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.

翻译：本文提出了一种空间聚类线性回归模型的扩展形式，即空间聚类空间自回归（SCSAR）模型，用于处理聚类过程中的空间异质性问题。具体而言，我们通过允许回归系数按照聚类结构在空间上变化，扩展了经典空间计量经济学模型，如空间自回归模型、空间误差模型和空间滞后模型。通过采用惩罚最大似然估计算法，我们联合估计了聚类隶属关系和回归系数，该算法鼓励相邻单元归属于具有共享回归系数的同一空间聚类。受2010年至2020年间欧洲农业生产基尼指数观测值上升的启发，我们采用所提出的方法来评估过去十年欧洲区域市场集中度指数是否存在局部空间溢出效应。实证结果支持了欧洲农业市场碎片化的假设，因为各区域可以通过将大陆划分为三组的聚类结构得到良好表征，大致对应于西部、中北部和东南部区域的划分。此外，我们还发现了所选解释变量对区域市场集中度产生的异质性局部效应。具体而言，我们发现与农业部门的社会、地域和经济重要性相关的变量似乎在空间维度（跨聚类）、相对于汇总模型以及时间维度上表现出不同的作用模式。