When does a paid research assistant become a co-author? What amount of work should a well compensated research assistant put into a paper before they're included as a co-author? Is there any norm? Suppose this is a field where 1 to 3 authors on any given journal paper is the standard amount (e.g., economics/finance/econometrics).

What if they do 30% of the paper? What if the paper requires (model building, programming, writing), and each component is about 33% of the paper, and the RA does all of one of these and helps a bit with another one of these?

I would think the answer is never, unless it was an unusually large contribution or the professor was feeling nice. I think this because otherwise they would've just gotten an experienced co-author who could bring much more to the table who they also don't have to compensate with any $$.
The decision of whether someone should be a coauthor is completely independent of monetary compensation: authorship depends on what sort of intellectual contribution each person has made, and it would be unethical to treat them differently based on their job (paid assistant, student, colleague, amateur, etc.).

People in different roles may be treated differently based on their contributions.  For example, an assistant who does no creative or insightful work, but instead just carries out explicit instructions in a straightforward way, should generally not be a coauthor.  (Still, the assistant should be thanked by name in the acknowledgments.)  When the assistant's work starts to involve exercising nontrivial skill and judgment, coauthorship may be appropriate.  If the assistant is doing a serious part of the creative intellectual work, then coauthorship is mandatory, even if the supervisor's role is deeper.