A Matrix Exponential Spatial Panel Model with Heterogeneous Coefficients

We extend the heterogeneous coefficients spatial autoregressive panel model (HSAR) from Aquaro, Bailey, and Pesaran (2015) to the case of a heterogeneous coefficients matrix exponential spatial specification (HMESS). The HSAR is capable of producing parameter estimates for each region in the sample, that follow a spatial autoregressive process. Spatial autoregressive processes apply geometric decay of influence to higher-order neighboring regions. The HMESS takes a similar approach as the HSAR to produce estimates for each region in the sample, but relies on a matrix exponential function to apply exponential decay to higher-order neighbors. The MESS introduced by LeSage and Pace (2007) for the case of cross-sectional spatial data samples has some potential computational advantages over the spatial autoregressive specification. In addition, the spatial dependence parameter in the MESS ranges from minus to plus infinity, which allows for use of normal priors assigned to this parameter in a Bayesian setting. We extend the cross-sectional MESS to the case of a heterogeneous coefficients model, and describe Bayesian Markov Chain Monte Carlo estimation. We illustrate the HMESS model with a panel wage curve relationship using quarterly unemployment and wage rates from 261 counties centered on the Bakken shale oil region in North Dakota and Montana.