The Divergence Index: A Decomposable Measure of Segregation and Inequality

Decomposition analysis is a critical tool for understanding the social and spatial dimensions of inequality, segregation, and diversity. In this paper, I propose a new measure - the Divergence Index - to address the need for a decomposable measure of segregation. Although the Information Theory Index has been used to decompose segregation within and between communities, I argue that it measures relative diversity not segregation. I demonstrate the importance of this conceptual distinction with two empirical analyses: I decompose segregation and relative homogeneity in the Detroit metropolitan area, and I analyze the relationship between the indexes in the 100 largest U.S. cities. I show that it is problematic to interpret the Information Theory Index as a measure of segregation, especially when analyzing local-level results or any decomposition of overall results. Segregation and diversity are important aspects of residential differentiation, and it is critical that we study each concept as the structure and stratification of the U.S. population becomes more complex.

[1]  Philip B. Coulter,et al.  Measuring Inequality: A Methodological Handbook , 1989 .

[2]  J. Jahn,et al.  The Measurement of Ecological Segregation , 1947 .

[3]  M. O'Kelly,et al.  Information theoretic approach to measurement of spatial inequality , 1979 .

[4]  Henri Theil,et al.  A note on the measurement of racial integration of schools by means of informational concepts , 1971 .

[5]  D. Lichter,et al.  Toward a New Macro-Segregation? Decomposing Segregation within and between Metropolitan Cities and Suburbs , 2015 .

[6]  C. Simkin. About Economic Inequality , 1998 .

[7]  W. Frey Diversity Explosion: How New Racial Demographics are Remaking America , 2014 .

[8]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[9]  Domenico Parisi,et al.  Multi-Scale Residential Segregation: Black Exceptionalism and America's Changing Color Line , 2011 .

[10]  D. H. Freeman Statistical Decomposition Analysis , 1974 .

[11]  O. D. Duncan,et al.  A METHODOLOGICAL ANALYSIS OF SEGREGATION INDEXES , 1955 .

[12]  S. Lieberson,et al.  Temporal Changes and Urban Differences in Residential Segregation: A Reconsideration , 1982, American Journal of Sociology.

[13]  R. Breen,et al.  Educational Assortative Mating and Earnings Inequality in the United States1 , 2011, American Journal of Sociology.

[14]  A. Shorrocks,et al.  Inequality Decomposition by Population Subgroups , 1984 .

[15]  C. Chree,et al.  [Letters to Editor] , 1925, Nature.

[16]  François Bourguignon,et al.  Decomposable Income Inequality Measures , 1979 .

[17]  Christophersen Er,et al.  The Welfare Approach to Measuring Inequality , 2007 .

[18]  R. Breen,et al.  Income Inequality and Education , 2015 .

[19]  M. White Segregation and diversity measures in population distribution. , 1986, Population index.

[20]  David O'Sullivan,et al.  Beyond the Census Tract: Patterns and Determinants of Racial Segregation at Multiple Geographic Scales , 2008, American sociological review.

[21]  Some further observations on the index of residential differentiation , 1981, Demography.

[22]  A. M. Carr-Saunders,et al.  Wealth and Welfare , 1913 .

[23]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[24]  Scott J. South,et al.  The Measurement of Intergroup Income Inequality: A Conceptual Review , 1983 .

[25]  Barrett A. Lee,et al.  Trajectories of Ethnoracial Diversity in American Communities, 1980-2010. , 2016, Population and development review.

[26]  W. E. Silver,et al.  Economics and Information Theory , 1967 .

[27]  M. Handcock,et al.  Relative Distribution Methods in the Social Sciences , 1999 .

[28]  Tomoya Mori,et al.  A Divergence Statistic for Industrial Localization , 2005, Review of Economics and Statistics.

[29]  John J. Peterson,et al.  Statistical Group Comparison , 2003, Technometrics.

[30]  Mary J. Fischer Shifting Geographies , 2008 .

[31]  K. Kuga,et al.  Additivity and the entropy concept: An axiomatic approach to inequality measurement , 1981 .

[32]  H. Dalton The Measurement of the Inequality of Incomes , 1920 .

[33]  Barbara S. Zoloth Alternative Measures of School Segregation , 1976 .

[34]  John R. Logan,et al.  Diversity and Disparities: America Enters a New Century , 2014 .

[35]  A. Shorrocks Decomposition procedures for distributional analysis: a unified framework based on the Shapley value , 2013 .

[36]  D. Lichter,et al.  The Geography of Exclusion: Race, Segregation, and Concentrated Poverty , 2012 .

[37]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[38]  A. Atkinson More on the measurement of inequality , 2008 .

[39]  James S. Coleman,et al.  Achievement and Segregation in Secondary Schools: A Further Look at Public and Private School Differences. , 1982 .

[40]  W. Heath The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies , 2008 .

[41]  S. Bandyopadhyay,et al.  Reference distributions and inequality measurement , 2013 .

[42]  Sean F. Reardon,et al.  2. Measures of Multigroup Segregation , 2002 .

[43]  James M. Sakoda,et al.  A generalized index of dissimilarity , 1981, Demography.

[44]  Sean F. Reardon,et al.  The geographic scale of Metropolitan racial segregation , 2008, Demography.

[45]  N. Denton,et al.  The Dimensions of Residential Segregation , 1988 .

[46]  Martina Morris,et al.  2. Relative Distribution Methods , 1998 .

[47]  A. Shorrocks,et al.  The Class of Additively Decomposable Inequality Measures , 1980 .

[48]  Harald Reuter,et al.  Diversity and complexity , 1988, Nature.

[49]  Rima Wilkes,et al.  Does Socioeconomic Status Matter? Race, Class, and Residential Segregation , 2006 .

[50]  H. Akaike A new look at the statistical model identification , 1974 .

[51]  B. Morgan,et al.  The Segregation of Socio-economic Groups in Urban Areas: a Comparative Analysis , 1975 .

[52]  Christopher Winship,et al.  The Desirability of Using the Index of Dissimilarity or any Adjustment of It for Measuring Segregation: Reply to Falk, Cortese, and Cohen , 1978 .

[53]  Delia Baldassarri,et al.  Love Thy Neighbor? Ethnoracial Diversity and Trust Reexamined1 , 2015, American Journal of Sociology.

[54]  Jack K. Cohen,et al.  Utilizing Standardized Indices of Residential Segregation: Comment on Winship , 1978 .

[55]  Sean F. Reardon,et al.  3. Measures of Spatial Segregation , 2004 .

[56]  I. Sasson,et al.  Trends in Life Expectancy and Lifespan Variation by Educational Attainment: United States, 1990–2010 , 2016, Demography.

[57]  Frank A. Cowell,et al.  Generalized entropy and the measurement of distributional change , 1980 .

[58]  Kendra Bischoff,et al.  School District Fragmentation and Racial Residential Segregation , 2008 .

[59]  Chad R. Farrell Bifurcation, Fragmentation or Integration? The Racial and Geographical Structure of US Metropolitan Segregation, 1990—2000 , 2008 .

[60]  François Bavaud,et al.  Information Theory, Relative Entropy and Statistics , 2009, Formal Theories of Information.

[61]  Deirdre Bloome Racial Inequality Trends and the Intergenerational Persistence of Income and Family Structure , 2014, American sociological review.

[62]  Claude S. Fischer,et al.  Appendices to : “ Distinguishing the Geographic Levels and Social Dimensions of U . S . Metropolitan Segregation , 1960-2000 , 2004 .

[63]  Charles F. Cortese Further Consideration on the Methodological Analysis of Segregation Indices. , 1976 .

[64]  Frank A. Cowell,et al.  On the Structure of Additive Inequality Measures , 1980 .

[65]  P. Allison Measures of Inequality , 1978 .

[66]  David O'Sullivan,et al.  Race and space in the 1990s: changes in the geographic scale of racial residential segregation, 1990-2000. , 2009, Social science research.

[67]  Richard Nock,et al.  Income distributions and decomposable divergence measures , 2010, J. Econ. Theory.

[68]  Theodore R. Anderson,et al.  Negroes in Cities: Residential Segregation and Neighborhood Change. , 1966 .

[69]  David R. James,et al.  Measures of segregation , 2019, Balancing School Choice and Equity.