Bayesian Approach to Lorenz Curve Using Time Series Grouped Data

This study is concerned with estimating the inequality measures associated with the underlying hypothetical income distribution from the times series grouped data on the income proportions. We adopt the Dirichlet likelihood approach where the parameters of the Dirichlet likelihood are set to the differences between the Lorenz curve of the hypothetical income distribution for the consecutive income classes and propose a state-space model which combines the transformed parameters of the Lorenz curve through a time series structure. The present article also studies the possibility of extending the likelihood model by considering a generalized version of the Dirichlet distribution where the mean is modeled based on the Lorenz curve with an additional hierarchical structure. The simulated data and real data on the Japanese monthly income survey confirmed that the proposed approach produces more efficient estimates on the inequality measures than the existing method that estimates the model independently without time series structures.