Abstract
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 two-equation 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.
Highlights
The seemingly unrelated regression (SUR) model is common in the Econometric literature (Zellner, 1962; Srivastava and Giles, 1987; Greene, 2003) but is less known elsewhere, its benefits have been explored by several authors, and more recently the SUR model is being applied in Agricultural Economics (O’ Dorell et al 1999), Wilde et al (1999)
Using a computer program which was written with TSP software package to estimate all the model parameters and the criteria, the performances of seven estimation methods; Ordinary Least Squares (OLS), Cochran – Orcutt (COCR), Maximum Likelihood Estimator (MLE), Multivariate Regression, Full Information Maximum Likelihood (FIML), Seemingly Unrelated Regression (SUR) and Three-Stage Least Squares (3SLS) were examined by subjecting the results obtained from each finite properties of the estimators into a multi-factor analysis of variance model
The summary of results from the Analysis of variance tables of the criteria showing the effect of the estimators, the correlation between the error term and autocorrelation on βi are presented in Table 1 below
Summary
The seemingly unrelated regression (SUR) model is common in the Econometric literature (Zellner, 1962; Srivastava and Giles, 1987; Greene, 2003) but is less known elsewhere, its benefits have been explored by several authors, and more recently the SUR model is being applied in Agricultural Economics (O’ Dorell et al 1999), Wilde et al (1999). The size and power properties of all tests deteriorate sharply as the number of equations increases, the system becomes more 581 dynamic, the exogenous variables become more auto correlated, and the sample size decreases. This performance has, in general, an unknown degree since the interaction amongst these factors does not permit a predictive summary, as might be hoped for by response surface-type approaches. (2017), among many others, have observed that the efficiency of the OLS estimator in a linear regression containing an auto correlated error term depends largely on the structure of X used. In a linear model with an auto correlated error term
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