Sophistication and Cautiousness in College Applications

Abstract

In the literature of school choice and college admissions, there is increasing empirical evidence that the equilibrium of centralized mechanisms may not be played in real-world settings (Abdulkadiroglu et al., 2006; Kapor et al., 2020). In this paper, we test the equilibrium of college admissions markets, and quantify the welfare cost of two types of application mistakes resulting from either sincere applications or pessimistic beliefs. First, we provide a clean test of equilibrium from a large field dataset of Chinese college admissions, by exploiting the variation in assignment mechanisms as well as the uniqueness of equilibrium. Our reduced-form evidence shows that equilibrium was not fully played in these markets and suggests that both types of application mistakes were made. Motivated by this observation, we estimate a parsimonious student decision model that incorporates two behavioral types, sincere and cautious, into the equilibrium. Our estimates show that these two behavioral types account for a significant fraction of students; however, China’s recent policy reforms from the Immediate Acceptance to the Chinese parallel mechanism have leveled the playing field for these students, especially for those with high priority.