  The Deferred Acceptance algorithm is a popular school allocation mechanism
thanks to its strategy proofness. However, with application costs, strategy
proofness fails, leading to an identification problem. In this paper, I address
this identification problem by developing a new Threshold Rank setting that
models the entire rank order list as a one-step utility maximization problem. I
apply this framework to study student assignments in Chile. There are three
critical contributions of the paper. I develop a recursive algorithm to compute
the likelihood of my one-step decision model. Partial identification is
addressed by incorporating the outside value and the expected probability of
admission into a linear cost framework. The empirical application reveals that
although school proximity is a vital variable in school choice, student ability
is critical for ranking high academic score schools. The results suggest that
policy interventions such as tutoring aimed at improving student ability can
help increase the representation of low-income low-ability students in better
quality schools in Chile.
