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School System Evaluation by Value Added Analysis Under Endogeneity

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  • Jorge Manzi
  • Ernesto San Martín
  • Sébastien Van Bellegem

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. Copyright The Psychometric Society 2014

Suggested Citation

  • Jorge Manzi & Ernesto San Martín & Sébastien Van Bellegem, 2014. "School System Evaluation by Value Added Analysis Under Endogeneity," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 130-153, January.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:1:p:130-153
    DOI: 10.1007/s11336-013-9338-0
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    Cited by:

    1. Canales, Andrea & Maldonado, Luis, 2018. "Teacher quality and student achievement in Chile: Linking teachers' contribution and observable characteristics," International Journal of Educational Development, Elsevier, vol. 60(C), pages 33-50.
    2. Melanie Birke & Sebastien Van Bellegem & Ingrid Van Keilegom, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 168-191, March.
    3. Vanhems, Anne & Van Keilegom, Ingrid, 2019. "Estimation Of A Semiparametric Transformation Model In The Presence Of Endogeneity," Econometric Theory, Cambridge University Press, vol. 35(1), pages 73-110, February.
    4. Luis Alejandro Lopez-Agudo & Oscar David Marcenaro Gutierrez, 2016. "Identifying effective teachers: The case study of Spain," Investigaciones de Economía de la Educación volume 11, in: José Manuel Cordero Ferrera & Rosa Simancas Rodríguez (ed.), Investigaciones de Economía de la Educación 11, edition 1, volume 11, chapter 18, pages 349-366, Asociación de Economía de la Educación.
    5. Garritt L. Page & Ernesto San Martín & Javiera Orellana & Jorge González, 2017. "Exploring complete school effectiveness via quantile value added," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 315-340, January.

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