Ultra-sparse small area estimation with super heavy-tailed priors for internal migration flows

Migration flows represent an important component of global sustainable development and demographic trends. However, the dynamic nature of the migration phenomenon, known issues of undercoverage of administrative records and long intercensal periods make estimation of internal migration a very challenging task. In this work we focus on the estimation of internal migration in Colombia, which is the subject of an ongoing armed conflict that has triggered forced and voluntary population movements from rural areas. Motivated by the high variability of migration flows across small areas in Colombia, we propose the use of super heavy-tailed (SHT) priors for sparse and ultra-sparse small area effects under a Fay–Herriot model. We establish theoretical properties of a family of log-Cauchy priors and a new SHT prior obtained by considering a four parameter beta (FPB) density. We provide especially suited Markov chain Monte Carlo (MCMC) algorithms that can also be applied to other global-local families of priors in small area contexts. In addition, we consider a simulation study to illustrate how our proposal improves the precision of posterior estimates in sparse and ultra-sparse settings compared to other existing priors in the literature. Finally, we apply our proposed methodology to the estimation of internal migration in Colombia and obtain results with improved precision that are consistent with the population dynamics in the country. Moreover, we provide practical suggestions for official statisticians and other practitioners who desire to use our proposed framework in their own SAE problems.