How to assign students to schools, that is the question. Placed at the core of the debate on public school choice, it has been widely discussed by researchers and policy makers. Traditional methods based on students’ neighbourhood are criticized because of their consequences in term of social segregation: neighbourhoods with low socio-economic indicators tend to have low quality schools. As a remedy, centralized systems allow students (or their parents) to choose schools beyond their neighbourhoods.

In the last two decades, many countries adopted centralized procedures to allocate students at different levels of public education (primary, secondary, high school and university).¹ Although details vary across countries and regions, all systems share four main ingredients. First, students’ preferences: a rank order list of schools by which each student indicates her most preferred school, the second most preferred school, and so on. Second, the number of seats available at each school. Third, transparent criteria (called schools’ priorities) defined by public authorities. These criteria are used to handle situations where the number of applicants exceeds schools’ capacity, and to decide who will be admitted. Finally, there is central clearinghouse which coordinates the system.

In general, the timing is as follows. The central clearinghouse announces schools’ capacities and priorities, and asks students to submit their preferences. Based on this information, an algorithm or mechanism is used to compute an assignment of students to schools. Clearly, preferences are students’ private information, and then, it is not guaranteed that they will be revealed truthfully. Depending on the mechanism in place, manipulations may arise. For this reason, market designers have advocated the use of strategy-proof mechanisms. This class of mechanisms reduces costly and risky manipulations by rewarding truth-telling students a no-worse outcome than other strategy.

A recent paper² analyses a situation where, different from the standard case, students have to submit their preferences before knowing schools’ priorities. The uncertainty about schools’ priorities induces students to choose which preferences submit based on their beliefs. The main goal of the paper is to study which strategies may arise at equilibrium, and to test theoretical predictions with real data.

The introduction of uncertainty is motivated by the high school match in Mexico City. Since 1996, Mexico City and its metropolitan area has adopted a centralized school choice system organized through a clearinghouse called Comisión Metropolitana de Instituciones Públicas de Educación Media Superior (COMIPEMS). Each year students are asked to submit a rank ordered list of high schools before taking a standardized exam. The exam score determines a strict and unique priority order, according to which a strategy-proof mechanism is used to allocate students to schools.³

In its theoretical analysis, the paper introduces a game with incomplete information, and shows that the type of strategies at equilibrium depends crucially on the probability that each student assigns to be admitted to schools. In particular, it is possible at equilibrium that some students do not top rank their most preferred school because their beliefs are such that the probability of being assigned to it is zero. This phenomenon is what the authors refer to as self-selection.⁴

The empirical analysis of the paper begins by presenting a first piece of evidence of self-selection. The authors consider a subsample of students who agree that their most desirable choice belongs to a set of top quality high schools affiliated to Universidad Nacional Autónoma de México (UNAM). This is achieved by using a survey question about which university students would like to attend in the future.  Then, it is argued for those who would like to attend UNAM that their top choice is one of the UNAM high schools.5 By looking at the submitted choices, the authors find that one fifth of them do not top rank any UNAM high school, or in other words, that they self-select.

In a second step, the paper explores which factors affect self-selection. Results suggest that secondary school average grade, family income, and parent education are the most important variables contributing to self-selection, after controlling for other factors (including distance). The explanation is as follows. Students look at their past secondary school performance to form beliefs about future exam scores. However, given the same grade, students’ beliefs depend on their socio-economic backgrounds. Students from low income families tend to be more pessimistic about their future performance, resulting in higher probability of self-selection. Moreover, the difference between high and low income families increases when lower grades are considered. For example, a student with a top 10% grade in secondary school self-selects with almost the same probability independent of her family’s income level. However, a student with a bottom 10% performance in secondary school is 13 percentage points more likely to self-select if she is from a low income than from a high income family.

Finally, it is evaluated, ex-post, to which extent the beliefs of self-selected students turn out to be correct. For this, the final exam score of each student is compared with the minimum acceptance threshold for the UNAM high schools, and it is found that 21% of the self-selected students obtained a score high enough to compete for a seat in one UNAM high school. Then, contrary to the complete information scenario, strategic behaviors lead to a different assignment that hurts some strategic students once uncertainty is resolved.

By studying in details the Mexico City high school match, the paper shows the existence of self-selection which is so far neglected in school choice design. As it was initially mentioned, school choice using strategy-proof mechanism is designed to provide students from all socio-economic backgrounds with equal opportunities to attend good schools. However, the evidence of self-selection presented in the paper ponders if this goal is fulfilled, and suggests the importance of some details such as timing of submission.

1. Recent experiences in some European countries are described at http://www.matching-in-practice.eu/.

2. Chen, L., and Pereyra, J.S., 2015, Self-selection in School Choice. Manuscript.

3. The mechanism used is known as the serial dictatorship.

4. As it is noted in the paper, COMIPEMS explicitly suggests students to consider their future exam scores when submitting preference. Thus, self-selection is not only possible in theory, but also can happen in practice when students follow that advice.

5. The main reason behind the identification strategy is based on the priority that students from UNAM high schools have in the admission to the university.