Bayesian small area estimation methods for business survey statistics

The positive skewness of study variables is a peculiarity a of business survey data. It is due to the presence of a majority of small firms, beside a minority of big ones. For this reason, thenormality assumption, typical of small area models, can fail. We aim at the estimation of value added for subsets of the population of Italian small and medium sized manufacturing firms classified according to geographical region, industrial sector and firms size. This disaggregation is needed to compare regions meaningfully, avoiding the confounding effect of different sectorial and firm size composition of a regional manufacturing industries. We use data on the Small and Medium Enterprises sample survey conducted yearly by the Italian National Statistical Institute. The target variable we consider, value added, is positivelyskewed and so is the sampling distribution of total estimators in small samples. We assume log-normality of direct estimators of total value added and we specify linear mixed models onthe log scale. We adopt a Bayesian approach to inference, with relevant posterior distributions approximated by MCMC methods. The models we consider are characterized by the presence of several random effects to account for variation between areas not accounted for by the covariates. The considered effects include sectorial, regional and a time effect describing year to year variation. Some of these random effects are not exchangeable: e.g. time effects will have a dependence structure such as the random walk we consider in our application. As a consequence the priors for various variance components should be specified carefully as they can keep an influence on some aspect of inference based on posterior distributions even in presence of good auxiliary information.