When do stable matching mechanisms fail? The role of standardized tests in Chinese college admissions

Abstract

In this paper, we investigate matching problems where priorities and preferences are misaligned. In the case of centralized Chinese college admissions, students are matched based on their test scores in standardized tests, a noisy realization of their aptitudes due to measurement errors. We show that in this case any matching mechanism that is stable with respect to score is not stable with respect to aptitude. The resulting instability leads to colleges' incentive to participate in early admissions (zizhu zhaosheng), a form of market unraveling. However, a manipulable mechanism such as the Immediate Acceptance mechanism, combined with limited information about priorities, may succeed in mending this market failure. We then design and conduct a laboratory experiment where we compare the performance of two mechanisms (the Immediate Acceptance mechanism and the Deferred Acceptance mechanism), under two timing conditions of the submission of students' rank-ordered lists of colleges (before the exam and after the exam), using a two-stage matching market design with the possibility of early offers. In the experiment, a significant level of market unraveling occurred under mechanisms that are not stable with respect to aptitude, confirming theoretical predictions. We also find that the Immediate Acceptance mechanism under pre-exam submission condition significantly reduces such unraveling.