Inequality measurement based on grouped data is usually performed by non-linear squares. We propose here an alternative approach building on the compositional nature of the shares of income derived from quantiles. Three parametric Lorenz curves are estimated after trasforming the income shares with the isometric logratio transform. The performance of our simplicial approach is then compared by means of a Monte Carlo Experiment with the methodology proposed by Chotikapanich and Griffiths (2002) based on the Dirichlet distribution and with the non-linear squares. To this purpose, the resulting bias in the Gini coefficient associated with the estimated curves is evaluated across increasing quantiles and different income distributions.

Crosato, L., & Monti, G. (2015). A simplicial approach to inequality measurement. In Proceedings of the 2015 SIS conference: Statistics and Demography: the Legacy of Corrado Gini.

A simplicial approach to inequality measurement

CROSATO, LISA;MONTI, GIANNA SERAFINA
2015

Abstract

Inequality measurement based on grouped data is usually performed by non-linear squares. We propose here an alternative approach building on the compositional nature of the shares of income derived from quantiles. Three parametric Lorenz curves are estimated after trasforming the income shares with the isometric logratio transform. The performance of our simplicial approach is then compared by means of a Monte Carlo Experiment with the methodology proposed by Chotikapanich and Griffiths (2002) based on the Dirichlet distribution and with the non-linear squares. To this purpose, the resulting bias in the Gini coefficient associated with the estimated curves is evaluated across increasing quantiles and different income distributions.
No
paper
Scientifica
Lorenz curve, Gini coefficient, income distribution, Aitchison Geometry, Dirichlet distribution
English
Statistics and Demography: the legacy of Corrado Gini
9788867874521
Crosato, L., & Monti, G. (2015). A simplicial approach to inequality measurement. In Proceedings of the 2015 SIS conference: Statistics and Demography: the Legacy of Corrado Gini.
Crosato, L; Monti, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/150807
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