Computing 3SLS Solutions of Simultaneous Equation Models with Possible Singular Variance-Covariance Matrix

In simultaneous equation models (SEMs) the assumption that the covariance matrix of the disturbances is non-singular cannot always be made. For example, allocation models and models with precise observations which may imply linear constraints on the parameters, have singular disturbance covariance matrix. The solution of such models can be obtained using the expensive computation of generalized inverse which can lead to loss of accuracy. The main motivation of this work is to provide computational strategies for solving an alternative formulation of the 3SLS estimation problem, where the disturbance covariance matrix is not required to be non- singular.