Estimating Seemingly Unrelated Regressions with First Order Autoregressive Disturbances

Abstract

In Seemingly Unrelated Regressions (SUR) model, disturbances are assumed to be correlated across equations and it will be erroneous to assume that disturbances behave independently, hence, the need for an efficient estimator. Literature has revealed gain in efficiency of the SUR estimator over the Ordinary Least Squares (OLS) estimator when the errors are correlated across equations. This work, however, considers methods of estimating a set of regression equations when disturbances are both contemporaneously and serially correlated. The Feasible Generalized Least Squares (FGLS), OLS and Iterative Ordinary Least Squares (IOLS) estimation techniques were considered and the form of autocorrelation examined. Prais-Winstein transformation was conducted on simulated data for the different sample sizes used to remove autocorrelations. Results from simulation studies showed that the FGLS was efficient both in small samples and large samples. Comparative performances of the estimators were investigated on the basis of the standard errors of the parameter estimates when estimating the model with and without AR(1) and the results showed that the estimators performed better with AR(1) as the sample size increased especially from 20. On the criterion of the Root Mean Square, the FGLS was found to have performed better with AR(1) and it was revealed that bias reduces as sample size increases. In all cases considered, the SUR estimator performed best. It was consistently most efficient than the OLS and IOLS estimators.