Bayesian small area estimation for skewed business survey variables

In business surveys, estimates of means and totals for subnational regions, industries and business classes can be too imprecise because of the small sample sizes that are available for subpopulations.We propose a small area technique for the estimation of totals for skewed target variables, which are typical of business data. We adopt a Bayesian approach to inference. We specify a prior distribution for the random effects based on the idea of local shrinkage, which is suitable when auxiliary variables with strong predictive power are available: another feature that is often displayed by business survey data. This flexible modelling of random effects leads to predictions in agreement with those based on global shrinkage for most of the areas, but enables us to obtain less shrunken and thereby less biased estimates for areas characterized by large model residuals. We discuss an application based on data from the Italian survey on small and medium enterprises. By means of a simulation exercise, we explore the frequentist properties of the estimators proposed. They are good, and differently from methods based on global shrinkage remain so also for areas characterized by large model residuals.