TY - JOUR
T1 - Anything Lorenz Curves Can Do, Top Shares Can Do
T2 - Assessing the TopBot Family of Inequality Measures
AU - Jasso, Guillermina
N1 - Funding Information:
Earlier versions of this article were presented at the MidYear Meeting of the ASA Methodology Section, Chicago, IL, April 2017; at the 10th Conference of the International Network of Analytical Sociologists (INAS), University of Oslo, Norway, June 2017; at DIW Berlin, July 2017; at the Seventh Meeting of the Society for the Study of Economic Inequality (ECINEQ), City University of New York, July 2017; and at the Joint Statistical Meetings, Baltimore, MD, August 2017 and at the XIX World Congress of the International Sociological Association (ISA), RC28, Toronto, Canada, July 2018. I am grateful to conference participants and to Charlotte Bartels, Jun Kobayashi, Arnout van der Rijt, Jürgen Schupp, Gert G. Wagner, Yu Xie, the anonymous referees, and the Editor for valuable comments and suggestions. I also gratefully acknowledge the intellectual and financial support of New York University. Finally, this paper is dedicated to Samuel Kotz (1930–2010); had he lived, he would have loved to work on it. The author(s) received no financial support for the research, authorship, and/or publication of this article.
Publisher Copyright:
© The Author(s) 2018.
PY - 2020/11
Y1 - 2020/11
N2 - Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on shares and ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure. The work reported in this article strengthens that evidence, making several contributions: First, it formalizes the shares and ratios, showing that as monotonic transformations of each other, they are different manifestations of a single inequality measure, here called TopBot. Second, it presents two standard forms of TopBot, which satisfy the principle of normalization. Third, it presents a new link between top shares and the Gini coefficient, showing that properties and results associated with the Lorenz curve pertain as well to top shares. Fourth, it investigates TopBot in mathematically specified probability distributions, showing that TopBot is monotonically related to classical measures such as the Gini, Atkinson, and Theil measures and the coefficient of variation. Thus, TopBot appears to be a genuine inequality measure. Moreover, TopBot is further distinguished by its ease of calculation and ease of interpretation, making it an appealing People’s measure of inequality. This work also provides new insights, for example, that, given nonlinearities in the (monotonic) relations among inequality measures, Spearman correlations are more appropriate than Pearson correlations and that weakening of correlations signals differences and shifts in distributional form, themselves signals of income dynamics.
AB - Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on shares and ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure. The work reported in this article strengthens that evidence, making several contributions: First, it formalizes the shares and ratios, showing that as monotonic transformations of each other, they are different manifestations of a single inequality measure, here called TopBot. Second, it presents two standard forms of TopBot, which satisfy the principle of normalization. Third, it presents a new link between top shares and the Gini coefficient, showing that properties and results associated with the Lorenz curve pertain as well to top shares. Fourth, it investigates TopBot in mathematically specified probability distributions, showing that TopBot is monotonically related to classical measures such as the Gini, Atkinson, and Theil measures and the coefficient of variation. Thus, TopBot appears to be a genuine inequality measure. Moreover, TopBot is further distinguished by its ease of calculation and ease of interpretation, making it an appealing People’s measure of inequality. This work also provides new insights, for example, that, given nonlinearities in the (monotonic) relations among inequality measures, Spearman correlations are more appropriate than Pearson correlations and that weakening of correlations signals differences and shifts in distributional form, themselves signals of income dynamics.
KW - Atkinson measure
KW - Gini coefficient
KW - Pareto distribution
KW - continuous univariate distributions
KW - general inequality parameter
KW - lognormal distribution
KW - power-function distribution
KW - principles of inequality measurement
KW - top shares
KW - top-to-bottom ratios
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U2 - 10.1177/0049124118769106
DO - 10.1177/0049124118769106
M3 - Article
AN - SCOPUS:85047377362
SN - 0049-1241
VL - 49
SP - 947
EP - 981
JO - Sociological Methods and Research
JF - Sociological Methods and Research
IS - 4
ER -