Efficient estimation in the linear simultaneous equations model with vector autoregressive disturbances

This paper obtains the score vector, the information matrix and the asymptotic Cramer-Rao lower bound for the parameters of the linear simultaneous equations model with vector autoregressive disturbances. The Cramer-Rao lower bound for the covariance matrix of a consistent estimator of the parameters of primary interest is obtained for the case where the autoregressive coefficients are known and for the case where these coefficients are unknown, thus enabling us to demonstrate how the lack of knowledge of the autoregressive coefficients increases the bound. These lower bounds are used then to evaluate the asymptotic efficiency of various estimators proposed in the literature.