Aysmptotic Bahaviour of Bayesian Seemingly Unrelated Regression Estimators with Different Collinearity Structures

Collinearity is a major drawback for efficiency gain of Seemingly Unrelated Regression (SUR) estimators. Any form of correlation between two explanatory variables defined as collinearity causes efficiency loss and unreliable estimates in SUR model. Use of prior information about SUR model parameters to address the problems associated to different Collinearity Structures (CSs), linear, quadratic, ratio and interactive, has not gained adequate attention in literature. This study was aimed at investigating behaviour of SUR estimators with different CSs under prior information as sample size, n increases from 5, 10, 20, 30, 50, 100, 250 and 500. The Bayesian Estimators (BEs) were derived, with analytically intractable Multivariate Normal Gamma (MNG) and Inverse Wishart (IW) non informative and informative priors. Result revealed that posterior standard deviations of SUR model with ratio collinearity decreased faster compared to other CSs as n increases under Non Informative Prior and Informative Prior. Also, The Bayesian estimators for the SUR model can effectively handle collinearity structures when prior information about unknown parameters is carefully incorporated.