A Dissimilarity Index of Multidimensional Inequality of Opportunity

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Oxford Poverty & Human Development Initiative (OPHI)
Oxford Department of International Development
Queen Elizabeth House (QEH), University of Oxford

OPHI WORKING PAPER NO. 39
A Dissimilarity Index of Multidimensional Inequality of
Opportunity
Gaston Yalonetzky *
November 2010
Abstract
A recent literature on inequality of opportunity offers quantitative tools for comparisons and measurement based on stochastic dominance criteria and traditional inequality indices. In this paper I suggest an additional way of assessing inequality of opportunity with two indices of dissimilarity across distributions. The indices are based on a traditional homogeneity test of multinomial distributions and are similar to the square coe¢ cient of variation (Reardon and Firebaugh, 2002). Their properties are studied, as well as their usefulness and limitations in applications when both circumstances and advantages/outcomes are multidimensional. An empirical application measures changes in inequality of opportunity from an old to a young cohort in Peru. The importance of assessing the sensitivity of the results to group definitions and group proportions is highlighted.

*Oxford Poverty & Human Development Initiative, University of Oxford. E-mail address: gaston.yalonetzky@qeh.ox.ac.uk.
This study has been prepared within the OPHI theme on multidimensional measurement.
OPHI gratefully acknowledges support for its research and activities from the Government of Canada through the
International Development Research Centre (IDRC) and the Canadian International Development Agency (CIDA), the
Australian Agency for International Development (AusAID), and the United Kingdom Department for International
Development (DFID).
ISSN 2040-8188

ISBN 978-1-907194-23-8

A Dissimilarity Index of Multidimensional Inequality of
Opportunity
Gaston Yalonetzky
November 7, 2010

Abstract
A recent literature on inequality of opportunity o¤ers quantitative tools for comparisons



References: Atkinson, A. (1970). On the measurement of economic inequality. Journal of Economic Theory 2 (3), 244– Atkinson, A. and F. Bourguignon (1982). The comparison of multi-dimensioned distributions of economic status Barros, R. P. d., F. Ferreira, J. Molinas, and J. Saavedra (2009). Measuring inequality of opportunity in Latin America and the Caribbean Barros, R. P. d., J. Molinas, and J. Saavedra (2008). Measuring inequality of opportunities for children Bossuroy, T. and D. Cogneau (2008). Social mobility and colonial legacy in …ve africa countries. Checchi, D. and V. Peragine (2005). Regional disparities and inequality of opportunity: the case of italy Cramer, H. (1946). Mathematical methods for statistics. Princeton University Press. Duclos, J.-Y., D. Sahn, and S. Younger (2006). Robust multidimensional poverty comparisons. The Economic Journal 116 (514), 943– Elbers, C., P. Lanjouw, J. Mistiaen, and B. Ozler (2008). Reinterpreting between-group inequality. Everitt, B. (1992). The analysis of contingency tables (Second ed.). Chapman & Hall. Ferreira, F. and J. Gignoux (2008). The measurement of inequality of opportunity: theory and application to latin america Fleurbaey, M. (2008). Fairness, Responsibility and Welfare. Oxford University Press. Foster, J. and A. Shneyerov (2000). Path independent inequality measures. Journal of Economic Theory 91, 199– Frechet, M. (1951). Sur les tableaux de correlation dont les marges sont donnes. Annales de l’ Giddens, A. (2006). Sociology (5 ed.). Polity Press. Hild, M. and A. Voorhoeve (2004). Equality of opportunity and opportunity dominance. Economics and Philosophy 20, 117– Hogg, R. and E. Tanis (1997). Probability and statistical inference. Prentice Hall. Hutchens, R. (2001). Numerical measures of segregation: desirable properties and their implications. Mathematical Social Sciences 42, 13– 29. James, D. and K. Taeuber (1985). Measures of segregation. Sociological Methodology 15, 1– 32. Kendall, M. and A. Stuart (1973). The Advanced Theory of Statistics (3 ed.), Volume 2. Gri¢ n. Lefranc, A., N. Pistolesi, and A. Trannoy (2009). Equality of opportunity and luck: de…nitions and testable conditions, with an application to income in france Openshaw, S. (1984). The modi…able areal unit problem. Number 38 in Concepts and techniques in modern geography Peragine, V. (2004). Ranking income distributions according to equality of opportunity. Journal of Economic Inequality 00, 1– Reardon, S. (2009). Measures of ordinal segregation. In Y. Fluckiger, S. Reardon, and J. Silber (Eds.), Occupational and Residential Segregation, Volume 17 of Research on Economic Inequality. Reardon, S. and G. Firebaugh (2002). Measures of multigroup segregation. Sociological Methodology 32, 33– 67. Roemer, J. (1998). Equality of Opportunity. Harvard University Press. Roemer, J. (2006). Economic development as opportunity equalization. Cowles Foundation Discussion Paper 1583. Sen, A. (1976). Real national income. The Review of Economic Studies 43 (1), 19– 39. Silber, J. and G. Yalonetzky (2010). Measuring inequality in life chances when one variable is ordinal. White, M. J. (1986). Segregation and diversity measures in population distribution. Population index 52 (2), 198–

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