Reduced rank regression for blocks of simultaneous equations

Reduced rank regression analysis provides maximum likelihood estimators of a matrix of regression coefficients of specified rank and of corresponding linear restrictions on such matrices. These estimators depend on the eigenvectors of an “effect” matrix in the metric of an error covariance matrix. In this paper it is shown that the maximum likelihood estimator of the restrictions can be approximated by a function of the effect matrix alone. The procedures are applied to a block of simultaneous equations. The block may be over-identified in the entire model and the individual equations just-identified within the block. The procedures are generalizations of the limited information maximum likelihood and two-stage least squares estimators.