Due to the increase in data availability in urban and regional studies, various spatial panel models have emerged to model spatial panel data, which exhibit spatial patterns and spatial dependencies between observations across time. Although estimation is usually based on maximum likelihood or generalized method of moments, these methods may fail to yield unique solutions if researchers are faced with high-dimensional settings. This article proposes a model-based gradient boosting algorithm, which enables estimation with interpretable results that is feasible in low- and high-dimensional settings. Due to its modular nature, the flexible model-based gradient boosting algorithm is suitable for a variety of spatial panel models, which can include random and fixed effects. The general framework also enables data-driven model and variable selection as well as implicit regularization where the bias-variance trade-off is controlled for, thereby enhancing accuracy of prediction on out-of-sample spatial panel data. Monte Carlo experiments concerned with the performance of estimation and variable selection confirm proper functionality in low- and high-dimensional settings while real-world applications including non-life insurance in Italian districts, rice production in Indonesian farms and life expectancy in German districts illustrate the potential application.

Researchers in urban and regional studies increasingly deal with spatial data that reflects geographic location and spatial relationships. As a framework for dealing with the unique nature of spatial data, various spatial regression models have been introduced. In this article, a novel model-based gradient boosting algorithm for spatial regression models with autoregressive disturbances is proposed. Due to the modular nature, the approach provides an alternative estimation procedure which is feasible even in high-dimensional settings where established quasi-maximum likelihood or generalized method of moments estimators do not yield unique solutions. The approach additionally enables data-driven variable and model selection in low- as well as high-dimensional settings. Since the bias-variance trade-off is also controlled in the algorithm, implicit regularization is imposed which improves prediction accuracy on out-of-sample spatial data. Detailed simulation studies regarding the performance of estimation, prediction and variable selection in low- and high-dimensional settings confirm proper functionality of the proposed methodology. To illustrative the functionality of the model-based gradient boosting algorithm, a case study is presented where the life expectancy in German districts is modeled incorporating a potential spatial dependence structure.