Estimation of Autoregressive Models with Two Types of Weak Spatial Dependence by Means of the W-Based and the Latent Variables Approach: Evidence from Monte Carlo Simulations

Abstract

We evaluate by means of Monte Carlo simulations the W-based spatial autoregressive model and the structural equation model with latent variables (SEM) to handle two types of simultaneously occurring weak spatial dependence: (i) spillover from a hotspot, and (iia) spillover from first-order, queen contiguous neighbours, (iib) inverse-distance-related spatial units, (iic) the first three nearest neighbours. Although it is possible to account for several different types of weak spatial lag dependence by several different weights matrices, the W-based approach usually proceeds on the basis of a single weights matrix that is implicitly assumed to adequately capture all types of spatial dependence. SEM on the other hand has been developed to explicitly distinguish between different types of weak spatial dependence in a model. In addition, whereas conventional higher order spatial econometric models entail specification and parameter space definition problems, SEM spatial dependence models can be routinely specified and estimated. In this paper we briefly discuss the pitfalls of including several types of weak spatial lag dependence (and thus different W matrices) in a standard W-based lag model and how these problems are mitigated by the SEM approach. Furthermore, the single W-based and the SEM approach are compared by means of simulations in terms of bias and root mean squared error (RMSE) for different values of the spatial lag parameters, specifications of the weights matrices, and sample sizes. We also include in the comparison the W-based approach with spatial dependence accounted for by the two weights matrices used to generate the data: That is, the correctly specified model. The simulation results show that compared with the single W-based models, SEM frequently has smaller bias and RMSE. Furthermore, SEM even outperforms the correctly specified W-based models (based on the same two weights matrices used for data generation) in many cases. These trends increase when the values of the spatial lag parameters increase. The dominance of SEM also increases with sample size. Finally, SEM is more stable in terms of both bias and RMSE over various dimensions.