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

In Japan, the Housing and Land Survey (HLS) provides grouped data on household incomes at the municipality level. Although this data could serve for effective local policy-making, there are some challenges in analysing the HLS data, such as the scarcity of information due to the grouping, the presence of the non-sampled areas and the very low frequency of the survey implementation. This paper tackles these challenges through a new spatio-temporal finite mixture model based on grouped data for modelling the income distributions of multiple spatial units at multiple points in time. The main idea of the proposed method is that all areas share the common latent distributions and the potential area-wise heterogeneity is captured by the mixing proportions that includes the spatial and temporal effects. Including these effects can smooth out the quantities of interest over time and space, impute missing values and predict future values. Applying the proposed method to the HLS data, we can obtain complete maps of income and poverty measures at an arbitrary point in time, which can be used for fast and efficient policy-making at a fine granularity.