Fuzzy group fixed-effects estimation with spatial clustering

The paper discusses the problem of estimating group heterogeneous fixed-effect panel data models under the assumption of fuzzy clustering, that is each unit belongs to all the clusters with a membership degree. To enhance spatial clustering, a spatio-temporal approach is considered. An iterative procedure, alternating panel data estimation and spatio-temporal clustering of the residuals, is proposed. The proposed method can be of relevance to researchers interested in using fuzzy group fixed-effect methods, but want to leverage spatial dimension for clustering units. Two empirical examples, the first on cigarette consumption in the US states and the second on non-life insurance demand in Italy, are presented to illustrate the performance of the proposed approach. The spatial fuzzy GFE model reveals important regional differences in both the US cigarette consumption and non-life insurance determinants in Italy. In the case of the US, we found a distinction in two main clusters, East and West. For the Italy provinces data, we find a distinction in North and South clusters. Regarding the regression results, for cigarette consumption data, different from the previous studies, we find that the smuggling effect is significant only in east regions, thus suggesting localised impacts of bootlegging. In the context of Italian non-life insurance demand, we find that while population density explains insurance consumption in northern provinces, the trust issues in the south explain the lower insurance demand.