Strategic mistakes in school assignment: Biased beliefs versus optimization errors
Theory shows that the manipulable Boston mechanism can result in higher expected student welfare than the strategy-proof deferred acceptance (DA) mechanism. Recent empirical studies find, however, the opposite and attribute this to students making strategic mistakes. Such mistakes can be due to biased beliefs about admission probabilities and to optimization errors. We use unique survey data combined with register data from the secondary-school match in Utrecht in 2016 to distinguish these two sources. We find that 18.1% of the students make a strategic mistake, that about two thirds of these mistakes are due to optimization errors instead of biased beliefs, and that optimization errors account for 85% of the associated welfare loss. Informing students about admission probabilities therefore has only a small effect on welfare. Under students' actual choices, mean welfare is lower under Boston than under DA. When all students play optimally, the welfare difference between the two mechanisms disappears but does not reverse. The results favor the strategy-proof DA mechanism.