gibbs</td></tr><tr><td>Kapor et al. (2020)</td><td>High S</td><td>New Haven (CT)</td><td>New Haven<sup>b</sup></td><td>Yes</td><td>Coarse+lottery</td><td>Portfolio</td><td>Probit</td><td>Gibbs</td></tr><tr><td>Xu and Hammond (2024)</td><td>Mid./High S</td><td>Wake County (NC)</td><td>IA</td><td>Yes</td><td>Coarse+lottery</td><td>Portfolio</td><td>Probit</td><td>Gibbs</td></tr><tr><td>De Haan et al. (2023)</td><td>Mid. S</td><td>Amsterdam (pre 2015)</td><td>Adaptive IA<sup>c</sup></td><td>Yes</td><td>Coarse+lottery</td><td>Portfolio</td><td>Logit</td><td>MSL</td></tr><tr><td>Calsamiglia et al. (2020)</td><td>Elem. S</td><td>Barcelona</td><td>IA</td><td>Yes</td><td>Coarse+lottery</td><td>Portfolio</td><td>Probit</td><td>MSL</td></tr><tr><td>He (2017)</td><td>Mid. S</td><td>Beijing</td><td>IA</td><td>No</td><td>Lottery</td><td>WTT/Portfolio/UD</td><td>Logit</td><td>MLE</td></tr><tr><td>Hwang (2015); Bayraktar and Hwang (2024)</td><td>High S</td><td>Seoul</td><td>IA</td><td>Yes</td><td>Coarse+lottery</td><td>UD</td><td>Logit/Probit</td><td>MEI</td></tr><tr><td colspan="9">Panel B. Deferred Acceptance</td></tr><tr><td>Laverde (2024)</td><td>Pre-K</td><td>Boston</td><td>DA</td><td>No</td><td>Coarse+lottery</td><td>STT</td><td>Logit</td><td>MLE</td></tr><tr><td>Pathak and Shi (2021)</td><td>Elem. S</td><td>Boston</td><td>DA</td><td>No</td><td>Coarse+lottery</td><td>WTT</td><td>Mixed logit</td><td>Gibbs/HMC</td></tr><tr><td>Idoux (2023)</td><td>Mid. S</td><td>NYC</td><td>DA</td><td>Yes</td><td>Coarse+lottery/Strict</td><td>Portfolio</td><td>Probit</td><td>Gibbs</td></tr><tr><td>Park and Hahm (2023)</td><td>Mid. S</td><td>NYC</td><td>DA</td><td>No<sup>d</sup></td><td>Coarse+lottery/Strict</td><td>WTT</td><td>Mixed logit</td><td>EM</td></tr><tr><td>Abdulkadiroğlu et al. (2017a)</td><td>High S</td><td>NYC</td><td>DA</td><td>Yes</td><td>Coarse+lottery/Strict</td><td>WTT</td><td>Probit</td><td>Gibbs</td></tr><tr><td>Narita (2018)</td><td>High S</td><td>NYC</td><td>DA</td><td>Yes</td><td>Coarse+lottery/Strict</td><td>WTT</td><td>Logit</td><td>MSL</td></tr><tr><td>Abdulkadiroğlu et al. (2020b)</td><td>High S</td><td>NYC</td><td>DA</td><td>Yes</td><td>Coarse+lottery/Strict</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Che et al. (2023)</td><td>High S</td><td>NYC</td><td>DA</td><td>Yes</td><td>Coarse+lottery/Strict</td><td>WTT/Stability</td><td>Probit</td><td>Gibbs</td></tr><tr><td>Nguyen (2021)</td><td>High S</td><td>NYC</td><td>DA</td><td>Yes</td><td>Coarse+lottery/Strict</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Corradini (2024)</td><td>High S</td><td>NYC</td><td>DA</td><td>Yes</td><td>Coarse+lottery/Strict</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Lee and Son (2024)</td><td>High S</td><td>NYC</td><td>DA</td><td>Yes</td><td>Coarse+lottery/Strict</td><td>Portfolio</td><td>Probit</td><td>GMM</td></tr><tr><td>Hahm and Park (2024)</td><td>Mid./High S</td><td>NYC</td><td>DA</td><td>No/Yes</td><td>Coarse+lottery/Strict</td><td>Stability</td><td>Mixed logit</td><td>EM</td></tr><tr><td>Oosterbeek et al. (2021)</td><td>Mid. S</td><td>Amsterdam (post 2015)</td><td>DA</td><td>No</td><td>Coarse+lottery</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Agte et al. (2024)</td><td>Elem. S</td><td>Chile</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT<sup>e</sup></td><td>Probit</td><td>Gibbs</td></tr><tr><td>Burgess et al. (2015)</td><td>Elem. S</td><td>England</td><td>DA/IA</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Ajayi (2024)</td><td>High S</td><td>Ghana</td><td>DA</td><td>Yes</td><td>Strict</td><td>Portfolio/Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Ajayi and Sidibé (2024)</td><td>High S</td><td>Ghana</td><td>DA</td><td>Yes</td><td>Strict</td><td>Portfolio</td><td>Probit</td><td>MSM</td></tr><tr><td>Bobba et al. (2023)</td><td>High S</td><td>Mexico City</td><td>SD</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Ngo and Dustan (2024)</td><td>High S</td><td>Mexico City</td><td>SD</td><td>Yes</td><td>Strict</td><td>WTT/Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Pariguana and Ortega-Hesles (2025)</td><td>High S</td><td>Mexico City</td><td>SD</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Logit</td><td>MLE</td></tr></tbody></table>

(Continued on next page)
<table><caption>**Table 1 – Preference Estimation in Centralized School Choice and College Admissions: Survey of Empirical Studies**
(Continued)</caption><thead><tr><th>Study</th><th>Matching market</th><th>Country or city</th><th>Assignment mechanism</th><th>List-length restrictions</th><th>Priorities</th><th>Empirical approach(es)</th><th>Model(s)</th><th>Estimation method(s)</th></tr></thead><tbody><tr><td colspan="9" style="text-align: center; font-weight: bold;">Panel B. Deferred Acceptance (continued)</td></tr><tr><td>Fack et al. (2019)</td><td>High S</td><td>Paris</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT/Stability/UD</td><td>Logit</td><td>MLE/MEI</td></tr><tr><td>Kessel and Olme (2018)</td><td>Elem. S</td><td>Botkyrka (Sweden)</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT</td><td>Mixed logit</td><td>MSL</td></tr><tr><td>Andersson et al. (2024)</td><td>Elem./Mid. S</td><td>Sweden</td><td>DA</td><td>Yes/No</td><td>Coarse+lottery/Strict</td><td>WTT/Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Akyol and Krishna (2017)</td><td>High S</td><td>Turkey</td><td>SD</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Nested logit</td><td>MSL</td></tr><tr><td>Beuermann et al. (2023)</td><td>Mid. S</td><td>Trinidad and Tobago</td><td>SD</td><td>Yes</td><td>Strict</td><td>Portfolio</td><td>logit</td><td>MLE</td></tr><tr><td>Vrioni (2024)</td><td>Higher Ed</td><td>Albania</td><td>DA</td><td>Yes</td><td>Strict</td><td>Portfolio</td><td>Logit</td><td>MSL</td></tr><tr><td>Barahona et al. (2023)</td><td>Higher Ed</td><td>Brazil</td><td>Iterative DA<sup>f</sup></td><td>Yes</td><td>Strict</td><td>Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Bordon and Fu (2015)</td><td>Higher Ed</td><td>Chile</td><td>DA</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Probit</td><td>MSM</td></tr><tr><td>Bucarey (2018)</td><td>Higher Ed</td><td>Chile</td><td>DA</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Mixed Logit</td><td>MSM</td></tr><tr><td>Larroucau and Rios (2020)</td><td>Higher Ed</td><td>Chile</td><td>DA</td><td>Yes</td><td>Strict</td><td>Portfolio</td><td>Probit</td><td>Gibbs</td></tr><tr><td>Larroucau and Rios (2023)</td><td>Higher Ed</td><td>Chile</td><td>DA</td><td>Yes</td><td>Strict</td><td>Portfolio</td><td>Mixed Logit</td><td>GII</td></tr><tr><td>Kapor et al. (2024)</td><td>Higher Ed</td><td>Chile</td><td>DA</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Probit</td><td>Gibbs</td></tr><tr><td>Campos et al. (2025)</td><td>Higher Ed</td><td>Chile</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Wang et al. (2025)</td><td>Higher Ed</td><td>Ningxia (China)</td><td>SD</td><td>Yes</td><td>Strict</td><td>Portfolio</td><td>Probit</td><td>MSM</td></tr><tr><td>Hernández-Chanto (2021)</td><td>Higher Ed</td><td>Costa Rica</td><td>SD</td><td>Yes</td><td>Strict</td><td>Portfolio</td><td>Probit</td><td>Gibbs</td></tr><tr><td>Chrisander and Bjerre-Nielsen (2023)</td><td>Higher Ed</td><td>Denmark</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT/Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Gandil (2025)</td><td>Higher Ed</td><td>Denmark</td><td>DA</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>De Groote et al. (2025)</td><td>Higher Ed</td><td>France</td><td>Multi-round DA<sup>h</sup></td><td>Yes</td><td>Coarse+lottery/Strict</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Grenet et al. (2022)</td><td>Higher Ed</td><td>Germany</td><td>Multi-offer DA<sup>g</sup></td><td>Yes</td><td>Strict</td><td>Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Kirkebøen (2012)</td><td>Higher Ed</td><td>Norway</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Hällsten (2010)</td><td>Higher Ed</td><td>Sweden</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT</td><td>Logit</td><td>MLE</td></tr><tr><td>Luflade (2019)</td><td>Higher Ed</td><td>Tunisia</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT/Portfolio</td><td>Mixed logit</td><td>MSL/MSM</td></tr><tr><td>Arslan (2021)</td><td>Higher Ed</td><td>Turkey</td><td>DA</td><td>Yes</td><td>Strict</td><td>WTT/Stability</td><td>Logit</td><td>MLE</td></tr><tr><td>Akyol et al. (2024)</td><td>Higher Ed</td><td>Turkey</td><td>DA</td><td>Yes</td><td>Strict</td><td>Stability</td><td>Latent class logit</td><td>MLE</td></tr></tbody></table>

Notes: Matching markets: Pre-K: Pre-kindergarten; Elem. S: Elementary school; Mid. S: Middle school; High S: High school; Higher Ed: Higher education; Assignment mechanisms: IA: Immediate Acceptance; DA: Deferred Acceptance; SD: Serial dictatorship. Priority rules: Coarse+lottery: coarse priorities (e.g., walk-zone, sibling attendance) combined with lottery tie-breaking; Strict: Strict priorities (e.g., test scores, home-school distance). Empirical approaches to estimating preferences: STT: Strict Truth-Telling; WTT: Weak Truth-Telling; Portfolio: Optimal portfolio choice; UD: Undominated strategies. Estimation methods: EM: Expectation-Maximization algorithm; Gibbs: Gibbs sampling; GII: Generalized Indirect Inference (Bruins et al., 2018); GMM: Generalized Method of Moments; HMC: Hamiltonian Monte Carlo; MEI: Moment Equalities and Inequalities; MLE: Maximum Likelihood Estimation; MSL: Maximum Simulated Likelihood; MSM: Method of Simulated Moments. a Cambridge (MA) uses a modified IA mechanism with dual capacities—for both programs and schools—limiting assignment feasibility. b Charlotte and New Haven use IA-like mechanisms where priority group takes precedence over ROL rank in determining assignments.

c The adaptive IA mechanism allows students to apply to their highest-ranked school with remaining seats in each round (Mennle and Seuken, 2017; Dur, 2019). d NYC data used by Park and Hahm (2023) reflects a period (2014–2015) when ROLs were unrestricted for middle schools; from 2017 onward, lists were capped at 12 programs. e Agte et al. (2024) estimate parents’ preferences under WTT while accommodating information frictions by modeling limited awareness of schools and misperceptions of their characteristics. f In Brazil, college admissions use an iterative version of DA in which students can revise up to two choices daily, guided by cutoff score updates (Bó and Hakimov, 2020, 2022). g Germany’s college admissions process begins with a multi-offer DA phase, allowing students to hold offers and update ROLS, before entering a final single-offer DA phase. h France’s former centralized college admission system (Admission Post-Bac) featured a three-round sequential implementation of the college-proposing DA, redistributing in each round the offers declined by students who opted for off-platform alternatives.
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