Estimating an Equilibrium Model of Horizontal Competition in Education

The quality of the match between students and schools affects learning but little is known about the magnitude of these effects or how they respond to changes in market structure. I develop a quantitative equilibrium model of school competition with horizontal competition in match quality. I estimate the model using data from Pakistan, a country with high private enrollment, and (1) quantify the importance of good matches, (2) show that profit-maximizing private schools' choices of quality advantage wealthier students, increasing inequality and reducing welfare and learning, and (3) provide intuition for when interventions in the market are valuable. I find that match matters: moving a student from her worst to best match school doubles yearly average test score gains. Setting match-specific quality socially optimally in private schools would greatly reduce inequality in learning between rich and poor students while increasing learning and welfare. These positive effects are amplified when students' enrollment decisions are more responsive to quality.