Spatial filtering and model interpretation for spatial Durbin Models

Spatial Filter for spatial autoregressive models like the spatial Durbin Model have seen a great interest in the recent literature. Pace et al. (2011) show that the spatial filtering methods developed by Griffith (2000) have desireable estimation properties for some parameters associated with spatial autoregessive models. However, spatial filtering faces two conceptual weaknesses: First the estimated parameters lack in general, and especially for the Spatial Durbin Model a proper interpretation. Second, there exists an inherent tradeoff between the estimator bias and its efficiency, depending on the spectrum of the used spatial weight matrix. This paper tackles both problems by introducing a new four step estimation procedure based on the eigenvectors of the spatial weight matrix. This new estimation procedure estimates all parameters of interest in a Spatial Durbin model and thus allows for a proper model interpretation. Additionally the estimation procedure's efficiency is only marginally influenced by the number of added eigenvectors, which allows us to use approximatly 95% of the available eigenvectors. By using Monte Carlo Simulations we observe that the estimaton procedure has a lower (or equal) bias and smaller (or equal) sample variance as the corresponding Maximum Likelihood estimator based on normality.