Spatio-Temporal Patterns in Portuguese Regional Fertility Rates: A Bayesian Approach for Spatial Clustering of Curves

Abstract

Abstract It is important for demographic analyses and policy-making to obtain accurate models of spatial diffusion, so that policy experiments can reflect endogenous spatial spillovers appropriately. Likewise, it is important to obtain accurate estimates and forecasts of demographic variables such as age-specific fertility rates, by regions and over time, as well as the uncertainty associated with such estimation. Here, we consider Bayesian hierarchical models with separable spatio-temporal dependence structure that can be estimated by borrowing strength from neighbouring regions and all years. Further, we do not consider the adjacency structure as a given, but rather as an object of inference. For this purpose, we use the local similarity of temporal patterns by developing a spatial clustering model based on Bayesian nonparametric smoothing techniques. The Bayesian inference provides the uncertainty associated with the clustering configurations that is typically lacking in classical analyses of large data sets in which a unique clustering representation can be insufficient. The proposed model is applied to 16-year data on age-specific fertility rates observed over 28 regions in Portugal, and provides statistical inference on the number of clusters, and local scaling and shrinkage levels. The corresponding central clustering configuration is able to capture spatial diffusion that has key demographic interpretations. Importantly, the exercise aids identification of peripheral regions with poor demographic prospects and development of regional policy for such places.