Moment restrictions for optimum GMM estimators under spatial simultaneous systems

It is widely known that for large samples maximum-likelihood based estimators are not
easy to implement for spatial models unless weights matrix satisfy certain basic conditions.
As an alternative recently in a series of paper Kelejian and Prucha (1999, 2004) proposed
a computationally feasible three step procedure for spatial models involving both lagged
dependent variable and spatially correlated disturbance term. The idea of this paper is to use
their set up for spatial simultaneous system, and construct a GMM type estimator based on
spatial first difference. The over-identification of the moment equation comes to the picture
by considering first two moments of a possibly heteroskedastic disturbance. Following
Chamberlains (1987) idea, a popular issue of optimum GMM based on conditional spatial
moment restrictions and asymptotic efficiency has been discussed.