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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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    References listed on IDEAS

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    1. Joshua D. Angrist & Alan B. Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 69-85, Fall.
    2. MANZI, Jorge & SAN MARTIN, Ernesto & VAN BELLEGEM, Sébastien, 2010. "School system evaluation by value-added analysis under endogeneity," CORE Discussion Papers 2010046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Picci, Giorgio, 1989. "Parametrization of factor analysis models," Journal of Econometrics, Elsevier, vol. 41(1), pages 17-38, May.
    4. Jee-Seon Kim & Edward Frees, 2007. "Multilevel Modeling with Correlated Effects," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 505-533, December.
    5. Blundell, Richard & Bond, Stephen, 1998. "Initial conditions and moment restrictions in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 87(1), pages 115-143, August.
    6. 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.
    7. 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.
    8. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, June.
    9. Florens, Jean-Pierre & Mouchart, Michel, 1985. "A Linear Theory for Noncausality," Econometrica, Econometric Society, vol. 53(1), pages 157-175, January.
    10. Saïd Hanchane & Tarek Mostafa, 2012. "Solving endogeneity problems in multilevel estimation: an example using education production functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1101-1114, November.
    11. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    12. Jee-Seon Kim & Edward Frees, 2006. "Omitted Variables in Multilevel Models," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 659-690, December.
    13. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    14. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164.
    15. 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..
    16. Paredes, Ricardo D. & Paredes, Valentina, 2009. "Chile: academic performance and educational management under a rigid employment regime," Revista CEPAL, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL), December.
    17. 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.
    18. 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.
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    1. repec:bla:scjsta:v:44:y:2017:i:1:p:168-191 is not listed on IDEAS
    2. Van Keilegom, Ingrid & Vanhems, Anne, 2016. "Estimation of a semiparametric transformation model in the presence of endogeneity," TSE Working Papers 16-654, Toulouse School of Economics (TSE).
    3. repec:bla:jorssa:v:180:y:2017:i:1:p:315-340 is not listed on IDEAS
    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.

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