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School System Evaluation by Value Added Analysis Under Endogeneity

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  • Jorge Manzi

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  • Ernesto San Martín

    ()

  • Sébastien Van Bellegem
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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. Copyright The Psychometric Society 2014

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    Bibliographic Info

    Article provided by Springer in its journal Psychometrika.

    Volume (Year): 79 (2014)
    Issue (Month): 1 (January)
    Pages: 130-153

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    Handle: RePEc:spr:psycho:v:79:y:2014:i:1:p:130-153

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    Related research

    Keywords: value added; endogeneity; hierarchical linear mixed model; instrumental variable; school effect;

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    1. Joshua Angrist & Alan Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Working Papers 834, Princeton University, Department of Economics, Industrial Relations Section..
    2. Peter Ebbes & Ulf Böckenholt & Michel Wedel, 2004. "Regressor and random-effects dependencies in multilevel models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 161-178.
    3. Richard Blundell & Steve Bond, 1995. "Initial conditions and moment restrictions in dynamic panel data models," IFS Working Papers W95/17, Institute for Fiscal Studies.
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    5. Claudio Sapelli & Bernardita Vial, 2002. "The Performance of Private and Public Schools in the Chilean Voucher System," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 39(118), pages 423-454.
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    9. Sean F. Reardon & Stephen W. Raudenbush, 2009. "Assumptions of Value-Added Models for Estimating School Effects," Education Finance and Policy, MIT Press, vol. 4(4), pages 492-519, October.
    10. Jee-Seon Kim & Edward Frees, 2007. "Multilevel Modeling with Correlated Effects," Psychometrika, Springer, vol. 72(4), pages 505-533, December.
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    12. Spencer, N. & Fielding, A., 2000. "A Comparison of Modelling Strategies for Value-Added Analyses of Educational Data," Papers 2000:7, University of Hertfordshire - Business Schoool.
    13. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164, September.
    14. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
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