Effects of Correlation between the Error Term and Autocorrelation on Some Estimators in a System of Regression Equations
Seemingly unrelated regression model developed to handle the problem of correlation among the error terms of a system of the regression equations is still not without a challenge, where each regression equation must satisfy the assumptions of the standard regression model. When dealing with time-series data, some of these assumptions, especially that of independence of the regressors and error terms leading to multicollinearity and autocorrelation respectively, are often violated. This study examined the effects of correlation between the error terms and autocorrelation on the performance of seven estimators and identify the estimator that yields the most preferred estimates under the separate or joint influence of the two correlation effects considered by the researcher. A twoequation model was considered, in which the first equation had multicollinearity and autocorrelation problems while the second one had no correlation problem. The error terms of the two equations were also correlated. The levels of correlation between the error terms and autocorrelation were specified between -1 and +1 at interval of 0.2 except when it approached unity. A Monte Carlo experiment of 1000 trials was carried out at five levels of sample sizes 20, 30, 50, 100, and 250 at two runs. The seven estimation methods namely; Ordinary Least Squares (OLS), Cochran – Orcutt (CORC), Maximum Likelihood Estimator (MLE), Multivariate Regression, Full Information Maximum Likelihood (FIML), Seemingly Unrelated Regression Model (SUR), and Three-Stage Least Squares (3SLS). Their performances were examined by subjecting the results obtained from each finite property of the estimators into a multi-factor analysis of variance model. The significant factors were further checked using their estimated marginal means and the Least Significant Difference (LSD) methodology to determine the best estimator. The findings generally show that the estimator of MLE is preferred to estimate all the parameters of the model in the presence of correlation between the error terms and autocorrelation at all the sample sizes. This study has applications in areas such as Economics, Econometrics, Social Sciences, Agricultural Economics, and some other fields where the correlation between the error terms and autocorrelation problems can be encountered.
