On Bayesian Analysis of Seemingly Unrelated Regression Model with Skew Distribution Error

Abstract

The simultaneous equation models (SEMs) are one of the standard statistical tools for analyzing multivariate regression when the errors are correlated with some covariates. A particular version of the SEMs is the Seemingly Unrelated Regression (SUR) models which consist of several regression equations with errors being correlated across the equations. There are many occasions in which the normality assumption for the error term might not hold in these models. Although transforming the error to comply with the normal density is a solution, the interpretation of the estimators for the parameters and the associated model might not be straightforward. However, taking into account the skew-normal distribution for the error might, sometimes, be a good alternative. In this paper such scenario is considered as well as a Bayesian framework to estimate the parameters, with a brief review of frequentist methodology. The full conditional posterior densities are derived and relevant statistical inferences are provided. A simulation study is conducted to evaluate the performance of the proposed method. Also, the utilized model is applied to fit relevant equations on Iran gross and income data collected in the year 2009.