If you want to introduce categorical intercepts, then it's best if you use dummy variables but not in the way you are doing it.
For example if you have three countries you use two dummy variables that have the following properties:
B0 - Normal intercept for first category where B1 and B2 are both zero
B1 - Normal intercept for second category where B2 = 0
B2 - Normal intercept for third category where B1 = 0.
Basically the way it works is this:
The model component for this qualitative variable is B0 + B1A1 + B2A2
First category - B0 represents intercept component for 1st category where B1 and B2 are both zero
Second category B0 + B1 represents intercept component for 2nd category where B1 = 1 but B2 = 0
Third category B0 + B2 represents intercept component for 3rd category where B2 = 1 but B1 = 0.
So try changing your second model into the above (ai into A0 + B1A1 + B2A2 where first category means A1 = 0, A2 = 0; second category means A1 = 1, A2 = 0; third category is A1 = 1, A2 = 1) and see what happens.
If these categories are independent, it should go well.