W-based Vs Latent Variables Spatial Autoregressive Models: Evidence from Monte Carlo Simulations

The paper evaluates by means of Monte Carlo simulations the estimator of the regression coefficient obtained by the classical W-based spatial autoregressive model and the structural equations model with latent variables (SEM) on the basis of data sets that contain two types of spatial dependence: spillover from (i) a hotspot and (iia) first order queen contiguity neighbors or (iib) inverse distance related neighbors. The classical models are either correctly specified or ignore (i), as is common in practice. SEM takes spatial dependence into account by means of a fixed number of nearest neighbors as well as the dependent variable in the hotspot weighted by inverse distance. The estimation results are analyzed in terms of bias and root mean squared error (RMSE) for different values of the spatial lag parameters, specifications of weights matrices and sample sizes. The simulation results show that compared to the misspecified models SEM frequently has smaller bias and RMSE and even outperforms the correctly specified models in many cases. These trends increase when the spatial lag parameter for spillover increases. The lead of SEM also increases by sample size. Finally, SEM is more stable in terms of both bias and RMSE over various dimensions.