A Bayesian Approach to the Sensitivity of Parameters Misspecification in The Seemingly Unrelated Regression Models

Abstract

The omission of important variables is often encountered in econometrics, which often results in the misspecification of the model. This study considered a misspecified joint seemingly unrelated regression (SUR) model within the Bayesian context. The explanatory variables were generated from a uniform distribution for sample sizes 5, 10, 30, 50, 100 and 1000. The coefficients of were generated from the multivariate normal distribution. Different levels of correlation (0.2, 0.4, 0.5, 0.7 and 0.9) among the independent variables were considered. The choice of hyperprior distribution was explored. Due to the incorrectly defined model, the intended attribute of unbiasedness in the estimated coefficients, which depends on the fitted model's correspondence with the actual underlying data-generating process, was not attained. Irregular patterns were seen in the posterior means and standard deviations except for a few large sample sizes. Keywords: Misspecification, Multicollinearity, Posterior mean, Posterior standard deviation, Seemingly unrelated regression.