What accounts for international differences in student performance?

"We use the PISA student-level achievement database to estimate international education production functions. Student characteristics, family backgrounds, home inputs, resources, teachers and institutions are all significantly related to math, science and reading achievement. Our models account for more than 85% of the between-country performance variation, with roughly 25% accruing to institutional variation. Student performance is higher with external exams and budget formulation, but also with school autonomy in textbook choice, hiring teachers and within-school budget allocations. School autonomy is more beneficial in systems with external exit exams. Students perform better in privately operated schools, but private funding is not decisive"--Forschungsinstitut zur Zukunft der Arbeit web site.