Dynamic Spatial Autoregressive Models with Time-Varying Spatial Weighting Matrices
54 Pages Posted: 14 Sep 2018 Last revised: 25 Sep 2019
Date Written: September 24, 2019
We propose a new spatio--temporal model with time--varying spatial weighting matrices. We allow for a general parameterization of the spatial matrix, such as: (i) a function of the inverse distances among pairs of units in space to the power of an unknown time--varying distance decay parameter, and (ii) a negative exponential function of the time--varying parameter as in (i).
The filtering procedure of the time--varying unknown parameters is performed using the information contained in the score of the conditional distribution of the observables. We provide conditions for the stationarity and ergodicity of the filtered sequence of the spatial matrices as well as for the consistency and asymptotic normality of the maximum likelihood estimator (MLE). An extensive Monte Carlo simulation study to investigate the finite sample properties of the maximum likelihood estimator is reported. In the empirical part of the paper we analyze the association between eight European countries' perceived risk. Our findings suggest that the economically strong countries have their perceived risk increased due to their spatial connection with the economically weaker countries. A second empirical analysis investigates the evolution of the spatial connection between the house prices in different areas of the UK. In this case we identify periods when the usually adopted sparse weighting matrix is not sufficient to describe the underlying spatial process.
Suggested Citation: Suggested Citation