On the Measurement of Dissimilarity and Related Orders
AbstractWe 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.
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Bibliographic InfoPaper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 274.
Length: 56 pages
Date of creation: Oct 2012
Date of revision:
dissimilarity; matrix majorization; Zonotopes; multi-group segregation; discrimination.;
Find related papers by JEL classification:
- J71 - Labor and Demographic Economics - - Labor Discrimination - - - Hiring and Firing
- D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-11-17 (All new papers)
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.:
- Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, Econometric Society, vol. 46(2), pages 303-16, March.
- George J. Borjas, 1991.
"Ethnic Capital and Intergenerational Mobility,"
NBER Working Papers
3788, National Bureau of Economic Research, Inc.
- Grant, S & Kajii, A & Polak, B, 1997.
"Intrinsic Preference for Information,"
Papers, Australian National University - Department of Economics
323, Australian National University - Department of Economics.
- Butler, Richard J & McDonald, James B, 1987. "Interdistributional Income Inequality," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 5(1), pages 13-18, January.
- Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, Elsevier, vol. 42(1), pages 13-29, July.
- Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 49(2), pages 183-201, April.
- Hutchens, Robert M., 1991. "Segregation curves, Lorenz curves, and inequality in the distribution of people across occupations," Mathematical Social Sciences, Elsevier, Elsevier, vol. 21(1), pages 31-51, February.
- Le Breton, Michel & Michelangeli, Alessandra & Peluso, Eugenio, 2012. "A stochastic dominance approach to the measurement of discrimination," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(4), pages 1342-1350.
- Federico Echenique & Roland G. Fryer Jr & Alex Kaufman, 2006. "Is School Segregation Good or Bad?," American Economic Review, American Economic Association, American Economic Association, vol. 96(2), pages 265-269, May.
- Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer, Springer, vol. 15(1), pages 1-14.
- Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, Elsevier, vol. 53(2), pages 185-195, March.
- Frankel, David M. & Volij, Oscar, 2011.
"Measuring school segregation,"
Journal of Economic Theory, Elsevier,
Elsevier, vol. 146(1), pages 1-38, January.
- Frankel, David M. & Volij, Oscar, 2010. "Measuring School Segregation," Staff General Research Papers, Iowa State University, Department of Economics 31808, Iowa State University, Department of Economics.
- Frankel, David M. & Volij, Oscar, 2011. "Measuring School Segregation," Staff General Research Papers, Iowa State University, Department of Economics 35115, Iowa State University, Department of Economics.
- FUSCO Alessio & SILBER Jacques, 2011. "Ordinal Variables and the Measurement of Polarization," CEPS/INSTEAD Working Paper Series 2011-33, CEPS/INSTEAD.
- George J. Borjas, 1994.
"Ethnicity, Neighborhoods, and Human Capital Externalities,"
NBER Working Papers
4912, National Bureau of Economic Research, Inc.
- Borjas, George J, 1995. "Ethnicity, Neighborhoods, and Human-Capital Externalities," American Economic Review, American Economic Association, American Economic Association, vol. 85(3), pages 365-90, June.
- Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 91(1), pages 1-13, February.
- Jenkins, Stephen P., 1994. "Earnings discrimination measurement : A distributional approach," Journal of Econometrics, Elsevier, Elsevier, vol. 61(1), pages 81-102, March.
- Olga Alonso-Villar & Coral del Río, 2008.
"Local versus overall segregation measures,"
Working Papers, Universidade de Vigo, Departamento de EconomÃa Aplicada
0802, Universidade de Vigo, Departamento de Economía Aplicada.
- Casilda Lasso de la Vega & Oscar Volij, 2013. "Segregation, Informativeness And Lorenz Dominance," Working Papers, Ben-Gurion University of the Negev, Department of Economics 1312, Ben-Gurion University of the Negev, Department of Economics.
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