Model ρ Bias β0 Efficiency β0 Bias β1 Efficiency β1 ε ~ N(0,1) GS a0=0.00 GS a0=0.50 GS a0=0.95 MCMC EM   0.25 0.25 0.25 0.25 0.25   0.00027 0.00013 0.00011 0.00517 0.00240   1.00000 0.87132 0.82339 6.55291 4.93114   0.00009 0.00007 0.00002 0.00053 0.00000   1.00000 0.73221 0.71291 4.81135 3.19351 GS a0=0.00 GS a0=0.50 GS a0=0.95 MCMC EM 0.50 0.50 0.50 0.50 0.50 0.00006 0.00005 0.00002 0.00736 0.00820 1.00000 0.96027 0.90345 4.09938 3.99210   0.00012 0.00010 0.00013 -0.00024 0.00000   1.00000 0.87130 0.65734 3.89316 2.31730   ε~t3 GS a0=0.00 GS a0=0.50 GS a0=0.95 MCMC EM   0.25 0.25 0.25 0.25 0.25   0.00008 0.00003 0.00005 0.27739 -0.13920   1.00000 0.91247 0.91136 3.56667 3.64298   0.00017 0.00011 0.00008 -0.00195 0.00010   1.00000 0.82553 0.79735 2.95862 2.76704 GS a0=0.00 GS a0=0.50 GS a0=0.95 MCMC EM 0.50 0.50 0.50 0.50 0.50 0.00012 0.00002 0.00006 0.00391 0.00430 1.00000 0.95731 0.94618 1.20034 3.54281 0.00007 0.00002 0.00003 0.00029 0.00010 1.00000 0.91337 0.86935 1.33942 2.70529 ε~x3 GS a0=0.00 GS a0=0.50 GS a0=0.95 MCMC EM   0.25 0.25 0.25 0.25 0.25   0.00000 0.00005 0.00008 -0.00771 0.02680   1.00000 0.99589 0.92721 2.24711 4.59660   0.00006 0.00009 0.00004 0.00032 -0.00010   1.00000 0.88395 0.83557 2.41503 3.99103 GS a0=0.00 GS a0=0.50 GS a0=0.95 MCMC EM 0.50 0.50 0.50 0.50 0.50 0.00013 0.00029 0.00018 0.00835 0.01920 1.00000 0.92774 0.89447 2.31421 3.75119 0.00000 0.00007 0.00002 0.00017 0.00000 1.00000 0.73221 0.63291 2.53098 2.15328

Table 1: Estimated bias and relative efficiency for different error distribution by using Gibbs sampler (GS), Bayesian MCMC, and EM algorithm.