Approximate Bayesian Computation for Lorenz Curves from Grouped Data

• Activity Number: 373
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Kazuhiko Kakamu* and Genya Kobayashi
• Companies: Kobe University and Chiba University
• Keywords: Approximate Bayesian computation ; Generalized beta (GB) distribution ; Gini coefficient ; Lorenz curve

Abstract

There are mainly two approaches to calculate the Gini coefficients from the grouped data in a parametric framework. One is to assume a hypothetical statistical distribution for income. The other is to fit a specific functional form to the Lorenz curve. It is known that the Gini coefficient for the same hypothetical distribution is estimated more accurately from the Lorenz curve than from the distribution. However, for a flexible class of size distributions, such as generalized beta distribution, the likelihood function for the Lorenz curve for the grouped data is not analytically available and its evaluation is computationally expensive. Approximate Bayesian computation is utilised to avoid the evaluation of the likelihood function and to estimate the parameters of the Lorenz curve. The proposed approach is illustrated with the generalized beta distribution using simulated and real datasets. The empirical results suggest that the Gini coefficients can be estimated more accurately by fitting the Lorenz curve using the proposed method than by fitting the income distribution directly.