The Large Core of College Admission Markets: Theory and Evidence – by Péter Biró

The Large Core of College Admission Markets:
Theory and Evidence

by Péter Biró

The Hungarian university admissions are organised in a nationwide, centralised scheme, where the students can apply for most programmes under two different financial terms: with or without scholarship. These potential “contracts” can be listed in an arbitrary preference order when submitting the applications to the matching scheme. In principle, the students prefer the same programme with scholarship than without it, however, when two different programmes are compared one with and the other without scholarship then they can have different preferences. Students from affluent families tend to care less about the financial terms, so their typical preference list contains both possible contracts for a programme right after each other, first with scholarship and then without scholarship. Whilst the students with worse social-economy background either only apply for contracts with scholarship, or they list first all acceptable programmes with scholarship and then they may put some contracts without scholarship to the end of their preference list.

The students are ranked by the universities according to their scores, which are coming mainly from their grades and performances at the entrance exams, but other factors can also be considered by the universities. The matching scheme uses the Gale-Shapley algorithm, and so it provides fair solutions according to the scores, thus by the merits of the students. The cutoff scores of all the programmes are published regarding the financial terms, which are simply the scores of the weakest students admitted under that contract. So, the fairness of the matching is transparent, since all the students admitted to a programme with a particular financial term met the cutoff score, and all the students rejected failed to meet it.

In this paper we investigate the potential effects of alternative admission policies, where the universities may decide on the financial terms of the admitted students based on different factors, mainly how affluent the families are, which is quite typical approach also in the US. We illustrate this alternative policy with a simple example, as follows. Suppose that we have a programme with two seats, one with scholarship and one without it. There are two applicants, a rich student who prefers the scholarship, but she is also willing to accept the contract without scholarship, and a poor student, who only applies without scholarship. If the rich student has higher admission score, then the resulting solution in the Hungarian scheme is that the rich student will be admitted with scholarship, and the poor student remains unmatched. An alternative decision, that can be considered better by the university, is when the scholarship contract is given to the poor student, and the rich student is also admitted just without scholarship.

In this research, we conducted a counter-factual analysis on the administrative dataset of the Hungarian university admission from 2007, provided by the KRTK Databank. We used a heuristic algorithm by making artificial swaps in the preference lists of some, supposedly rich, students, switching the positions of two subsequent contracts listed in their preference lists for the same programme, now having the scholarship option behind the tuition fee option. In the end we obtained some alternative matchings, that can also be considered fair by a more general choice function of the universities, where they are flexible about awarding their scholarships, and they mainly care about the set of students admitted. In this case we could demonstrate that the total number of students admitted could increase by 1.9%. Moreover, we show that among the students gaining from the alternative admission policy there are much more students with low social-economic background and rural addresses, than among the students who would loose with this alternative policy.

Reference:
Péter Biró, Avinatan Hassidim, Assaf Romm, Ran I. Shorrer, Sándor Sóvágó
The Large Core of College Admission Markets – Theory and Evidence 
The Review of Economics and Statistics 2025;
doi: https://doi.org/10.1162/REST.a.1628