A computationally efficient method for solving sur models with orthogonal regressor

Abstract

A computationally efficient method to estimate seemingly unrelated regression equations models with orthogonal regressors is presented. The method considers the estimation problem as a generalized linear least squares problem (GLLSP). The basic tool for solving the GLLSP is the generalized QR decomposition of the block-diagonal exogenous matrix and Cholesky factor C⊗IT of the covariance matrix of the disturbances. Exploiting the orthogonality property of the regressors the estimation problem is reduced into smaller and independent GLLSPs. The solution of each of the smaller GLLSPs is obtained by a single-column modification of C. This reduces significantly the computational burden of the standard estimation procedure, especially when the iterative feasible estimator of the model is needed. The covariance matrix of the estimators is also derived.