This monograph reviews a set of widely used summary inequality measures, and the lesser-known relative distribution method provides the basic rationale behind each measure and discusses their interconnections. It also introduces model-based decomposition of inequality over time using quantile regression. This approach enables researchers to estimate two different contributions to changes in inequality between two time points.
This supplementary monograph is appropriate for any graduate-level, intermediate, or advanced statistics course across the social and behavioral sciences, as well as for individual researchers.
Providing basic foundations for measuring inequality
from the perspective of distributional properties
This text reviews a set of widely used summary inequality measures, and the lesser known relative distribution method provides the basic rationale behind each and discusses their interconnections. It also introduces model-based decomposition of inequality over time using quantile regression. This approach enables researchers to estimate two different contributions to changes in inequality between two time points.
Key Features
- Clear statistical explanations provide fundamental statistical basis for understanding the new modeling framework
- Straightforward empirical examples reinforce statistical knowledge and ready-to-use procedures
- Multiple approaches to assessing inequality are introduced by starting with the basic distributional property and providing connections among approaches
This supplementary text is appropriate for any graduate-level, intermediate, or advanced statistics course across the social and behavioral sciences, as well as individual researchers.
| About the Authors |
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viii | |
| Series Editor's Introduction |
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ix | |
| Acknowledgments |
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1 | (4) |
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2 PDFs, CDFs, Quantile Functions, and Lorenz Curves |
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5 | (14) |
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Ranks, PDFs, CDFs, and Moments |
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5 | (5) |
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10 | (3) |
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13 | (3) |
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16 | (1) |
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Appendix: A Location Shift Changes the Lorenz Curve |
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17 | (2) |
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3 Summary Inequality Measures |
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19 | (25) |
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Summary Inequality Measures |
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19 | (21) |
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Relating Inequality Measures to Probability Distributions |
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19 | (6) |
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Inequality Measures Based on Quantile Functions and Lorenz Curves |
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25 | (5) |
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Inequality Measures Derived From Social Welfare Functions |
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30 | (4) |
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Inequality Measures Developed From Information Theory |
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34 | (6) |
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Inequality Measures for Variables With Nonpositive Values |
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40 | (1) |
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41 | (1) |
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42 | (2) |
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4 Choices of Inequality Measures |
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44 | (21) |
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Weak Principle of Transfers |
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44 | (2) |
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Strong Principle of Transfers |
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46 | (1) |
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47 | (1) |
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48 | (1) |
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48 | (9) |
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Choose Inequality Measures for One Population |
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57 | (2) |
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Lorenz Dominance and Population Comparison |
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59 | (4) |
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63 | (1) |
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64 | (1) |
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5 Relative Distribution Methods |
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65 | (28) |
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Relative Rank, Relative Distribution, Relative Density |
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65 | (5) |
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Relative Proportions and Relative Density |
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70 | (3) |
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Decomposition of Relative Density |
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73 | (9) |
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Summary Measures of Relative Distribution |
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82 | (8) |
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82 | (4) |
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86 | (4) |
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Trends of Relative Distributions |
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90 | (2) |
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92 | (1) |
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93 | (18) |
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The Asymptotic Approach With Survey Design Effect |
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94 | (7) |
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101 | (8) |
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104 | (2) |
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Bootstrap Inferences for Relative Distribution Measures |
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106 | (1) |
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Bootstrapping With Survey Sampling Designs |
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107 | (1) |
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Performance of the Asymptotic and Bootstrap Approaches |
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108 | (1) |
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109 | (2) |
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7 Analyzing Inequality Trends |
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111 | (10) |
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120 | (1) |
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8 An Illustrative Application: Inequality in Income and Wealth in the United States, 1991-2001 |
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121 | (22) |
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121 | (5) |
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Observed Income and Wealth Inequality |
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126 | (4) |
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Testing Trends of Income and Wealth Inequality |
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130 | (6) |
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Decomposing Trends of Income and Wealth Inequality |
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136 | (4) |
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140 | (2) |
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142 | (1) |
| References |
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143 | (4) |
| Index |
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147 | |
Lingxin Hao is a professor of sociology at Johns Hopkins University. Her specialties include quantitative methodology, social inequality, sociology of education, migration, and family and public policy. She is the lead author of two QASS monographs Quantile Regression and Assessing Inequality. Her research has appeared in the Sociological Methodology, Sociological Methods and Research, American Journal of Sociology, Demography, Social Forces, Sociology of Education, and Child Development, among others. Daniel Q. Naiman (PhD, Mathematics, 1982, University of Illinois at Urbana-Champaign) is Professor and Chair of the Applied Mathematics and Statistics at the Johns Hopkins University. He was elected as a Fellow of the Institute of Mathematical Statistics in 1997, and was an Erskine Fellow at the University of Canterbury in 2005. Much of his mathematical research has been focused on geometric and computational methods for multiple testing. He has collaborated on papers applying statistics in a variety of areas: bioinformatics, econometrics, environmental health, genetics, hydrology, and microbiology. His articles have appeared in various journals including Annals of Statistics, Bioinformatics, Biometrika, Human Heredity, Journal of Multivariate Analysis, Journal of the American Statistical Association, and Science.
