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 such data can be invaluable for effective local policymaking, their analysis is often hindered by several challenges, including limited information inherent in the grouped format, the presence of missing areas, and the low frequency of survey implementation. To address these issues, we propose a novel grouped-data-based spatio-temporal finite mixture model for estimating income distributions across multiple spatial units and time points. A unique feature of the proposed method is that all areas share common latent distributions, while the mixing proportions, incorporating spatial and temporal effects, capture the potential area-wise heterogeneity. Consequently, the inclusion of these effects enables smoothing quantities of interest over space and time, imputing missing values, and predicting future trends. By applying the proposed method to the HLS data, we generate complete maps of income and inequality measures at any given time, thereby facilitating rapid and efficient policymaking with fine granularity.