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School System Evaluation by Value Added Analysis Under Endogeneity

Published online by Cambridge University Press:  01 January 2025

Jorge Manzi ,
Ernesto San Martín  and
Sébastien Van Bellegem
Jorge Manzi
Affiliation:
School of Psychology, Pontificia Universidad Católica de Chile Measurement Center MIDE UC
Ernesto San Martín*
Affiliation:
Measurement Center MIDE UC Department of Statistics, Pontificia Universidad Católica de Chile Faculty of Education, Pontificia Universidad Católica de Chile Center for Operations Research and Econometrics, Université catholique de Louvain
Sébastien Van Bellegem
Affiliation:
Center for Operations Research and Econometrics, Université catholique de Louvain
*
Requests for reprints should be sent to Ernesto SanMartín, Department of Statistics, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Macul, Santiago, Chile. E-mail: esanmart@mat.puc.cl
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Abstract

Value added is a common tool in educational research on effectiveness. It is often modeled as a (prediction of a) random effect in a specific hierarchical linear model. This paper shows that this modeling strategy is not valid when endogeneity is present. Endogeneity stems, for instance, from a correlation between the random effect in the hierarchical model and some of its covariates. This paper shows that this phenomenon is far from exceptional and can even be a generic problem when the covariates contain the prior score attainments, a typical situation in value added modeling. Starting from a general, model-free definition of value added, the paper derives an explicit expression of the value added in an endogeneous hierarchical linear Gaussian model. Inference on value added is proposed using an instrumental variable approach. The impact of endogeneity on the value added and the estimated value added is calculated accurately. This is also illustrated on a large data set of individual scores of about 200,000 students in Chile.

Keywords

value addedendogeneityhierarchical linear mixed modelinstrumental variableschool effect

Information

Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 1 , January 2014 , pp. 130 - 153
Copyright
Copyright © 2013 The Psychometric Society

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