A recursive algorithm for solving SUR models

The main computational tool for solving SUR or simultaneous equations models is the generalized QR decomposition (GQRD) of an exogenous matrix A and the Cholesky factorization of a dispersion matrix C. Initially the GQRD computes the QRD of A and then the RQD of QC, where Q is an orthogonal matrix. Sequential and parallel strategies have been proposed for computing the GQRD by exploiting the block-diagonal and Kronecker structures of A and C, respectively. The RQD of QC is the most expensive of these operations. An algorithm is presented here that avoids the explicit computation of the RQD of QC. It is based on the strategies for solving augmented systems and updated SUR models. A modification to handle SUR models with unequal observation sizes is discussed.