Bayesian Estimation of Normal Linear Regression Model with Heteroscedasticity Error Structures

Abstract

Non-constant error variance in Normal Linear Regression Model (NLRM) is an econometric problem generally referred to as heteroscedasticity. Its presence renders statistical inference invalid. Classical approach to its detection, estimation and remediation are widely discussed in the econometric literature. However, estimation of a NLRM using the Bayesian approach when heteroscedasticity problem is present is a major gap in the existing stock of knowledge on this subject. This approach has grown widely in recent times because it combines out-of-sample information with observed data. The study derived Bayesian estimators of the NLRM in the presence of functional forms of heteroscedasticity. Variance was treated as a linear function and as an exponential function of exogenous variables. The estimators are found to be unbiased and consistent and the precision values tend to zero. The estimates obtained from the estimators approximately 95% draws fall within each of the corresponding credible interval. Therefore, the results obtained for the derived Bayesian estimators for different functional forms of heteroscedasticity considered are similar, thus, providing a credible alternative to the existing classical methods which depend solely on the sample information.