On Seemingly Unrelated Regression and Single Equation Estimators Under Heteroscedastic Error and Non-Gaussian Responses

Abstract

This study investigated the efficiency of Seemingly Unrelated Regression (SUR) estimator of Feasible Generalized Least Square (FGLS) compared to robust MM-BISQ, M-Huber, and Ordinary Least Squares (OLS) estimators when the variances of the error terms are non-constant and the distribution of the response variables is not Gaussian. The finite properties and relative performance of these other estimators to OLS were examined under four forms of heteroscedasticity of the error terms, levels of Contemporaneous Correlation (Cc) with gamma responses. The efficiency of four estimation techniques for the SUR model was examined using the Root Mean Square Error (RMSE) criterion to determine the best estimator(s) under different conditions at various sample sizes. The simulation results revealed that the SUR estimator (FGLS) showed superior performance in the small sample situations when the contemporaneous correlation ( ) is almost perfect ( =0.95) with the gamma response model while MM-BISQ was the best under low contemporaneous correlation. The relative efficiencies of MM-BISQ, M-Huber and FGLS estimators over the OLS are respectively 89%, 71%, and 14% in a small sample 30) and 49%, 32% and 1% in large sample sizes  under gamma response model. The study concluded that MM-BISQ and M-Huber estimators are the most efficient estimators for modeling systems of simultaneous equations with non-Gaussian responses under either homoscedastic or multiplicative heteroscedastic error terms irrespective of the sample size.Keywords—, Contemporaneous correlation, Feasible Generalized Least Square, Heteroscedasticity, Homoscedasticity, Seemingly unrelated Regression.