This paper 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 vari- ables. We focus on the spatial Durbin model (SDM) specification in this study that nests most models used in the regional growth literature, and develop a simple Bayesian model averaging approach that provides a unified and formal treatment of these aspects of model uncertainty for SDM growth models. The approach expands on the work by LeSage and Fischer (2008) by reducing the computational costs through the use of Bayesian information criterion model weights and a matrix exponential specification of the SDM model. The spatial Durbin 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 expo- nential. In particular, the matrix exponential has a simple matrix determinant which vanishes for the case of a spatial weight matrix with a trace of zero (LeSage and Pace 2007). This allows for a larger domain of spatial growth regression models to be analysed 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 dataset of income per capita growth for 273 European regions. (authors' abstract)

Several recent empirical studies, particularly in the regional economic growth literature, emphasize the importance of explicitly accounting for uncertainty surrounding model specification. Standard approaches to deal with the problem of model uncertainty involve the use of Bayesian model-averaging techniques. However, Bayesian model-averaging for spatial autoregressive models suffers from severe drawbacks both in terms of computational time and possible extensions to more flexible econometric frameworks. To alleviate these problems, this paper presents two global-local shrinkage priors in the context of high-dimensional matrix exponential spatial specifications. A simulation study is conducted to evaluate the performance of the shrinkage priors. Results suggest that they perform particularly well in high-dimensional environments, especially when the number of parameters to estimate exceeds the number of observations. Moreover, we use pan-European regional economic growth data to illustrate the performance of the proposed shrinkage priors.

This paper considers the problem of model uncertainty associated with variable selection and specification of the spatial weight matrix in spatial growth regression models in general and growth regression models based on the matrix exponential spatial specification in particular. A natural solution, supported by formal probabilistic reasoning, is the use of Bayesian model averaging which assigns probabilities on the model space and deals with model uncertainty by mixing over models, using the posterior model probabilities as weights. This paper proposes to adopt Bayesian information criterion model weights since they have computational advantages over fully Bayesian model weights. The approach is illustrated for both identifying model covariates and unveiling spatial structures present in pan-European growth data. (authors' abstract) / Series: Department of Economics Working Paper Series