Implementation of Spatial Error Model through Maximum Likelihood

The implementation of spatial models through maximum likelihood is a great challenge due to the presence of Jacobian term in the log likelihood function. In literature, the implementation is usually performed using pseudo-likelihood. However, pseudo-likelihood doesn’t provide the consistent and efficient estimators. The present study implements the Spatial Error Model (SEM) through maximum likelihood. The maximum likelihood method provides the desirable properties like consistency, asymtotic efficiency, asymtotic normalilty and in some cases, it achieves unbiasness, Anselin (1988). The implementation through maximum likelihood is carried using Differential Evolution technique. The obtained results through maximum likelihood and pseudo-likelihood are compared and discussed