Spatial System Estimators for Panel Models: A Sensitivity and Simulation Study

System of panel models are popular models in applied sciences and the question of spatial errors has created the recent demand for spatial system estimation of panel models. Therefore we propose new diagnostic methods to explore if the spatial component will change significantly the outcome of non-spatial estimates of seemingly unrelated regression (SUR) systems. We apply a local sensitivity approach to study the behavior of generalized least squares (GLS) estimators in two spatial autoregression SUR system models: a SAR model with SUR errors (SAR-SUR) and a SUR model with spatial errors (SUR-SEM). Using matrix derivative calculus we establish a sensitivity matrix for spatial panel models and we show how a first order Taylor approximation of the GLS estimators can be used to approximate the GLS estimators in spatial SUR models. In a simulation study we demonstrate the good quality of our approximation results.