A new method for dealing simultaneously with spatial autocorrelation and spatial heterogeneity in regression models

Although spatial heterogeneity and spatial dependence are two cornerstones of spatial econometrics, models and methods for dealing at the same time with both issues are still rare in the literature, with few notable exceptions. The same can be said for studies on the performance of spatial econometric models under misspecification of explanatory variables and unknown structure of the spatial weight matrix. In this article, we introduce a new class of data generating processes (DGP), called MGWR-SAR, in which the regression parameters and the spatial autocorrelation coefficient can vary over the space. For the estimation of these new models, we resort to the Spatial Two-Stage Least Squares (S2SLS) technique. We rely on a Monte Carlo experiment for testing the performance of classical models, such as OLS, GWR (Geographically Weighted Regression), mixed GWR and SAR (Spatial AutoRegressive model), as well as our proposals, paying special attention to simulated data under the realistic assumption that they suffer from multicollinearity/concurvity problems and/or misspecification of the covariates. The results suggest that certain model specifications amongst the newly proposed family MGWR-SAR are the more robust. Furthermore, to complete our proposal, we also suggest a specification procedure to identify the correct spatial weight matrix for DGPs with spatial heterogeneity and spatial autocorrelation of the endogenous. We conclude the article with an empirical study on the Lucas County house price dataset, confirming the good performance of the proposed estimators.