An estimation method for the seemingly unrelated regression model with contemporaneous covariances based on an efficient recursive algorithm

Abstract

This paper develops an iterative estimation procedure for estimating both the parameters and covariances of the seemingly unrelated regression model with contemporaneous covariances. The method is based on the use of an efficient recursive estimation algorithm for the SUR model with known contemporaneous covariances. The components of each observation vector are used one at a time to simultaneously estimate the parameters using a Bayesian “state vector” approach. This is computationally efficient, since the only matrix inversion required is one by one. The covariances are estimated using the residuals from the fitted model. The procedure iterates between estimating the parameters and estimating the covariances until convergence. The algorithm yields the parameter estimator and an estimator for its distribution, thus providing a sound basis for inferential procedures on the parameters.