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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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. San Martin, Ernesto & Rolin, Jean-Marie, 2013. "Identification of parametric Rasch-type models," LIDAM Reprints ISBA 2013002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. 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, May.
    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.
    6. 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.
    7. Neil H. Spencer & Antony Fielding, 2002. "A Comparison of Modelling Strategies for Value-Added Analyses of Educational Data," Computational Statistics, Springer, vol. 17(1), pages 103-116, March.
    8. 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.
    9. 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.
    10. Jee-Seon Kim & Edward Frees, 2006. "Omitted Variables in Multilevel Models," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 659-690, December.
    11. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164.
    12. 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.
    13. Manzi, Jorge & San Martin, Ernesto & Van Bellegem, Sébastien, 2010. "School System Evaluation By Value-Added Analysis under Endogeneity," IDEI Working Papers 631, Institut d'Économie Industrielle (IDEI), Toulouse.
    14. Picci, Giorgio, 1989. "Parametrization of factor analysis models," Journal of Econometrics, Elsevier, vol. 41(1), pages 17-38, May.
    15. Jee-Seon Kim & Edward Frees, 2007. "Multilevel Modeling with Correlated Effects," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 505-533, December.
    16. 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.
    17. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sebastien, 2012. "Instrumental regression in partially linear models," LIDAM Reprints ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Andrew Ray & Tanya McCormack & Helen Evans, 2009. "Value Added in English Schools," Education Finance and Policy, MIT Press, vol. 4(4), pages 415-438, October.
    19. Florens, Jean-Pierre & Mouchart, Michel, 1985. "A Linear Theory for Noncausality," Econometrica, Econometric Society, vol. 53(1), pages 157-175, January.
    20. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    21. Derek C. Briggs & Jonathan P. Weeks, 2011. "The Persistence of School-Level Value-Added," Journal of Educational and Behavioral Statistics, , vol. 36(5), pages 616-637, October.
    22. 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..
    23. 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.
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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. Garritt L. Page & Ernesto San Martín & David Torres Irribarra & Sébastien Van Bellegem, 2024. "Temporally Dynamic, Cohort-Varying Value-Added Models," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 1074-1103, September.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Page, Garritt L. & San Martin, Ernesto & Torres Irribarra, David & Van Bellegem, Sébastien, 2024. "Temporally Dynamic, Cohort-Varying Value-Added Models," LIDAM Discussion Papers CORE 2024009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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