Preference Estimation in Deferred Acceptance with Partial School Rankings

TL;DR

This paper introduces a new model for estimating student preferences in school choice, addressing identification issues with partial rankings and applying it to Chilean data to inform policy interventions.

Contribution

It develops a recursive likelihood algorithm and a linear cost framework to handle partial rankings and identification problems in school choice models.

Findings

School proximity influences student preferences but ability is more critical for high-ranked schools.

Policy interventions like tutoring can improve low-income students' access to better schools.

The model successfully captures student decision-making with partial rank data.

Abstract

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.