This is the 19th in this year’s series of posts by PhD students on the job market.
Governments all across the globe are using centralized allocation algorithms for assigning students to schools. This is expected to eliminate any selection by schools and improve diversity in the schooling system by providing equal access to all. In Chile, school segregation based on socioeconomic status has increased in the last few decades, driven by students from middle-income households shifting from public to voucher schools. To stem this trend, the Chilean government introduced a centralized student assignment. But does this work as intended and what factors influence the outcome of this system?
In my job market paper I examine the Chilean system, specifically to understand how its selection design impacts reaching its objective to increase the representation of students from low socio-economic status in better quality schools in Chile. Anonymized administrative data for this work was provided by the Ministry of Education in Chile. Researchers and policymakers prefer algorithms that do not give parents incentives to manipulate their preferences (strategy-proof). Consequently, the Deferred Acceptance (DA) algorithm is extensively used for student assignments as it is viewed as strategy-proof (Abdulkadiroğlu and Sönmez, 2003). However, DA's strategy proofness fails with positive application costs when parents report a partial list of schools (Fack, Grenet and He, 2019). Therefore, the observed partial ranking need not be useful to back out the underlying preference ordering parameters.
Multiple factors can contribute to partial ranking of schools. Often parents have access to a guaranteed school, and so they do not want to list schools below this guaranteed school. Parents are aware of the oversubscribed schools and would like to skip the impossible schools if the likelihood of admission is very low and does not compensate for the application cost. Partial ranking due to these factors can lead to non-strategy proof equilibrium.
To address identification under application costs in DA, I incorporate the value of the outside option and the probability of admission in an additive cost framework in the school choice model. From this, I can identify the determinants of true utility ordering over schools. I differentiate between ranked and non-ranked alternatives using the rank cut-off in my school choice framework. I contribute to the methodology on rank-ordered choices by modeling the student's decision to rank multiple schools as a single step process. This new framework is applied to Chilean DA for high school assignments. I find that travel distance is important for parents but the sensitivity varies by student household income and test score. Secondly, I find evidence suggesting that parents have a preference for schools where the academic rigor matches to student ability. My results show that students coming from low-income households are likely to apply to high-score schools irrespective of travel distance when their ability is closer to the academic standards of the school. This central finding -- that student ability match is key to decision making once I condition on travel distance and income in the context of Chile -- is surprising compared to DA results in other contexts such as in Boston, where travel costs emerge as the key determinant of school diversity (Laverde, 2020).
Guaranteed school, oversubscribed schools, and unobserved costs in the Chilean DA
About 60% of parents rank at most three schools for high school admission. There are several unique features of the Chilean system that leads to a partial ranking over schools and variations in the rank cut-off. First, in Chile's case, the outside option depends on two features for middle to high school transition. If the student's pre-DA school offers the grade at which the student seeks admission, the student is guaranteed admission at the pre-DA school when the algorithm fails to allocate the student at any of the listed schools in ROL. On the contrary, if the pre-DA school does not offer a higher grade, which is the case for many middle schools, the student gets allocated to the nearest public school with a vacancy. Second, there is a high negative correlation between vacancy and school academic quality. Students enrolled in high-score schools pre-DA are less likely to participate in DA. In my sample in 2017, out of 496 schools that participated in DA for high school admissions, the median vacancy for schools in the top 10% of score distribution (language score) was 8 compared to a median of 31 for the entire sample of schools. This correlation makes it critical to explicitly account for indicators of the probability of admission in the school choice model. Lastly, unobserved costs such as the mental cost of adding schools to the list vary by the level of parental sophistication. I incorporate these three components in my estimation to identify the parameters of the underlying preference ordering.
Identification can be achieved for Chile with full support. If there is a positive density of all types of students around different school types, this variation in student location of a similar type can be critical for identification. In other words, let's assume one can use student income and the ability to define student type. School types are defined by academic quality as a simplifying assumption. If similar typed low income and low ability students are located around high and low academic quality schools, then this distance variation based on location can be used for identification. The student location provides variation in the outside option. If there is variation in outside options for similar type students, this can be used to explain the length of the ranking list for these students. Empirical analysis reveals a notable variation in the placement of similar type students around different schools and the outside value due to geographic location.
Importance of travel cost in school rankings and ability match
I find that travel distance is critical, but sensitivity to distance varies substantially by student ability and family income. I observe two significant results. Higher-income households have only a marginal advantage in overcoming the travel cost to good quality schools. However, student ability proxied by pre-DA test scores is the most crucial determinant of listing the best quality schools. Once I condition the marginal effects on family income, I find that higher ability students do end up applying to good quality schools irrespective of income levels. For instance, the graphs below display the travel time isochrones from the best school (green marker) in Limari province in Chile. An x minute isochrone to the best school connects all points that are x minutes away (travel time by car) from this school. The red (blue) marker indicates a high (low) predicted probability of application to the best school. This figure shows that once we condition the marginal effects on travel distance and family income, ability match determines the predicted probability of applying to the best score school.
These results suggest that reducing travel costs alone might not improve students' representation from low socioeconomic status in higher-quality schools. Policies geared towards improving student ability, especially for students belonging to low-income households, can go a long way in improving their representation in high-quality schools.
Shanjukta Nath is a Ph.D. Candidate at the University of Maryland.
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