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Achievement Gap Estimates and Deviations from Cardinal Comparability

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Abstract

This paper assesses the sensitivity of standard empirical methods for measuring group differences in achievement to violations in the cardinal comparability of achievement test scores. The paper defines a distance measure over possible weighting functions (scalings) of test scores. It then constructs worst-case bounds for the bias in the estimated achievement gap (or achievement gap change) that could result from using the observed rather than the true test scale, given that the true and observed scales are no more than a fixed distance from each other. The worst-case weighting functions have simple, closed-form expressions consisting of achievement thresholds, flat regions in which test scores are uninformative, and regions in which the observed test scores are actually cardinally comparable. The paper next estimates these worst-case weighting functions for black/white and high-/low-income achievement gaps and gap changes using data from several commonly employed surveys. The results of this empirical exercise suggest that cross-sectional achievement gap estimates tend to be quite robust to scale misspecification. In contrast, achievement gap change estimates seem to be quite sensitive to the choice of test scale. Standard empirical methods may not robustly identify the sign of the trend in achievement inequality between students from different racial groups and income classes. Furthermore, ordinal methods may be more powerful and will continue to have the correct size when the test scale has been misspecified.

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  • Eric R. Nielsen, 2015. "Achievement Gap Estimates and Deviations from Cardinal Comparability," Finance and Economics Discussion Series 2015-40, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2015-40
    DOI: 10.17016/FEDS.2015.040
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    References listed on IDEAS

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    Cited by:

    1. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    2. Schröder, Carsten & Yitzhaki, Shlomo, 2017. "Revisiting the evidence for cardinal treatment of ordinal variables," European Economic Review, Elsevier, vol. 92(C), pages 337-358.
    3. Eric R. Nielsen, 2019. "Test Questions, Economic Outcomes, and Inequality," Finance and Economics Discussion Series 2019-013, Board of Governors of the Federal Reserve System (U.S.).
    4. Jesse Rothstein, 2019. "Inequality of Educational Opportunity? Schools as Mediators of the Intergenerational Transmission of Income," Journal of Labor Economics, University of Chicago Press, vol. 37(S1), pages 85-123.
    5. Attanasio, Orazio & Cattan, Sarah & Fitzsimons, Emla & Meghir, Costas & Rubio-Codina, Marta, 2015. "Estimating the Production Function for Human Capital: Results from a Randomized Control Trial in Colombia," IZA Discussion Papers 8856, Institute of Labor Economics (IZA).
    6. Rothstein , Jesse, 2017. "Inequality of Educational Opportunity? Schools as Mediators of the Intergenerational Transmission of Income," Department of Economics, Working Paper Series qt02t2c4nn, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    7. Jacob, B & Rothstein, J, 2016. "The measurement of student ability in modern assessment systems," Department of Economics, Working Paper Series qt24r2j30b, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    8. ALIEVA Aigul & HILDEBRAND Vincent & VAN KERM Philippe, 2018. "How does the achievement gap between immigrant and native-born pupils progress from primary to secondary education?," LISER Working Paper Series 2018-20, LISER.
    9. Brian Jacob & Jesse Rothstein, 2016. "The Measurement of Student Ability in Modern Assessment Systems," Journal of Economic Perspectives, American Economic Association, vol. 30(3), pages 85-108, Summer.

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    Keywords

    Achievement gaps; econometrics; health; education; and welfare; inequalty; measurement; robustness;
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