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analysis average high school average student socioeconomic average student test Catholic voucher schools characteristics and school Chile Chilean pesos controlling for student decentralization of decisionmaking decisionmaking authority Decomposition of estimated degree of decentralization estimated variance high school grades implementing projects Inter-American Development Bank job satisfaction March 2002 March math test scores McEwan and Carnoy measure of student Municipal Private voucher municipal schools paid Catholic voucher percent of teachers percent of total principal components analysis Private paid Catholic private paid schools Private voucher Private private voucher schools school characteristics school choice school management measures school management policies school schedule school-level averages shared financing standard deviation student achievement student background student socioeconomic background student test scores teacher absenteeism teacher and school teacher autonomy teacher characteristics teacher reports teacher-level teachers with university total variance unexplained variance Universidad de Chile university education unobserved variance decomposition variation in student voucher Private paid vulnerability index