Effects of atypical observations on the estimation of seemingly unrelated regression model

Abstract

The Seemingly Unrelated Regression Equation model is a generalization of a linear regression model that consists of several regression equations in order to achieve efficient estimates. Unfortunately, the assumptions underlying most SUR estimators give little/no consideration to outlying observations which may be present in the data. These atypical observations may have some apparent distorting effects on the estimates produced by these estimators. This study thus examined the effect of outliers on the performances of SUR and OLS estimators using Monte Carlo simulation method. The Cholesky method was used to partition the variance-covariance matrix by decomposing it into the upper and lower non-singular triangular matrices. Varying degree of outliers; 0%, 5%, and 10% were each introduced into five sample sizes; 20, 40, 60, 100 and 500 respectively. The performances of the estimators were evaluated using Absolute Bias (ABIAS) and Mean Square Error (MSE). The results showed that at 0% outliers (when outliers were absent), the ABIAS and MSE of the SUR and OLS estimators showed similar results. At 5% and 10% outliers, the magnitude in ABIAS and MSE for both estimators increased but the SUR estimator showed better performance than the OLS estimator. As the sample size increases, ABIAS and MSE of the estimators decreased consistently for the various degrees of outliers considered with SUR consistently better than OLS