School Choice Design, Risk Aversion and Cardinal Segregation

Abstract

We embed the problem of public school choice design in a model of local provision of education. We define cardinal (student) segregation as that emerging when families with identical ordinal preferences submit different rankings of schools in a centralised school choice procedure. With the Boston Mechanism (BM), when higher types are less risk-averse, and there is sufficient vertical differentiation of schools, any equilibrium presents cardinal segregation. Transportation costs facilitate the emergence of cardinal segregation as does competition from private schools. Furthermore, the latter renders the best public schools more elitist. The Deferred Acceptance mechanism is resilient to cardinal segregation.

School Choice and Neighborhood Sorting: Equilibrium Consequences of Geographic School Admissions

“…First, incorporating a private school into the market has been shown to be important for the equilibrium outcomes of school choice systems by providing an 'outside option' to richer households (Epple and Romano 2003;Calsamiglia, Fu, and Güell 2020;Calsamiglia, Martínez-Mora, and Miralles 2020). The relevance of this private school option will depend on its quality (relative to the public schools) and price, and the admissions system used.…”

“…Transport costs have been included by a handful of previous studies (Epple and Romano 2003;Calsamiglia, Martínez-Mora, and Miralles 2020;Agostinelli, Luflade, and Martellini 2021;Park and Hahm 2023;Pietrabissa 2023) but no other theoretical models of school and neighborhood choice. 7 In relation to these papers, we expand on the mechanisms through which 6.…”

Optimal assignment mechanisms with imperfect verification

“…The concern is not so much with risk aversion per se, but with what might correlate with that risk aversion. For example, there is suggestive evidence that low‐income students tend to be more risk averse (see, for example, Calsamiglia and Guell (2018) and Calsamiglia, Martinez‐Mora, and Miralles (2021) for a theoretical analysis). As a result, when we thinkin about our model to assign students to schools or colleges, a reasonable concern is that the optimal mechanism further increases income inequality.…”

Timing of preference submissions under the Boston mechanism

“…The literature primarily evaluates various matching mechanisms according to desirable criteria, such as strateyproofness, efficiency, and stability in a complete information environment. More recent work has been done to account for incomplete information (L. Chen & Pereyra, 2019; Ehlers & Massó, 2007), expand standard criteria for fairness (Alcalde & Romero‐Medina, 2017; Özek, 2017; Troyan et al, 2020), and efficiency (Abdulkadiroğlu et al, 2011; Miralles, 2009), include richer setup such as housing choices (Avery & Pathak, 2021; Calsamiglia et al, 2021; Xu, 2019), and linking the matching literature to coalition formation problems (Leo et al, 2021; Pápai, 2004). In particular, this study contributes to a growing literature investigating the timing of preference submissions in centralized college admission problems.…”