Study of Spatial Autoregressive Regression With Heteroskedasticity Using the Generalized Method of Moments and Bayesian Approach

Kajian Regresi Spasial Autoregresif dengan Heteroskedastik Menggunakan Generalized Method of Moments dan Pendekatan Bayes

Abstract

Spatial dependence and spatial heteroskedasticity are problems in spatial regression. Spatial autoregressive regression (SAR) concerns only to the dependence on lag. The estimation of SAR parameters containing heteroskedasticity using the maximum likelihood estimation (MLE) method provides biased and inconsistent estimators. The alternative method that can be used are generalized method of moments (GMM) and Bayesian method. GMM uses a combination of linear and quadratic moment functions simultaneously so that the computation is easier than MLE. Bayesian method solves heteroskedasticity by modeling the structure of variance-covariance matrix. The bias are used to evaluate the GMM and Bayes in estimating parameters of SAR model with heteroskedasticity disturbances in simulation data. The results show that GMM and Bayes provides the bias of parameter estimates relatively consistent and smaller with larger number of observations. GMM and Bayes methods are applied to district/city GRDP data in Indonesia. The result show GMM method with Eksponential Distance Weights (EDW) matrix produces the minimum variance and the largest pseudo-R²