Efficiency of heterosceastic linear model

In order to investigate the asymptotic efficiency of estimators under two different simulation techniques, normal-normal double sided Heteroscedastic error structure was adopted. We explored Direct Monte Carlo method of A. Zellner (2010) and Metropolis Hasting Algorithm experiments, an approach of Markov Chain Monte Carlo.
We truncated the model with one error component of two sided error structure. A Metropolis-Hasting Algorithm and Direct Monte Carlo adopted to perform simulation on joint posterior distribution of heteroscedastic linear econometric model. Since Ordinary Least squares is invalid and inefficient in the presence of heteroscedastic, heteroscedastic linear model was conjugated with informative priors to form posterior distribution. Maximum Likelihood Estimation was compared with Bayesian Maximum Likelihood Estimation, Mean Squares Error criterion was use to identify which estimator and/or simulation method outperform other. We chose the following sample sizes: 25; 50; 100; and 200. Thus 10,000 simulations with varying degree of heteroscedastic error structures were adopted. This is subjected to the level of convergence.
The overall using minimum mean squares error criterion revealed improving performance asymptotically regardless of the degree of heteroscedasticity. The results showed that Direct Monte Carlo Method outperformed Markov Chain Monte Carlo Method and Maximum Likelihood Estimator with minimum mean square error at any degree of heteroscedasticity.