Competition between Private and Public Schools, Vouchers, and Peer-Group Effects

TLDR

Students vary in ability and income, and achievement depends on both individual ability and peers’ abilities. The model features tax‑financed tuition‑free public schools and competitive tuition‑financed private schools, where private schools offer tuition discounts to high‑ability, low‑income students and charge premiums to low‑ability, high‑income students. Equilibrium produces a strict hierarchy of school quality and two‑dimensional sorting by ability and income, and tuition vouchers enlarge the private sector, intensify sorting, and favor high‑ability students over low‑ability ones.

Abstract

A theoretical and computational model with tax-financed, tuition-free public schools and competitive, tuition-financed private schools is developed. Students differ by ability and income. Achievement depends on own ability and on peers' abilities. Equilibrium has a strict hierarchy of school qualities and two-dimensional student sorting with stratification by ability and income. In private schools, high-ability, low-income students receive tuition discounts, while low-ability, high-income students pay tuition premia. Tuition vouchers increase the relative size of the private sector and the extent of student sorting, and benefit high-ability students relative to low-ability students.