Approximate Bayesian computation for Lorenz curves from grouped data

Abstract

This paper proposes a new Bayesian approach to estimate the Gini coefficient from the Lorenz curve based on grouped data. The proposed approach assumes a hypothetical income distribution and estimates the parameter by directly working on the likelihood function implied by the Lorenz curve of the income distribution from the grouped data. It inherits the advantages of two existing approaches through which the Gini coefficient can be estimated more accurately and a straightforward interpretation about the underlying income distribution is provided. Since the likelihood function is implicitly defined, the approximate Bayesian computational approach based on the sequential Monte Carlo method is adopted. The usefulness of the proposed approach is illustrated through the simulation study and the Japanese income data.

Bayesian approach to Lorenz curve using time series grouped data

“…Also the posterior distributions seem to robust with respect to the prior specification. Contrary, the posterior distributions under the separate approach are wide spread and exhibit prior sensitivity, as also demonstrated by Kobayashi and Kakamu (2019). of Japan have demonstrated that the parameters can be estimated more stably and the posterior distributions obtained from the proposed approach have much smaller uncertainty than separately estimating the parameters based on the Dirichlet distribution using the data only from a single period.…”

“…Furthermore, the data do not contain information on the Dirichlet precision parameter λ and λ is seen as a nuisance parameter or tuning parameter. Although the value of λ can potentially have an impact on the estimates of the parameters and Gini coefficient (Kobayashi and Kakamu, 2019), there exists no clear guideline on the choice of its value when it is fixed nor the choice of its prior distribution when the model is estimated within the Bayesian framework.…”

“…Chotikapanich and Griffith (2005) considered the Bayesian estimation based on the Dirichlet likelihood and the posterior estimation is carried out using the Markov chain Monte Carlo (MCMC) method. More recently, Kobayashi and Kakamu (2019) proposed the likelihood-free approach to the Lorenz curve based on the approximate Bayesian computation (ABC) that does not rely on the Dirichlet likelihood and can be implemented even when an analytical form of the Lorenz curve is not available.…”