Bootstrap Approach for Estimating Seemingly Unrelated Regressions with Varying Degrees of Autocorrelated Disturbances

The Seemingly Unrelated Regressions (SUR) model proposed in 1962 by Arnold Zellner has gained a wide acceptability and its practical use is enormous. In this research, two methods of estimation techniques were examined in the presence of varying degrees of first order Autoregressive [AR(1)] coefficients in the error terms of the model. Data was simulated using bootstrapping approach for sample sizes of 20, 50, 100, 500 and 1000.  Performances of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators were examined under a definite form of the variance-covariance matrix used for estimation in all the sample sizes considered. The results revealed that the GLS estimator was efficient both in small and large sample sizes. Comparative performances of the estimators were studied with 0.3 and 0.5 as assumed coefficients of AR(1) in the first and second regressions and these coefficients were further interchanged for each regression equation, it was deduced that standard errors of the parameters decreased with increase in the coefficients of AR(1) for both estimators with the SUR estimator performing better as sample size increased. Examining the performances of the SUR estimator with varying degrees of AR(1) using Mean Square Error (MSE), the SUR estimator performed better with autocorrelation coefficient of 0.3 than that of 0.5 in both regression equations with best MSE obtained to be 0.8185 using $\rho = 0.3$ in the second regression equation for sample size of 50