Measuring cumulative deprivation and affluence based on the diagonal dependence diagram

Koen Decancq

No 652198, Working Papers of Department of Economics, Leuven from KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven

Abstract: In this paper, I introduce the diagonal dependence diagram to chart dependence around the main diagonal of a multivariate distribution. This diagonal dependence diagram is a useful tool to quantify phenomena such as cumulative deprivation and affluence. A society is said to exhibit more cumulative deprivation when more persons occupy bottom positions in all dimensions of well-being. Analogously, there is more cumulative affluence in a society when more persons occupy top positions in all dimensions. The diagonal dependence diagram consists of two curves which are obtained by taking the diagonal section of the underlying copula and survival functions, respectively. I show the elementary multivariate re-arrangements underlying dominance in terms of both curves. The area under each curve leads to a natural index of diagonal dependence. Interestingly, the average of both indices equals a multivariate generalization of Spearman's footrule and is closely related to the cograduation index proposed by Gini.

Keywords: Copula; Cumulative Deprivation; Cumulative Affluence; Diagonal Dependence; Spearman's Footrule; Gini's cograduation index (search for similar items in EconPapers)
Pages: 27
Date: 2020
Note: paper number DPS 20.02
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Published in FEB Research Report Department of Economics

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Journal Article: Measuring cumulative deprivation and affluence based on the diagonal dependence diagram (2020)
Working Paper: Measuring cumulative deprivation and affluence based on the diagonal dependence diagram (2020)
Working Paper: Measuring cumulative deprivation and affluence based on the diagonal dependence diagram (2020)
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