Maximum likelihood estimation of matrix exponential spatial specification on seemingly unrelated regression-spatial autoregressive model

Spatial Seemingly unrelated regression estimation with matrix exponential specification (abbreviated as SUR-MESS(1,0)) is a new alternative when estimation of a spatial seemingly unrelated regression model with spatial autoregressive (abbreviated as SUR-SAR) has difficulty using large data. The difficulties faced are numerical iteration in obtaining parameters, theoretical complexity, and computational difficulties in calculating the Jacobian matrix so that it is not effective and efficient. With these difficulties, it is necessary to develop a new approach or model, one of which uses the Matrix Exponential Spatial Specification (MESS). The MESS specification for alternative SAR models is MESS(1,0). The existence of several properties possessed by MESS(1,0) causes this model to be better than SAR when using maximum likelihood estimation (MLE). The purpose of this research is to find the estimator of SUR-MESS(1,0) with MLE. The results of simulation studies using large data; the computational time for estimating the SUR-MESS(1,0) model is much shorter than the SUR-SAR model. Some highlights of the proposed method are:•SUR-MESS(1,0) is a new model built as an alternative to the SUR-SAR model when using large data.•The SUR-MESS(1,0) has analytical and computational advantages during parameter estimation when using MLE.•The SUR-MESS(1,0) has similar estimation results to the SUR-SAR.