zbMATH — the first resource for mathematics

Measuring school segregation. (English) Zbl 1244.91074
Summary: Using only ordinal axioms, we characterize several multigroup school segregation indices: the Atkinson indices for the class of school districts with a given fixed number of ethnic groups and the Mutual Information index for the class of all districts. Properties of other school segregation indices are also discussed. In an empirical application, we document a weakening of the effect of ethnicity on school assignment from 1987/1988 to 2007/2008. We also show that segregation between districts within cities currently accounts for 33% of total segregation. Segregation between states, driven mainly by the distinct residential patterns of Hispanics, contributes another 32%.

91C05 Measurement theory in the social and behavioral sciences
Full Text: DOI
[1] Aczél, J., Lectures on functional equations and their applications, (1966), Academic Press New York and London · Zbl 0139.09301
[2] Atkinson, A.B., On the measurement of inequality, J. econ. theory, 2, 244-263, (1970)
[3] Bell, W., A probability model for the measurement of ecological segregation, Social forces, 32, 357-364, (1954)
[4] Blackwell, D., Equivalent comparisons of experiments, Ann. math. statist., 24, 265-272, (1953) · Zbl 0050.36004
[5] H. Bohnenblust, L. Shapley, S. Sherman, Reconnaissance in game theory, RAND Working Paper, RM-208, 1949.
[6] Boozer, M.A.; Krueger, A.B.; Wolkin, S., Race and school quality Since Brown v. board of education, Brookings pap. econ. act. microeconomics, 269-338, (1992)
[7] Bourguignon, F., Decomposable income inequality measures, Econometrica, 47, 901-920, (1979) · Zbl 0424.90013
[8] Card, D.; Rothstein, J., Racial segregation and the black-white test score gap, J. public econ., 91, 2158-2184, (2007)
[9] Clotfelter, C.T., Public school segregation in metropolitan areas, Land econ., 75, 487-504, (1999)
[10] Coleman, J.S.; Hoffer, T.; Kilgore, S., Achievement and segregation in secondary schools: a further look at public and private school differences, Soc. educ., 55, 162-182, (1982)
[11] Cover, T.M.; Thomas, J.A., Elements of information theory, (1991), Wiley and Sons New York, NY · Zbl 0762.94001
[12] Cutler, D.; Glaeser, E.; Vigdor, J., When are ghettos bad? lessons from immigration segregation in the united states, J. urban econ., 63, 759-774, (2008)
[13] Dalton, H., The measurement of the inequality of incomes, Econ. J., 30, 348-361, (1920)
[14] Echenique, F.; Fryer, R.G., A measure of segregation based on social interactions, Quart. J. econ., 122, 441-485, (2007)
[15] Flückiger, Y.; Silber, J., The measurement of segregation in the labor force, (1999), Physica-Verlag Heidelberg and New York
[16] Foster, J.E., An axiomatic characterization of the Theil measure of income inequality, J. econ. theory, 65, 105-121, (1983) · Zbl 0522.90020
[17] Fuchs, V., A note on sex segregation in professional occupations, Explorations econ. res., 2, 105-111, (1975)
[18] Grant, S.; Kajii, A.; Polak, B., Intrinsic preference for information, J. econ. theory, 83, 233-259, (1998) · Zbl 0915.90080
[19] Guryan, J., Desegregation and black dropout rates, Amer. econ. rev., 94, 919-943, (2005)
[20] E.A. Hanushek, J.F. Kain, S.G. Rivkin, New evidence about Brown v. board of education: the complex effects of school racial composition on achievement, NBER Working Paper, W8741, 2004.
[21] C.M. Hoxby, Peer effects in the classroom: learning from gender and race variation, NBER Working Paper, 7867, 2000.
[22] Hutchens, R., Numerical measures of segregation: desirable properties and their implications, Math. soc. sci., 42, 13-29, (2001) · Zbl 0980.91063
[23] Hutchens, R., One measure of segregation, Int. econ. rev., 45, 555-578, (2003)
[24] Jahn, J.; Schmidt, C.F.; Schrag, C., The measurement of ecological segregation, Amer. soc. rev., 12, 293-303, (1947)
[25] James, F.J., A new generalized ‘exposure-based’ segregation index, Soc. methods res., 14, 301-316, (1986)
[26] James, D.R.; Taeuber, K.E., Measures of segregation, Soc. methodology, 15, 1-32, (1985)
[27] Johnson, R.; Poulsen, M.; Forrest, J., Ethnic and racial segregation in U.S. metropolitan areas, 1980-2000: the dimensions of segregation revisited, Urban aff. rev., 42, 479-504, (2007)
[28] Lieberson, S., Measuring population diversity, Amer. soc. rev., 34, 850-862, (1969)
[29] Massey, D.S.; Denton, N.A., The dimensions of racial segregation, Social forces, 67, 281-315, (1988)
[30] D. McLaughlin, CCD data file: thirteen-year longitudinal common core of data non-fiscal survey database: school years 1986-87 - 1998-99, U.S. Department of Education, National Center for Education Statistics, 2003.
[31] Mora, R.; Ruiz-Castillo, J., Additively decomposable segregation indices: the case of gender segregation by occupations and human capital levels in Spain, J. econ. inequality, 1, 147-179, (2003)
[32] R. Mora, J. Ruiz-Castillo, The axiomatic properties of an entropy based index of segregation, Universidad Carlos III de Madrid working paper, 05-62, 2005.
[33] Mora, R.; Ruiz-Castillo, J., Gender segregation by occupations in the public and the private sector: the case of Spain, Investigaciones econ., 28, 399-428, (2004)
[34] Morgan, B.S., The segregation of socioeconomic groups in urban areas: a comparative analysis, Urban stud., 12, 47-60, (1975)
[35] Philipson, T., Social welfare and measurement of segregation, J. econ. theory, 60, 322-334, (1993) · Zbl 0805.90025
[36] Reardon, S.F.; Firebaugh, G., Measures of multigroup segregation, Soc. methodology, 32, 33-67, (2002)
[37] Rivkin, S.G., Residential segregation and school integration, Soc. educ., 67, 279-292, (1994)
[38] Sakoda, J., A generalized index of dissimilarity, Demography, 18, 245-250, (1981)
[39] Shorrocks, A.F., The class of additively decomposable inequality measures, Econometrica, 39, 613-625, (1980) · Zbl 0435.90040
[40] Shorrocks, A.F., Inequality decompositions by population subgroups, Econometrica, 48, 1369-1386, (1984) · Zbl 0601.90029
[41] Taeuber, K.E.; James, D.R., Racial segregation among public and private schools, Soc. educ., 55, 133-143, (1982)
[42] Theil, H., Economics and information theory, (1967), North-Holland Amsterdam
[43] Theil, H., Principles of econometrics, (1971), Wiley and Sons New York, NY · Zbl 0221.62002
[44] Theil, H., Statistical decomposition analysis, (1972), North-Holland Amsterdam
[45] Theil, H.; Finizza, A.J., A note on the measurement of racial integration in schools, J. math. soc., 1, 187-193, (1971)
[46] von Neumann, J.; Morgenstern, O., Theory of games and economic behavior, (1944), Princeton University Press Princeton, NJ · Zbl 0063.05930
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.