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09-05-2022 | Original Paper

Financial aid in college admissions: need-based versus merit-based

Author: Eun Jeong Heo

Published in: Social Choice and Welfare | Issue 1-2/2023

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Abstract

In college admission, financial aid plays an important role in students’ enrollment decision as well as their preparation for college application. We analyze how different types of financial aid affect these decisions and admission outcomes. We consider two financial aid regimes—need-based and merit-based—in a simple college admission model and characterize respective equilibria. We find that a more competitive college has a higher admission cutoff under a need-based regime than under a merit-based regime. A less competitive college, on the other hand, benefits from a merit-based regime as it admits students with a higher average ability than it does under no aid. We next allow colleges to choose their own financial aid system so as to account for a stylized fact in the US college admissions. We show that when one college is ranked above the other, it is a dominant strategy for the higher-ranked college to offer need-based aid and for the lower-ranked college to offer merit-based aid.

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Appendix
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Footnotes
1
An example is affirmative action. Most colleges adopt it in admission process and it has been studied extensively in economics. On the theory side, for instance, Afacan and Salman (2016), Kojima (2012), and Dŏgan (2016) study its welfare impact on students in the market design context. It has also been analyzed as a contest: see Fain (2009), Fu (2006), Bodoh-Creed and Hickman (2018).
 
2
There are many empirical studies on the impact of financial aid on educational investment in high schools. For instance, see Dinkelman and Martínez (2014).
 
3
The effort cost here represents an opportunity cost of exerting effort, which varies with family income levels. For instance, extra spending on private-tutoring or extracurricular activities accounts more of household budget for low-income families than it does for high-income families, incurring a higher opportunity cost.
 
4
The majority of colleges are currently adopting need-blind admission policy: the survey by the National Association for College Admission Counseling indicates that 92% of public colleges and 81% of private colleges adopt this practice in 2007 (Heller et al. 2008). Under this policy, admission decision is not affected by a student’s financial status (or type in our model), so we assume that a common admission cutoff applies both types of students. As discussed above, a student’s financial status is reported and verified through the FAFSA form, not by the college’s admission office.
 
5
In this paper, we focus on institutional financial aid that comes out of each college’s budget/endowment, for instance, in the form of grants and scholarships: any federal aid or loan is not included in our analysis.
 
6
These colleges include Harvard, Yale, Stanford and others. For instance, visit college.harvard.edu/financial-aid/types-aid. The financial aid office explicitly informs that their scholarships are based entirely on need, not merit.
 
8
Given the college admissions in practice, extra effort makes a student stronger to some extent in the applications, but there are many other factors that jointly affect the outcome. Therefore, it is hard to justify that the student can outperform more than a quarter of a college’s capacity solely by exerting effort such as private tutoring, consulting, or extracurricular activities that we mentioned in Introduction. This assumption also allows us to guarantee the existence of (deterministic) equilibrium in Sect. 3.
 
9
Under each financial aid regime we define below, the amount of aid per student is larger than \(c_H\) and \(c_L\) under the assumption \(c_L, c_H\le \frac{3M}{2}\).
 
10
As discussed in Introduction, these cutoffs do not have to be determined by a standardized testing only, but it can be determined by overall performance of students in college admissions process, for instance, on a weighted sum of their SAT scores, GPA, strength of application essays, and other achievements in high school.
 
11
We regard this case as a baseline setup in this manuscript, but we could also think of other formulations, such as the equal distribution of the budget across all admitted students at each college. Under this formulation, for instance, the budget M will be distributed to all students enrolling in each college and therefore, each student receives \(\frac{3M}{2}\) amount of financial support, regardless of their types. This formulation improves the admitted students’ welfare, but the preference threshold identified above in comparing the two colleges remains the same, because both colleges offer the same amount of aid the student’s payoff is quasi-linear in monetary transfer. The equilibrium characterization above remains the same as well.
 
12
This assumption is also consistent with the statistics of financial aid in most colleges. For instance, only 300 out of 16,082 full-time undergraduates received non-need-based aid in 2015 at Boston University. This observation prevails in other years and in other colleges.
 
13
In college admissions, L-type students can apply for need-based aid even if they receive merit-based aid from a college. In this case, students should report it in the FAFSA form, where the cost of attendance (COA) is calculated by subtracting the amount of merit-based aid that they receive. The amount of need-based aid is adjusted accordingly, but the total amount of aid that these students end up receiving is usually larger than the amount of need-based only. This observation supports our assumption \(F\ge \text {argmax}_{w_B\in \{mb,nb\}}F_A(n,w_B)\) and \(F\ge \text {argmax}_{w_A\in \{mb,nb\}}F_B(w_A,nb)\). Due to need-based aid, on the other hand, these L-type students also receive a larger amount in total than the merit-based aid that H-type students receive. In practice, many financial aid offices advise students to apply for both types of financial aid if possible, in case they “need financial assistance beyond a merit award” (Boston University).
 
14
Even if \({\underline{y}}>0\), our analysis in Sect. 3 carries over, as long as preference thresholds between available options are properly defined.
 
15
Note that \(([x_A^*-\delta ,x_A^*]\setminus [{\bar{x}}_A^*-\delta , {\bar{x}}_A^*])\cap [{\underline{x}}-\delta , {\underline{x}}]\) is empty, because \({\bar{x}}_A^*>{\underline{x}}\).
 
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Metadata
Title
Financial aid in college admissions: need-based versus merit-based
Author
Eun Jeong Heo
Publication date
09-05-2022
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 1-2/2023
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-022-01405-7

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