Spatio-temporal smoothing, interpolation and prediction of income distributions based on grouped data

Abstract: The Housing and Land Survey (HLS) of Japan provides municipality-level grouped data on household incomes. Although these data can be used for effective local policymaking, their analyses are hindered by several challenges, such as limited information attributed to grouping, the presence of non-sampled areas, and the very low frequency of implementing surveys. To address these challenges, we propose a novel grouped-data-based spatio-temporal finite mixture model for estimating the income distributions of multiple spatial units at multiple time points. A unique feature of the proposed method is that all the areas share common latent distributions and that the mixing proportions, including spatial and temporal effects, capture the potential area-wise heterogeneity. Thus, incorporating these effects can smooth out the quantities of interest over time and space, impute missing values, and predict future values. By treating the HLS data with the proposed method, we obtain complete maps of the income and inequality measures at an arbitrary time, which can facilitate rapid and efficient policymaking with fine granularity.