A Symmetric Information Theoretic Index For The Measurement Of Inequality
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A Symmetric Information-theoretic Index for the Measurement of Inequality
"The application of information theory to the measurement of income inequality has yielded an impressive array of measurement techniques known as Generalized Entropy (GE) measures. Special cases of this class of index include Theil's T and L measures which are considered axiomatically superior to other types of metrics including the popular Gini coefficient. In this paper we show that the parallel between information theory and inequality measurement has not yet been fully explored and propose a new inequality measure based upon this concept. The proposed measure is already established as a tool for use in statistical classification and signal processing problems and is known in these fields as the J-Divergence or Symmetric Kullback-Leibler Divergence. As an inequality metric the measure is shown to be axiomatically complete and is in possession of an additional property allowing for an alternate type of decomposition analysis. The new type of decomposition makes the contribution of any individual or subgroup to the inequality metric directly observable such that the overall index may be reconciled with a weighted sum of each group contribution. We illustrate with an example using income micro-data from the United States where we evaluate the contributions of various racial groups to overall inequality. We also provide a standard decomposition of the inequalities between and within the racial groups to contrast the techniques"--Abstract.
Assessing Inequality
Providing basic foundations for measuring inequality from the perspective of distributional properties This monograpg 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. 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.
The Information Theory of Comparisons
This book finds a broad domain of relevance in statistics and the social sciences. Its conceptual development is supported by applications to economics and income distribution, finance, education, demographics and actuarial science, political studies, psychology, and general statistics. Fresh perspectives on directional complexity have generated an informational theory of ‘more versus less’, with representative polar outcomes as good or bad, or rich or poor. New duality metrics for spread and asymmetry have resulted, motivated by internal perspectives on the part of subjects, such as attitudes to their comparative (dis)advantage. This book is a readable review of these developments. Concepts and applications are described in tandem with each other. They consolidate recent contributions to the research literature, augmented with fresh insights and applications. Dynamic extensions include modeling shifting social attitudes, while the broader agenda encompasses topical areas such as subjectivist probability, investment decision making, and income distribution.