Spatial autoregressive models with unknown heteroskedasticity: A comparison of Bayesian and robust GMM approach

• This study considers heteroskedasticity of an unknown form in spatial models.
• Properties of the robust GMME are compared with the Bayesian MCMC estimator.
• This study is the first to compare these heteroskedasticity robust approaches.
• A Monte Carlo study provides evaluation of the performance of the robust estimators.
• In the final section, two empirical applications are provided.

Most of the estimators suggested for the estimation of spatial autoregressive models are generally inconsistent in the presence of an unknown form of heteroskedasticity in the disturbance term. The estimators formulated from the generalized method of moments (GMM) and the Bayesian Markov Chain Monte Carlo (MCMC) frameworks can be robust to unknown forms of heteroskedasticity. In this study, the finite sample properties of the robust GMM estimator are compared with the estimators based on the Bayesian MCMC approach for the spatial autoregressive models with heteroskedasticity of an unknown form. A Monte Carlo simulation study provides evaluation of the performance of the heteroskedasticity robust estimators. Our results indicate that the MLE and the Bayesian estimators impose relatively greater bias on the spatial autoregressive parameter when there is negative spatial dependence in the model. In terms of finite sample efficiency, the Bayesian estimators perform better than the robust GMM estimator. In addition, two empirical applications are provided to evaluate relative performance of heteroskedasticity robust estimators.