Research
Effects of Multicollinearity and Correlation between the Error Terms on Some Estimators in a System of Regression Equations
One of the assumptions of a single equation model is that there is one -way causation between the dependent variable Y and the independent variables X. When the assumption is not valid, as, in many econometric models, of lack of correlation between the independent variables and the error terms (U) is further violated, Ordinary Least Square estimator would no longer efficient, that was why this study examined the effects of multicollinearity and a correlation between the error terms on the performance of seven estimators and identified the estimator that yields the most preferred estimates under the separate or joint influence of the two correlation effects under consideration. A twoequation model in which the two correlation problems were introduced was used in this study. The error terms of the two equations were also correlated. The levels of correlation between the error terms and multicollinearity were specified between -1 and +1 at an interval of 0.2 except when the correlation value 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 (MR), Full Information Maximum Likelihood (FIML), Seemingly Unrelated Regression Model (SUR) and Three-Stage Least Squares (3SLS) and their performances were thoroughly checked by subjecting the results obtained from each finite properties of the estimators into a multi-factor ANOVA model. The significant factors of the results were further examined using their estimated marginal means and the Least Significant Difference (LSD) methodology to determine the best estimator. The results when there is no correlation show that the OLS, CORC, and MLE estimators are generally preferred. Furthermore, the estimators of MR, FIML, SUR, and 3SLS are preferred for computing all the parameters of the model in the presence of multicollinearity and correlation between the error terms at all the sample sizes chosen.
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.
