There is a semi-new paper (pdf) by Youjin Hahn, Liang Choon Wang, and Hee-Seung Yang, the abstract is this:
We show that private high school students outperform public high school students in Seoul, South Korea, where secondary school students are randomly assigned into schools within school districts. Both private and public schools in Seoul must admit students randomly assigned to them, charge the same fees, and use the same curricula under the so-called equalization policy’, but private schools enjoy greater autonomy in hiring and other staffing decisions and their principals and teachers face stronger incentives to deliver good students’ performance. Our findings suggest that providing schools greater autonomy in their personnel and resource allocation decisions while keeping school principals accountable can be effective in improving students’ outcomes.
That is from G Heller Sahlgren, who has numerous tweets of interest on Korean schooling.