Preference Formation and Peer Effects in University Admission: The Further Deferred Acceptance – FDA

We theoretically show that the FDA dominates the DA in terms of student welfare given the presence of costly preference formation and peer effects. Both ingredients of the model are non-standard in the literature, and we use survey and administrative data to empirically test their validity. The performance of the FDA relative to the DA is quantitatively evaluated through lab experiments as well as counterfactual analyses with real data, i.e. simulating outcomes under both mechanisms based on estimated preferences.
We first focus on the question of how the timing of offers influences the matching outcome, using data from the Germany university admissions. At the first stage, the students and universities can interact in ways that are similar to a decentralized market. Students in the system can apply to up to 12 university programs. Students may receive multiple offers and are given the opportunity to accept an offer and exit the system or reject offers. They can also remain inactive. Students who have not accepted an offer at the end of this stage have to rank the programs they have applied to, and the Gale-Shapley mechanism is run for these remaining students and seats.
Importantly, whether a student receives offers earlier or later from the universities she applied to is exogenous to the (preliminary) rank order list submitted by the student. Moreover, we observe that the point in time at which a university sends out its offers is independent of the selectivity of the program.

We find that receiving an early offer from a university increases the likelihood of the student enrolling at this university. More precisely, (i) conditional on a choice being ex post feasible, having received an early offer from a program increases the probability of accepting that program; and (ii) the earlier the offer, the larger the effect.
This project sheds light on a practical solution to market design problems with costly preference formation and peer effects. Given the low cost of switching from the DA to the FDA, the latter can be a viable option for policy makers in real-life contexts such as France’s Admission Post Bac and AFFELNET, among numerous others.

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This research has led to the production of several research articles. Some are theoretical, and other are experimental and empirical. The methods that are developed in our research articles can be used in future studies of school choice and college admissions by ourselves and other researchers.

Market design has been one of the most successful fields of economics in terms of how research has improved practices in real life. As recognition, the 2012 Nobel Prize in Economics was awarded to Alvin Roth and Lloyd Shapley "for the theory of stable allocations and the practice of market design". However, many research questions and practical problems remain unresolved. This project aims to advance our understanding of market design for university admission by relaxing two restrictions in the literature. First, it is typically assumed that students can form a preference ranking of all universities at no cost. Second, externalities such as peer effects are mostly not allowed. Unfortunately, both assumptions are unlikely to be satisfied in real applications. For example, students usually choose from a large set of options about which they have limited information, and thus have difficulties to formulate a full preference ranking. Also, students may prefer to study close to where their friends study.

Our project investigates a new mechanism that was recently introduced in Germany addressing the problems that can arise when the two assumptions do not hold. It is a variant of the Gale-Shapley Deferred-Acceptance (DA) mechanism which has been at the very center of market design. The DA enjoys desirable theoretical properties such as stability and strategy-proofness and has been adopted in various educational settings such as school choice in Boston, New York City, and Paris.

In contrast to the DA, the German mechanism has two important features: First, students "apply to" a set of universities and are only required to rank them after all universities make first-round offers. Second, students may receive multiple first-round offers and can decide which one to keep. Compared with the DA, the ranking decision and the acceptance/rejection of first-round offers are further deferred, which empowers students to acquire more information and to coordinate among themselves. We thus name it as the Further-Deferred-Acceptance (FDA) mechanism.

We will theoretically show that the FDA dominates the DA in terms of student welfare given the presence of costly preference formation and peer effects. Both ingredients of the model are non-standard in the literature, and we will use survey and administrative data to empirically test their validity. The performance of the FDA relative to the DA will also be quantitatively evaluated through lab experiments as well as counterfactual analyses with real data, i.e. simulating outcomes under both mechanisms based on estimated preferences.

This project will shed light on a practical solution to market design problems with costly preference formation and peer effects. Given the low cost of switching from the DA to the FDA, the latter can be a viable option to many policy makers in real-life contexts such as France’s Admission Post Bac and AFFELNET, among numerous others.