  Estimating income distributions plays an important role in the measurement of
inequality and poverty over space. The existing literature on income
distributions predominantly focuses on estimating an income distribution for a
country or a region separately and the simultaneous estimation of multiple
income distributions has not been discussed in spite of its practical
importance. In this work, we develop an effective method for the simultaneous
estimation and inference for area-wise spatial income distributions taking
account of geographical information from grouped data. Based on the multinomial
likelihood function for grouped data, we propose a spatial state-space model
for area-wise parameters of parametric income distributions. We provide an
efficient Bayesian approach to estimation and inference for area-wise latent
parameters, which enables us to compute area-wise summary measures of income
distributions such as mean incomes and Gini indices, not only for sampled areas
but also for areas without any samples thanks to the latent spatial state-space
structure. The proposed method is demonstrated using the Japanese
municipality-wise grouped income data. The simulation studies show the
superiority of the proposed method to a crude conventional approach which
estimates the income distributions separately.
