Small area estimation of labor productivity for the Italian manufacturing SME cross-classified by region, industry and size

In this paper we propose a new small area estimation methodology aimed at the estimation of Value Added, Labor Cost and related competitiveness indicators 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 in regional comparisons in order to avoid the confounding effect of sectorial and firm size composition of a region's manufacturing industry. We use data on the Small and Medium Enterprises sample survey conducted by the Italian National Statistical Institute (year 2009) that provided us this information in the framework of the BLUE-ETS project. The estimates obtained with our method are more reliable than those that would have been obtained using standard survey weighted estimators, and offer therefore the basis for more sound economic analysis. The small area methods that we propose are model based and take into account the peculiarities of business such as the skewness of target variables' distributions. For this reason the model we propose is based on the log-normal distribution. We consider a multivariate model in which two different variables (Value Added and Labor Cost) and jointly modeled in order to exploit their correlation. We adopt a Bayesian approach to inference. The problem of prior specification is considered and two alternative solutions compared. Since we produce estimates for several variables and hundreds of subset of the target population results are difficult to summarize. A general conclusion may be that, for Italy, the North-South divide in productivity levels is more apparent in capital and knowledge intensive sectors, especially when industrial districts are present. The productivity gap tends to grow for larger firms, but there exists several exception to this rule. Many industries traditionally associated to the Italian productive system (furniture, clothing, textile) are characterized by low labor productivity levels: in these cases the productivity gap between Northern and Southern regions is less pronounced or absent. As the paper is mostly about the methodology needed to obtain the estimates, it is relevant not only for those interested in Italian economy. The same ideas may be applied to data from other countries. The relevance of the mentioned indicators is highlighted by the increasing divergences in economic competitiveness among regions within the different EU member states observed in these last years.