On the Measurement of Dissimilarity and Related Orders
We consider populations partitioned into groups, whose members are distributed across a finite number of classes such as, for instance, types of occupation, residential locations, social status of fathers, levels of education, health or income. Our aim is to assess the dissimilarity between the patterns of distributions of the different groups. These evaluations are relevant for the analysis of multi-group segregation, socioeconomic mobility, equalization of opportunity and discrimination. We conceptualize the notion of dissimilarity making use of reasonable transformations of the groups' distributions, based on sequences of transfers and exchanges of population masses across classes and/or groups. Our analysis clarifies the substantial differences underlying the concept of dissimilarity when applied to ordered or to permutable classes. In both settings, we illustrate the logical connections of dissimilarity evaluations with matrix majorization preorders, and provide equivalent implementable criteria to test unambiguous reductions in dissimilarity. Furthermore, we show that inequality evaluations can be interpreted as special cases of dissimilarity assessments and discuss relations with concepts of segregation and discrimination.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Frankel, David M. & Volij, Oscar, 2011.
"Measuring school segregation,"
Journal of Economic Theory,
Elsevier, vol. 146(1), pages 1-38, January.
- Frankel, David M. & Volij, Oscar, 2010. "Measuring School Segregation," Staff General Research Papers Archive 31808, Iowa State University, Department of Economics.
- Frankel, David M. & Volij, Oscar, 2011. "Measuring School Segregation," Staff General Research Papers Archive 35115, Iowa State University, Department of Economics.
- Grant, Simon & Kajii, Atsushi & Polak, Ben, 1998. "Intrinsic Preference for Information," Journal of Economic Theory, Elsevier, vol. 83(2), pages 233-259, December.
- Grant, S & Kajii, A & Polak, B, 1997. "Intrinsic Preference for Information," Papers 323, Australian National University - Department of Economics.
- Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
- Jenkins, Stephen P., 1994. "Earnings discrimination measurement : A distributional approach," Journal of Econometrics, Elsevier, vol. 61(1), pages 81-102, March.
- Borjas, George J, 1995. "Ethnicity, Neighborhoods, and Human-Capital Externalities," American Economic Review, American Economic Association, vol. 85(3), pages 365-390, June.
- George J. Borjas, 1994. "Ethnicity, Neighborhoods, and Human Capital Externalities," NBER Working Papers 4912, National Bureau of Economic Research, Inc.
- Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
- Alonso-Villar, Olga & del Río, Coral, 2010. "Local versus overall segregation measures," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 30-38, July.
- Olga Alonso-Villar & Coral del Río, 2008. "Local versus overall segregation measures," Working Papers 0802, Universidade de Vigo, Departamento de Economía Aplicada.
- George J. Borjas, 1992. "Ethnic Capital and Intergenerational Mobility," The Quarterly Journal of Economics, Oxford University Press, vol. 107(1), pages 123-150.
- A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 183-201.
- Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 1-14.
- Federico Echenique & Roland G. Fryer Jr & Alex Kaufman, 2006. "Is School Segregation Good or Bad?," American Economic Review, American Economic Association, vol. 96(2), pages 265-269, May.
- Le Breton, Michel & Michelangeli, Alessandra & Peluso, Eugenio, 2012. "A stochastic dominance approach to the measurement of discrimination," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1342-1350.
- Hutchens, Robert M., 1991. "Segregation curves, Lorenz curves, and inequality in the distribution of people across occupations," Mathematical Social Sciences, Elsevier, vol. 21(1), pages 31-51, February.
- Butler, Richard J & McDonald, James B, 1987. "Interdistributional Income Inequality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 13-18, January.
- FUSCO Alessio & SILBER Jacques, 2011. "Ordinal Variables and the Measurement of Polarization," LISER Working Paper Series 2011-33, LISER.
- Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, Oxford University Press, vol. 91(1), pages 1-13.
- Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March. Full references (including those not matched with items on IDEAS)