Bayesian Analysis of Spatial Econometrics Regression Models

Spatial regression models are often used for modeling spatial economic data. The main purpose of studying these models is to obtain parameter estimates and then predict at new locations. For this purpose, the maximum likelihood approach is first investigated and in order to increase the accuracy of parameter estimation and reduce the computation time, the conventional Bayesian approach and an approximate Bayesian approach are examined for three regression models, spatial Lag model, spatial Durbin model and spatial error model. Finally, in a simulation study and a real example of housing data in Tehran, the performance of models and approaches are compared. The existence of a spatial effect and a direct relationship between housing price and area in the data is accepted. Using the Relative Root Mean Square Error for these two data sets, it was concluded that the approximate Bayesian approach for spatial econometric models has a better performance than the maximum likelihood and the conventional Bayesian approaches. In addition, it was found that the computational time of the Bayesian approach is about twice as long as the approximate Bayesian approach.