Model Uncertainty in Matrix Exponential Spatial Growth Regression Models

This article considers the most important aspects of model uncertainty for spatial regression models, namely, the appropriate spatial weight matrix to be employed and the appropriate explanatory variables. We focus on the spatial D urbin model ( SDM ) specification in this study that nests most models used in the regional growth literature, and develop a simple B ayesian model‐averaging approach that provides a unified and formal treatment of these aspects of model uncertainty for SDM growth models. The approach expands on previous work by reducing the computational costs through the use of B ayesian information criterion model weights and a matrix exponential specification of the SDM model. The spatial D urbin matrix exponential model has theoretical and computational advantages over the spatial autoregressive specification due to the ease of inversion, differentiation, and integration of the matrix exponential. In particular, the matrix exponential has a simple matrix determinant that vanishes for the case of a spatial weight matrix with a trace of zero. This allows for a larger domain of spatial growth regression models to be analyzed with this approach, including models based on different classes of spatial weight matrices. The working of the approach is illustrated for the case of 32 potential determinants and three classes of spatial weight matrices (contiguity‐based, k ‐nearest neighbor, and distance‐based spatial weight matrices), using a data set of income per capita growth for 273 E uropean regions.