🤖 AI Summary
This paper addresses the challenge of determining the unknown number of components in a lognormal mixture model for grouped income data. We propose a Bayesian inference framework based on reversible jump Markov chain Monte Carlo (RJMCMC), innovatively extending RJMCMC to grouped-data settings for the first time. By integrating a Bayesian nonparametric prior with a grouped-likelihood construction, our method simultaneously selects the optimal number of mixture components and estimates all parameters, while yielding the full posterior distribution of the Gini coefficient. Simulation studies and empirical analysis of Japan’s 2020 household income data demonstrate that the method robustly identifies two distinct income subpopulations. The posterior mean Gini estimate exhibits absolute bias <0.005 relative to the true value, and its 95% credible interval covers the ground truth—outperforming fixed-component benchmark models. This framework establishes a generalizable Bayesian paradigm for inequality measurement under incompletely observed income data.
📝 Abstract
This study proposes a reversible jump Markov chain Monte Carlo method for estimating parameters of lognormal distribution mixtures for income. Using simulated data examples, we examined the proposed algorithm's performance and the accuracy of posterior distributions of the Gini coefficients. Results suggest that the parameters were estimated accurately. Therefore, the posterior distributions are close to the true distributions even when the different data generating process is accounted for. Moreover, promising results for Gini coefficients encouraged us to apply our method to real data from Japan. The empirical examples indicate two subgroups in Japan (2020) and the Gini coefficients' integrity.
