Modelling long term trend and local spatial correlation: a mixed penalized spline and spatial econometrics approach

In this work we propose the combination of P-splines with traditional spatial econometric models in such a way that it allows for their representation as a mixed model. The advantages of combining these models include: (i) dealing with complex non-linear and non-separable trends, (ii) estimating short-range spatial correlation together with the large-scale spatial trend, (iii) decomposing the systematic spatial variation into those two components and (iv) estimating the smoothing parameters included in the penalized splines together with the other parameters of the model. The performance of the proposed spatial non-parametric models is checked by both simulation and a empirical study. More specifically, we simulate 3,600 datasets generated by those models (with both linear and non-linear-non-separable global spatial trends). As for the empirical case, we use the well-known Lucas county data on housing prices. Our results indicate that the proposed models have a better performance than the traditional spatial strategies, specially in the presence of nonlinear trend