I have a 2 large open economy model. I put in all symmetric conditions between two countries into the model. The steady state returned are exactly the same between the two countries except the bond holdings. One country has b= 3×10-20 while the other has b*=-2×10-19. Actually I set initial values b=b*=0. So can I disregard the difference in b and b* at that magnititude? Cheers!

In case of a linear model, 0 should be 0. For nonlinear models, Everything smaller than 10-10 is really safe while everything smaller than E-6 or E-7 is usually also OK.