Spatial autoregressive models with heteroskedastic normal perturbations

Homoscedasticity in spatial data has always been an important assumption to simplify and speed up parameter estimation. However, the presence of heteroscedasticity is common in spatial data; this work presents a methodology based on maximum likelihood for the estimation and inference of SAR models with heteroscedasticity. The proposal is easy to implement and is not computationally intensive. Through simulation exercises, it was demonstrated that the proposed algorithm offers outstanding results in the recovery of both mean and variance parameters and greater precision compared to other methods. Applying the algorithm to regional wage information in Poland revealed subtle differences compared to previous estimates that did not consider heteroscedasticity and allowed the variance to be successfully modeled from the explanatory variables.