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	Educational Production Function	Educational Hierarchical Linear Modeling
分野	Education	Education
系統	Regression model	Regression model
提唱年	1979	2002
提唱者	Economics of education (Coleman; Hanushek; Todd & Wolpin)	Stephen Raudenbush & Anthony Bryk
種類	Regression relating educational inputs to achievement outputs	Multilevel regression for hierarchically nested educational data
原典	Hanushek, E. A. (1979). Conceptual and empirical issues in the estimation of educational production functions. Journal of Human Resources, 14(3), 351–388.	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage. ISBN: 9780761919049
別名	Education Production Function, Schooling Production Function, Input-Output Model of Education, Achievement Production Function	Multilevel Models in Education, Students-in-Schools HLM, School Effects Multilevel Model, Random-Effects Models for Educational Data
関連	3	4
概要	The educational production function is the economist's framework for relating the inputs of schooling — class size, teacher quality, expenditure, family background — to an output, usually measured achievement. Borrowing the production-function metaphor from the economics of the firm, it estimates by how much achievement changes when an input changes. It is the analytic backbone of decades of debate over what resources matter for learning, and the methodological challenges of estimating it honestly — endogeneity, omitted variables, and the cumulative history of inputs — define much of the field.	Educational hierarchical linear modeling (HLM) is a multilevel regression framework for data in which students are nested within classrooms and classrooms within schools. Formalized for education by Raudenbush and Bryk, it lets the intercept and slopes of a student-level regression vary across schools, simultaneously estimating student-level relationships, school-level relationships, and the cross-level interactions between them — while producing correct standard errors that single-level regression on clustered data cannot.