We propose a semiparametric P-Spline model to deal with spatial panel data. This model includes a non-parametric spatio-temporal trend, a spatial lag of the dependent variable, and a time series autoregressive noise. Specifically, we consider a spatio-temporal ANOVA model, disaggregating the trend into spatial and temporal main effects, as well as second- and third-order interactions between them. Algorithms based on spatial anisotropic penalties are used to estimate all the parameters in a closed form without the need for multidimensional optimization. Monte Carlo simulations and an empirical analysis of regional unemployment in Italy show that our model represents a valid alternative to parametric methods aimed at disentangling strong and weak cross-sectional dependence when both spatial and temporal heterogeneity are smoothly distributed.

我们提出了一个半参数的P样条模型来处理空间面板数据。该模型包括非参数时空趋势，因变量的空间滞后以及时间序列自回归噪声。具体来说，我们考虑时空方差分析模型，将趋势分解为时空主效应，以及它们之间的二阶和三阶相互作用。基于空间各向异性惩罚的算法用于以封闭形式估算所有参数，而无需进行多维优化。蒙特卡洛模拟和对意大利区域性失业的实证分析表明，当空间和时间异质性都平稳分布时，我们的模型可以替代参数方法，以消除强横断面和弱横断面相关性。