I like it. It is biased against poor people, since only rich people would have the money to have a third kid. (Oh, god. The third child would become a status symbol, wouldn't it.)
But... it is hard to raise lots of kids well when you're poor, so that sorta seems like it perfectly fits the criteria.
It still runs into the issue of how to enforce it. What if someone has the 2nd child even if the don't pass the requirements? What if someone has the 3rd kid but can't afford the taxes? At the end of the day, either you force abortions (ick) or you end up hurting kids (removing them from parents, not giving them equal opportunity, etc).
The only enforcement I can think of that has the least ethical issues is forced, reversible sterilization. After your first, you are sterilized. Once you pass the application for the second or third, sterilization is reversed during the time you are making the approved babies, then reapplied after their births.