Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe

In this paper, we present an extension of the spatially-clustered linear regression models, namely, the spatially-clustered spatial autoregression (SCSAR) model, to deal with spatial heterogeneity issues in clustering procedures. In particular, we extend classical spatial econometrics models, such as the spatial autoregressive model, the spatial error model, and the spatially-lagged model, by allowing the regression coefficients to be spatially varying according to a cluster-wise structure. Cluster memberships and regression coefficients are jointly estimated through a penalized maximum likelihood algorithm which encourages neighboring units to belong to the same spatial cluster with shared regression coefficients. Motivated by the increase of observed values of the Gini index for the agricultural production in Europe between 2010 and 2020, the proposed methodology is employed to assess the presence of local spatial spillovers on the market concentration index for the European regions in the last decade. Empirical findings support the hypothesis of fragmentation of the European agricultural market, as the regions can be well represented by a clustering structure partitioning the continent into three-groups, roughly approximated by a division among Western, North Central and Southeastern regions. Also, we detect heterogeneous local effects induced by the selected explanatory variables on the regional market concentration. In particular, we find that variables associated with social, territorial and economic relevance of the agricultural sector seem to act differently throughout the spatial dimension, across the clusters and with respect to the pooled model, and temporal dimension.