Comparing Cross-Country Estimates of Lorenz Curves Using a Dirichlet Distribution Across Estimators and Datasets

Chang, Andrew C.; Li, Phillip; Martin, Shawn M.

doi:10.17016/FEDS.2017.062

Working Paper

Comparing Cross-Country Estimates of Lorenz Curves Using a Dirichlet Distribution Across Estimators and Datasets

Abstract: Chotikapanich and Griffiths (2002) introduced the Dirichlet distribution to the estimation of Lorenz curves. This distribution naturally accommodates the proportional nature of income share data and the dependence structure between the shares. Chotikapanich and Griffiths (2002) fit a family of five Lorenz curves to one year of Swedish and Brazilian income share data using unconstrained maximum likelihood and unconstrained non-linear least squares. We attempt to replicate the authors' results and extend their analyses using both constrained estimation techniques and five additional years of data. We successfully replicate a majority of the authors' results and find that some of their main qualitative conclusions also hold using our constrained estimators and additional data.

Keywords: Constrained Estimation; Dirichlet; Dirichlet Distribution; Gini Coefficient; Income Distribution; Lorenz curves; Maximum Likelihood; Non-linear Least Squares; replications; Share Data;

JEL Classification: C24; C51; C87; D31;

https://doi.org/10.17016/FEDS.2017.062